903 Replies to “Michael Egnor talks with podcaster Lucas Skrobot about how we can know we are not zombies

  1. 1
    bornagain77 says:

    As to,

    “a philosophical zombie,,,, is identical to a human being but has no first-person (subjective) experience. (i.e. no qualia).,,, I’m not concerned here to argue whether a p-zombie is practically possible but rather whether it is conceptually possible. Specifically, does a p-zombie break any physical laws of science?
    If a p-zombie is conceptually possible—that is, if it does not violate any scientific principles—then it is reasonable to conclude that whatever gives us first-person subjective experience must be something that is not physical, as the term is understood scientifically. If p-zombies, who lack consciousness, are conceptually consistent with physical science, then consciousness is something outside the purview of physical science.”
    – Michael Egnor
    https://mindmatters.ai/2020/07/neurosurgeon-explains-why-you-are-not-a-zombie/

    I have to disagree with Dr. Egnor with his claim that “consciousness is something outside the purview of physical science.”. While the mental attribute of qualia itself may forever be outside the ‘outside the purview of physical science’ ,,, (i.e. Mary’s room)

    11.2.1 Qualia – Perception (“The Hard Problem” )
    Philosopher of the mind Frank Jackson imagined a thought experiment —Mary’s Room— to explain qualia and why it is such an intractable problem for science. The problem identified is referred to as the knowledge argument. Here is the description of the thought experiment:
    “Mary is a brilliant scientist who is, for whatever reason, forced to investigate the world from a black and white room via a black and white television monitor. She specializes in the neurophysiology of vision and acquires, let us suppose, all the physical information there is to obtain about what goes on when we see ripe tomatoes, or the sky, and use terms like ‘red’, ‘blue’, and so on. She discovers, for example, just which wavelength combinations from the sky stimulate the retina, and exactly how this produces via the central nervous system the contraction of the vocal cords and expulsion of air from the lungs that results in the uttering of the sentence ‘The sky is blue’. (…) What will happen when Mary is released from her black and white room or is given a color television monitor? Will she learn anything or not?”
    Jackson believed that Mary did learn something new: she learned what it was like to experience color.
    “It seems just obvious that she will learn something about the world and our visual experience of it. But then is it inescapable that her previous knowledge was incomplete. But she had all the physical information. Ergo there is more to have than that, and Physicalism [materialism] is false.”
    https://www.urantia.org/study/seminar-presentations/is-there-design-in-nature#Emergence

    ,,, While the mental attribute of qualia itself may forever be outside the ‘outside the purview of physical science’ ,,, (i.e. Mary’s room), there are other defining attributes of consciousness that do lend themselves to scientific examination.

    In short, Qualia is not the only attribute of mind that distinguishes it from the material brain. As Dr. Egnor himself pointed out, besides qualia, the immaterial mind can also be distinguished from the material brain by the mental attributes of, “Intentionality,,, Persistence of Self-Identity,,, Restricted Access,,, Incorrigibility,,, Free Will,,,”

    The Mind and Materialist Superstition – Michael Egnor – 2008
    Six “conditions of mind” that are irreconcilable with materialism: –
    Excerpt: Intentionality,,, Qualia,,, Persistence of Self-Identity,,, Restricted Access,,, Incorrigibility,,, Free Will,,,
    http://www.evolutionnews.org/2.....13961.html

    You can read more in-depth definitions of each of the six properties of immaterial mind in Dr. Egnor’s article.

    Likewise, J. Warner Wallace has a very similar list, (but not an exact match to Dr. Egnor’s list), of six properties of immaterial mind that are irreconcilable with reductive materialism.

    Six reasons why you should believe in non-physical minds – 01/30/2014
    1) First-person access to mental properties
    2) Our experience of consciousness implies that we are not our bodies
    3) Persistent self-identity through time
    4) Mental properties cannot be measured like physical objects
    5) Intentionality or About-ness
    6) Free will and personal responsibility
    http://winteryknight.com/2014/.....cal-minds/

    And while, as Dr. Egnor pointed out, qualia is forever beyond ‘the purview of physical science’, other mental attributes do lend themselves to examination by physical science. Specifically, ‘Persistence of Self-Identity through time’ (which may also be termed ‘the experience of ‘the Now”), and ‘free will’, although both being irreconcilable with reductive materialism, nonetheless, both of those defining attributes of immaterial mind that Dr. Egnor listed, unlike qualia, do make their presence known to us in recent experimental evidence from quantum mechanics.

    As to defining the specific mental attribute of the ‘Persistence of Self-Identity through time’ (and/or ‘the experience of ‘the Now”) in particular, it is first important to note that we each have a unique perspective of being outside of time. In fact we each seemingly watch from some mysterious outside perspective of time as time seemingly passes us by. Simply put, we seem to be standing on an island of ‘now’ as the river of time continually flows past us.

    In the following video, Dr. Suarez states that the irresolvable dilemma for reductive materialists as such, “it is impossible for us to be ‘persons’ experiencing ‘now’ if we are nothing but particles flowing in space time. Moreover, for us to refer to ourselves as ‘persons’, we cannot refer to space-time as the ultimate substratum upon which everything exists, but must refer to a Person who is not bound by space time. (In other words) We must refer to God!”

    Nothing: God’s new Name – Antoine Suarez – video
    Paraphrased quote: (“it is impossible for us to be ‘persons’ experiencing ‘now’ if we are nothing but particles flowing in space time. Moreover, for us to refer to ourselves as ‘persons’, we cannot refer to space-time as the ultimate substratum upon which everything exists, but must refer to a Person who is not bound by space time. i.e. We must refer to God!”)
    https://www.youtube.com/watch?v=SOr9QqyaLlA

    In further defining the mental attribute of ‘the experience of the now’, in the following article Stanley Jaki states that “There can be no active mind without its sensing its existence in the moment called now.,,, ,,,There is no physical parallel to the mind’s ability to extend from its position in the momentary present to its past moments, or in its ability to imagine its future. The mind remains identical with itself while it lives through its momentary nows.”

    The Mind and Its Now – Stanley L. Jaki, May 2008
    Excerpts: There can be no active mind without its sensing its existence in the moment called now.,,,
    Three quarters of a century ago Charles Sherrington, the greatest modern student of the brain, spoke memorably on the mind’s baffling independence of the brain. The mind lives in a self-continued now or rather in the now continued in the self. This life involves the entire brain, some parts of which overlap, others do not.
    ,,,There is no physical parallel to the mind’s ability to extend from its position in the momentary present to its past moments, or in its ability to imagine its future. The mind remains identical with itself while it lives through its momentary nows.
    ,,, the now is immensely richer an experience than any marvelous set of numbers, even if science could give an account of the set of numbers, in terms of energy levels. The now is not a number. It is rather a word, the most decisive of all words. It is through experiencing that word that the mind comes alive and registers all existence around and well beyond.
    ,,, All our moments, all our nows, flow into a personal continuum, of which the supreme form is the NOW which is uncreated, because it simply IS.
    http://metanexus.net/essay/mind-and-its-now

    And ‘the experience of ‘the now” also happens to be exactly where Albert Einstein got into trouble with leading philosophers of his day and also happens to be exactly where Einstein, eventually, got into trouble with quantum mechanics itself.

    Around 1935, Einstein was asked by Rudolf Carnap (who was a philosopher):

    “Can physics demonstrate the existence of ‘the now’ in order to make the notion of ‘now’ into a scientifically valid term?”
    – Rudolf Carnap – Philosopher

    Einstein’s denied that it was possible, and stated:

    “The experience of ‘the now’ cannot be turned into an object of physical measurement, it can never be a part of physics.”
    – Einstein

    Prior to that encounter with Carnap, Einstein also had another disagreement with another famous philosopher, Henri Bergson, over what the proper definition of time should be (Bergson was also very well versed in the specific mental attribute of the ‘experience of the now’). In fact, that disagreement with Henri Bergson over what the proper definition of time should be was actually one of the primary reasons that Einstein failed to ever receive a Nobel prize for his work on relativity:

    Einstein, Bergson, and the Experiment that Failed: Intellectual Cooperation at the League of Nations! – Jimena Canales
    page 1177
    Excerpt: Bergson temporarily had the last word during their meeting at Société française de philosophie. His intervention negatively affected Einstein’s Nobel Prize, which was given “for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect” and not for relativity. The reasons behind this decision, as stated in the prize’s presentation speech, were related to Bergson’s intervention: “Most discussion [of Einstein’s work] centers on his Theory of Relativity. This pertains to epistemology and has therefore been the subject of lively debate in philosophical circles. It will be no secret that the famous philosopher Bergson in Paris has challenged this theory, while other philosophers have acclaimed it wholeheartedly.”51 For a moment, their debate dragged matters of time out of the solid terrain of “matters of fact” and into the shaky ground of “matters of concern.”52
    https://dash.harvard.edu/bitstream/handle/1/3210598/canales-Einstein,%20Bergson%20and%20the%20Experiment%20that%20Failed%282%29.pdf?sequence=2

    The specific statement that Einstein made to Carnap on the train, “The experience of ‘the now’ cannot be turned into an object of physical measurement, it can never be a part of physics.” was a very interesting statement for Einstein to make to the philosopher since “The experience of ‘the now’ has, from many recent experiments in quantum mechanics, established itself as very much being a defining part of our physical measurements in quantum mechanics.

    For instance, the following delayed choice experiment with atoms demonstrated that, “It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,”

    Reality doesn’t exist until we measure it, (Delayed Choice) quantum experiment confirms – Mind = blown. – FIONA MACDONALD – 1 JUN 2015
    Excerpt: “It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,” lead researcher and physicist Andrew Truscott said in a press release.
    http://www.sciencealert.com/re.....t-confirms

  2. 2
    bornagain77 says:

    Likewise, the following violation of Leggett’s inequality stressed the quantum-mechanical assertion that reality does not exist when we’re not observing it.

    Quantum physics says goodbye to reality – Apr 20, 2007
    Excerpt: They found that, just as in the realizations of Bell’s thought experiment, Leggett’s inequality is violated – thus stressing the quantum-mechanical assertion that reality does not exist when we’re not observing it. “Our study shows that ‘just’ giving up the concept of locality would not be enough to obtain a more complete description of quantum mechanics,” Aspelmeyer told Physics Web. “You would also have to give up certain intuitive features of realism.”
    http://physicsworld.com/cws/article/news/27640

    The Mind First and/or Theistic implications of quantum experiments such as the preceding are fairly obvious. As Professor Scott Aaronson of MIT once quipped, “Look, we all have fun ridiculing the creationists,,, But if we accept the usual picture of quantum mechanics, then in a certain sense the situation is far worse: the world (as you experience it) might as well not have existed 10^-43 seconds ago!”

    “Look, we all have fun ridiculing the creationists who think the world sprang into existence on October 23, 4004 BC at 9AM (presumably Babylonian time), with the fossils already in the ground, light from distant stars heading toward us, etc. But if we accept the usual picture of quantum mechanics, then in a certain sense the situation is far worse: the world (as you experience it) might as well not have existed 10^-43 seconds ago!”
    – Scott Aaronson – MIT associate Professor quantum computation – Lecture 11: Decoherence and Hidden Variables

    Thus, contrary to what Einstein himself thought was possible for experimental physics, physicists have now shown, in overwhelming fashion, that ‘the experience of the now’ is very much a part of experimental physics. In fact, due to advances in quantum mechanics, it would now be much more appropriate to rephrase Einstein’s answer to the philosopher Rudolph Carnap in this way:

    “It is impossible for “the experience of ‘the now’” to ever be divorced from physical measurement, it will always be a part of physics.”

    The ‘experience of the now’ also makes itself known in experimental science through what is termed the quantum zeno effect.

    An old entry in wikipedia described the Quantum Zeno effect as such “an unstable particle, if observed continuously, will never decay.”

    Perspectives on the quantum Zeno paradox – 2018
    The quantum Zeno effect is,, an unstable particle, if observed continuously, will never decay.
    https://iopscience.iop.org/article/10.1088/1742-6596/196/1/012018/pdf

    Likewise, the present day entry on wikipedia about the Quantum Zeno effect also provocatively states that “a system can’t change while you are watching it”

    Quantum Zeno effect
    Excerpt: Sometimes this effect is interpreted as “a system can’t change while you are watching it”
    https://en.wikipedia.org/wiki/Quantum_Zeno_effect

    Atheistic materialists have tried to get around the Quantum Zeno effect by postulating that interactions with the environment are sufficient to explain the Quantum Zeno effect.

    Perspectives on the quantum Zeno paradox – 2018
    Excerpt: The references to observations and to wavefunction collapse tend to raise unnecessary questions related to the interpretation of quantum mechanics. Actually, all that is required is that some interaction with an external system disturb the unitary evolution of the quantum system in a way that is effectively like a projection operator.
    https://iopscience.iop.org/article/10.1088/1742-6596/196/1/012018/pdf

    Yet, the following interaction-free measurement of the Quantum Zeno effect demonstrated that the presence of the Quantum Zeno effect can be detected without interacting with a single atom.

    Interaction-free measurements by quantum Zeno stabilization of ultracold atoms – 14 April 2015
    Excerpt: In our experiments, we employ an ultracold gas in an unstable spin configuration, which can undergo a rapid decay. The object—realized by a laser beam—prevents this decay because of the indirect quantum Zeno effect and thus, its presence can be detected without interacting with a single atom.
    http://www.nature.com/ncomms/2.....S-20150415

    In short, the quantum zeno effect, regardless of how atheistic materialists may feel about it, is experimentally shown to be a real effect that is not reducible to any materialistic explanation. And thus the original wikipedia statement of, “an unstable particle, if observed continuously, will never decay”, stands, as far as the science itself is concerned, as being a true statement to make.

    Moreover, on top of the quantum zeno effect, the mental attribute of ‘the experience of the now’ is also now verified by recent experiments in quantum mechanics that have now shown that “entropy is always dependent on the observer.”

    As the following article states, the deletion of data, under certain conditions, can create a cooling effect instead of generating heat. The cooling effect appears when the strange quantum phenomenon of entanglement is invoked.,,, In the new paper, the researchers,,, show that when the bits to be deleted are quantum-mechanically entangled with the state of an observer, then the observer could even withdraw heat from the system while deleting the bits. Entanglement links the observer’s state to that of the computer in such a way that they know more about the memory than is possible in classical physics.,,,
    In measuring entropy, one should bear in mind that an object does not have a certain amount of entropy per se, instead an object’s entropy is always dependent on the observer. Applied to the example of deleting data, this means that if two individuals delete data in a memory and one has more knowledge of this data, she perceives the memory to have lower entropy and can then delete the memory using less energy.,,,

    Quantum knowledge cools computers: New understanding of entropy – June 1, 2011
    Excerpt: Recent research by a team of physicists,,, describe,,, how the deletion of data, under certain conditions, can create a cooling effect instead of generating heat. The cooling effect appears when the strange quantum phenomenon of entanglement is invoked.,,,
    The new study revisits Landauer’s principle for cases when the values of the bits to be deleted may be known. When the memory content is known, it should be possible to delete the bits in such a manner that it is theoretically possible to re-create them. It has previously been shown that such reversible deletion would generate no heat. In the new paper, the researchers go a step further. They show that when the bits to be deleted are quantum-mechanically entangled with the state of an observer, then the observer could even withdraw heat from the system while deleting the bits. Entanglement links the observer’s state to that of the computer in such a way that they know more about the memory than is possible in classical physics.,,,
    In measuring entropy, one should bear in mind that an object does not have a certain amount of entropy per se, instead an object’s entropy is always dependent on the observer. Applied to the example of deleting data, this means that if two individuals delete data in a memory and one has more knowledge of this data, she perceives the memory to have lower entropy and can then delete the memory using less energy.,,,
    No heat, even a cooling effect;
    In the case of perfect classical knowledge of a computer memory (zero entropy), deletion of the data requires in theory no energy at all. The researchers prove that “more than complete knowledge” from quantum entanglement with the memory (negative entropy) leads to deletion of the data being accompanied by removal of heat from the computer and its release as usable energy. This is the physical meaning of negative entropy.
    Renner emphasizes, however, “This doesn’t mean that we can develop a perpetual motion machine.” The data can only be deleted once, so there is no possibility to continue to generate energy. The process also destroys the entanglement, and it would take an input of energy to reset the system to its starting state. The equations are consistent with what’s known as the second law of thermodynamics: the idea that the entropy of the universe can never decrease. Vedral says “We’re working on the edge of the second law. If you go any further, you will break it.”
    http://www.sciencedaily.com/re.....134300.htm

    And as the following 2017 article states: James Clerk Maxwell (said), “The idea of dissipation of energy depends on the extent of our knowledge.”,,,
    quantum information theory,,, describes the spread of information through quantum systems.,,,
    Fifteen years ago, “we thought of entropy as a property of a thermodynamic system,” he said. “Now in (quantum) information theory, we wouldn’t say entropy is a property of a system, but a property of an observer who describes a system.”,,,

    The Quantum Thermodynamics Revolution – May 2017
    Excerpt: the 19th-century physicist James Clerk Maxwell put it, “The idea of dissipation of energy depends on the extent of our knowledge.”
    In recent years, a revolutionary understanding of thermodynamics has emerged that explains this subjectivity using quantum information theory — “a toddler among physical theories,” as del Rio and co-authors put it, that describes the spread of information through quantum systems. Just as thermodynamics initially grew out of trying to improve steam engines, today’s thermodynamicists are mulling over the workings of quantum machines. Shrinking technology — a single-ion engine and three-atom fridge were both experimentally realized for the first time within the past year — is forcing them to extend thermodynamics to the quantum realm, where notions like temperature and work lose their usual meanings, and the classical laws don’t necessarily apply.
    They’ve found new, quantum versions of the laws that scale up to the originals. Rewriting the theory from the bottom up has led experts to recast its basic concepts in terms of its subjective nature, and to unravel the deep and often surprising relationship between energy and information — the abstract 1s and 0s by which physical states are distinguished and knowledge is measured.,,,
    Renato Renner, a professor at ETH Zurich in Switzerland, described this as a radical shift in perspective. Fifteen years ago, “we thought of entropy as a property of a thermodynamic system,” he said. “Now in (quantum) information theory, we wouldn’t say entropy is a property of a system, but a property of an observer who describes a system.”,,,
    https://www.quantamagazine.org/quantum-thermodynamics-revolution/

    The reason why I am very impressed with the preceding experiments demonstrating that the mental attribute of ‘the experience of the now’ is very much a part of entropy, is that the second law of thermodynamics, entropy, is very foundational to any definition of time that we may have.

    As the following article states, “Entropy explains time; it explains every possible action in the universe;,,”,, “Even gravity,,,, can be expressed as a consequence of the law of entropy.,,,”

    Shining Light on Dark Energy – October 21, 2012
    Excerpt: It (Entropy) explains time; it explains every possible action in the universe;,,
    Even gravity, Vedral argued, can be expressed as a consequence of the law of entropy.,,,
    The principles of thermodynamics are at their roots all to do with information theory. Information theory is simply an embodiment of how we interact with the universe —,,,
    http://crev.info/2012/10/shini.....rk-energy/

  3. 3
    bornagain77 says:

    On top of the fact that “(Entropy) explains time; it explains every possible action in the universe”, Entropy is also, by a wide margin, the most finely tuned of the initial conditions of the Big Bang. Finely tuned to an almost incomprehensible degree of precision, 1 part in 10 to the 10 to the 123rd power. As Roger Penrose himself stated that, “This now tells us how precise the Creator’s aim must have been: namely to an accuracy of one part in 10^10^123.”

    “This now tells us how precise the Creator’s aim must have been: namely to an accuracy of one part in 10^10^123.”
    Roger Penrose – How special was the big bang? – (from the Emperor’s New Mind, Penrose, pp 339-345 – 1989)

    “The time-asymmetry is fundamentally connected to with the Second Law of Thermodynamics: indeed, the extraordinarily special nature (to a greater precision than about 1 in 10^10^123, in terms of phase-space volume) can be identified as the “source” of the Second Law (Entropy).”
    Roger Penrose – The Physics of the Small and Large: What is the Bridge Between Them?

    In the following video, Dr, Bruce Gordon touches upon just how enormous that number truly is. Dr. Gordon states, “you would need a hundred million, trillion, trillion, trillion, universes our size, with a zero on every proton and neutron in all of those universes just to write out this number. That is how fine tuned the initial entropy of our universe is.”

    “An explosion you think of as kind of a messy event. And this is the point about entropy. The explosion in which our universe began was not a messy event. And if you talk about how messy it could have been, this is what the Penrose calculation is all about essentially. It looks at the observed statistical entropy in our universe. The entropy per baryon. And he calculates that out and he arrives at a certain figure. And then he calculates using the Bekenstein-Hawking formula for Black-Hole entropy what the,,, (what sort of entropy could have been associated with,,, the singularity that would have constituted the beginning of the universe). So you’ve got the numerator, the observed entropy, and the denominator, how big it (the entropy) could have been. And that fraction turns out to be,, 1 over 10 to the 10 to the 123rd power. Let me just emphasize how big that denominator is so you can gain a real appreciation for how small that probability is. So there are 10^80th baryons in the universe. Protons and neutrons. No suppose we put a zero on every one of those. OK, how many zeros is that? That is 10^80th zeros. This number has 10^123rd zeros. OK, so you would need a hundred million, trillion, trillion, trillion, universes our size, with zero on every proton and neutron in all of those universes just to write out this number. That is how fine tuned the initial entropy of our universe is. And if there were a pre-Big Bang state and you had some bounces, then that fine tuning (for entropy) gets even finer as you go backwards if you can even imagine such a thing. ”
    Dr Bruce Gordon – Contemporary Physics and God Part 2 – video – 1:50 minute mark – video
    https://youtu.be/ff_sNyGNSko?t=110

    In fact, entropy is also the primary reason why our own material, temporal, bodies grow old and eventually die in this universe,,,

    Entropy Explains Aging, Genetic Determinism Explains Longevity, and Undefined Terminology Explains Misunderstanding Both – 2007
    Excerpt: There is a huge body of knowledge supporting the belief that age changes are characterized by increasing entropy, which results in the random loss of molecular fidelity, and accumulates to slowly overwhelm maintenance systems [1–4].,,,
    http://www.plosgenetics.org/ar.....en.0030220

    And yet, to repeat the last sentence from the quantum information paper, “we wouldn’t say entropy is a property of a system, but a property of an observer who describes a system.”

    The Quantum Thermodynamics Revolution – May 2017
    Excerpt: “Now in (quantum) information theory, we wouldn’t say entropy is a property of a system, but a property of an observer who describes a system.”,,,
    https://www.quantamagazine.org/quantum-thermodynamics-revolution/

    That statement is just fascinating! Why in blue blazes should the finely tuned entropic actions of the universe, entropic actions which also happen to explain time itself, even care if I am consciously observing them, and/or describing them, unless ‘the experience of ‘the now’ really is more foundational to reality than the finely tuned 1 in 10^10^123 entropy of the universe is? To state the obvious, this finding of entropy being “a property of an observer who describes a system.” is very friendly to a Mind First, and/or to a Theistic view of reality.
    For instance Romans chapter 8: verses 20 and 21 itself states, “For the creation was subjected to frustration, not by its own choice, but by the will of the one who subjected it, in hope that the creation itself will be liberated from its bondage to decay and brought into the glorious freedom of the children of God.”

    Romans 8:20-21
    For the creation was subjected to frustration, not by its own choice, but by the will of the one who subjected it, in hope that the creation itself will be liberated from its bondage to decay and brought into the glorious freedom of the children of God.

    “We have the sober scientific certainty that the heavens and earth shall ‘wax old as doth a garment’….
    Dark indeed would be the prospects of the human race if unilluminated by that light which reveals ‘new heavens and a new earth.’”
    Sir William Thomson, Lord Kelvin (1824 – 1907) – pioneer in many different fields, particularly electromagnetism and thermodynamics.

    Psalm 102:25-27
    Of old You laid the foundation of the earth, And the heavens are the work of Your hands. They will perish, but You will endure; Yes, they will all grow old like a garment; Like a cloak You will change them, And they will be changed. But You are the same, And Your years will have no end.

    Besides the Quantum Zeno effect, Quantum information theory and the experimental realization of Maxwell’s demon thought experiment all confirming that the mental attribute of ‘the experience of the now’ is very much a part of present day quantum physics, Quantum Mechanics also now shows that Stanley Jaki’s contention that “There is no physical parallel to the mind’s ability to extend from its position in the momentary present to its past moments, or in its ability to imagine its future” is confirmed by recent experimental breakthroughs in quantum mechanics.

    As to the ability of the mind to extend from its experience of the now to past moments in time, in recent experiments in quantum mechanics, it is now found that “quantum mechanics can even mimic an influence of future actions on past events”

    Quantum physics mimics spooky action into the past – April 23, 2012
    Excerpt: According to the famous words of Albert Einstein, the effects of quantum entanglement appear as “spooky action at a distance”. The recent experiment has gone one remarkable step further. “Within a naïve classical world view, quantum mechanics can even mimic an influence of future actions on past events”, says Anton Zeilinger.
    http://phys.org/news/2012-04-q.....ction.html

    Quantum Weirdness Now a Matter of Time – 2016
    Bizarre quantum bonds connect distinct moments in time, suggesting that quantum links — not space-time — constitute the fundamental structure of the universe.
    Excerpt: Not only can two events be correlated, linking the earlier one to the later one, but two events can become correlated such that it becomes impossible to say which is earlier and which is later.,,,
    “If you have space-time, you have a well-defined causal order,” said Caslav Brukner, a physicist at the University of Vienna who studies quantum information. But “if you don’t have a well-defined causal order,” he said — as is the case in experiments he has proposed — then “you don’t have space-time.”,,,
    Quantum correlations come first, space-time later. Exactly how does space-time emerge out of the quantum world? Bruner said he is still unsure.
    https://www.quantamagazine.org/20160119-time-entanglement/

    And as the following 2017 article states, “a decision made in the present can influence something in the past.”

    Physicists provide support for retrocausal quantum theory, in which the future influences the past
    July 5, 2017 by Lisa Zyga
    Excerpt: retrocausality means that, when an experimenter chooses the measurement setting with which to measure a particle, that decision can influence the properties of that particle (or another particle) in the past, even before the experimenter made their choice. In other words, a decision made in the present can influence something in the past.
    https://phys.org/news/2017-07-physicists-retrocausal-quantum-theory-future.html

    And to drive this point further home, in the following 2018 article Professor Crull provocatively states “entanglement can occur across two quantum systems that never coexisted,,, it implies that the measurements carried out by your eye upon starlight falling through your telescope this winter somehow dictated the polarity of photons more than 9 billion years old.”

    You thought quantum mechanics was weird: check out entangled time – Feb. 2018
    Excerpt: Just when you thought quantum mechanics couldn’t get any weirder, a team of physicists at the Hebrew University of Jerusalem reported in 2013 that they had successfully entangled photons that never coexisted. Previous experiments involving a technique called ‘entanglement swapping’ had already showed quantum correlations across time, by delaying the measurement of one of the coexisting entangled particles; but Eli Megidish and his collaborators were the first to show entanglement between photons whose lifespans did not overlap at all.,,,
    Up to today, most experiments have tested entanglement over spatial gaps. The assumption is that the ‘nonlocal’ part of quantum nonlocality refers to the entanglement of properties across space. But what if entanglement also occurs across time? Is there such a thing as temporal nonlocality?,,,
    The data revealed the existence of quantum correlations between ‘temporally nonlocal’ photons 1 and 4. That is, entanglement can occur across two quantum systems that never coexisted.
    What on Earth can this mean? Prima facie, it seems as troubling as saying that the polarity of starlight in the far-distant past – say, greater than twice Earth’s lifetime – nevertheless influenced the polarity of starlight falling through your amateur telescope this winter. Even more bizarrely: maybe it implies that the measurements carried out by your eye upon starlight falling through your telescope this winter somehow dictated the polarity of photons more than 9 billion years old.
    https://aeon.co/ideas/you-thought-quantum-mechanics-was-weird-check-out-entangled-time

    It is also very interesting to point out that these experiments demonstrating ‘quantum entanglement in time’ are very friendly to Dr. Michael Egnor’s (Theistic) contention (via Aristotle) that “Perception at a distance is no more inconceivable than action at a distance.”

    Perception and the Cartesian Theater – Michael Egnor – December 8, 2015
    Excerpt: Perception at a distance is no more inconceivable than action at a distance. The notion that a perception of the moon occurs at the moon is “bizarre” (Torley’s word) only if one presumes that perception is constrained by distance and local conditions — perhaps perception would get tired if it had to go to the moon or it wouldn’t be able to go because it’s too cold there. Yet surely the view that the perception of a rose held up to my eye was located at the rose wouldn’t be deemed nearly as bizarre. At what distance does perception of an object at the object become inconceivable?
    http://www.evolutionnews.org/2.....01471.html

  4. 4
    bornagain77 says:

    And it is also interesting to note that this finding or ‘quantum entanglement in time’ also refutes Dr Vincent Torley’s strenuous objection against Dr Egnor. Dr. Torley strenuously objected that perception cannot possibly occur ‘at a distance’ since a Supernova that we might be observing “ceased to exist nearly 200 millennia ago, long before the dawn of human history.”

    The Squid and the Supernova: A Reply to Professor Egnor – December 9, 2015 – vjtorley
    Excerpt: In February 1987, a supernova appeared in the Southern skies, and remained visible for several months. ,,, The problem is that the object itself ceased to exist nearly 200 millennia ago, long before the dawn of human history. Even if the squid that witnessed the explosion were capable of having perceptions which are located in intergalactic space, as Egnor contends, they are surely incapable of having perceptions which go back in time.
    ,,,perception is a bodily event, and that an event involving my body cannot take place at a point which is separate from my body. An event involving my body may occur inside my body, or at the surface of my body, but never separately from it. Thus it simply makes no sense to assert that I am here, at point X, but that my perceptions – or for that matter, my actions – are located at an external point Y.
    https://uncommondescent.com/intelligent-design/the-squid-and-the-supernova-a-reply-to-professor-egnor/

    Yet, despite Dr. Torley’s strenuous (materialistic) objection against Dr. Egnor’s claim that “Perception at a distance is no more inconceivable than action at a distance.” and to repeat Professor Crull’s provocative statement, the findings of quantum entanglement in time “implies that the measurements carried out by your eye upon starlight falling through your telescope this winter somehow dictated the polarity of photons more than 9 billion years old.”

    In short, quantum mechanics itself could care less about Dr. Torley’s materialistic presuppositions.

    In further confirmation of Stanley Jaki’s contention that, “There is no physical parallel to the mind’s ability to extend from its position in the momentary present to its past moments, or in its ability to imagine its future.”, in further confirmation of that contention, not only does “quantum mechanics show us that “a decision made in the present can influence something in the past.”, but quantum mechanics also shows us that our present conscious choices ultimately determine what type of future will be presented to us in our measurements of quantum systems.
    As leading experimentalist Anton Zeilinger states in the following video, “what we perceive as reality now depends on our earlier decision what to measure. Which is a very, very, deep message about the nature of reality and our part in the whole universe. We are not just passive observers.”

    “The Kochen-Speckter Theorem talks about properties of one system only. So we know that we cannot assume – to put it precisely, we know that it is wrong to assume that the features of a system, which we observe in a measurement exist prior to measurement. Not always. I mean in certain cases. So in a sense, what we perceive as reality now depends on our earlier decision what to measure. Which is a very, very, deep message about the nature of reality and our part in the whole universe. We are not just passive observers.”
    Anton Zeilinger –
    Quantum Physics Debunks Materialism – video (7:17 minute mark)
    https://www.youtube.com/watch?feature=player_detailpage&v=4C5pq7W5yRM#t=437

    As well, with contextuality we find that, “In the quantum world, the property that you discover through measurement is not the property that the system actually had prior to the measurement process. What you observe necessarily depends on how you carried out the observation”

    Contextuality is ‘magic ingredient’ for quantum computing – June 11, 2012
    Excerpt: Contextuality was first recognized as a feature of quantum theory almost 50 years ago. The theory showed that it was impossible to explain measurements on quantum systems in the same way as classical systems.
    In the classical world, measurements simply reveal properties that the system had, such as colour, prior to the measurement. In the quantum world, the property that you discover through measurement is not the property that the system actually had prior to the measurement process. What you observe necessarily depends on how you carried out the observation.
    Imagine turning over a playing card. It will be either a red suit or a black suit – a two-outcome measurement. Now imagine nine playing cards laid out in a grid with three rows and three columns. Quantum mechanics predicts something that seems contradictory – there must be an even number of red cards in every row and an odd number of red cards in every column. Try to draw a grid that obeys these rules and you will find it impossible. It’s because quantum measurements cannot be interpreted as merely revealing a pre-existing property in the same way that flipping a card reveals a red or black suit.
    Measurement outcomes depend on all the other measurements that are performed – the full context of the experiment.
    Contextuality means that quantum measurements can not be thought of as simply revealing some pre-existing properties of the system under study. That’s part of the weirdness of quantum mechanics.
    http://phys.org/news/2014-06-w.....antum.html

    Thus, Stanley Jaki’s contention that “There is no physical parallel to the mind’s ability to extend from its position in the momentary present to its past moments, or in its ability to imagine its future.”, is now experimentally established to be true by the fact that “a decision made in the present can influence something in the past.” and is also established by the fact that, “We are not just passive observers,,, what we perceive as reality now depends on our earlier decision what to measure”.

    Thus, (contrary to what Einstein himself thought was possible for experimental physics), advances in quantum mechanics have now shown, in overwhelming fashion, that ‘the experience of the now’ is very much a part of experimental physics.

    Likewise, as mentioned previously, the mental attribute of free will also makes its presence known by recent advances in quantum mechanics.

    As Steven Weinberg, an atheist himself, states in the following article, In the instrumentalist approach (in quantum mechanics) humans are brought into the laws of nature at the most fundamental level.,,, the instrumentalist approach turns its back on a vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else.,,, In quantum mechanics these probabilities do not exist until people choose what to measure,,, Unlike the case of classical physics, a choice must be made,,,

    The Trouble with Quantum Mechanics – Steven Weinberg – January 19, 2017
    Excerpt: The instrumentalist approach,, (the) wave function,, is merely an instrument that provides predictions of the probabilities of various outcomes when measurements are made.,,
    In the instrumentalist approach,,, humans are brought into the laws of nature at the most fundamental level. According to Eugene Wigner, a pioneer of quantum mechanics, “it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness.”11
    Thus the instrumentalist approach turns its back on a vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else. It is not that we object to thinking about humans. Rather, we want to understand the relation of humans to nature, not just assuming the character of this relation by incorporating it in what we suppose are nature’s fundamental laws, but rather by deduction from laws that make no explicit reference to humans. We may in the end have to give up this goal,,,
    Some physicists who adopt an instrumentalist approach argue that the probabilities we infer from the wave function are objective probabilities, independent of whether humans are making a measurement. I don’t find this tenable. In quantum mechanics these probabilities do not exist until people choose what to measure, such as the spin in one or another direction. Unlike the case of classical physics, a choice must be made,,,
    http://quantum.phys.unm.edu/46.....inberg.pdf

    In fact Weinberg, again an atheist, rejected the instrumentalist approach precisely because “humans are brought into the laws of nature at the most fundamental level” and because it undermined the Darwinian worldview from within. Yet, regardless of how he and other atheists may prefer the world to behave, quantum mechanics itself could care less how atheists prefer the world to behave.

    For instance, this recent 2019 experimental confirmation of the “Wigner’s Friend” thought experiment established that “measurement results,, must be understood relative to the observer who performed the measurement”.

    More Than One Reality Exists (in Quantum Physics) By Mindy Weisberger – March 20, 2019
    Excerpt: “measurement results,, must be understood relative to the observer who performed the measurement”.
    https://www.livescience.com/65029-dueling-reality-photons.html

    Experimental test of local observer-independence – 2019
    Excerpt: The scientific method relies on facts, established through repeated measurements and agreed upon universally, independently of who observed them. In quantum mechanics, the objectivity of observations is not so clear, most dramatically exposed in Eugene Wigner’s eponymous thought experiment where two observers can experience seemingly different realities. The question whether these realities can be reconciled in an observer-independent way has long remained inaccessible to empirical investigation, until recent no-go-theorems constructed an extended Wigner’s friend scenario with four observers that allows us to put it to the test. In a state-of-the-art 6-photon experiment, we realise this extended Wigner’s friend scenario, experimentally violating the associated Bell-type inequality by 5 standard deviations. If one holds fast to the assumptions of locality and free-choice, this result implies that quantum theory should be interpreted in an observer-dependent way.
    https://arxiv.org/pdf/1902.05080.pdf

    Moreover, although there have been several major loopholes in quantum mechanics over the past several decades that atheists have tried to appeal to in order to try to avoid the ‘spooky’ Theistic implications of quantum mechanics, over the past several years each of those major loopholes have each been closed one by one. The last major loophole that was left to be closed was the “setting independence” and/or the ‘free-will’ loophole:

    Closing the ‘free will’ loophole: Using distant quasars to test Bell’s theorem – February 20, 2014
    Excerpt: Though two major loopholes have since been closed, a third remains; physicists refer to it as “setting independence,” or more provocatively, “free will.” This loophole proposes that a particle detector’s settings may “conspire” with events in the shared causal past of the detectors themselves to determine which properties of the particle to measure — a scenario that, however far-fetched, implies that a physicist running the experiment does not have complete free will in choosing each detector’s setting. Such a scenario would result in biased measurements, suggesting that two particles are correlated more than they actually are, and giving more weight to quantum mechanics than classical physics.
    “It sounds creepy, but people realized that’s a logical possibility that hasn’t been closed yet,” says MIT’s David Kaiser, the Germeshausen Professor of the History of Science and senior lecturer in the Department of Physics. “Before we make the leap to say the equations of quantum theory tell us the world is inescapably crazy and bizarre, have we closed every conceivable logical loophole, even if they may not seem plausible in the world we know today?”
    https://www.sciencedaily.com/releases/2014/02/140220112515.htm

    And now Anton Zeilinger and company have recently, as of 2018, pushed the ‘free will loophole’ back to 7.8 billion years ago, thereby firmly establishing the ‘common sense’ fact that the free will choices of the experimenter in the quantum experiments are truly free and are not determined by any possible causal influences from the past for at least the last 7.8 billion years, and that the experimenters themselves are therefore shown to be truly free to choose whatever measurement settings in the experiments that he or she may so desire to choose so as to ‘logically’ probe whatever aspect of reality that he or she may be interested in probing.

    Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars – Anton Zeilinger – 14 June 2018
    Abstract: In this Letter, we present a cosmic Bell experiment with polarization-entangled photons, in which measurement settings were determined based on real-time measurements of the wavelength of photons from high-redshift quasars, whose light was emitted billions of years ago; the experiment simultaneously ensures locality. Assuming fair sampling for all detected photons and that the wavelength of the quasar photons had not been selectively altered or previewed between emission and detection, we observe statistically significant violation of Bell’s inequality by 9.3 standard deviations, corresponding to an estimated p value of approx. 7.4 × 10^21. This experiment pushes back to at least approx. 7.8 Gyr ago the most recent time by which any local-realist influences could have exploited the “freedom-of-choice” loophole to engineer the observed Bell violation, excluding any such mechanism from 96% of the space-time volume of the past light cone of our experiment, extending from the big bang to today.
    https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.080403

  5. 5
    bornagain77 says:

    Thus regardless of how Steven Weinberg and other atheists may prefer the universe to behave, with the closing of the last remaining free will loophole in quantum mechanics, “humans are indeed brought into the laws of nature at the most fundamental level”, and thus these recent findings from quantum mechanics directly undermine, as Weinberg himself stated, the “vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else.”

    Moreover allowing free will and/or Agent causality into the laws of physics at their most fundamental level has some fairly profound implications for us personally.

    First and foremost, allowing the Agent causality of God ‘back’ into physics, as the Christian founders of modern science originally envisioned,,,, (Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders),,, and as quantum mechanics itself now empirically demands (with the closing of the free will loophole by Anton Zeilinger and company), rightly allowing the Agent causality of God ‘back’ into physics provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead provides an empirically backed reconciliation, via the Shroud of Turin, between quantum mechanics and general relativity into the much sought after ‘Theory of Everything”. Here are a few posts where I lay out and defend some of the evidence for that claim:

    November 2019 – despite the fact that virtually everyone, including the vast majority of Christians, hold that the Copernican Principle is unquestionably true, the fact of the matter is that the Copernican Principle is now empirically shown, (via quantum mechanics and general relativity, etc..), to be a false assumption.
    https://uncommondescent.com/intelligent-design/so-then-maybe-we-are-privileged-observers/#comment-688855

    (February 19, 2019) To support Isabel Piczek’s claim that the Shroud of Turin does indeed reveal a true ‘event horizon’, the following study states that ‘The bottom part of the cloth (containing the dorsal image) would have born all the weight of the man’s supine body, yet the dorsal image is not encoded with a greater amount of intensity than the frontal image.’,,,
    Moreover, besides gravity being dealt with, the shroud also gives us evidence that Quantum Mechanics was dealt with. In the following paper, it was found that it was not possible to describe the image formation on the Shroud in classical terms but they found it necessary to describe the formation of the image on the Shroud in discrete quantum terms.
    https://uncommondescent.com/intelligent-design/experiment-quantum-particles-can-violate-the-mathematical-pigeonhole-principle/#comment-673178

    The evidence for the Shroud’s authenticity keeps growing. (Timeline of facts) – November 08, 2019
    What Is the Shroud of Turin? Facts & History Everyone Should Know – Myra Adams and Russ Breault
    https://www.christianity.com/wiki/jesus-christ/what-is-the-shroud-of-turin.html

    To give us a small glimpse of the power that was involved in Christ’s resurrection from the dead, the following recent article found that, ”it would take 34 Thousand Billion Watts of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.”

    Astonishing discovery at Christ’s tomb supports Turin Shroud – NOV 26TH 2016
    Excerpt: The first attempts made to reproduce the face on the Shroud by radiation, used a CO2 laser which produced an image on a linen fabric that is similar at a macroscopic level. However, microscopic analysis showed a coloring that is too deep and many charred linen threads, features that are incompatible with the Shroud image. Instead, the results of ENEA “show that a short and intense burst of VUV directional radiation can color a linen cloth so as to reproduce many of the peculiar characteristics of the body image on the Shroud of Turin, including shades of color, the surface color of the fibrils of the outer linen fabric, and the absence of fluorescence”.
    ‘However, Enea scientists warn, “it should be noted that the total power of VUV radiations required to instantly color the surface of linen that corresponds to a human of average height, body surface area equal to = 2000 MW/cm2 17000 cm2 = 34 thousand billion watts makes it impractical today to reproduce the entire Shroud image using a single laser excimer, since this power cannot be produced by any VUV light source built to date (the most powerful available on the market come to several billion watts )”.
    Comment
    The ENEA study of the Holy Shroud of Turin concluded that it would take 34 Thousand Billion Watts of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.
    http://westvirginianews.blogsp.....in-is.html

    Verse:

    Colossians 1:15-20
    The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross.

    Thus in conclusion, and as Dr. Egnor pointed out, although the mental attribute of qualia is forever beyond ‘the purview of physical science”, we are not left completely in the dark as to seeing how the immaterial mind might relate to the physical world. Specifically, the mental attributes of the ‘experience of the now’ and of free will do lend themselves very much to scientific investigation and confirm, in over the top fashion, that, as Richard Conn Henry put the current situation in quantum mechanics, “The Universe is immaterial — mental and spiritual. Live, and enjoy.”

    “The Universe is immaterial — mental and spiritual. Live, and enjoy.”
    Richard Conn Henry – The mental Universe – 06 July 2005
    https://www.nature.com/articles/436029a

  6. 6
    Retired Physicist says:

    We really need an open thread around here so I can post fun things like this.

    Apeirogons are generalized polygons whose sides are countably infinite.

    https://en.m.wikipedia.org/wiki/Apeirogon

  7. 7
    ET says:

    RP:

    Apeirogons are generalized polygons whose sides are countably infinite.

    How do you know?

  8. 8
    Bob O'H says:

    He spent a week in a hotel counting the sides.

    It would have been a weekend but more guests kept on turning up, so RP had to change rooms repeatedly.

  9. 9
    Retired Physicist says:

    @Bob it seemed like I was changing rooms forever.

  10. 10
    Bob O'H says:

    Next time you go there, you should check the rooms carefully. They might look rectangular, but they’re actually arranged around a circle.

  11. 11
    ET says:

    Ok wait, if infinite rooms are filled with infinite guests, how do more guests show up? If they can just pop into existence then so can then the rooms to accommodate them can also pop into existence. You get the rooms from the same place Hilbert got the newly arriving guests, from his arse. No need for anyone to move.

  12. 12
    JVL says:

    ET: Ok wait, if infinite rooms are filled with infinite guests, how do more guests show up?

    There are infinitely many of them so the queue extends forever.

    If they can just pop into existence then so can then the rooms to accommodate them can also pop into existence.

    They already exist, just like the positive integers. An infinitely long line of rooms and guests.

    You get the rooms from the same place Hilbert got the newly arriving guests, from his arse. No need for anyone to move.

    Which room in the infinite hotel would you like then? Pick a positive integer, any positive integer. We will have that room and can make it available.

  13. 13
    ET says:

    JVL:

    There are infinitely many of them so the queue extends forever.

    Infinitely many? That isn’t a thing. But that is still a non-sequitur.

    They already exist, just like the positive integers. An infinitely long line of rooms and guests.

    That isn’t what Hilbert said.

    Hilbert said there was a hotel with infinite rooms, that were filled by infinite guests. Then another guest shows up, making it infinity + 1, which is incorrect.

    The issue is there isn’t any queue. The guests would turn and enter the room they are next to

  14. 14
    asauber says:

    Andrew’s Infinite Public Service Announcement:

    Conceptually, mixing infinite in with finite gives you absurdity.

    Carry on.

    Andrew

  15. 15
    JVL says:

    ET: Hilbert said there was a hotel with infinite rooms, that were filled by infinite guests. Then another guest shows up, making it infinity + 1, which is incorrect.

    What’s incorrect about it? It’s just a thought ‘experiment’. Infinity + 1 = infinity. Simple.

    The issue is there isn’t any queue. The guests would turn and enter the room they are next to

    Yup, that’s correct. I was just messin’ with you earlier.

  16. 16
    JVL says:

    Asauber: Conceptually, mixing infinite in with finite gives you absurdity.

    If you can’t do the math, stay out of the kitchen . . . or something.

  17. 17
    bornagain77 says:

    “If you can’t do the math, stay out of the kitchen ”

    says the man with no ‘mathematical kitchen’ to cook in,

    What Does It Mean to Say That Science & Religion Conflict? – M. Anthony Mills – April 16, 2018
    Excerpt: Barr rightly observes that scientific atheists often unwittingly assume not just metaphysical naturalism but an even more controversial philosophical position: reductive materialism, which says all that exists is or is reducible to the material constituents postulated by our most fundamental physical theories. ,,,
    In fact, more problematic for the materialist than the non-existence of persons is the existence of mathematics. Why? Although a committed materialist might be perfectly willing to accept that you do not really exist, he will have a harder time accepting that numbers do not exist. The trouble is that numbers — along with other mathematical entities such as classes, sets, and functions — are indispensable for modern science. And yet — here’s the rub — these “abstract objects” are not material. Thus, one cannot take science as the only sure guide to reality and at the same time discount disbelief in all immaterial realities.
    https://www.realclearreligion.org/articles/2018/04/16/what_does_it_mean_to_say_that_science_and_religion_conflict.html

  18. 18
    ET says:

    JVL:

    What’s incorrect about it?

    There isn’t any such thing as infinity + 1

  19. 19
    asauber says:

    “If you can’t do the math, stay out of the kitchen”

    JVL,

    This has nothing to do with math.

    Andrew

  20. 20
    JVL says:

    Bornagain77: says the man with no ‘mathematical kitchen’ to cook in,

    Because I cannot conceive of mathematics working any differently than it does I do not believe mathematics depends on any kind of design. I may be wrong but I think math HAS to be the way it is.

    ET: There isn’t any such thing as infinity + 1

    Of course there is! If you have an infinite number of things and you add one more you still have an infinite amount of things. Simple.

    Asauber: This has nothing to do with math.

    I was just being silly.

  21. 21
    asauber says:

    JVL,

    Let me put it to you philosophically, which happens before you start math.

    Finity = context. Infinity = context removed.

    They don’t work together, other than in someone’s imagination.

    Andrew

  22. 22
    JVL says:

    Asauber: Let me put it to you philosophically, which happens before you start math.

    Finity = context. Infinity = context removed.

    They don’t work together, other than in someone’s imagination.

    Well, I don’t have the heart to tell several centuries of mathematicians who have been using infinity that they are wrong. You’re going to have to do it.

    Did you ever take Calculus by the way? And take a limit as x goes to infinity? Just wondering.

  23. 23
    asauber says:

    “mathematicians who have been using infinity”

    JVL,

    Of course they are using it. But it’s all in their heads. 😉

    Andrew

  24. 24
    asauber says:

    JVL,

    And I didn’t say mathematicians are “wrong”. You are just trying to put words in my mouth.

    Andrew

  25. 25
    JVL says:

    Asauber: Of course they are using it. But it’s all in their heads. ????

    But then so are a lot of higher level mathematical operations and manipulations.

    And I didn’t say mathematicians are “wrong”. You are just trying to put words in my mouth.

    Well, I don’t know what you meant then when you said they don’t work together.

    When you take a limit to infinity you start with something finite and let it grow without bound so you are using the concepts of finite and infinite together. The mathematics is pretty simple and straightforward and has been used for quite a while now. I don’t think it’s just in the mathematicians head since, I believe, any being of any kind in any reality would come upon the same procedure and use it the same way. How could it be otherwise?

  26. 26
    asauber says:

    “When you take a limit to infinity you start with something finite and let it grow without bound so you are using the concepts of finite and infinite together.”

    JVL,

    “so are a lot of higher level mathematical operations and manipulations”

    Of course. Abstractly.

    “you start with something finite”

    And you end with something finite, right?

    Andrew

  27. 27
    ET says:

    JVL:

    If you have an infinite number of things and you add one more you still have an infinite amount of things.

    What “one more”? You already have everything.

  28. 28
    JVL says:

    Asauber: And you end with something finite, right?

    It depends. For example: in Calculus when you’re trying to figure out if an infinite series converges or diverges you might get a finite result (it converges) or you might get an infinite answer (it diverges).

    Have you taken Calculus? There’s tons of examples.

    On of my favourites is: take the function 1/x for x > 1 and rotate it about the x-axis. You get a horn-shaped thing (sometimes nicknamed the horn of Gabriel). It turns out, if you do the math right, that that object has a finite volume but an infinite surface area. So, again, the finite and infinite are manifest in the same object.

    Fractals are another good example: they have infinite perimeter but finite area.

  29. 29
    asauber says:

    “So, again, the finite and infinite are manifest in the same object.”

    JVL,

    Sure. In your imagination.

    Andrew

  30. 30
    JVL says:

    ET: What “one more”? You already have everything.

    Not necessarily. Take the set of all even integers. That’s an infinite set. Add in the integer ‘3’ which is not an even integer. You still have an infinite number of integers. Add in all the odd integers and you still have an infinite set. Add in all the values like 0.5, 1.5, 2.5, 3.5 . . . you still have an infinite set.

    Hilbert’s metaphor isn’t something I find very useful to be honest. Just doing the math works and makes more sense.

    Math is like a language, the pleasure you get out of it depends on how well you speak it.

  31. 31
    ET says:

    Thank you for proving that the set of even integers is smaller than the set of all integers.

  32. 32
    JVL says:

    Asauber: Sure. In your imagination..

    NOT in my imagination. Anyone who knows the mathematical procedures would get the same result. The procedures work for finite objects you could actually measure and touch. Use the same procedures on something that’s infinite and you can get infinite and finite results depending on what procedure you followed.

    Math HAS to work that way. Or it wouldn’t work at all. It’s not made up or imagined. It’s pure logic.

  33. 33
    asauber says:

    “It’s pure logic.”

    JVL,

    You are stuck on something. I’m not sure what it is. Pure logic resides in your mind. I don’t think you can find it anywhere else.

    Andrew

  34. 34
    JVL says:

    ET: Thank you for proving that the set of even integers is smaller than the set of all integers.

    Is an incorrect conclusion. As shown by the work of Cantor and others.

    You can match up the integers with the even integers one-to-one so that no even integer is unpaired with and integer and no integer is unpaired with an even integer. You tell me an integer and I’ll tell you what even integer its matched with. You tell me an even integer and I’ll tell you an integer it’s matched up with. Nothing is left out.

    That can only happen if both sets have the same number of elements. If they had different number of elements there would be something unmatched. But there isn’t.

    So, the set of all even integers is the same ‘size’ as the set of all integers. QED

    That same kind of matching procedure works for finite sets as well: if you can match two sets up one-to-one they must be the same size. In fact, that’s how we count how many objects there are: we are matching up the positive integers with the elements of a set.

  35. 35
    JVL says:

    Asuaber: You are stuck on something. I’m not sure what it is. Pure logic resides in your mind. I don’t think you can find it anywhere else.

    Math has to work the way it does. It can’t be any different. Therefore it must exist outside of my mind or imagination.

    If you start with the same basic counting techniques humans arrived at millenniums ago and extend it you will get the same mathematical truths we know now. Maybe not in the same order, maybe expressed differently but the same truths. That’s not down to me or you; that’s something invariant.

    Try and find some other kind of mathematics. See if it’s just in your mind.

  36. 36
    asauber says:

    “That’s not down to me or you;”

    JVL,

    But it is. No mind, no math.

    Andrew

  37. 37
    bornagain77 says:

    JVL:

    Because I cannot conceive of mathematics working any differently than it does I do not believe mathematics depends on any kind of design. I may be wrong but I think math HAS to be the way it is.

    LOL, Too funny, a Darwinian materialist appeals to logical necessity to try to claim that mathematics does not depend ‘on any kind of design’.

    To point out the glaringly obvious elephant in the living room, both mathematics and logic have no place to stand within the Darwinist’s materialistic worldview.

    Naturalism and Self-Refutation – Michael Egnor – January 31, 2018
    Excerpt: Mathematics is certainly something we do. Is mathematics “included in the space-time continuum [with] basic elements … described by physics”?,,,
    What is the physics behind the Pythagorean theorem? After all, no actual triangle is perfect, and thus no actual triangle in nature has sides such that the Pythagorean theorem holds. There is no real triangle in which the sum of the squares of the sides exactly equals the square of the hypotenuse. That holds true for all of geometry. Geometry is about concepts, not about anything in the natural world or about anything that can be described by physics. What is the “physics” of the fact that the area of a circle is pi multiplied by the square of the radius? And of course what is natural and physical about imaginary numbers, infinite series, irrational numbers, and the mathematics of more than three spatial dimensions? Mathematics is entirely about concepts, which have no precise instantiation in nature as described by physics.,,,
    Clark would likely argue that the concepts of mathematics are the products of our brains, which are purely material things. But that’s merely an assertion based on metaphysical presupposition, without any basis in physics or science. The hallmarks of the mind — intentionality, qualia, restricted access, the generation of propositions and logic, etc., have nothing whatsoever to do with matter. Matter, as understood by physics, isn’t intentional — it isn’t about anything. Matter is not inherently subjective, it doesn’t generate propositions or logic, etc.,,,
    Furthermore, the very framework of Clark’s argument — logic — is neither material nor natural. Logic, after all, doesn’t exist “in the space-time continuum” and isn’t described by physics. What is the location of modus ponens? How much does Gödel’s incompleteness theorem weigh? What is the physics of non-contradiction? How many millimeters long is Clark’s argument for naturalism? Ironically the very logic that Clark employs to argue for naturalism is outside of any naturalistic frame.
    The strength of Clark’s defense of naturalism is that it is an attempt to present naturalism’s tenets clearly and logically. That is its weakness as well, because it exposes naturalism to scrutiny, and naturalism cannot withstand even minimal scrutiny. Even to define naturalism is to refute it.
    https://evolutionnews.org/2018/01/naturalism-and-self-refutation/

    As the old joke goes about God telling the scientist to go ‘get your own dirt’,,

    God was once approached by a scientist who said, “Listen God, we’ve decided we don’t need you anymore. These days we can clone people, transplant organs and do all sorts of things that used to be considered miraculous.”
    God replied, “Don’t need me huh? How about we put your theory to the test. Why don’t we have a competition to see who can make a human being, say, a male human being.”
    The scientist agrees, so God declares they should do it like he did in the good old days when he created Adam.
    “Fine” says the scientist as he bends down to scoop up a handful of dirt.”
    “Whoa!” says God, shaking his head in disapproval. “Not so fast. You get your own dirt.”
    https://www.reddit.com/r/Jokes/comments/b0faut/get_your_own_dirt/

    Likewise JVL, go get your own mathematics,

    KEEP IT SIMPLE by Edward Feser – April 2020
    Excerpt: Mathematics appears to describe a realm of entities with quasi-­divine attributes. The series of natural numbers is infinite. That one and one equal two and two and two equal four could not have been otherwise. Such mathematical truths never begin being true or cease being true; they hold eternally and immutably. The lines, planes, and figures studied by the geometer have a kind of perfection that the objects of our ­experience lack. Mathematical objects seem ­immaterial and known by pure reason rather than through the senses. Given the centrality of mathematics to scientific explanation, it seems in some way to be a cause of the natural world and its order.
    How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect.
    https://www.firstthings.com/article/2020/04/keep-it-simple

  38. 38
    ET says:

    I see that the concepts of addition an subtraction and addition still elude JVL. Strange that set subtraction refutes Cantor’s alleged proof.

  39. 39
    ET says:

    Cantor’s diagonal just proves that the sets are countable.

  40. 40
    JVL says:

    Asauber: But it is. No mind, no math.

    I disagree. I think it takes a mind to experience or perceive math but the math is there regardless.

    You are an experiencialist. I’m not.

  41. 41
    JVL says:

    BornAgain77: LOL, Too funny, a Darwinian materialist appeals to logical necessity to try to claim that mathematics does not depend ‘on any kind of design’.

    If you can propose another kind of mathematics then I’ll be very, very interested. If you can’t then . . . .

  42. 42
    JVL says:

    ET: I see that the concepts of addition an subtraction and addition still elude JVL. Strange that set subtraction refutes Cantor’s alleged proof.

    Uh huh. If you’d like to propose a different system for handling infinities and then face the heat and answer questions about your system then by all means do so.

    Cantor’s diagonal just proves that the sets are countable.

    SOME sets are countably infinite.

    If you’ve got a better system lay it out and let us query it.

  43. 43
    asauber says:

    “I think it takes a mind to experience or perceive math but the math is there regardless.”

    JVL.

    Where is it?

    Andrew

  44. 44
    JVL says:

    Asauber: Where is it?

    It exists outside of space and time. It just is.

    You cannot get away from one plus two equals three. You might use different words or terms but the basic mathematics stays true. Always.

  45. 45
    bornagain77 says:

    “It exists outside of space and time. It just is.”

    Godel begs to differ.

    Moreover, exactly how do you, a Darwinist who believes we are purely material beings, account for the fact that we can grasp mathematical concepts that have no material basis? Again, you, as a Darwinian materialist, simply have no place to stand. Whereas, we, as Christian Theists who rightly believe that we have immaterial minds, readily do have foundation to stand upon.

    As Wallace himself stated,

    “Nothing in evolution can account for the soul of man. The difference between man and the other animals is unbridgeable. Mathematics is alone sufficient to prove in man the possession of a faculty unexistent in other creatures. Then you have music and the artistic faculty. No, the soul was a separate creation.”
    – Alfred Russel Wallace – 1910

  46. 46
    asauber says:

    “It exists outside of space and time.”

    JVL,

    How Twilight Zone of you. lol

    Andrew

  47. 47
    JVL says:

    BornAgain77: Godel begs to differ.

    So?

    Moreover, exactly how do you, a Darwinist who believes we are purely material beings, account for the fact that we can grasp mathematical concepts that have no material basis? Again, you, as a Darwinian materialist, simply have no place to stand. Whereas, we, as Christian Theists who rightly believe that we have immaterial minds, readily do have foundation to stand upon.

    The more intelligent and successful creatures are more aware of the basic rules that underlie the universes’s existence. It’s simple. The more advanced the intelligence the better able they are at grasping the basic rules and using and extending them. No god or soul needed. Just a better understanding of how things work.

    You look at the universe and look for justifications for your belief in God. Everything you find beautiful or complicated is an indication of your deity. I don’t see it that way. I see the universe being built on some basic structures and rules and as we advance and pay attention we grasp those things better and better.

    You don’t need a soul, you just need to pay attention and remember.

  48. 48
    asauber says:

    “the basic rules”

    JVL,

    People are trying to give you an opportunity to present coherent ideas and you keep failing.

    How did the basic rules come about?

    Andrew

  49. 49
    JVL says:

    Asauber: People are trying to give you an opportunity to present coherent ideas and you keep failing.

    What? Because I’m not saying what you want to hear?

    How did the basic rules come about?

    The basic rules of what? Mathematics? Physics? Chemistry?

    Chemistry is a subset of physics. The rules of chemistry are based on the underlying physics.

    Physics is a reflection of the basic underlying structures of the universe. It’s complicated but let’s say you start with electrons, protons and neutrons. The interactions between those particles give rise to a lot of other rules and laws. We are learning to delve deeper than those three particles. We are learning to dig further down. There’s no indication it’s planned or dictated. It’s all just the way it is. Perhaps the very fabric of the universe can only react in certain ways?

    Mathematics I don’t think can be another way. That doesn’t mean that it was dictated or defined. I don’t know why anyone would look at it and just say: see, that indicated some kind of design. I hear that more from people who haven’t studied mathematics. I mean really studied it. That means a Bachelor’s degree or more.

  50. 50
    asauber says:

    “The basic rules of what? Mathematics? Physics? Chemistry?”

    JVL,

    You tell me. You are the one who brought it up.

    Andrew

  51. 51
    ET says:

    Yes, JVL ascribes to the “this all just happened to happen” scenario. Untestable and takes more faith to believe than Christianity.

  52. 52
    bornagain77 says:

    BA77: “Godel begs to differ.”

    JVL: “So?”

    Nothing to see here eh JVL?

    The Naked Gun – “Nothing to see here!” (1080p)
    https://www.youtube.com/watch?v=aKnX5wci404

    Contrary to JVL’s nonchalant attitude towards evidence that directly falsifies his claim, and as the following article states, “Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous.”

    Taking God Out of the Equation – Biblical Worldview – by Ron Tagliapietra – January 1, 2012
    Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties.
    1. Validity … all conclusions are reached by valid reasoning.
    2. Consistency … no conclusions contradict any other conclusions.
    3. Completeness … all statements made in the system are either true or false.
    The details filled a book, but the basic concept was simple and elegant. He (Godel) summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem.
    Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation.
    Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3).
    https://uncommondescent.com/philosophy/why-god-appears-to-be-a-mathematician/#comment-703707

    Physicists (and mathematicians) today, especially with the proof of Godel’s incompleteness theorems sitting right before them, simply have no basis for their belief that mathematics, all by its lonesome, can somehow function as a God substitute,

    THE GOD OF THE MATHEMATICIANS – DAVID P. GOLDMAN – August 2010
    Excerpt: we cannot construct an ontology that makes God dispensable. Secularists can dismiss this as a mere exercise within predefined rules of the game of mathematical logic, but that is sour grapes, for it was the secular side that hoped to substitute logic for God in the first place. Gödel’s critique of the continuum hypothesis has the same implication as his incompleteness theorems: Mathematics never will create the sort of closed system that sorts reality into neat boxes.
    http://www.firstthings.com/art.....ematicians

    Stephen Hawking himself, an atheist, honestly admitted that “Gödel’s incompleteness theorem (1931), proves that there are limits to what can be ascertained by mathematics. Kurt Gödel halted the achievement of a unifying all-encompassing theory of everything in his theorem that: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove”

    “Gödel’s incompleteness theorem (1931), proves that there are limits to what can be ascertained by mathematics. Kurt Gödel halted the achievement of a unifying all-encompassing theory of everything in his theorem that: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove”
    – Stephen Hawking & Leonard Miodinow, The Grand Design (2010)

    As well, Steven Weinberg, also an atheist, also honestly admitted that, ” “I don’t think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don’t describe the world as we know it. And we will always be left with a question ‘why are the laws of nature what they are rather than some other laws?’. And I don’t see any way out of that.”

    “I don’t think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don’t describe the world as we know it. And we will always be left with a question ‘why are the laws of nature what they are rather than some other laws?’. And I don’t see any way out of that.
    The fact that the constants of nature are suitable for life, which is clearly true, we observe,,,”
    (Weinberg then comments on the multiverse conjecture of atheists)
    “No one has constructed a theory in which that is true. I mean,, the (multiverse) theory would be speculative, but we don’t even have a theory in which that speculation is mathematically realized. But it is a possibility.”
    – Steven Weinberg – as stated to Richard Dawkins at the 8:15 minute mark of the following video
    – Leonard Susskind – Richard Dawkins and Steven Weinberg – 1 in 10^120 – Cosmological Constant points to intelligent design – video
    https://youtu.be/z4E_bT4ecgk?t=495

    In fact, there are an infinite number of mathematical theorems that could have described the universe but don’t, As Gregory Chaitin pointed out, “what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms. ”

    The Limits Of Reason – Gregory Chaitin – 2006
    Excerpt: Unlike Gödel’s approach, mine is based on measuring information and showing that some mathematical facts cannot be compressed into a theory because they are too complicated. This new approach suggests that what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.
    http://www.umcs.maine.edu/~chaitin/sciamer3.pdf

    Mathematics, contrary to what the vast majority of theoretical physicists believe today, simply never will have the capacity within itself to function as a God substitute.

    As Dr. Bruce Gordon explains, “The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,,
    Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.”

    BRUCE GORDON: Hawking’s irrational arguments – October 2010
    Excerpt: ,,,The physical universe is causally incomplete and therefore neither self-originating nor self-sustaining. The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy.
    This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,,
    Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.” Anything else invokes random miracles as an explanatory principle and spells the end of scientific rationality.,,,
    Universes do not “spontaneously create” on the basis of abstract mathematical descriptions, nor does the fantasy of a limitless multiverse trump the explanatory power of transcendent intelligent design. What Mr. Hawking’s contrary assertions show is that mathematical savants can sometimes be metaphysical simpletons. Caveat emptor.
    http://www.washingtontimes.com.....arguments/

    Moreover, an essential belief in the rise of modern science, a belief that distinctly separated it from Platonic philosophy that preceded it, (a philosophy that held math to exist separate from God), was the Christian’s belief that mathematics, especially any mathematics that might describe this universe, was, and is, the product of the Mind of God.

    KEEP IT SIMPLE by Edward Feser – April 2020
    Excerpt: How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect.
    There is also a very different answer, in which the mathematical realm is a rival to God rather than a path to him. According to this view, mathematical objects such as numbers and geometrical figures exist not only independently of the ­material world, but also independently of any mind, including the divine mind. They occupy a “third realm” of their own, the realm famously described in Plato’s Theory of Forms. God used this third realm as a blueprint when creating the physical world, but he did not create the realm itself and it exists outside of him. This position is usually called Platonism since it is commonly thought to have been ­Plato’s own view, as distinct from that of his Neoplatonic followers who relocated mathematical objects and other Forms into the divine mind. (I put to one side for present purposes the question of how historically accurate this standard narrative is.)
    https://www.firstthings.com/article/2020/04/keep-it-simple

    And as Paul Davies observed, “All the early scientists, like Newton, were religious in one way or another. They saw their science as a means of uncovering traces of God’s handiwork in the universe. What we now call the laws of physics they regarded as God’s abstract creation: thoughts, so to speak, in the mind of God. So in doing science, they supposed, one might be able to glimpse the mind of God – an exhilarating and audacious claim.”

    “All the early scientists, like Newton, were religious in one way or another. They saw their science as a means of uncovering traces of God’s handiwork in the universe. What we now call the laws of physics they regarded as God’s abstract creation: thoughts, so to speak, in the mind of God. So in doing science, they supposed, one might be able to glimpse the mind of God – an exhilarating and audacious claim.”
    – Paul Davies
    http://ldolphin.org/bumbulis/

  53. 53
    bornagain77 says:

    In fact, in 1619, Johannes Kepler, shortly after discovering the laws of planetary motion, stated,

    “O, Almighty God, I am thinking Thy thoughts after Thee!”
    – Johannes Kepler, 1619, The Harmonies of the World.

    Likewise in 1687, Sir Isaac Newton, after discovering the law of universal gravitation, (which has been referred to as the first major unification in physics), stated that, “This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being.,,,This Being governs all things, not as the soul of the world, but as Lord over all;”

    “This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being. And if the fixed stars are the centres of other like systems, these, being formed by the like wise counsel, must be all subject to the dominion of One; especially since the light of the fixed stars is of the same nature with the light of the sun, and from every system light passes into all the other systems: and lest the systems of the fixed stars should, by their gravity, fall on each other mutually, he hath placed those systems at immense distances one from another. This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont to be called Lord God pantokrator, or Universal Ruler;,,, The Supreme God is a Being eternal, infinite, absolutely perfect;,,, from his true dominion it follows that the true God is a living, intelligent, and powerful Being; and, from his other perfections, that he is supreme, or most perfect. He is eternal and infinite, omnipotent and omniscient; that is, his duration reaches from eternity to eternity; his presence from infinity to infinity; he governs all things, and knows all things that are or can be done. He is not eternity or infinity, but eternal and infinite; he is not duration or space, but he endures and is present. He endures for ever, and is every where present”:
    Sir Isaac Newton – Principia; 1687, GENERAL SCHOLIUM.
    http://gravitee.tripod.com/genschol.htm

    As well, as Ian H. Hutchinson noted in the following article on Faraday and Maxwell, “Lawfulness was not, in their thinking, inert, abstract, logical necessity, or complete reducibility to Cartesian mechanism; rather, it was an expectation they attributed to the existence of a divine lawgiver.,,, For them, the coherence of nature resulted from its origin in the mind of its Creator.”

    The Genius and Faith of Faraday and Maxwell – Ian H. Hutchinson – 2014
    Conclusion: Lawfulness was not, in their thinking, inert, abstract, logical necessity, or complete reducibility to Cartesian mechanism; rather, it was an expectation they attributed to the existence of a divine lawgiver. These men’s insights into physics were made possible by their religious commitments. For them, the coherence of nature resulted from its origin in the mind of its Creator.
    http://www.thenewatlantis.com/.....nd-maxwell

    As well in quantum mechanics and relativity, we find that both Eugene Wigner and Einstein are on record as to regarding it as a ‘miracle’ that mathematics is applicable to the universe. In fact, Einstein went so far as to disparage ‘professional atheists’ when he called it a miracle:

    On the Rational Order of the World: a Letter to Maurice Solovine – Albert Einstein – March 30, 1952
    Excerpt: “You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton’s theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the ‘miracle’ which is constantly reinforced as our knowledge expands.
    There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles.”
    -Albert Einstein
    http://inters.org/Einstein-Letter-Solovine

    The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner – 1960
    Excerpt: ,,certainly it is hard to believe that our reasoning power was brought, by Darwin’s process of natural selection, to the perfection which it seems to possess.,,,
    It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.,,,
    The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
    http://www.dartmouth.edu/~matc.....igner.html

    Moreover, when we rightly allow the Agent causality of God ‘back’ into physics, as the Christian founders of modern science originally envisioned,,,, (Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders),,, and as quantum mechanics itself now empirically demands (with the closing of the free will loophole by Anton Zeilinger and company), when we rightly allow the Agent causality of God ‘back’ into physics then that provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead provides an empirically backed reconciliation, (via the Shroud of Turin), between quantum mechanics and general relativity into the much sought after ‘Theory of Everything”. Here are a few posts where I lay out and defend some of the evidence for that claim:

    November 2019 – despite the fact that virtually everyone, including the vast majority of Christians, hold that the Copernican Principle (and/or the principle of mediocrity) is unquestionably true, the fact of the matter is that the Copernican Principle is now empirically shown, (via quantum mechanics and general relativity, etc..), to be a false assumption.
    https://uncommondescent.com/intelligent-design/so-then-maybe-we-are-privileged-observers/#comment-688855

    (February 19, 2019) To support Isabel Piczek’s claim that the Shroud of Turin does indeed reveal a true ‘event horizon’, the following study states that ‘The bottom part of the cloth (containing the dorsal image) would have born all the weight of the man’s supine body, yet the dorsal image is not encoded with a greater amount of intensity than the frontal image.’,,,
    Moreover, besides gravity being dealt with, the shroud also gives us evidence that Quantum Mechanics was dealt with. In the following paper, it was found that it was not possible to describe the image formation on the Shroud in classical terms but they found it necessary to describe the formation of the image on the Shroud in discrete quantum terms.
    https://uncommondescent.com/intelligent-design/experiment-quantum-particles-can-violate-the-mathematical-pigeonhole-principle/#comment-673178

    The evidence for the Shroud’s authenticity keeps growing. (Timeline of facts) – November 08, 2019
    What Is the Shroud of Turin? Facts & History Everyone Should Know – Myra Adams and Russ Breault
    https://www.christianity.com/wiki/jesus-christ/what-is-the-shroud-of-turin.html

    To give us a small glimpse of the power that was involved in Christ’s resurrection from the dead, the following recent article found that, ”it would take 34 Thousand Billion Watts (34 trillion Watts) of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.”

    Astonishing discovery at Christ’s tomb supports Turin Shroud – NOV 26TH 2016
    Excerpt: The first attempts made to reproduce the face on the Shroud by radiation, used a CO2 laser which produced an image on a linen fabric that is similar at a macroscopic level. However, microscopic analysis showed a coloring that is too deep and many charred linen threads, features that are incompatible with the Shroud image. Instead, the results of ENEA “show that a short and intense burst of VUV directional radiation can color a linen cloth so as to reproduce many of the peculiar characteristics of the body image on the Shroud of Turin, including shades of color, the surface color of the fibrils of the outer linen fabric, and the absence of fluorescence”.
    ‘However, Enea scientists warn, “it should be noted that the total power of VUV radiations required to instantly color the surface of linen that corresponds to a human of average height, body surface area equal to = 2000 MW/cm2 17000 cm2 = 34 thousand billion (34 trillion) watts makes it impractical today to reproduce the entire Shroud image using a single laser excimer, since this power cannot be produced by any VUV light source built to date (the most powerful available on the market come to several billion watts )”.
    Comment
    The ENEA study of the Holy Shroud of Turin concluded that it would take 34 Thousand Billion Watts of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.
    http://westvirginianews.blogsp.....in-is.html

    Verse:

    Colossians 1:15-20
    The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross.

  54. 54
    JVL says:

    ET: Yes, JVL ascribes to the “this all just happened to happen” scenario. Untestable and takes more faith to believe than Christianity.

    The math works. It can be proved. It’s the most testable discipline ever.

  55. 55
    JVL says:

    BornAgain77:

    I did not say nor do I believe that mathematics is a replacement or substitute for God. You choose to look at is as evidence for God. I think that’s misplaced and incorrect. I think mathematics has nothing to do with God. But you think all of existence is due to God so there is nothing I can say that will get you to change your mind. Your belief is unfalsifiable so I’m not going to try and argue with you about it.

    If you want to talk about mathematics that’s fine. If you are going to use mathematics as support for God (and I gather you haven’t studied math much yourself) then we’ve got nothing to say to each other really.

  56. 56
    bornagain77 says:

    JVL: “I did not say nor do I believe that mathematics is a replacement or substitute for God.”

    All evidence to the contrary be damned eh JVL?

    JVL: “It (mathematics) exists outside of space and time. It just is.”

    BA77: “Godel begs to differ.”

    JVL: “So”

    And, irony of ironies, JVL accuses me of holding an unfalsifiable position in the face of he himself refusing to accept Godel’s falsification of his position.

  57. 57
    ET says:

    JVL:

    The math works. It can be proved.

    What are you talking about? There isn’t any math for all of this just happening to happen. The only reason math exists is because the universe was designed using it. It permeates our existence.

  58. 58
    JVL says:

    ET: What are you talking about? There isn’t any math for all of this just happening to happen. The only reason math exists is because the universe was designed using it. It permeates our existence.

    I disagree. I can not see any way math could work differently.

  59. 59
    JVL says:

    BornAgain77: And, irony of ironies, JVL accuses me of holding an unfalsifiable position in the face of he himself refusing to accept Godel’s falsification of his position.

    I agree with Godel’s mathematics but interpreting it as theology . . . nah. That’s why I said “so?”, it’s your use of Godel’s mathematics to make a religious statement. That doesn’t wash.

  60. 60
    BobRyan says:

    JVL:

    If math exists, which you believe, then where did it originate? I am sure you know that new formulas are not referred to as having been created, but of discovering what already exists. Without intelligence designing the entire universe, there can be no math to discover. Something created the formulas, just as something created the laws of physics.

  61. 61
    asauber says:

    So at the end of the day, JVL is just another unresponsive troll. Again. Good Times, though.

    Andrew

  62. 62
    ET says:

    JVL- You aren’t even responding to my comments. It’s as if you cannot comprehend what I am posting, Mathematics cannot work any differently because it permeates our universe. It permeates our universe because mathematics was used in its Intelligent Design.

    Materialism doesn’t work. It cannot account for mathematics. That’s because it cannot account for this universe. There isn’t any math that supports materialism.

  63. 63
    JVL says:

    ET: You aren’t even responding to my comments. It’s as if you cannot comprehend what I am posting, Mathematics cannot work any differently because it permeates our universe. It permeates our universe because mathematics was used in its Intelligent Design.

    How was it used then? Do you think the math existed before the design was conceived?

    Materialism doesn’t work. It cannot account for mathematics. That’s because it cannot account for this universe. There isn’t any math that supports materialism.

    Math has nothing to do with theology or materialism. It’s separate from any world view and supports none.

  64. 64
    JVL says:

    Asuaber: So at the end of the day, JVL is just another unresponsive troll. Again. Good Times, though.

    Sorry for not agreeing with you.

  65. 65
    ET says:

    JVL:

    How was it used then?

    Most likely the same way we use it to design things today. Or very similar.

    Do you think the math existed before the design was conceived?

    Yes.

    Math has nothing to do with theology or materialism.

    That’s your opinion. However, materialism is incoherent and is a non-starter.

  66. 66
    JVL says:

    BobRyan: If math exists, which you believe, then where did it originate?

    I think it’s always been there. I don’t see how 2 + 2 can equal anything but 4, ever.

    I am sure you know that new formulas are not referred to as having been created, but of discovering what already exists

    Depends on the mathematician.

    Without intelligence designing the entire universe, there can be no math to discover.

    Why? If math can be no other way then what does intelligent design have to do with it? Design implies choices were made. I don’t think there are choices with mathematics. It is what it is.

    Something created the formulas, just as something created the laws of physics.

    I disagree. The fact that the infinite series 1 + 1/2 + 1/4 + 1/8 + 1/16 + . . . . converges has nothing to do with a designer. You couldn’t decide to make that come out to be something else.

    Can you conceive of a different kind of mathematics? If you can’ then doesn’t that mean it has to be the way it is? If that’s true then there’s no choice about it. That means, if intelligent design is true, that the math existed before the design was implemented.

  67. 67
    JVL says:

    ET: Most likely the same way we use it to design things today. Or very similar.

    Give an example of something you think was designed and how math was used in the design process.

    Yes.

    So we agree!

    That’s your opinion. However, materialism is incoherent and is a non-starter.

    I say math has nothing to do with materialism, especially if materialism is incoherent since math is very coherent.

    If math existed before choices were made in the design process then math has nothing to do with design. It might have been used during the design process but it exists apart from design. So math was not designed.

  68. 68
    ET says:

    Bridges require mathematics. Tall buildings require mathematics. Rocket launches and recovery depend on mathematics.

    If math existed before choices were made in the design process then math has nothing to do with design.

    That doesn’t follow.

    It might have been used during the design process but it exists apart from design.

    That doesn’t follow, either.

    So math was not designed.

    How do you figure?

    Math was designed so that the universe could then follow.

  69. 69
    ET says:

    If math can be no other way then what does intelligent design have to do with it?

    Mathematics was part of the Intelligent Design.

    Design implies choices were made.

    Does it? Just because choices were made does not mean mathematics was not intelligently designed. Perhaps there was a different math that didn’t work in the physical realm

  70. 70
    JVL says:

    ET: Bridges require mathematics. Tall buildings require mathematics. Rocket launches and recovery depend on mathematics.

    Those were not part of the design intelligent design is talking about. Give an example of something BIOLOGICAL you think was designed and how math was used.

    That doesn’t follow.

    You agreed that math existed before biological design was implemented. So it’s independent from that design process. It existed before then. So it was not affected by the design process. So it exists apart from the biological design you believe happened.

    Math was designed so that the universe could then follow.

    So, how could math have been designed differently? How could math have been designed without using math?

    Mathematics was part of the Intelligent Design.

    So, step 1? Again, if math was designed then it could have been done differently. How could it have been done differently?

    Does it? Just because choices were made does not mean mathematics was not intelligently designed. Perhaps there was a different math that didn’t work in the physical realm

    Like what? Give an example.

  71. 71
    ET says:

    LoL! @ JVL- You lose and now you try to change the subject. The entire universe required mathematics, Jerad. The laws that govern the universe are purely mathematical.

    You agreed that math existed before biological design was implemented.

    It had to. Mathematics was used to design the universe.

    Again, if math was designed then it could have been done differently.

    Not necessarily.

  72. 72
    JVL says:

    ET: You lose and now you try to change the subject. The entire universe required mathematics, Jerad. The laws that govern the universe are purely mathematical.

    That doesn’t mean math was designed does it? I say math was NOT designed because it has to be the way it is.

    It had to. Mathematics was used to design the universe.

    Like how? Give an example.

    Not necessarily.

    Give an example.

  73. 73
    ET says:

    JVL:

    I say math was NOT designed because it has to be the way it is.

    Just because it has to be the way it is does not mean it wasn’t intelligently designed.

    Mathematics was used to design the universe in a similar fashion to the way we use it for engineering.

    Give an example.

    Of what? You want an example that math couldn’t be different? Are you daft?

  74. 74
    JVL says:

    ET: Just because it has to be the way it is does not mean it wasn’t intelligently designed.

    Design implies choices were made, yes? If something has to be a certain way then there are no choices, yes?

    Of what? You want an example that math couldn’t be different? Are you daft?

    Okay, so you think math has to be the way it is? How are there any choices in that? How can it be designed then?

    Design implies choices. If there are no choices there is no design.

    If math has to be the way it is then it wasn’t designed. If you think it was designed then you should be able to come up with choices or alternative to the way math works as we understand it. You should be able to come up with a different kind of math.

    Can you do that?

    If there are no alternatives then was it designed? I say no.

  75. 75
    ET says:

    JVL:

    Design implies choices were made, yes?

    Not necessarily.

    Even if there aren’t any alternatives mathematics had to come into existence somehow. And seeing that it was required to design the universe it is obvious we did not invent it.

  76. 76
    ET says:

    Oh noes! Car designers did not have any choice but to make the wheels round! Houses all have roofs and walls! No choice!!! And bridges they can’t be just anywhere.

  77. 77
    JVL says:

    ET: Not necessarily.

    You think you can have design without choices being made? That’s the same as necessity isn’t it? How does the explanatory filter view that?

    Even if there aren’t any alternatives mathematics had to come into existence somehow. And seeing that it was required to design the universe it is obvious we did not invent it.

    Yes so . . . was mathematics designed? I say no.

    Oh noes! Car designers did not have any choice but to make the wheels round! Houses all have roofs and walls! No choice!!! And bridges they can’t be just anywhere.

    Wheels don’t have to be round. Houses can be in caves. Bridges are partially dependent on land rights and available spaces aside from the geographic considerations.

    https://www.youtube.com/watch?v=vk7s4PfvCZg

    https://en.wikipedia.org/wiki/Non-circular_gear

    And, guess what: you still haven’t been able to provide an example of a different kind of mathematics. So, I say, mathematics was not designed or decided upon. It just is. It’s pre-design, if design in nature exists.

  78. 78
    ET says:

    How do you think mathematics came to be, then, JVL? Your turn- your “math just is” is a cop out.

    A cave as a house still has a roof and walls. Bridges are only where they are needed.

    I don’t have to give an example of a different kind of math. That has nothing to do with what I said. What I said is more of a thought experiment. That is why you are so confused.

    The bike on youtube is close to useless. And I never said anything about gears

  79. 79
    JVL says:

    ET: How do you think mathematics came to be, then, JVL? Your turn- your “math just is” is a cop out.

    How did your designer come to be?

    I think mathematics is just part of the fabric of reality. No being had to design it or create it.

    I don’t have to give an example of a different kind of math. That has nothing to do with what I said. What I said is more of a thought experiment. That is why you are so confused.

    You don’t HAVE to do anything. But if you can’t come up with a different kind of mathematics then you have less of platform to say it was designed. Designed means having choices. Means things could have been different. Could math have been different? If you haven’t got an example then maybe you’re wrong.

    The bike on youtube is close to useless. And I never said anything about gears

    Wheels don’t have to be round. Sorted.

  80. 80
    asauber says:

    “I think mathematics is just part of the fabric of reality.”

    JVL,

    That’s very poetic but it doesn’t explain why or how there is math.

    Andrew

  81. 81
    JVL says:

    Asauber: That’s very poetic but it doesn’t explain why or how there is math.

    Do you have an explanation of how math came to be? And, if it was designed, how it could have been different? Design means there are choices. What choices did the designer make regarding mathematics?

  82. 82
    ET says:

    JVL:

    How did your designer come to be?

    Question-begging.

    I think mathematics is just part of the fabric of reality.

    That’s the way the universe was designed.

    But if you can’t come up with a different kind of mathematics then you have less of platform to say it was designed.

    Just because you can say something stupid that doesn’t make it so.

    If you haven’t got an example then maybe you’re wrong.

    That doesn’t follow.

    Wheels don’t have to be round.

    Yes, they do. If you put a non-round wheel on a car, either the wheel or something on the car, will break. The road will be torn up, too.

  83. 83
    ET says:

    JVL:

    Design means there are choices.

    To design or not to design is a choice. To have the laws that govern nature to be the way they are, was also a choice- to have intelligent observers or not, was a choice that affected that prior choice.

    Choices abound, choices all around. But do keep flailing about.

  84. 84
    bornagain77 says:

    JVL holds that the ‘beyond space and time’ math that describes this universe ‘just is’ and that it is not contingent upon the Mind of God for its existence and also holds that God did not choose the particular mathematical form that this universe takes.

    JVL’s position, as far as the philosophy of science is concerned, is a major step backwards. JVL’s position is very similar, if not exactly like, the position that was held by the ancient Greeks.

    The ancient Greeks held to a necessartarian view of mathematics. A view in which mathematics, to use JVL’s term ‘just is’. And that necessartarian, i.e. ‘just is’, view of mathematics, played a major role in preventing the rise of modern science. As Peter Williams notes in the following article, “Both Greek and biblical thought asserted that the world is orderly and intelligible. But the Greeks held that this order is necessary and that one can therefore deduce its structure from first principles. Only biblical thought held that God created both form and matter, meaning that the world did not have to be as it is and that the details of its order can be discovered only by observation. ”

    Is Christianity Unscientific? – Peter S. Williams
    Excerpt: “Both Greek and biblical thought asserted that the world is orderly and intelligible. But the Greeks held that this order is necessary and that one can therefore deduce its structure from first principles. Only biblical thought held that God created both form and matter, meaning that the world did not have to be as it is and that the details of its order can be discovered only by observation. ”
    https://www.bethinking.org/does-science-disprove-god/is-christianity-unscientific

    And as Henry F. Schaefer III noted in the following video, “The emergence of modern science was associated with a disdain for the rationalism of Greek philosophers who pronounced on how the world should behave, with insufficient attention to how the world in fact did behave.”

    “The emergence of modern science was associated with a disdain for the rationalism of Greek philosophers who pronounced on how the world should behave, with insufficient attention to how the world in fact did behave.”
    – Henry F. Schaefer III – Making Sense of Faith and Science – 23:30 minute mark
    https://youtu.be/C7Py_qeFW4s?t=1415

    In fact, it was only with the quote-unquote ‘outlawing’ of the ancient Greek philosophers’s deterministic and necessitarian views of creation that modern science was finally able to achieve a viable birth.

    As the following article states, “If science suffered only stillbirths in ancient cultures, how did it come to its unique viable birth? The beginning of science as a fully fledged enterprise took place in relation to two important definitions of the Magisterium of the Church. The first was the definition at the Fourth Lateran Council in the year 1215, that the universe was created out of nothing at the beginning of time. The second magisterial statement was at the local level, enunciated by Bishop Stephen Tempier of Paris who, on March 7, 1277, condemned 219 Aristotelian propositions, so outlawing the deterministic and necessitarian views of creation.
    These statements of the teaching authority of the Church expressed an atmosphere in which faith in God had penetrated the medieval culture and given rise to philosophical consequences. The cosmos was seen as contingent in its existence and thus dependent on a divine choice which called it into being; the universe is also contingent in its nature and so God was free to create this particular form of world among an infinity of other possibilities. Thus the cosmos cannot be a necessary form of existence; and so it has to be approached by a posteriori investigation. The universe is also rational and so a coherent discourse can be made about it. Indeed the contingency and rationality of the cosmos are like two pillars supporting the Christian vision of the cosmos.”

    The War against the War Between Science and Faith Revisited – July 2010
    Excerpt: …as Whitehead pointed out, it is no coincidence that science sprang, not from Ionian metaphysics, not from the Brahmin-Buddhist-Taoist East, not from the Egyptian-Mayan astrological South, but from the heart of the Christian West, that although Galileo fell out with the Church, he would hardly have taken so much trouble studying Jupiter and dropping objects from towers if the reality and value and order of things had not first been conferred by belief in the Incarnation. (Walker Percy, Lost in the Cosmos),,,
    Jaki notes that before Christ the Jews never formed a very large community (priv. comm.). In later times, the Jews lacked the Christian notion that Jesus was the monogenes or unigenitus, the only-begotten of God. Pantheists like the Greeks tended to identify the monogenes or unigenitus with the universe itself, or with the heavens. Jaki writes: Herein lies the tremendous difference between Christian monotheism on the one hand and Jewish and Muslim monotheism on the other. This explains also the fact that it is almost natural for a Jewish or Muslim intellectual to become a pa(n)theist. About the former Spinoza and Einstein are well-known examples. As to the Muslims, it should be enough to think of the Averroists. With this in mind one can also hope to understand why the Muslims, who for five hundred years had studied Aristotle’s works and produced many commentaries on them failed to make a breakthrough. The latter came in medieval Christian context and just about within a hundred years from the availability of Aristotle’s works in Latin,,
    If science suffered only stillbirths in ancient cultures, how did it come to its unique viable birth? The beginning of science as a fully fledged enterprise took place in relation to two important definitions of the Magisterium of the Church. The first was the definition at the Fourth Lateran Council in the year 1215, that the universe was created out of nothing at the beginning of time. The second magisterial statement was at the local level, enunciated by Bishop Stephen Tempier of Paris who, on March 7, 1277, condemned 219 Aristotelian propositions, so outlawing the deterministic and necessitarian views of creation.
    These statements of the teaching authority of the Church expressed an atmosphere in which faith in God had penetrated the medieval culture and given rise to philosophical consequences. The cosmos was seen as contingent in its existence and thus dependent on a divine choice which called it into being; the universe is also contingent in its nature and so God was free to create this particular form of world among an infinity of other possibilities. Thus the cosmos cannot be a necessary form of existence; and so it has to be approached by a posteriori investigation. The universe is also rational and so a coherent discourse can be made about it. Indeed the contingency and rationality of the cosmos are like two pillars supporting the Christian vision of the cosmos.
    http://www.scifiwright.com/201.....revisited/

    As to the last sentence of the preceding quote, “Indeed the contingency and rationality of the cosmos are like two pillars supporting the Christian vision of the cosmos”, it is important to note just how radical of a departure this ‘contingency vs. necessatarian’ transformation in the philosophy of mathematics was.

    As Edward Fesser notes in the following article, for Christian scholastic philosophers of the medieval period “Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts,” whereas for ancient Greek philosophers, “mathematical objects such as numbers and geometrical figures exist not only independently of the material world, but also independently of any mind, including the divine mind.”

    KEEP IT SIMPLE – by Edward Feser – April 2020
    Excerpt: Mathematics appears to describe a realm of entities with quasi-divine attributes. The series of natural numbers is infinite. That one and one equal two and two and two equal four could not have been otherwise. Such mathematical truths never begin being true or cease being true; they hold eternally and immutably. The lines, planes, and figures studied by the geometer have a kind of perfection that the objects of our experience lack. Mathematical objects seem immaterial and known by pure reason rather than through the senses. Given the centrality of mathematics to scientific explanation, it seems in some way to be a cause of the natural world and its order.
    How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect.
    There is also a very different answer, in which the mathematical realm is a rival to God rather than a path to him. According to this view, mathematical objects such as numbers and geometrical figures exist not only independently of the material world, but also independently of any mind, including the divine mind. They occupy a “third realm” of their own, the realm famously described in Plato’s Theory of Forms. God used this third realm as a blueprint when creating the physical world, but he did not create the realm itself and it exists outside of him. This position is usually called Platonism since it is commonly thought to have been Plato’s own view, as distinct from that of his Neoplatonic followers who relocated mathematical objects and other Forms into the divine mind. (I put to one side for present purposes the question of how historically accurate this standard narrative is.)
    https://www.firstthings.com/article/2020/04/keep-it-simple

    In the minds of the Christian founders of modern science, mathematics, especially any mathematics that might describe the universe, was certainly not held to be necessary, as the ancient Greeks held and JVL currently holds, but any mathematics that might describe was instead held to be contingent upon God’s thoughts.

    Perhaps the best example that I can give for the fact that the Christian founders of modern science held mathematics, especially any mathematics that might describe the universe, to be God’s thoughts is the following quote by Kepler, (which he made shortly after discovering the laws of planetary motion),,

    “O, Almighty God, I am thinking Thy thoughts after Thee!”
    – Johannes Kepler, 1619, The Harmonies of the World.

    Several quotes along similar lines we presented in post #53
    https://uncommondescent.com/neuroscience/michael-egnor-talks-with-podcaster-lucas-skrobot-about-how-we-can-know-we-are-not-zombies/#comment-706255

    Thus JVL is actually defending a necessitarian view of mathematics that the ancient Greeks also held. A fruitless view of mathematics that played a major role in preventing the rise of modern science since a necessitarian view of gives rise to the “Greek philosophers who pronounced on how the world should behave, with insufficient attention to how the world in fact did behave”.

    In short, a necessitarian view of mathematics and/or creation, undermines empirical science itself since those who hold to a necessitarian view of mathematics, apparently, didn’t, and still don’t, believe that it was possible for the universe to take any other mathematical form than the one it currently has..

    On this point they are sadly, and profoundly mistaken.

    Godel’s incompleteness theorem is more that enough, in and of itself, to prove this point. But to add even more weight to the claim that the mathematics that describe this universe could have been different. The free will loop-hole in quantum mechanics has now been closed by Anton Zeilinger and company.

    On top of that, “Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information.”

    Algorithmic Information Theory, Free Will and the Turing Test – Douglas S. Robertson?Excerpt: Chaitin’s Algorithmic Information Theory shows that information is conserved under formal mathematical operations and, equivalently, under computer operations. This conservation law puts a new perspective on many familiar problems related to artificial intelligence. For example, the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information.?http://cires.colorado.edu/~dou...../info8.pdf

    And as James Franklin noted, “the intellect (is) immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.,,,”

    The mathematical world – James Franklin – 7 April 2014
    Excerpt: the intellect (is) immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.,,,
    – James Franklin is professor of mathematics at the University of New South Wales in Sydney.
    http://aeon.co/magazine/world-.....-be-about/

    Thus the Christian Theist has multiple lines of strong evidence, (many more lines than what I have presented here in this short post), that he can appeal to to support his claim that the mathematics that describe this universe is contingent upon the Mind of God for its existence, and indeed that God chose this particular mathematical form that this universe has taken. Whereas JVL has, basically, only his ignorance of the history of science, and his ignorance of the evidence itself, to appeal to,

    It is truly sad that he repeatedly chooses ignorance over God:

  85. 85
    kairosfocus says:

    JVL,

    I am late to the party, but observe:

    >>Do you have an explanation of how math came to be?>>

    1: Yes, as you know I have examined a core of Mathematics, showing that once a distinct possible world is, a certain logically ordered structure linked to quantity obtains. Indeed, we then see that such core aspects necessarily extend to any possible world, i.e. all of them, securing universality and global relevance. Which in turn answers Wigner on the astonishing power of Mathematics.

    2: So, this is not a matter of clever rhetorical games dependent on whatever ideas, suggestions or gaps may obtain with particular interlocutors, but something established as a base for further thought.

    3: There is, however, a second order question: how are possible worlds just that, possible?

    4: To answer that, notice, that were there ever utter, genuine nothingness — utter non-being — then as such has no causal capability, such would forever obtain. Further, transfinite regress cannot be traversed in finite stage steps, i.e. an actual infinity of successive contingent worlds with finite duration [years, say] is also ruled out, as is retro-causation by which a not yet future state reaches back to generate the chain that leads to itself. That, too would be pulling a world out of a non-existent hat.

    5: That is, there is adequate, finitely remote root cause for the actual world we inhabit and others that may or do actually exist. Such, is a reality root, necessary being. Once a world is, something always was, a something of different order from ourselves. Something, capable of creating worlds.

    6: So, there are consequences to there being possible worlds.

    >> And, if it was designed, how it could have been different?>>

    7: Possibility of a distinct world W implies near neighbour worlds such as W’ that lack some particular attribute or aspect A unique to W and singling it out. This of course then leads to world partition W = {A|~A} thence 0,1,2 etc, and on to structured core sets and frameworks of Mathematics.

    8: Distinct identity directly implies just that, distinction, i.e. actualisability of what else could also be, here W’. So, we have general possibility of alternatives pivoting on locally unique defining thus structural attributes such as A,

    9: In addition, a given world will be structured and does not preclude that other worlds may be structured in equally distinct but distinguishable ways. So, we see for example how we may have different logic-model worlds creating distinct mathematical domains that nonetheless share core necessary structures present in any possible world. N, Z, Q, R, C etc and linked things come instantly to mind as such in-common structures as we just saw.

    >> Design means there are choices.>>

    10: Yes, and distinct possibilities are inherent in there being unique possible worlds. So, choice would exist connected to actualising one or the other of neighbours W and W’ or even both.

    11: Choice, of course, is inherent in design.

    >>What choices did the designer make regarding mathematics?>>

    12: Choices connected to actualising particular worlds with structures such as a particular physics and cosmology. Some structural-quantitative aspects of a PW are in common, others will be distinct to particular worlds such as our own.

    13: There is abundant evidence that our world sits at a deeply isolated operating point amenable to C-Chemistry, Aqueous medium, terrestrial planet in galactic and circumstellar habitable zone life.

    14: As there is no reason to hold neighbouring but life-inhibiting worlds logically impossible of being there is good reason to hold that we thus see signs of design.

    KF

  86. 86
    JVL says:

    ET: That’s the way the universe was designed.

    Designed means choices were made. If math could have been different how?

    Just because you can say something stupid that doesn’t make it so.

    If math was part of the design then choices were made which means things could have been different. How could math be different?

    To design or not to design is a choice. To have the laws that govern nature to be the way they are, was also a choice- to have intelligent observers or not, was a choice that affected that prior choice.

    I’m talking about mathematics which I say is invariant no matter what nature is like.

  87. 87
    JVL says:

    BornAgain77: Thus JVL is actually defending a necessitarian view of mathematics that the ancient Greeks also held. A fruitless view of mathematics that played a major role in preventing the rise of modern science since a necessitarian view of gives rise to the “Greek philosophers who pronounced on how the world should behave, with insufficient attention to how the world in fact did behave”.

    You may be right about the mindset most conducive to the rise of modern science, certainly the weight granted to people like Aristotle slowed things down. But I’m talking about mathematics and the Greeks were excellent mathematics. Arguably no major advancements were made after the Greek era for another 1000 years. They figured out that the square root of 2 is irrational! Euclid’s Elements are still studied and still true. And just about everyone knows the Pythagorean theorem. They may have slowed down science but they discovered the mathematics upon which science sits.

  88. 88
    JVL says:

    Kairosfocus: 12: Choices connected to actualising particular worlds with structures such as a particular physics and cosmology. Some structural-quantitative aspects of a PW are in common, others will be distinct to particular worlds such as our own.

    But what about the mathematics? Could the underlying mathematics be different? If you say yes then how? Can you give an actual example.

  89. 89
    doubter says:

    Kairosfocus @85

    5: That is, there is adequate, finitely remote root cause for the actual world we inhabit and others that may or do actually exist. Such, is a reality root, necessary being. Once a world is, something always was, a something of different order from ourselves. Something, capable of creating worlds.

    6: So, there are consequences to there being possible worlds.
    >> And, if it was designed, how it could have been different?>>

    Excuse the digression, but one thing has always puzzled me, that may have already been solved by philosophers generations ago. This is the proposition that, if God is truly omnipotent, it would seem that He could create a world where the to us fundamental laws of logic and mathematics are different.

    If not, the laws of logic and mathematics are ultimate realities prior to and out of the control of God. But He is supposed to be truly omnipotent.

    Could He create if He chose a world reality where 2 + 2 = 5, where the laws of logic are different? Are there such world realities, forever inaccessible to humans?

    This notion does not seem acceptable, so where is the flaw in this reasoning?

  90. 90
    bornagain77 says:

    JVL asks,

    If math was part of the design then choices were made which means things could have been different. How could math be different?

    Simple, and to repeat, there are an infinite number of different axioms that could have been chosen that could have given rise to an infinite number of different mathematical frameworks,

    Algorithmic Information Theory, Free Will and the Turing Test – Douglas S. Robertson?Excerpt: Chaitin’s Algorithmic Information Theory shows that information is conserved under formal mathematical operations and, equivalently, under computer operations. This conservation law puts a new perspective on many familiar problems related to artificial intelligence. For example, the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information.?http://cires.colorado.edu/~dou...../info8.pdf

    As Chaitin pointed out, “an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.”

    The Limits Of Reason – Gregory Chaitin – 2006
    Excerpt: Unlike Gödel’s approach, mine is based on measuring information and showing that some mathematical facts cannot be compressed into a theory because they are too complicated. This new approach suggests that what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.
    http://www.umcs.maine.edu/~chaitin/sciamer3.pdf

    For instance, the parallel postulate and/or axiom of Euclidian geometry does not hold for the Riemannian geometry and/or the four-dimensional Minkowski space that lies at the basis of relativity.

    Riemannian geometry
    Riemannian geometry, also called elliptic geometry, one of the non-Euclidean geometries that completely rejects the validity of Euclid’s fifth postulate and modifies his second postulate. Simply stated, Euclid’s fifth postulate is: through a point not on a given line there is only one line parallel to the given line. In Riemannian geometry, there are no lines parallel to the given line. Euclid’s second postulate is: a straight line of finite length can be extended continuously without bounds. In Riemannian geometry, a straight line of finite length can be extended continuously without bounds, but all straight lines are of the same length. The tenets of Riemannian geometry, however, admit the other three Euclidean postulates,,,
    https://www.britannica.com/science/Riemannian-geometry

    Four-dimensional space – with 4-D animation:
    Excerpt: The idea of adding a fourth dimension began with Joseph-Louis Lagrange in the mid 1700s and culminated in a precise formalization of the concept in 1854 by Bernhard Riemann.,,,
    Higher dimensional spaces have since become one of the foundations for formally expressing modern mathematics and physics. Large parts of these topics could not exist in their current forms without the use of such spaces.,,,
    Einstein’s concept of spacetime uses such a 4D space, though it has a Minkowski structure that is a bit more complicated than Euclidean 4D space.
    https://en.wikipedia.org/wiki/Four-dimensional_space

    Thus the fact that the math that describes this universe ‘could have been different’ was in fact the way that it was. The math that actually describes the space-time of this universe is very different than Euclidian math and that difference between the two mathematical systems lies in the different axioms of each mathematical system. And again, to repeat, axioms are a matter of choice, not necessity,

    Algorithmic Information Theory, Free Will and the Turing Test – Douglas S. Robertson?Excerpt: Chaitin’s Algorithmic Information Theory shows that information is conserved under formal mathematical operations and, equivalently, under computer operations. This conservation law puts a new perspective on many familiar problems related to artificial intelligence. For example, the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information.?http://cires.colorado.edu/~dou...../info8.pdf

    And again, “an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.”

    The Limits Of Reason – Gregory Chaitin – 2006
    Excerpt: Unlike Gödel’s approach, mine is based on measuring information and showing that some mathematical facts cannot be compressed into a theory because they are too complicated. This new approach suggests that what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.
    http://www.umcs.maine.edu/~chaitin/sciamer3.pdf

    Thus JVL’s claim that math ‘just is’ and that math could not have been different, is simply a naively false claim for him to make. The math that describes this universe could have been infinitely different depending on then infinite number of axioms that God could have chosen to implement.

    Of supplemental note:

    ever since modern science was born in medieval Christian Europe, science has had a history of looking for ‘platonic perfection’, and assuming the Mind of God to be behind that ‘platonic perfection’. That is to say, that science has a history of reaching for perfect agreement between the immaterial mathematics that describe a facet of this universe and the experimental results that measure those mathematical predictions.,,,
    And indeed for most of the history of modern science in the Christian west, finding ‘platonic perfection’ for the mathematical descriptions of the universe has been a very elusive goal. This all changed with the discoveries of Special Relativity, General Relativity and Quantum Mechanics. That is to say, as far as experimental testing will allow, there is no discrepancy to be found between what the mathematical descriptions of Relativity and Quantum Mechanics predict and what our most advanced scientific testing of those predictions are able to measure.
    https://uncommondescent.com/intelligent-design/what-elements-of-fine-tuning-of-our-universe-vs-the-multiverse-would-pass-this-test-of-science-truth/#comment-680868

  91. 91
    JVL says:

    BornAgain77: Simple, and to repeat, there are an infinite number of different axioms that could have been chosen that could have given rise to an infinite number of different mathematical frameworks,

    Can you come up with a consistent form of mathematics different from ours? One that works for the most basic problems?

    As Chaitin pointed out, “an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.”

    Quite true, as per Godel’s work. But theorems are NOT axioms.

    For instance, the parallel postulate and/or axiom of Euclidian geometry does not hold for the Riemannian geometry and/or the four-dimensional Minkowski space that lies at the basis of relativity.

    Yup, it’s like going from Newtonian mechanics to Einstein. But 2 + 2 still = 4. The area of a circle on a plane is the same. (Don’t tell ET that under non-Euclidian geometry parallel lines meet at infinity, he won’t like that.) But the axiom you’re throwing out was defined by MEN, it’s not an inherent or obvious rule to depend on. In other words, if God designed mathematics he did NOT come up with the parallel axiom, men did. In fact, since not using the parallel postulate means you can better model part of God’s creation then I would say that God was probably working with non-Euclidian geometry in the first place! Human’s thought parallel lines never meet and then changed their minds.

    Thus the fact that the math that describes this universe ‘could have been different’ was in fact the way that it was. The math that actually describes the space-time of this universe is very different than Euclidian math and that difference between the two mathematical systems lies in the different axioms of each mathematical system. And again, to repeat, axioms are a matter of choice, not necessity,

    But, again, the underlying arithmetic is the same. Algebra is the same. Number theory is the same. Throwing out the parallel postulate (which, again, was a human assumption) oddly enough works when modelling certain phenomena (and it was ‘discovered’ before there were applications) but that doesn’t change how numbers work together. Subtraction, addition, multiplication, division, exponents, logarithm, integrals, derivatives, etc, all that stuff still works.

    Thus JVL’s claim that math ‘just is’ and that math could not have been different, is simply a naively false claim for him to make. The math that describes this universe could have been infinitely different depending on then infinite number of axioms that God could have chosen to implement.

    Okay, give me an example then of a consistent axiomatic mathematical system that would be completely different from ours but still work for real world problems. This is my point; I don’t hear anyone coming up with an example. You can talk and pontificate all you like but if you can’t come up with an example then maybe what you propose does not exist.

  92. 92
    kairosfocus says:

    Doubter, the attributes of God are compossible and indeed bound up inextricably in one another. As any possible world will have a distinct identity as outlined certain core aspects of math flow from that and are necessary. The issue shifts as noted to there being the possibility of worlds, pointing to causally adequate world root, thus a second level of cause. In context, non core aspects of math can be explored through contingent logic model worlds, which opens up math fields of study and different physics for PWs. In all these the core is there. Have to go. KF

  93. 93
    kairosfocus says:

    JVL, see the just above and earlier, you are again unresponsive to core points.one for RW now. KF

  94. 94
    ET says:

    JVL:

    Designed means choices were made

    Why do you keep saying that? You can’t prove it so stop being a strawman loser.

    I’m talking about mathematics which I say is invariant no matter what nature is like.

    You are erecting a strawman and then attacking it like some sort of demented child.

  95. 95
    ET says:

    JVL:

    (Don’t tell ET that under non-Euclidian geometry parallel lines meet at infinity, he won’t like that.)

    Meet @ infinity? Infinity is not a place. Look, JVL, you don’t understand the terminology. You don’t understand infinity. And you are totally clueless about design.

  96. 96
    ET says:

    JVL has some demented and perverted view of design. I have already provided engineering examples in which choices could NOT be made. And then once we consider engineering STANDARDs, we can see there are plenty of times where choices could NOT be made in design.

    JVL is ignorant of design. And he thinks his belligerent ignorance is an argument.

  97. 97
    bornagain77 says:

    JVL in response to this fact, “axioms are a matter of choice, not necessity,” states that,

    the underlying arithmetic is the same. Algebra is the same. Number theory is the same. Throwing out the parallel postulate (which, again, was a human assumption) oddly enough works when modelling certain phenomena (and it was ‘discovered’ before there were applications) but that doesn’t change how numbers work together. Subtraction, addition, multiplication, division, exponents, logarithm, integrals, derivatives, etc, all that stuff still works.

    And yet if we were to choose different axioms then ‘all that stuff’ would not work.

    Peano axioms
    In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of whether number theory is consistent and complete.
    The need to formalize arithmetic was not well appreciated until the work of Hermann Grassmann, who showed in the 1860s that many facts in arithmetic could be derived from more basic facts about the successor operation and induction.[1] In 1881, Charles Sanders Peirce provided an axiomatization of natural-number arithmetic.[2] In 1888, Richard Dedekind proposed another axiomatization of natural-number arithmetic, and in 1889, Peano published a simplified version of them as a collection of axioms in his book, The principles of arithmetic presented by a new method (Latin: Arithmetices principia, nova methodo exposita).
    The Peano axioms contain three types of statements. The first axiom asserts the existence of at least one member of the set of natural numbers. The next four are general statements about equality; in modern treatments these are often not taken as part of the Peano axioms, but rather as axioms of the “underlying logic”.[3] The next three axioms are first-order statements about natural numbers expressing the fundamental properties of the successor operation. The ninth, final axiom is a second order statement of the principle of mathematical induction over the natural numbers. A weaker first-order system called Peano arithmetic is obtained by explicitly adding the addition and multiplication operation symbols and replacing the second-order induction axiom with a first-order axiom schema.
    https://en.wikipedia.org/wiki/Peano_axioms

    In fact, the fact that basic arithmetic is incomplete was the main point of Godel first incompleteness theorem, i.e. “as long as your logical system is complicated enough to include addition and multiplication, then your logical system is incomplete.”

    Gödel’s first incompleteness theorem says that if you have a consistent logical system (i.e., a set of axioms with no contradictions) in which you can do a certain amount of arithmetic4, then there are statements in that system which are unprovable using just that system’s axioms.In other words, as long as your logical system is complicated enough to include addition and multiplication, then your logical system is incomplete. There are things you can’t prove true or false!
    https://infinityplusonemath.wordpress.com/2017/08/04/godels-incompleteness-theorems/

    In short, JVL is simply completely wrong in his assumption that math could not have been different. All of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.

  98. 98
    JVL says:

    Kairosfocus: Doubter, the attributes of God are compossible and indeed bound up inextricably in one another. As any possible world will have a distinct identity as outlined certain core aspects of math flow from that and are necessary. The issue shifts as noted to there being the possibility of worlds, pointing to causally adequate world root, thus a second level of cause. In context, non core aspects of math can be explored through contingent logic model worlds, which opens up math fields of study and different physics for PWs. In all these the core is there. Have to go

    I just want to know if someone can present a consistent axiomatic mathematics that is significantly different from ours!

    JVL, see the just above and earlier, you are again unresponsive to core points.one for RW now.

    I see you guys talking about different laws of physics and chemistry and different mathematics but I don’t see anyone giving me an example except non-Euclidean geometry. Throwing out the parallel postulate is just tossing a man-made axiom, an assumption about mathematics. I want to know how you could start from ground zero and get something different. Can you give me an example? If you can’t then how can you be sure one exists?

  99. 99
    JVL says:

    ET: Why do you keep saying that? You can’t prove it so stop being a strawman loser.

    Look, if you tell me you designed something then that means you made choices that could have been different. Like cars or bridges or bicycles or novels or landscapes or pottery or just about anything man-made. We can all see different ways you might have done something. You designed it, you made choices. I’m not sure the basic core of mathematics can be altered or different. I’m not sure there are choices that can be made. I’m not sure you can ‘design’ root-level mathematics. If you can then please give me an example.

    Meet @ infinity? Infinity is not a place. Look, JVL, you don’t understand the terminology. You don’t understand infinity. And you are totally clueless about design.

    🙂 Sometimes I say things just to wind you up.

    has some demented and perverted view of design. I have already provided engineering examples in which choices could NOT be made. And then once we consider engineering STANDARDs, we can see there are plenty of times where choices could NOT be made in design.

    Okay, fine. But you can at least design part of a car or a bridge or a wheel. You can make choices of how big the wheel is, how wide it is, what its made of, etc. I’m saying that I don’t think you can change the core of mathematics (arithmetic, algebra, probability, etc). If that’s true then I don’t think you can say that mathematics was ‘designed’ or ‘chosen’.

    JVL is ignorant of design. And he thinks his belligerent ignorance is an argument.

    Look, if you design something then you must make choices between alternatives. At least at some level. I’m not sure there are choices in setting up mathematics. But if someone can come up with an example I’m happy to consider it.

  100. 100
    JVL says:

    Bornagain77: And yet if we were to choose different axioms then ‘all that stuff’ would not work.

    Your example of the Peano axioms is interesting but that was just an attempt to put our basic mathematics on the same kind of standing as Euclidean geometry (with its famous five axioms). They didn’t create something different. I’m asking: can you start with different axioms and come up with something different? Yes or no?

    In fact, the fact that basic arithmetic is incomplete was the main point of Godel first incompleteness theorem, i.e. “as long as your logical system is complicated enough to include addition and multiplication, then your logical system is incomplete.”

    I’m not talking about whether or not you can deduce all theorems with a mechanistic approach starting with a set of axioms. I’m asking: can you create a whole new system of mathematics using different base axioms. Yes or no? If yes then an example please.

    In short, JVL is simply completely wrong in his assumption that math could not have been different. All of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.

    Then show me a different mathematical system, a really different mathematical system, based on different axioms. Math is not a spectator sport: if you want to play you’ve got to put on a uniform and hit the field.

  101. 101
    ET says:

    JVL- please shut up. You don’t know anything about design. And I have already told you about the choices. That you are a willfully ignorant troll doesn’t help you.

  102. 102
    bornagain77 says:

    Whatever JVL, I am confident that the unbiased reader can now clearly see that you are wrong in your assumption that math ‘just is’.

  103. 103
    asauber says:

    “math ‘just is’”

    JVL has proven itself quite the simpleton.

    Andrew

  104. 104
    Mac McTavish says:

    If math can’t be different, as JVL claims, is this not further evidence for the fine tuning argument?

  105. 105
    kairosfocus says:

    JVl, you have you answer, there are certain math structures that are pre axiomatic and will be in common to abstract logic model worlds erected through axiomatisations. Not to mention when we go on to sets of cosmos-building laws. KF

  106. 106
    JVL says:

    ET: please shut up. You don’t know anything about design. And I have already told you about the choices. That you are a willfully ignorant troll doesn’t help you.

    Bornagain77: Whatever JVL, I am confident that the unbiased reader can now clearly see that you are wrong in your assumption that math ‘just is’.

    Asauber: JVL has proven itself quite the simpleton.

    Look, it’s really simple. I assert that math has to be the way it is, at the basic level like arithmetic, algebra, probabilities, etc. I don’t think that part can be due to design.

    I agree that axioms matter a lot. That’s the logical basis for any axiomatic system.

    My challenge to you guys is: if you think mathematics was even partially designed then please proved and example of a designed mathematical system that is significantly different from ours at the basic level.

    If you can’t do that then how do you know it’s possible to do so?

    So far, all you’ve done is heap aspersions on me. Let’s see if you can establish your belief that mathematics could have been designed by providing a designed mathematics that differs from ours.

  107. 107
    JVL says:

    Mac McTavish: If math can’t be different, as JVL claims, is this not further evidence for the fine tuning argument?

    No, because you can’t fine tune something that is not tuneable.

  108. 108
    JVL says:

    Kairosfocus: you have you answer, there are certain math structures that are pre axiomatic and will be in common to abstract logic model worlds erected through axiomatisations. Not to mention when we go on to sets of cosmos-building laws.

    That sounds like you agree with me! That certain parts of mathematics are not design-able.

    Thank you for that.

    If that’s not what you mean then what pre-axiomatic math structures are you talking about?

  109. 109
    ET says:

    JVL:

    I assert that math has to be the way it is, at the basic level like arithmetic, algebra, probabilities, etc. I don’t think that part can be due to design.

    Even if it couldn’t be any other way doesn’t mean it wasn’t designed and isn’t part of the design.

    So far, all you’ve done is heap aspersions on me.

    Well deserved. Your “challenge” just exposes your clueless desperation. How can we show you math that doesn’t exist in our universe using terminology from our universe?

    How does our inability to mimic the Designer of the universe have anything to do with math being designed in and for this universe?

  110. 110
    ET says:

    JVL:

    No, because you can’t fine tune something that is not tuneable.

    How do you know?

  111. 111
    JVL says:

    ET: Well deserved. Your “challenge” just exposes your clueless desperation. How can we show you math that doesn’t exist in our universe using terminology from our universe?

    If you can’t do it, how do you know it can be done?

    How does our inability to mimic the Designer of the universe have anything to do with math being designed in and for this universe?

    If you can’t do it, how do you know it can be done?

    Is having faith science? Or mathematics?

    How do you know?

    Explain how you can fine tune something that is not tuneable?

    All I want is for you to provide me an example of what you think is possible. If you can’t provide and example then how do you know it IS possible?

    Math is not a spectator sport. You have to be able to ‘do it’.

  112. 112
    ET says:

    JVL:

    If you can’t do it, how do you know it can be done?

    How can we show you math that doesn’t exist in our universe using terminology from our universe? Answer the question.

    Explain how you can fine tune something that is not tuneable?

    At the start, by making it non-tunable.

  113. 113
    JVL says:

    ET: How can we show you math that doesn’t exist in our universe using terminology from our universe? Answer the question.

    How do you know it’s possible if you can’t show it? How do you know you’re not just making stuff up that doesn’t actually exist? “OOO, I can’t tell you but I know” just doesn’t cut it.

    You don’t know if all the stuff you’re taling about is even possible. You can’t use your own ignorance of your own beliefs as proof you’re correct.

    At the start, by making it non-tunable.

    How can you make something non-tunable? If you tuned it to be non-tunable why couldn’t you retune it later?

  114. 114
    bornagain77 says:

    Of note, change the Peano axioms and you will have a different mathematical system.

    Nonstandard Arithmetics
    ,, the second and more radical way of obtaining nonstandard arithmetic is to add something inconsistent with the Peano axioms and jettison some of these. (This is analogous to how non-Euclidean geometries were first produced.) In principle, this could produce many different systems, but I know of only one in the literature.,,
    A more radical way still of producing a nonstandard arithmetic , for which there is now a general theory, is to drop the consistency requirement.,,,
    https://books.google.com/books?id=1PD1CAAAQBAJ&pg=PA67&lpg=PA67&dq=peano+axioms+alternative&source=bl&ots=pq6pyb6yy6&sig=ACfU3U3Ce_zrmkYLOrJOLrk-LQbEgseFSw&hl=en&sa=X&ved=2ahUKEwi87f_54sDqAhXZXc0KHXWcCS4Q6AEwBXoECAsQAQ#v=onepage&q=peano%20axioms%20alternative&f=false

    Again, all of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity. That is exactly what made Godel’s incompleteness theorem so devastating to David Hilbert and others who wished for mathematics to be complete within itself.?

    Hilbert tasked mathematicians with proving that set theory and all of infinitistic mathematics is finitistically reducible, and therefore trustworthy. “We must know; we will know!” he said in a 1930 address in Königsberg — words later etched on his tomb.
    However, the Austrian-American mathematician Kurt Gödel showed in 1931 that, in fact, we won’t. In a shocking result, Gödel proved that no system of logical axioms (or starting assumptions) can ever prove its own consistency; to prove that a system of logic is consistent, you always need another axiom outside of the system. This means there is no ultimate set of axioms — no theory of everything — in mathematics. When looking for a set of axioms that yield all true mathematical statements and never contradict themselves, you always need another axiom. Gödel’s theorem meant that Hilbert’s program was doomed: The axioms of finitistic mathematics cannot even prove their own consistency, let alone the consistency of set theory and the mathematics of the infinite.?

    Again, JVL is completely wrong in his assertion that ‘math just is’.

    This following video is also very interesting for revealing how Godel’s incompleteness theorem was brought about,
    ?

    BBC-Dangerous Knowledge – Part 1 of 5
    https://vimeo.com/122917065?
    Part 2
    https://vimeo.com/30641992

  115. 115
    JVL says:

    Bornagain77: Of note, change the Peano axioms and you will have a different mathematical system.

    Yup, you would. Show me an example.

    Again, all of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.

    Yup, agreed. Show me an example of an axiomatic mathematical system that differs significantly from ours that works for some of our basic problems. Arithmetic, algebra, statistics, etc.

    I don’t disagree with the theory, I just want to see an example that shows it is possible.

  116. 116
    Mac McTavish says:

    JVL

    No, because you can’t fine tune something that is not tuneable.

    Are you claiming that the argument being made for the fine tuning of the universe is a flawed argument because there is no evidence that it can be tuned?

  117. 117
    bornagain77 says:

    JVL, you are the one claiming that ‘math just is’. So for you to agree with the statement, “all of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.”,,,

    For you to agree with that statement,,

    JVL: “Yup, agreed.”

    ,, is for you to concede that you are wrong in you belief that ‘math just is’

    After conceding that you are wrong in your presupposition of ‘math just is’, you then wanted an example, to which I had already provided a reference in my post which stated,

    “the second and more radical way of obtaining nonstandard arithmetic is to add something inconsistent with the Peano axioms and jettison some of these. (This is analogous to how non-Euclidean geometries were first produced.) In principle, this could produce many different systems, but I know of only one in the literature.,,”

    So there is an example out there somewhere, and no, I will not dig it up for you. You can dig it up for yourself if you want. Personally, I am more than satisfied that you have conceded the primary fact that defeats your argument, i.e. “all of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.”,,,

    JVL: “Yup, agreed.”

  118. 118
    JVL says:

    Mac McTavish: Are you claiming that the argument being made for the fine tuning of the universe is a flawed argument because there is no evidence that it can be tuned?

    Ummm. .. . yeah. More or less.

  119. 119
    JVL says:

    Bornagain77: is for you to concede that you are wrong in you belief that ‘math just is’

    I agree that in general that a system depends on its axioms. What I am wondering is: is it possible for mathematics as we understand it to be significantly different from what we experience. And I’d like an example from those whose assert it could be something different.

    So, what I am asserting is: I do not think that mathematics can be significantly different from what we know. So yes: I think it just is. Considering the discussion of axioms I think mathematics will always depend on the same basic axioms.

    If I am wrong then someone should be able to provide a counter example. Can you provide such a counter example? Yes or no?

    So there is an example out there somewhere, and no, I will not dig it up for you. You can dig it up for yourself if you want. Personally, I am more than satisfied that you have conceded the primary fact that defeats your argument, i.e. “all of math, including basic arithmetic, is dependent on axioms, and axioms are always a matter of choice, not necessity.”,,,

    I haven’t denied that. What I am asking is: can you come up with an axiomatic system of mathematics that differs greatly from what we have now? A system that deals with arithmetic and algebra and geometry and probability, etc.

    So far, you haven’t found an example.

  120. 120
    ET says:

    How can we show you math that doesn’t exist in our universe using terminology from our universe? Answer the question.

    You can’t use your own ignorance of your own beliefs as proof you’re correct.

    The ignorance is all yours. The strawman you are whipping is proof that you are clueless.

    How can you make something non-tunable?

    Super tight specifications that do not allow for tolerances.

    If you tuned it to be non-tunable why couldn’t you retune it later?

    Strawman soup today, eh? It was designed and built to be non-tunable.

    You can tune a piano but you can’t tuna fish

  121. 121
    ET says:

    JVL:

    I do not think that mathematics can be significantly different from what we know.

    In this universe it can’t be. And even if can’t be any different in any verse it doesn’t mean it wasn’t designed. It is already very flexible.

  122. 122
    bornagain77 says:

    LOL, JVL, do your own research, I gave you a big hint where to look. Myself, I am more than satisfied with your honest concession that you were wrong in your original presupposition of “math just is”. i.e. JVL: “Yup, agreed.”

    You are just wasting my time after you conceded that axioms are a matter of choice, not necessity.

    i.e. The game is over, the fat lady has sung, and the stadium lights are being shut off.

  123. 123
    jerry says:

    Mathematics is different from the real world. In the real world only positive integers exist but even these positive integers are abstractions that just exist in our heads. That does not mean that all the mathematical concepts that are used are not useful but they are abstractions. Maybe similar to Plato’s shadows.

    In our universe there is no pi or e or square root of 2 or infinity whether infinitely big or infinitely small. And definitely not any imaginary or complex numbers.

    All are incredibly useful. But all are mental abstractions. There is no such thing as a circle or right angle or polygon or even a straight line in the physical world. Only in our heads. That does not mean we don’t observe close approximations to these concepts but in reality they do not exist.

    Mathematics is not a science but logical truisms. The modern world thrives on these abstractions and their logical underpinnings but that is all they are.

    And how far is all this from the OP about zombies.

  124. 124
    bornagain77 says:

    As to mathematics and fine-tuning. As mentioned previously, the parallel postulate and/or axiom of Euclidian geometry does not hold for the Riemannian geometry and/or the four-dimensional Minkowski space that lies at the basis of relativity.

    Riemannian geometry
    Riemannian geometry, also called elliptic geometry, one of the non-Euclidean geometries that completely rejects the validity of Euclid’s fifth postulate and modifies his second postulate. Simply stated, Euclid’s fifth postulate is: through a point not on a given line there is only one line parallel to the given line. In Riemannian geometry, there are no lines parallel to the given line. Euclid’s second postulate is: a straight line of finite length can be extended continuously without bounds. In Riemannian geometry, a straight line of finite length can be extended continuously without bounds, but all straight lines are of the same length. The tenets of Riemannian geometry, however, admit the other three Euclidean postulates,,,
    https://www.britannica.com/science/Riemannian-geometry

    Four-dimensional space – with 4-D animation:
    Excerpt: The idea of adding a fourth dimension began with Joseph-Louis Lagrange in the mid 1700s and culminated in a precise formalization of the concept in 1854 by Bernhard Riemann.,,,
    Higher dimensional spaces have since become one of the foundations for formally expressing modern mathematics and physics. Large parts of these topics could not exist in their current forms without the use of such spaces.,,,
    Einstein’s concept of spacetime uses such a 4D space, though it has a Minkowski structure that is a bit more complicated than Euclidean 4D space.
    – per wikipedia

    And yet, although the universe is based on four-dimensional Minkowski space, we find that the universe is “actually very close to the most unlikely state of all, absolute flatness.”

    “The Universe today is actually very close to the most unlikely state of all, absolute flatness. And that means it must have been born in an even flatter state, as Dicke and Peebles, two of the Princeton astronomers involved in the discovery of the 3 K background radiation, pointed out in 1979. Finding the Universe in a state of even approximate flatness today is even less likely than finding a perfectly sharpened pencil balancing on its point for millions of years, for, as Dicke and Peebles pointed out, any deviation of the Universe from flatness in the Big Bang would have grown, and grown markedly, as the Universe expanded and aged. Like the pencil balanced on its point and given the tiniest nudges, the Universe soon shifts away from perfect flatness.”
    ~ John Gribbin, In Search of the Big Bang

    As to the fine-tuning of the ‘most unlikely’ flatness, and as the following author comments, the universe must have been flat to 1 part within 1×10^57 parts over its entire 13.8 billion year history which, “seems like an insane coincidence”.

    How do we know the universe is flat? Discovering the topology of the universe – by Fraser Cain – June 7, 2017
    Excerpt: With the most sensitive space-based telescopes they have available, astronomers are able to detect tiny variations in the temperature of this background radiation.
    And here’s the part that blows my mind every time I think about it. These tiny temperature variations correspond to the largest scale structures of the observable universe. A region that was a fraction of a degree warmer become a vast galaxy cluster, hundreds of millions of light-years across.
    The cosmic microwave background radiation just gives and gives, and when it comes to figuring out the topology of the universe, it has the answer we need. If the universe was curved in any way, these temperature variations would appear distorted compared to the actual size that we see these structures today.
    But they’re not. To best of its ability, ESA’s Planck space telescope, can’t detect any distortion at all. The universe is flat.,,,
    Since the universe is flat now, it must have been flat in the past, when the universe was an incredibly dense singularity. And for it to maintain this level of flatness over 13.8 billion years of expansion, in kind of amazing.
    In fact, astronomers estimate that the universe must have been flat to 1 part within 1×10^57 parts.
    Which seems like an insane coincidence.
    https://phys.org/news/2017-06-universe-flat-topology.html

    Since the universe is “ever-so-boringly flat. On large, cosmic scales, parallel lines stay parallel forever, interior angles of triangles add up to 180 degrees, and so on. All the rules of Euclidean geometry that you learned in high school apply.”,

    And yet, as the author goes on to comment, “But there’s no reason for our universe to be flat.”

    Why We Need Cosmic Inflation
    By Paul Sutter, Astrophysicist | October 22, 2018
    Excerpt: As best as we can measure, the geometry of our universe appears to be perfectly, totally, ever-so-boringly flat. On large, cosmic scales, parallel lines stay parallel forever, interior angles of triangles add up to 180 degrees, and so on. All the rules of Euclidean geometry that you learned in high school apply.
    But there’s no reason for our universe to be flat. At large scales it could’ve had any old curvature it wanted. Our cosmos could’ve been shaped like a giant, multidimensional beach ball, or a horse-riding saddle. But, no, it picked flat.
    https://www.space.com/42202-why-we-need-cosmic-inflation.html

    The author should be grateful that the universe is ‘ever-so-boringly flat’. If the universe were not so ‘ever-so-boringly flat’ science and technology would not be possible for humans.

    How do we know the universe is flat? Discovering the topology of the universe – by Fraser Cain – June 7, 2017
    Excerpt: We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,,
    Since the universe is flat now, it must have been flat in the past, when the universe was an incredibly dense singularity. And for it to maintain this level of flatness over 13.8 billion years of expansion, in kind of amazing.
    In fact, astronomers estimate that the universe must have been flat to 1 part within 1×10^57 parts.
    Which seems like an insane coincidence.
    https://phys.org/news/2017-06-universe-flat-topology.html

    Simply put, without some remarkable degree of exceptional, and stable, flatness for the universe, (as well as exceptional stability for all the other constants), Euclidean (3-Dimensional) geometry would not be applicable to our world. or to the universe at large, and this would make science and engineering for humans, for all practical purposes, all but impossible.

    Scientists Question Nature’s Fundamental Laws – Michael Schirber – 2006
    Excerpt: “There is absolutely no reason these constants should be constant,” says astronomer Michael Murphy of the University of Cambridge. “These are famous numbers in physics, but we have no real reason for why they are what they are.”
    The observed differences are small-roughly a few parts in a million-but the implications are huge (if they hold up): The laws of physics would have to be rewritten, not to mention we might need to make room for six more spatial dimensions than the three that we are used to.”,,,
    The speed of light, for instance, might be measured one day with a ruler and a clock. If the next day the same measurement gave a different answer, no one could tell if the speed of light changed, the ruler length changed, or the clock ticking changed.
    http://www.space.com/2613-scie.....-laws.html

    This ‘insane coincidence’ of flatness adds considerable weight to both Einstein’s and Wigner’s claim that the applicability of math to the universe is, by all rights, a miracle:

    On the Rational Order of the World: a Letter to Maurice Solovine – Albert Einstein – March 30, 1952
    Excerpt: “You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton’s theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the ‘miracle’ which is constantly reinforced as our knowledge expands.
    There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles.”
    -Albert Einstein – Letter to Solovine
    The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner – 1960
    Excerpt: ,,certainly it is hard to believe that our reasoning power was brought, by Darwin’s process of natural selection, to the perfection which it seems to possess.,,,
    It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.,,,
    The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
    http://www.dartmouth.edu/~matc.....igner.html

    Thus in conclusion, although JVL blew off as inconsequential the fact that Euclid’s parallel postulate does not hold for the four-dimensional space time of relativity, the fact of the matter is that the ‘insanely’ finely tuned flatness of the four-dimensional space time of relativity allows us to apply Euclidian mathematics to the real world so as to enable us to practice science, engineering, and technology in the first place. In other words, the universe gives every appearance of having been designed so as to enable intelligent creatures to practice science.

    And remember, the entire concept of a line is an axiom in mathematics, and axioms in mathematics are always the result of choices, not necessity.

    Algorithmic Information Theory, Free Will and the Turing Test – Douglas S. Robertson?Excerpt: Chaitin’s Algorithmic Information Theory shows that information is conserved under formal mathematical operations and, equivalently, under computer operations. This conservation law puts a new perspective on many familiar problems related to artificial intelligence. For example, the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information.
    http://cires1.colorado.edu/~do...../info8.pdf

    Verse:

    Job 38:4-5
    “Where were you when I laid the earth’s foundation? Tell me, if you understand. Who marked off its dimensions? Surely you know! Who stretched a measuring line across it?

  125. 125
    Mac McTavish says:

    JVL

    Mac McTavish: “Are you claiming that the argument being made for the fine tuning of the universe is a flawed argument because there is no evidence that it can be tuned?”

    Ummm. .. . yeah. More or less.

    I always thought there was something flawed in the fine tuning argument with respect to design.

  126. 126
    bornagain77 says:

    as to:

    Mac McTavish: “Are you claiming that the argument being made for the fine tuning of the universe is a flawed argument because there is no evidence that it can be tuned?”

    JVL: Ummm. .. . yeah. More or less.

    Mac McTavish: I thought there was something flawed in the fine tuning argument with respect to design.

    The only flaw is that you would give any credence whatsoever to JVL’s claim that fine-tuning of the constants of the universe had to be exactly the way they are. The constants, like mathematical axioms themselves, are certainly not derived by mathematical necessity:

    As Luke Barnes noted, “Today, our deepest understanding of the laws of nature is summarized in a set of equations. Using these equations, we can make very precise calculations of the most elementary physical phenomena, calculations that are confirmed by experimental evidence. But to make these predictions, we have to plug in some numbers that cannot themselves be calculated but are derived from measurements of some of the most basic features of the physical universe. These numbers specify such crucial quantities as the masses of fundamental particles and the strengths of their mutual interactions. After extensive experiments under all manner of conditions, physicists have found that these numbers appear not to change in different times and places, so they are called the fundamental constants of nature.”

    The Fine-Tuning of Nature’s Laws – Luke A. Barnes – Fall 2015
    Excerpt: Today, our deepest understanding of the laws of nature is summarized in a set of equations. Using these equations, we can make very precise calculations of the most elementary physical phenomena, calculations that are confirmed by experimental evidence. But to make these predictions, we have to plug in some numbers that cannot themselves be calculated but are derived from measurements of some of the most basic features of the physical universe. These numbers specify such crucial quantities as the masses of fundamental particles and the strengths of their mutual interactions. After extensive experiments under all manner of conditions, physicists have found that these numbers appear not to change in different times and places, so they are called the fundamental constants of nature.
    These constants represent the edge of our knowledge. Richard Feynman called one of them — the fine-structure constant, which characterizes the amount of electromagnetic force between charged elementary particles like electrons — “one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man.” An innovative, elegant physical theory that actually predicts the values of these constants would be among the greatest achievements of twenty-first-century physics.
    Many have tried and failed. ,,,
    Tweaking the Constants
    Let’s consider a few examples of the many and varied consequences of messing with the fundamental constants of nature, the initial conditions of the universe, and the mathematical form of the laws themselves.
    You are made of cells; cells are made of molecules; molecules of atoms; and atoms of protons, neutrons, and electrons. Protons and neutrons, in turn, are made of quarks. We have not seen any evidence that electrons and quarks are made of anything more fundamental (though other fundamental particles, like the Higgs boson of recent fame, have also been discovered in addition to quarks and electrons). The results of all our investigations into the fundamental building blocks of matter and energy are summarized in the Standard Model of particle physics, which is essentially one long, imposing equation. Within this equation, there are twenty-six constants, describing the masses of the fifteen fundamental particles, along with values needed for calculating the forces between them, and a few others. We have measured the mass of an electron to be about 9.1 x 10^-28 grams, which is really very small — if each electron in an apple weighed as much as a grain of sand, the apple would weigh more than Mount Everest. The other two fundamental constituents of atoms, the up and down quarks, are a bit bigger, coming in at 4.1 x 10^-27 and 8.6 x 10^-27 grams, respectively. These numbers, relative to each other and to the other constants of the Standard Model, are a mystery to physics. Like the fine-structure constant, we don’t know why they are what they are.
    However, we can calculate all the ways the universe could be disastrously ill-suited for life if the masses of these particles were different. For example, if the down quark’s mass were 2.6 x 10^-26 grams or more, then adios, periodic table! There would be just one chemical element and no chemical compounds, in stark contrast to the approximately 60 million known chemical compounds in our universe.
    With even smaller adjustments to these masses, we can make universes in which the only stable element is hydrogen-like. Once again, kiss your chemistry textbook goodbye, as we would be left with one type of atom and one chemical reaction. If the up quark weighed 2.4 x 10^-26 grams, things would be even worse — a universe of only neutrons, with no elements, no atoms, and no chemistry whatsoever.
    ,,, Compared to the range of possible masses that the particles described by the Standard Model could have, the range that avoids these kinds of complexity-obliterating disasters is extremely small. Imagine a huge chalkboard, with each point on the board representing a possible value for the up and down quark masses. If we wanted to color the parts of the board that support the chemistry that underpins life, and have our handiwork visible to the human eye, the chalkboard would have to be about ten light years (a hundred trillion kilometers) high.,,,
    http://www.thenewatlantis.com/.....tures-laws

  127. 127
    JVL says:

    Bornagain77: VL, do your own research, I gave you a big hint where to look.

    I’m not going to research your assertion that basic mathematics can be very much different from what we have. That means your assertion is unsupported.

    You are just wasting my time after you conceded that axioms are a matter of choice, not necessity.

    But that doesn’t support your assertion if you cannot construct an alternative form of mathematics the works by making axiom choices. I guess we’ll never know . . .

    i.e. The game is over, the fat lady has sung, and the stadium lights are being shut off.

    You shouldn’t mix your metaphors so much.

  128. 128
    bornagain77 says:

    I gave you a link. which referenced an example of a different system,

    “the second and more radical way of obtaining nonstandard arithmetic is to add something inconsistent with the Peano axioms and jettison some of these. (This is analogous to how non-Euclidean geometries were first produced.) In principle, this could produce many different systems, but I know of only one in the literature.,,

    You refused to chase that example down. It is not on me to do your research for you. Especially when you have already conceded the main point under consideration, i.e. that mathematical axioms are always a matter of choice not mathematical necessity.

    You can’t have it both ways JVL. You cannot claim that basic arithmetic had to be exactly the way it is, i.e. ‘math just is’, while at the same time conceding that the Peano axioms which underlie basic arithmetic itself are a matter of choice.

    Moreover, as an atheist who believes in Darwinian evolution, and who therefore believes that you have no immaterial mind and/or soul, you have no explanation as to why humans are even able to grasp this, as you yourself admitted, ‘beyond space and time’ immaterial realm of mathematics. Whether you honestly admit it or not, that is a rather glaring hole in your entire argument for atheism.

    The self-refuting holes in your arguments against design literally pop out with every post you write. The only thing that has been consistent in your argumentation is that you are against the inference to design no matter what type of argument you have to make, even if the arguments are blatantly self-contradictory.

    This is NOT honest scientific inquiry on your part, but is a stubborn, dogmatic, refusal on your part to, no matter what the evidence says to the contrary, to budge from your a-priori atheistic bias against any type of inference to God.

    MATTHEW 13:15
    For this people’s heart has grown dull, and with their ears they can barely hear, and their eyes they have closed, lest they should see with their eyes and hear with their ears and understand with their heart and turn, and I would heal them.’

  129. 129
    JVL says:

    Bornagain77:

    In the book you linked to:

    On pages 67 and 68 the possibility of alternative arithmetics is discussed (I am unable to copy-and-paste passages for some reason). It is mentioned that one scheme is tantamount to creating extensions to standard arithmetic not rivals; in other words basically the same at the base level. Another approach talks about creating finite arithmetics which are useful under very limited conditions; not the sort of thing you would come up with first. You get those things AFTER you already have standard arithmetic. That section concludes with mentioning dropping the consistency requirement. Then there is a long discussion culminating in a fictional example. In the example different observers use arithmetic to calculate the result of some cosmological event. And get different results (pages 74 – 76).

    First of all I asked if you could create a consistent alternate arithmetic. Secondly the example in the book is a bit daft because I do not see how a race of being could develop science to the high point given in the example with an inconsistent arithmetic? In the example they don’t even know their arithmetic is inconsistent until they compare their results from measuring different cosmic events and later comparing with beings on other planets. So, they have arithmetic consistent enough to build a high level of scientific sophistication but one that is inconsistent? Really? If someone can wrap their head around the example I’d love to hear about it. And, it seems to me, even the author assumed they already had consistent arithmetic like ours to start with.

    As I said, all the finite arithmetic systems I have seen were derived AFTER standard arithmetic was in wide scale use. And they were derived by mathematicians. Witht he possible exceptions of some primitive tribes who never went on to develop any kind of science or business.

    Sorry, I’m just not buying it. It all sounds like intellectual exercises on the fringes or derivations from that standard form just for limited and particular purposes. And mostly arrived at after standard arithmetic was mastered. I don’t see an alternative, consistent type of arithmetic that would solve the same kind of problems ours does.

  130. 130
    ET says:

    Again the mathematics of our universe is FLEXIBLE. So flexible there doesn’t need to be any alternative. The CHOICE was to make it flexible so it can be used in a wide variety of scenarios.

  131. 131
    JVL says:

    ET: Again the mathematics of our universe is FLEXIBLE. So flexible there doesn’t need to be any alternative. The CHOICE was to make it flexible so it can be used in a wide variety of scenarios.

    How is it flexible? How is flexible baked into mathematics?

  132. 132
    Retired Physicist says:

    @jvl Yeah, how on earth could a race of beings on a planet have two space pineapples, and add another space pineapple, and not have three space pineapples? If you have 12 space pineapples, and you want to distribute them equally among three beings, how could you not get four space pineapples apiece? Nonsense of the highest order.

  133. 133
    bornagain77 says:

    JVL you state:

    In the example they don’t even know their arithmetic is inconsistent until they compare their results from measuring different cosmic events and later comparing with beings on other planets.

    So you agree that he gave an example but you disagree that it is consistent because it does not agree with ‘cosmic events’? Do you even read what you write?

    So a system of mathematics can only be consistent if it agrees with cosmic events? But that is the entire point, there are consistent mathematical laws that don’t describe the universe. As Steven Weinberg, an atheist, told Richard Dawkins, “we can already think of mathematically consistent laws that don’t describe the world as we know it. And we will always be left with a question ‘why are the laws of nature what they are rather than some other laws?’. And I don’t see any way out of that.”

    “I don’t think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don’t describe the world as we know it. And we will always be left with a question ‘why are the laws of nature what they are rather than some other laws?’. And I don’t see any way out of that.
    The fact that the constants of nature are suitable for life, which is clearly true, we observe,,,”
    (Weinberg then comments on the multiverse conjecture of atheists)
    “No one has constructed a theory in which that is true. I mean,, the (multiverse) theory would be speculative, but we don’t even have a theory in which that speculation is mathematically realized. But it is a possibility.”
    Steven Weinberg – as stated to Richard Dawkins at the 8:15 minute mark of the following video
    – Leonard Susskind – Richard Dawkins and Steven Weinberg – 1 in 10^120 – Cosmological Constant points to intelligent design – video
    https://youtu.be/z4E_bT4ecgk?t=495

    Moreover, as I pointed out in post 124, (and you apparently ignored), the fact that we can even practice science in the first place is dependent on the ‘insanely’ fine-tuned flatness of the universe that allows everything to, mathematically, ‘make sense’ for us:

    “We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,,
    Since the universe is flat now, it must have been flat in the past, when the universe was an incredibly dense singularity. And for it to maintain this level of flatness over 13.8 billion years of expansion, in kind of amazing.
    In fact, astronomers estimate that the universe must have been flat to 1 part within 1×10^57 parts.
    Which seems like an insane coincidence.”

    The universe, being the 4-D spacetime geometry that it is, simply did not have to be flat, and thus mathematics did not have to ‘make sense’ for us! i.e. There could very well have been no correlation between the math that we take for granted (i.e. Euclidian geometry) and the physical world!

    As best as we can measure, the geometry of our universe appears to be perfectly, totally, ever-so-boringly flat. On large, cosmic scales, parallel lines stay parallel forever, interior angles of triangles add up to 180 degrees, and so on. All the rules of Euclidean geometry that you learned in high school apply.
    But there’s no reason for our universe to be flat. At large scales it could’ve had any old curvature it wanted. Our cosmos could’ve been shaped like a giant, multidimensional beach ball, or a horse-riding saddle. But, no, it picked flat.

    You claimed that ‘math just is” and that the ‘fine-tuning just is”. You are wrong on both of your claims.

  134. 134
    JVL says:

    Retired Physicist:

    Yup, mathematics is not a spectator sport. Certainly it is appropriate for pure mathematicians to explore every single nook and cranny of the mathematical landscape but it doesn’t mean all of that theorising sheds any light on the practical, basic core of mathematics.

  135. 135
    ET says:

    JVL:

    How is it flexible? How is flexible baked into mathematics?

    The use of VARIABLES make it flexible. The fact that we do NOT need calculus to figure a grocery bill makes it flexible.

    Your inability to think still isn’t an argument, Jerad

  136. 136
    JVL says:

    Bornagain77: So you agree that he gave an example but you disagree that it is consistent because it does not agree with ‘cosmic events’? Do you even read what you write?

    No, I say it’s inconsistent because the author of the books clearly states he is exploring a kind of arithmetic where the consistency axiom IS THROWN OUT! The author clearly has picked the example because the arithmetic is inconsistent.

    Are you actually paying attention or just trying to score points? Did you actually read the section of the book you linked to?

    Moreover, as I pointed out in post 124, (and you apparently ignored), the fact that we can even practice science in the first place is dependent on the ‘insanely’ fine-tuned flatness of the universe that allows everything to, mathematically, ‘make sense’ for us:

    Doesn’t the mathematics have to be consistent then? How can you understand the cosmos if you get everybody gets different answers from each other to simple, basic mathematical calculations?

    The universe, being the 4-D spacetime geometry that it is, simply did not have to be flat, and thus mathematics did not have to ‘make sense’ for us! i.e. There could very well have been no correlation between the math that we take for granted (i.e. Euclidian geometry) and the physical world!

    But the math is consistent to itself. That’s the difference. You cannot model things if your mathematics is not consistent. Lots and lots of mathematics is developed well before an application is found. But when it looks like some obscure form of mathematics might reflect and uphold some new theory of physics it would all fall to pieces if the mathematics wasn’t consistent. Which is is in all the real world examples you cite.

    Axioms in pure mathematics are arbitrary. Some very weird mathematical structures and approaches end up having real world applications. But all of that work initially came from a consistent arithmetic framework And I haven’t seen an alternative consistent arithmetic framework that can be built upon to create the wide variety of mathematics we have now that solves some really basic physical problems.

  137. 137
    JVL says:

    ET: The use of VARIABLES make it flexible. The fact that we do NOT need calculus to figure a grocery bill makes it flexible.

    Variables are placeholders for values that might change. That’s not part of the basic framework or mathematics. How the math actually works.

    Why don’t you read through that book that Bornagain77 referenced and see if you can understand the example I discussed. Go on, give it a try.

  138. 138
    bornagain77 says:

    Whatever JVL, the authors both said that the universe did not have to ‘make sense’ to us mathematically. You disagreed. So what? You also disagree with both Einstein and Wigner.

    On the Rational Order of the World: a Letter to Maurice Solovine – Albert Einstein – March 30, 1952
    Excerpt: “You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton’s theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the ‘miracle’ which is constantly reinforced as our knowledge expands.
    There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles.”
    -Albert Einstein – Letter to Solovine

    The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner – 1960
    Excerpt: ,,certainly it is hard to believe that our reasoning power was brought, by Darwin’s process of natural selection, to the perfection which it seems to possess.,,,
    It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.,,,
    The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

    I’ll let unbiased readers decide for themselves whether they want to give more credence to you, an atheistic troll on the internet, or to Einstein and Wigner. For me, the choice isn’t even close.

  139. 139
    ET says:

    Wow. Jerad I understand that English confuses you. Variables make mathematics FLEXIBLE.

    Why don’t you get an education that allows you to think. Then perhaps we can talk

  140. 140
    JVL says:

    Bornagain77: Whatever JVL, the authors both said that the universe did not have to ‘make sense’ to us mathematically. You disagreed. So what? You also disagree with both Einstein and Wigner.

    Wow, clearly you just don’t understand the mathematics. Incredible. You copy and paste stuff you think upholds your view and your really don’t understand what’s going on at all.

    I have agreed that, in a purely abstract sense, mathematical axioms are arbitrary. Some mathematicians have created types of ‘arithmetic’ which are either inconsistent (as noted in the book you linked to) or limited (as also noted in the book you linked to). So, so far, no one has been able to show me an alternative, consistent form of arithmetic that differs significantly from ours that can be used to solve the same basic real-world problems.

    But you thought: Oh, this hideous, awful atheistic materialist must be wrong; I’m going to find something that looks like it contradicts him.

    I’m talking about mathematics, you seem to think that has something to do with world views and theology.

    It doesn’t. It’s just mathematics. That is not subject to theology or philosophy or any world views.

  141. 141
    JVL says:

    ET: Wow. Jerad I understand that English confuses you. Variables make mathematics FLEXIBLE.

    Variables just take the place of unknown quantities. They don’t change the basic underlying mathematical structures. The can be replaced with real values or functions or . . . whatever they are standing in place of.

    Clearly you just don’t understand what variables do. The don’t change basic, underlying mathematics.

    Why don’t you get an education that allows you to think. Then perhaps we can talk

    I have done. Now I’m waiting for you to catch up.

    I notice you haven’t even bothered to read the book excerpts that Bornagain77 linked to. Perhaps you should try and do that before you offer an opinion.

  142. 142
    jerry says:

    Why doesn’t everyone try to define mathematics. It may be why people keep talking past each other.

    I’ll give you a hint. No one can define it.

    Ask yourself what is a number? I once wrote a paper on this for a philosophy class. For example what is the number three.

  143. 143
    Mac McTavish says:

    Jerry For example what is the number three.
    That’s easy. It is 1/14th the answer to life, the universe and everything.

  144. 144
    bornagain77 says:

    JVL, You claim that mathematics has nothing to do with the theology, i.e. the ‘miraculous’ and/or with God. You also claim I know nothing about mathematics since I think it does. (i.e. fallacious ‘argument to the man’) The quotes from Einstein and Wigner are unambiguous. THEY disagree with you. They hold it to be miraculous that mathematics should be applicable to the universe, and Einstein even went so far as to chastise ‘professional atheists’ in the process of calling it a miracle. I will take their word over your word any day of the week since you are merely an atheistic troll on the internet with, as far as I can tell from my limited interaction with you, an agenda. Seeking to score points no matter how dishonest you have to be, and in comparison to you, they, both Einstein and Wigner, are, frankly, both mathematical geniuses in their respective fields who’s shoes you are not worthy to tie.

  145. 145
    jerry says:

    Jerry For example what is the number three.
    That’s easy. It is 1/14th the answer to life, the universe and everything

    Now define the number 17. And then define “1/14th” and life and universe.

  146. 146
    ET says:

    LoL! @ JVL! Get a dictionary and look up the word “flexible”. To catch up with you would require I get a lobotomy.

  147. 147
    kairosfocus says:

    Jerry:

    Why doesn’t everyone try to define mathematics

    My fav answer is a mod from my first Uni Math Prof, Harald Neiderreiter of Austria: [the study of] the logic of structure and quantity.

    The first part is our part, where we can get partly creative.

    The second is substance, connected to possible worlds and particularly logic-model worlds — including our actualised world. Where, it turns out there are Math facts that are self evident and/or discoverable that are antecedent to axiomatisations C19 – 20 style. Where, too, if a proposed axiomatic system is incompatible with core math facts it simply will gain no traction, often because it becomes an incoherent chaos.

    Such would be rejected.

    As for my comments above, I am pointing out that we need to ask how worlds become possible, given that utter nothingness would be permanent were it ever to obtain as non-being has no causal powers. Similarly, circular retrocausality is trying to pull an original world out of the not yet, i.e. from non being. Likewise, a proposed endlessly successive past of stages [years for simplicity] cannot be traversed stepwise to now. We are left with a finitely remote, necessary being world root capable of causing worlds with rational creatures capable of freedom to reason.

    Such leads to huge logic of being consequences.

    So, we need a reality root to get to possible worlds and the actual one. That in any possible world N, Q, Z, R, C will be with much consequent on that, is downstream of how do we get to possible worlds including an actual one with creatures capable of doing Mathematics.

    KF

    PS: See my onward discussion here https://journals.blythinstitute.org/ojs/index.php/cbi/article/view/62/59

  148. 148
    JVL says:

    Bornagain77:

    You are welcome to take whatever text or quotes you find most enlightening as definitive. The quotes and opinions are peripheral to the mathematics though.

    I still haven’t seen a consistent, alternative form of mathematics that can handle all the simple and basic issues humans needed to deal with thousands of years ago. I do not think it’s possible to have a system of mathematics that meets those criteria markedly different from what we’ve got. I am open to any counter example anyone wishes to present but, so far, no one has presented one.

  149. 149
    kairosfocus says:

    MMT, see the just linked, noting how N etc are necessary abstracta embedded in what it takes to get to a distinct possible world. Also, following von Neumann (another Austrian, there is a theory about a Martian settlement . . .):

    {} –> 0
    {0} –> 1
    {0.1} –> 2
    {0,1,2} –> 3
    . . .
    {0,1,2,3 . . .} –> w, first transfinite ordinal.

    And, oddly enough the logic of being import lurking behind such does point to the roots of reality, thus the meaningfulness of our observed cosmos.

    KF

  150. 150
    kairosfocus says:

    JVL, you are being evasive on central issues again. KF

  151. 151
    JVL says:

    ET: LoL! @ JVL! Get a dictionary and look up the word “flexible”. To catch up with you would require I get a lobotomy.

    I notice you haven’t addressed the book Bornagain77 linked to. Of course he won’t call you on it ’cause you guys scrupulously choose not to criticise each other. But I will assert that the mathematics in that book is above the level that you and Bornagain77 can deal with. You can prove me wrong, if you have the ability. I’m betting you won’t even try.

    I’ll wait and see what you do.

  152. 152
    JVL says:

    Kairosfocus: JVL, you are being evasive on central issues again.

    Really? Can you provide an example of a consistent system of arithmetic that is significantly different from ours that can still handle the same basic problems our system does?

    This has nothing to do with theology. This has nothing to do with values. This is pure mathematics.

  153. 153
    kairosfocus says:

    RP, 147 above may help. JB’s related article here may further help. KF

  154. 154
    kairosfocus says:

    JVL, side tracking evasion pivoting on setting up and knocking over a strawman. I point you to 85 above. KF

  155. 155
    ET says:

    JVL:

    I notice you haven’t addressed the book Bornagain77 linked to.

    Am I supposed to care about this book? Does it have any affect on my life?

    Of course he won’t call you on it ’cause you guys scrupulously choose not to criticise each other.

    And yet we have had at it a few times. Strange, that.

    But I will assert that the mathematics in that book is above the level that you and Bornagain77 can deal with.

    Am I supposed to care what you assert? You can’t even grasp the language you use. You don’t seem to understand infinity. You may have taken more advanced mathematics than I have. It definitely hasn’t helped you form a coherent argument nor understand what other people are saying.

  156. 156
    JVL says:

    ET: Am I supposed to care about this book? Does it have any affect on my life?

    It may mean you’re not up to the conversation.

    Am I supposed to care what you assert? You can’t even grasp the language you use. You don’t seem to understand infinity. You may have taken more advanced mathematics than I have. It definitely hasn’t helped you form a coherent argument nor understand what other people are saying.

    There is another interpretation. that you don’t quite grasp the concepts involved. Perhaps if you could be bothered to look at some of the references given we might be able to make a determination of your capacity.

  157. 157
    jerry says:

    Kf,

    Mathematics is essentially logic. It will exist as such in any world we can dream of. Is there a world where logic does not hold?

    I was in a PhD program in math and we had a discussion on just what math was and essentially what came out of it was that math is logic. None of the professors or students could define it otherwise.

    I made the point above that the only numbers that exist are positive integers and in reality they are in our head too. They are not in nature though we can certainly count but for that we have to have a concept of what is meant by number. In our universe there are no negative numbers, no pi, no e, no rational or irrational numbers, nothing infinite nor anything infinitely small.

    As I said above they are extremely useful but are just in our head. We can write all the equations, symbols and terminology we want but they are all just abstract creations. Extremely useful but not real.

  158. 158
    JVL says:

    Kairosfocus: JVL, side tracking evasion pivoting on setting up and knocking over a strawman. I point you to 85 above

    I have been very clear in my statements and questions. Perhaps you’d like to actually address the issues I have raised? Especially considering I find your comments in #85 above to be a bit off topic, to be honest.

  159. 159
    bornagain77 says:

    As expected, JVL hand waves off Einstein and Wigner and pretends he has a more expert opinion than they on mathematics and how it relates to the universe. Hubris is too mild a term.

  160. 160
    JVL says:

    Bornagain77: As expected, JVL hand waves off Einstein and Wigner and pretends he has a more expert opinion than they. Hubris is too mild a term.

    🙂 It’s okay with me if you have consistently failed to address my questions and challenges with pointless references and digressions.

    As I said before: your mathematics ability is clearly not up to the task. Being able to copy and paste just doesn’t cut it.

  161. 161
    bornagain77 says:

    JVL responds with a lie, a ad hominem, and another hand wave. Pathetic.

  162. 162
    kairosfocus says:

    Jerry, yes the logic of structure and quantity. KF

  163. 163
    kairosfocus says:

    JVL, the questions have been digressions and have ignored substantial, relevant remarks. KF

  164. 164
    ET says:

    JVL:

    It may mean you’re not up to the conversation.

    With you? No thanks.

    There is another interpretation. that you don’t quite grasp the concepts involved.

    Or you’re just horse’s arse.

    I do NOT care about your irrelevant tangent. I have much better things to do.

  165. 165
    ET says:

    It’s as if there are two different conversations- 1) What people say and 2) What JVL responds with which usually has nothing to do with 1.

  166. 166
    kairosfocus says:

    ET, language. KF

  167. 167
    bornagain77 says:

    As to the ‘miracle’ that directly faces us in the applicability of mathematics to the universe, (via Einstein and Wigner).

    Ever since modern science was born in medieval Christian Europe, scientists have had a history of looking for ‘platonic perfection’ in our mathematical descriptions of the universe, and assuming the Mind of God to be behind that ‘platonic perfection that was being sought after’.

    That is to say, that science has had a history of reaching for perfect agreement between the immaterial mathematics that might describe a certain facet of this universe and the experimental results that measure those mathematical predictions. And assuming God to be behind the assumed platonic perfection that was being sought after.

    Copernicus, (who was heavily influenced by Platonic thinking), imagined (incorrectly) that the planets move in perfect circles (rather than ellipses).

    Later, when Newton was challenged with the extreme mathematical difficulty of multiple orbits (perturbation theory), and for allowing God could adjust the orbits of the planets, was chastised by Leibniz, (and even by Laplace) for having “very narrow ideas about the wisdom and the power of God.”.. i.e. For having a narrow view of the perfection of God.

    “Leibniz, in his controversy with Newton on the discovery of infinitesimal calculus, sharply criticized the theory of Divine intervention as a corrective of the disturbances of the solar system. “To suppose anything of the kind”, he said, “is to exhibit very narrow ideas of the wisdom and power of God’.”
    – Pierre-Simon Laplace
    https://books.google.com/books?id=oLtHAAAAIAAJ&pg=PA73&lpg=PA73

    As a side-note, I hold that Newton, Leibniz, (and even Laplace himself), would be very pleased with what modern science has now revealed about the wisdom and power of God in setting up the solar system.

    “You might also think that these disparate bodies are scattered across the solar system without rhyme or reason. But move any piece of the solar system today, or try to add anything more, and the whole construction would be thrown fatally out of kilter. So how exactly did this delicate architecture come to be?”
    R. Webb – Unknown solar system 1: How was the solar system built? – New Scientist – 2009

    Is the Solar System Stable? By Scott Tremaine – 2011
    Excerpt: So what are the results? Most of the calculations agree that eight billion years from now, just before the Sun swallows the inner planets and incinerates the outer ones, all of the planets will still be in orbits very similar to their present ones. In this limited sense, the solar system is stable. However, a closer look at the orbit histories reveals that the story is more nuanced. After a few tens of millions of years, calculations using slightly different parameters (e.g., different planetary masses or initial positions within the small ranges allowed by current observations) or different numerical algorithms begin to diverge at an alarming rate. More precisely, the growth of small differences changes from linear to exponential:,,,
    As an example, shifting your pencil from one side of your desk to the other today could change the gravitational forces on Jupiter enough to shift its position from one side of the Sun to the other a billion years from now. The unpredictability of the solar system over very long times is of course ironic since this was the prototypical system that inspired Laplacian determinism.
    Fortunately, most of this unpredictability is in the orbital phases of the planets, not the shapes and sizes of their orbits, so the chaotic nature of the solar system does not normally lead to collisions between planets. However, the presence of chaos implies that we can only study the long-term fate of the solar system in a statistical sense, by launching in our computers an armada of solar systems with slightly different parameters at the present time—typically, each planet is shifted by a random amount of about a millimeter—and following their evolution. When this is done, it turns out that in about 1 percent of these systems, Mercury’s orbit becomes sufficiently eccentric so that it collides with Venus before the death of the Sun. Thus, the answer to the question of the stability of the solar system—more precisely, will all the planets survive until the death of the Sun—is neither “yes” nor “no” but “yes, with 99 percent probability.”
    https://www.ias.edu/about/publications/ias-letter/articles/2011-summer/solar-system-tremaine

    But anyways, back to the topic at hand, for most of the history of modern science in the Christian west, finding ‘platonic perfection’, i.e. perfect agreement, between our mathematical predictions for the universe, and our experimental measurements of those mathematical predictions, has been a very elusive goal. The primary example being Newton’s theory of gravity, (which I remind was based on Euclidean geometry), and the failure to describe the precession of Mercury’s orbit within the Euclidian geometry of Newton’s theory.

    This lack of perfect agreement between our mathematical predictions for the universe, and our experimental observations of those mathematical predictions, all changed with the discoveries of the 4-dimensional spacetimes of Special Relativity & General Relativity, and the discovery of the infinite dimensional Hilbert space of Quantum Mechanics. That is to say, as far as experimental testing will allow, there is no discrepancy to be found between what the higher dimensional mathematical descriptions of Relativity and Quantum Mechanics predict and what our most advanced scientific testing of those predictions are able to measure.

    “Recent experiments have confirmed, to within one part in one hundred million billion (10^17), that the speed of light does not change when an observer is in motion.”
    Douglas Ell – “Counting To God” – pg. 41 – 2014

    “When this paper was published (referring to the circa 1970 Hawking, Penrose paper) we could only prove General Relativity’s reliability to 1% precision, today we can prove it to 15 places of decimal.”
    Hugh Ross PhD. Astrophysics – quote taken from 8:40 mark of the following video debate
    Hugh Ross vs Lewis Wolpert – Is there evidence for a Cosmic Creator
    https://www.youtube.com/watch?v=VLMrDO0_WvQ

    Introduction to The Strange World of Quantum Mechanics
    Excerpt: quantum mechanics is the most successful theory that humanity has ever developed; the brightest jewel in our intellectual crown. Quantum mechanics underlies our understanding of atoms, molecules, solids, and nuclei. It is vital for explaining aspects of stellar evolution, chemical reactions, and the interaction of light with matter. It underlies the operation of lasers, transistors, magnets, and superconductors. I could cite reams of evidence backing up these assertions, but I will content myself by describing a single measurement. One electron will be stripped away from a helium atom that is exposed to ultraviolet light below a certain wavelength. This threshold wavelength can be determined experimentally to very high accuracy: it is
    50.425 929 9 ± 0.000 000 4 nanometers.
    The threshold wavelength can also be calculated from quantum mechanics: this prediction is
    50.425 931 0 ± 0.000 002 0 nanometers.
    The agreement between observation and quantum mechanics is extraordinary. If you were to predict the distance from New York to Los Angeles with this accuracy, your prediction would be correct to within the width of your hand. In contrast, classical mechanics predicts that any wavelength of light will strip away an electron, that is, that there will be no threshold at all.
    http://www.oberlin.edu/physics.....intro.html

    Experimental non-classicality of an indivisible quantum system – Zeilinger 2011
    Excerpt: Page 491: “This represents a violation of (Leggett’s) inequality (3) by more than 120 standard deviations, demonstrating that no joint probability distribution is capable of describing our results.” The violation also excludes any non-contextual hidden-variable model. The result does, however, agree well with quantum mechanical predictions, as we will show now.,,,
    https://vcq.quantum.at/fileadmin/Publications/Experimental%20non-classicality%20of%20an%20indivisible.pdf

    As well, quantum electrodynamics (QED), which is a combination of special relativity and quantum mechanics, also now joins the list of perfect mathematical descriptions of the universe in which we can find no deviation from what the mathematics predict and what our best experimental testing can discern. In other words, as far as we can tell, ‘platonic perfection’ is reached for QED:

    The Most Precisely Tested Theory in the History of Science – May 5, 2011
    Excerpt: So, which of the two (general relativity or QED) is The Most Precisely Tested Theory in the History of Science?
    It’s a little tough to quantify a title like that, but I think relativity can claim to have tested the smallest effects. Things like the aluminum ion clock experiments showing shifts in the rate of a clock set moving at a few m/s, or raised by a foot, measure relativistic shifts of a few parts in 10^16. That is, if one clock ticks 10,000,000,000,000,000 times, the other ticks 9,999,999,999,999,999 times. That’s an impressively tiny effect, but the measured value is in good agreement with the predictions of relativity.
    In the end, though, I have to give the nod to QED, because while the absolute effects in relativity may be smaller, the precision of the measurements in QED is more impressive. Experimental tests of relativity measure tiny shifts, but to only a few decimal places. Experimental tests of QED measure small shifts, but to an absurd number of decimal places. The most impressive of these is the “anomalous magnetic moment of the electron,” expressed is terms of a number g whose best measured value is:
    g/2 = 1.001 159 652 180 73 (28)
    Depending on how you want to count it, that’s either 11 or 14 digits of precision (the value you would expect without QED is exactly 1, so in some sense, the shift really starts with the first non-zero decimal place), which is just incredible. And QED correctly predicts all those decimal places (at least to within the measurement uncertainty, given by the two digits in parentheses at the end of that).
    http://scienceblogs.com/princi.....sted-theo/

    This point was driven further home with the discovery of the hypergeometric object of the amplitudhedron:

    Bohemian Gravity – Rob Sheldon – September 19, 2013
    Excerpt: Quanta magazine carried an article about a hypergeometric object that is as much better than Feynman diagrams as Feynman was better than Heisenberg’s S-matrices. But the discoverers are candid about it,
    “The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity. “Both are hard-wired in the usual way we think about things,” said Nima Arkani-Hamed, a professor of physics at the Institute for Advanced Study in Princeton, N.J., and the lead author of the new work, which he is presenting in talks and in a forthcoming paper. “Both are suspect.””
    What are these suspect principles? None other than two of the founding principles of materialism–that there do not exist “spooky-action-at-a-distance” forces, and that material causes are the only ones in the universe.,,,
    http://rbsp.info/PROCRUSTES/bohemian-gravity/

    As Nima Arkani-Hamed himself, the discoverer of the amplituhedron, stated “It seems inconceivable that this intricate web of perfect mathematical descriptions is random or happenstance. This mystery must have an explanation.”,,,

    Physicist: It’s Not The Answers We Lack, It’s The Question – February 24, 2019
    Excerpt: “It seems inconceivable that this intricate web of perfect mathematical descriptions is random or happenstance. This mystery must have an explanation. But what might such an explanation look like?”
    Nima Arkani-Hamed
    https://uncommondescent.com/intelligent-design/physicist-its-not-the-answers-we-lack-its-the-question/

  168. 168
    bornagain77 says:

    And as was already mentioned previously in this thread, another very important place where ‘platonic perfection’ is now shown to be ‘perfectly reached’ in the universe, (as far as our most precise testing will allow), is for the ‘flatness’ of the universe.

    “When a geometry is described by a set of axioms, the notion of a line is usually left undefined (a so-called primitive object).”
    per wikipedia

    How do we know the universe is flat? Discovering the topology of the universe – by Fraser Cain – June 7, 2017
    Excerpt: With the most sensitive space-based telescopes they have available, astronomers are able to detect tiny variations in the temperature of this background radiation.
    And here’s the part that blows my mind every time I think about it. These tiny temperature variations correspond to the largest scale structures of the observable universe. A region that was a fraction of a degree warmer become a vast galaxy cluster, hundreds of millions of light-years across.
    The cosmic microwave background radiation just gives and gives, and when it comes to figuring out the topology of the universe, it has the answer we need. If the universe was curved in any way, these temperature variations would appear distorted compared to the actual size that we see these structures today.
    But they’re not. To best of its ability, ESA’s Planck space telescope, can’t detect any distortion at all. The universe is flat.,,,
    We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,,
    Since the universe is flat now, it must have been flat in the past, when the universe was an incredibly dense singularity. And for it to maintain this level of flatness over 13.8 billion years of expansion, in kind of amazing.
    In fact, astronomers estimate that the universe must have been flat to 1 part within 1×10^57 parts.
    Which seems like an insane coincidence.
    https://phys.org/news/2017-06-universe-flat-topology.html

    Moreover, this ‘insane coincidence’ of ‘plantonic perfection’ being reached for the axiomatic ‘primitive object’ of the line just so happens to be necessary for us to even be able to practice math and science, (and apply technology in our world), in the first place:

    How do we know the universe is flat? Discovering the topology of the universe – by Fraser Cain – June 7, 2017
    Excerpt: We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,,
    https://phys.org/news/2017-06-universe-flat-topology.html

    Why We Need Cosmic Inflation
    By Paul Sutter, Astrophysicist | October 22, 2018
    Excerpt: As best as we can measure, the geometry of our universe appears to be perfectly, totally, ever-so-boringly flat. On large, cosmic scales, parallel lines stay parallel forever, interior angles of triangles add up to 180 degrees, and so on. All the rules of Euclidean geometry that you learned in high school apply.
    But there’s no reason for our universe to be flat. At large scales it could’ve had any old curvature it wanted. Our cosmos could’ve been shaped like a giant, multidimensional beach ball, or a horse-riding saddle. But, no, it picked flat.
    https://www.space.com/42202-why-we-need-cosmic-inflation.html

    Simply put, if the universe were not ‘ever-so-boringly’ flat (and if the universal constants were not also ‘ever-so-boringly’ constant), but the universe were instead governed by randomness, as atheists presuppose, or governed by some other of the infinitude of ‘platonic topologies’ that were possible, modern science and technology would have never gotten off the ground here on earth.

    Scientists Question Nature’s Fundamental Laws – Michael Schirber – 2006
    Excerpt: “There is absolutely no reason these constants should be constant,” says astronomer Michael Murphy of the University of Cambridge. “These are famous numbers in physics, but we have no real reason for why they are what they are.”,,,
    The observed differences are small-roughly a few parts in a million-but the implications are huge (if they hold up): The laws of physics would have to be rewritten, not to mention we might need to make room for six more spatial dimensions than the three that we are used to.”,,,
    The speed of light, for instance, might be measured one day with a ruler and a clock. If the next day the same measurement gave a different answer, no one could tell if the speed of light changed, the ruler length changed, or the clock ticking changed.
    Per space DOT com

    Nor, if platonic perfection were not present for the flatness of the universe would we have eventually been able to deduce the ‘platonic perfection’ that is revealed in the ‘higher dimensional’ mathematics that lay behind Relativity and Quantum Mechanics.
    More interesting still, these findings of ‘platonic perfection’ for the higher dimensional mathematics that lay behind Relativity and Quantum Mechanics are VERY friendly to overriding Christian presuppositions of life after death as well as the presupposition of God upholding this universe in its continual existence.

    Quantum Mechanics, Special Relativity, General Relativity and Christianity – video
    https://www.youtube.com/watch?v=h4QDy1Soolo

    For an example of just how friendly this ‘platonic perfection’ is to Christian presuppositions, let’s look at special relativity and general relativity in particular.

    There are a couple of thought experiments that Einstein utilized to work out the basics of special relativity and then general relativity.

    Introduction to special relativity
    Excerpt: Einstein’s approach was based on thought experiments, calculations, and the principle of relativity, which is the notion that all physical laws should appear the same (that is, take the same basic form) to all inertial observers.,,,
    Each observer has a distinct “frame of reference” in which velocities are measured,,,,http://en.wikipedia.org/wiki/I.....relativity

    In the first thought experiment for special relativity, Einstein imagined that he was riding on a bus near the speed of light,

    “In the spring of 1905, Einstein was riding on a bus and he looked back at the famous clock tower that dominates Bern Switzerland. And then he imagined, “What happens if that bus were racing near the speed of light.”, (narrator: “In his imagination, Einstein looks back at the clock tower and what he sees is astonishing. As he reaches the speed of light, the hands of the clock appear frozen in time”), “Einstein would later write, “A storm broke in my mind. All of the sudden everything, everything, kept gushing forward.”, (narrator: “Einstein knows that, back at the clock tower, time is passing normally, but on Einstein’s light speed bus, as he reaches the speed of light, the light from the clock can no longer catch up to him. The faster he races through space, the slower he moves through time. This insight sparks the birth of Einstein’s Special Theory of relativity, which says that space and time are deeply connected. In fact, they are one and the same. A flexible fabric called spacetime.”)
    – Michio Kaku
    Einstein: Einstein’s Miracle Year (‘Insight into Eternity’ – Thought Experiment – 6:29 minute mark) – video
    https://youtu.be/QQ35opgrhNA?t=389

    Whereas in his second thought experiment, which he termed ‘the happiest thought of my life’, Einstein imagined a man freely falling in an elevator:

    “Ultimately, the thing that gives (Einstein) that clue turns out to be his old faithful way of reasoning; the thought experiment.”,,, He’s in his office at the patent office looking out the window. And he imagined men working on a roof. And he begins to wonder what would happen if one of those men were to fall off the roof.” Kaku, “And then he had the happiest thought of his life. The inspiration of the ages.”,, “He had a vision, the man would not be actually feeling his own weight.”,, “He would be Weight-Less!”,, “And then he imagined, if you are in a elevator and somebody cuts the cord, what happens to you?”,, “You fall, but the elevator falls at the same rate you do, so you are Weight-Less inside the elevator. So then Einstein got it.”,, “I is as though gravity has been switched off. What’s really going on?”,, “There is no such thing as gravitational pull. The earth has curved the space around me and (the curvature of) space is pushing me into this chair. Space itself can be curved.”
    Einstein History Channel HD
    https://youtu.be/QQ35opgrhNA?t=987

    Introduction to Tensor Calculus for General Relativity
    Excerpt: The second essential idea underlying GR is that at every spacetime point there exist locally inertial reference frames, corresponding to locally flat coordinates carried by freely falling observers, in which the physics of GR is locally indistinguishable from that of special relativity. This is Einstein’s famous strong equivalence principle and it makes general relativity an extension of special relativity to a curved spacetime.
    http://web.mit.edu/edbert/GR/gr1.pdf

  169. 169
    bornagain77 says:

    And similar to when time, as we understand it, comes to complete stop in Special Relativity when we reach the speed of light, in General Relativity time, as we understand it, also comes to a complete stop when we reach what is termed to be the ‘event horizon’ of a black hole, As wikipedia states, “Travel to regions of space where extreme gravitational time dilation is taking place, such as near a black hole, could yield time-shifting results analogous to those of near-lightspeed space travel.”

    Time dilation
    Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to them will be measured to tick slower than a clock that is at rest in their frame of reference. This case is sometimes called special relativistic time dilation. The faster the relative velocity, the greater the time dilation between one another, with the rate of time reaching zero as one approaches the speed of light (299,792,458 m/s). This causes massless particles that travel at the speed of light to be unaffected by the passage of time.,,,
    Gravitational time dilation is experienced by an observer that, at a certain altitude within a gravitational potential well, finds that their local clocks measure less elapsed time than identical clocks situated at higher altitude (and which are therefore at higher gravitational potential).
    Gravitational time dilation is at play e.g. for ISS astronauts. While the astronauts’ relative velocity slows down their time, the reduced gravitational influence at their location speeds it up, although at a lesser degree. Also, a climber’s time is theoretically passing slightly faster at the top of a mountain compared to people at sea level. It has also been calculated that due to time dilation, the core of the Earth is 2.5 years younger than the crust.[32] “A clock used to time a full rotation of the earth will measure the day to be approximately an extra 10 ns/day longer for every km of altitude above the reference geoid.”[33] Travel to regions of space where extreme gravitational time dilation is taking place, such as near a black hole, could yield time-shifting results analogous to those of near-lightspeed space travel.
    Contrarily to velocity time dilation, in which both observers measure the other as aging slower (a reciprocal effect), gravitational time dilation is not reciprocal. This means that with gravitational time dilation both observers agree that the clock nearer the center of the gravitational field is slower in rate, and they agree on the ratio of the difference.
    https://en.wikipedia.org/wiki/Time_dilation#Gravitational_time_dilation

    It is important to point out that these ‘eternities’ found at both Special Relativity and General Relativity have fairly direct theological implications. As Dr. Richard Swenson states,

    “The laws of relativity have changed timeless existence from a theological claim to a physical reality. Light, you see, is outside of time, a fact of nature proven in thousands of experiments at hundreds of universities. I don’t pretend to know how tomorrow can exist simultaneously with today and yesterday. But at the speed of light they actually and rigorously do. Time does not pass.”
    Dr. Richard Swenson – More Than Meets The Eye, Chpt. 11

    Einstein himself seemed to concede this theological implication of his theory when he, upon his good friend Michele Besso’s death, stated that, “Now he has departed from this strange world a little ahead of me. That signifies nothing. For those of us who believe in physics, the distinction between past, present and future is only a stubbornly persistent illusion.”

    Einstein and Michele Besso
    Upon Besso’s death in 1955, Einstein wrote a letter of condolence to the Besso family—less than a month before his own death—which contained the following quote “Now he has departed from this strange world a little ahead of me. That signifies nothing. For those of us who believe in physics, the distinction between past, present and future is only a stubbornly persistent illusion.”
    http://quotingeinstein.blogspo.....besso.html

    And in what was, basically, an extension of Einstein’s thought experiment for General Relativity, Kip Thorne worked out what would happen to a hypothetical astronaut who was unfortunate enough to fall into a black hole,

    “Einstein’s equation predicts that, as the astronaut reaches the singularity (of the black-hole), the tidal forces grow infinitely strong, and their chaotic oscillations become infinitely rapid. The astronaut dies and the atoms which his body is made become infinitely and chaotically distorted and mixed-and then, at the moment when everything becomes infinite (the tidal strengths, the oscillation frequencies, the distortions, and the mixing), spacetime ceases to exist.”
    Kip S. Thorne – “Black Holes and Time Warps: Einstein’s Outrageous Legacy” pg. 476
    http://books.google.com/books?.....38;f=false
    Kip Thorne and Charles Misner, and John Wheeler wrote Gravitation (1973), considered a definitive textbook on general relativity.

    In short, what makes the eternity of General Relativity profoundly different than the eternity found at Special Relativity, is that the entropy associated with Special Relativity is extremely ordered whereas the entropy associated with General Relativity is extremely chaotic

    How Special Was The Big Bang?
    “But why was the big bang so precisely organized (to 1 in 10^10^123 for the initial entropy), whereas the big crunch (or the singularities in black holes) would be expected to be totally chaotic? It would appear that this question can be phrased in terms of the behaviour of the WEYL part of the space-time curvature at space-time singularities. What we appear to find is that there is a constraint WEYL = 0 (or something very like this) at initial space-time singularities-but not at final singularities-and this seems to be what confines the Creator’s choice to this very tiny region of phase space.”
    Roger Penrose – (from the Emperor’s New Mind, Penrose, pp 339-345 copyright 1989, Penguin Books)
    http://www.ws5.com/Penrose/

    In fact, gain in entropy, which is the primary reason why our material bodies grow old and eventually die in this universe,,,

    Entropy Explains Aging, Genetic Determinism Explains Longevity, and Undefined Terminology Explains Misunderstanding Both – 2007
    Excerpt: There is a huge body of knowledge supporting the belief that age changes are characterized by increasing entropy, which results in the random loss of molecular fidelity, and accumulates to slowly overwhelm maintenance systems [1–4].,,,
    http://www.plosgenetics.org/ar.....en.0030220

    ,, gain in entropy is found to be greatest at black holes. As the following article stated,, ‘supermassive black holes are the largest contributor to the observable universe’s entropy.’

    Entropy of the Universe – Hugh Ross – May 2010
    Excerpt: Egan and Lineweaver found that supermassive black holes are the largest contributor to the observable universe’s entropy. They showed that these supermassive black holes contribute about 30 times more entropy than what the previous research teams estimated.
    http://www.reasons.org/entropy-universe

    Thus the ‘eternity’ that is found at a black hole can rightly be called an ‘eternity of decay, death, and destruction’.
    Needless to say, to those of us who are of, shall we say, a spiritually minded persuasion, this finding of an eternity of destruction and decay should be fairly sobering.

    To continue on, the evidence from Special Relativity, (which is currently one of our most powerful theories in science), strongly supports the physical reality of a timeless eternity and of a heavenly dimension that exists above this temporal dimension. The timeless eternity aspect of both Special and General Relativity was already covered in this post. ,,, so to continue on, the only way it is possible for time not to pass for light, and yet for light to move from point A to point B in our universe, is if light is of a higher dimensional nature of time than the temporal time that we are currently living in. If this were not the case, then light would simply be ‘frozen within time’ to our temporal frame of reference.

    And indeed that is exactly what we find. “Hermann Minkowski- one of the math professors of a young Einstein in Zurich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space.” In fact, Hermann Minkowski’s work in higher dimensional mathematics proved to be vital for Einstein in his eventual formulation of General Relativity.

    Spacetime
    Excerpt: In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zurich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the definition of a spacetime interval that combines distance and time. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded.
    Minkowski’s geometric interpretation of relativity was to prove vital to Einstein’s development of his 1915 general theory of relativity, wherein he showed that spacetime becomes curved in the presence of mass or energy.,,,
    Einstein, for his part, was initially dismissive of Minkowski’s geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity.[10]:151–152 Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime.
    https://en.wikipedia.org/wiki/Spacetime

    One way for us to more easily understand this higher dimensional framework for time that light exist in is for us to visualize what would happen if a hypothetical observer approached the speed of light.
    In the following video clip, at around the 2:40 minute mark, (a video which was made by two Australian University Physics Professors), we find that the 3-Dimensional world ‘folds and collapses’ into a tunnel shape as a ‘hypothetical’ observer approaches the ‘higher dimension’ of the speed of light.

    Optical Effects of Special Relativity – video – full relativistic effects featured at around the 2:40 minute mark
    https://youtu.be/JQnHTKZBTI4?t=161

  170. 170
    bornagain77 says:

    Interestingly, as was visualized at the 3:00 minute mark of the preceding video, (i.e. all of the light concentrating into the direction of travel, i.e. the light visualized at the ‘end of the tunnel’ in the video), is termed to be the ‘headlight effect’

    Relativistic aberration
    Relativistic aberration is the relativistic version of aberration of light, including relativistic corrections that become significant for observers who move with velocities close to the speed of light. It is described by Einstein’s special theory of relativity.,,,
    One consequence of this is that a forward observer should normally be expected to intercept a greater proportion of the object’s light than a rearward one; this concentration of light in the object’s forward direction is referred to as the “searchlight effect” (or headlight effect).
    https://en.wikipedia.org/wiki/Relativistic_aberration

    Now that we have outlined the basics of what we know to be physically true from special relativity, It is very interesting to note that many of the characteristics found in heavenly Near Death Experience testimonies are exactly what we would expect to see from what we now know to be physically true about Special Relativity.

    For instance, many times people who have had a Near Death Experience mention that their perception of time was radically altered. In the following video clip, Mickey Robinson gives his Near Death testimony of what it felt like for him to experience a ‘timeless eternity’.

    ‘In the ‘spirit world,,, instantly, there was no sense of time. See, everything on earth is related to time. You got up this morning, you are going to go to bed tonight. Something is new, it will get old. Something is born, it’s going to die. Everything on the physical plane is relative to time, but everything in the spiritual plane is relative to eternity. Instantly I was in total consciousness and awareness of eternity, and you and I as we live in this earth cannot even comprehend it, because everything that we have here is filled within the veil of the temporal life. In the spirit life that is more real than anything else and it is awesome. Eternity as a concept is awesome. There is no such thing as time. I knew that whatever happened was going to go on and on.’
    In The Presence Of Almighty God – The NDE of Mickey Robinson – video (testimony starts at 27:45 minute mark)
    https://www.youtube.com/watch?v=voak1RM-pXo

    And here are a few more quotes from people who have experienced Near Death, that speak of how their perception of time was radically altered as they were outside of their material body during their NDEs.

    ‘Earthly time has no meaning in the spirit realm. There is no concept of before or after. Everything – past, present, future – exists simultaneously.’
    – Kimberly Clark Sharp – Near Death Experiencer

    ‘There is no way to tell whether minutes, hours or years go by. Existence is the only reality and it is inseparable from the eternal now.’
    – John Star – NDE Experiencer

    As well, Near Death Experiencers also frequently mention going through a tunnel, towards an extremely brilliant light, to a higher heavenly dimension:

    Ask the Experts: What Is a Near-Death Experience (NDE)? – article with video
    Excerpt: “Very often as they’re moving through the tunnel, there’s a very bright mystical light … not like a light we’re used to in our earthly lives. People call this mystical light, brilliant like a million times a million suns…”
    – Jeffrey Long M.D. – has studied NDE’s extensively

    The Tunnel and the Near-Death Experience
    Excerpt: One of the nine elements that generally occur during NDEs is the tunnel experience. This involves being drawn into darkness through a tunnel, at an extremely high speed, until reaching a realm of radiant golden-white light.

    In the following video, Barbara Springer gives her testimony as to what it felt like for her to go through the tunnel towards ‘the light’:

    “I started to move toward the light. The way I moved, the physics, was completely different than it is here on Earth. It was something I had never felt before and never felt since. It was a whole different sensation of motion. I obviously wasn’t walking or skipping or crawling. I was not floating. I was flowing. I was flowing toward the light. I was accelerating and I knew I was accelerating, but then again, I didn’t really feel the acceleration. I just knew I was accelerating toward the light. Again, the physics was different – the physics of motion of time, space, travel. It was completely different in that tunnel, than it is here on Earth. I came out into the light and when I came out into the light, I realized that I was in heaven.”
    Barbara Springer – Near Death Experience – The Tunnel – video
    https://www.youtube.com/watch?v=gv2jLeoAcMI

    And in the following audio clip, Vicki Noratuk, who has been blind from birth, (besides being able to ‘miraculously” see for the first time in her life during her Near Death Experience), Vicki also gives testimony of going through a tunnel at a ‘horrifically’ rapid rate of speed:

    “I was in a body, and the only way that I can describe it was a body of energy, or of light. And this body had a form. It had a head, it had arms and it had legs. And it was like it was made out of light. And it was everything that was me. All of my memories, my consciousness, everything.”,,, “And then this vehicle formed itself around me. Vehicle is the only thing, or tube, or something, but it was a mode of transportation that’s for sure! And it formed around me. And there was no one in it with me. I was in it alone. But I knew there were other people ahead of me and behind me. What they were doing I don’t know, but there were people ahead of me and people behind me, but I was alone in my particular conveyance. And I could see out of it. And it went at a tremendously, horrifically, rapid rate of speed. But it wasn’t unpleasant. It was beautiful in fact.,, I was reclining in this thing, I wasn’t sitting straight up, but I wasn’t lying down either. I was sitting back. And it was just so fast. I can’t even begin to tell you where it went or whatever it was just fast!” –
    Vicki’s NDE – Blind since birth –
    https://www.youtube.com/watch?v=e65KhcCS5-Y

    And in the following quotes, the two Near Death Experiencers both testify that they firmly believed that they were in a higher heavenly dimension that is above this three-dimensional world, and that the reason that they have a very difficult time explaining what their Near Death Experiences actually felt like is because we simply don’t currently have the words to properly describe that higher dimension:

    “Regardless, it is impossible for me to adequately describe what I saw and felt. When I try to recount my experiences now, the description feels very pale. I feel as though I’m trying to describe a three-dimensional experience while living in a two-dimensional world. The appropriate words, descriptions and concepts don’t even exist in our current language. I have subsequently read the accounts of other people’s near-death experiences and their portrayals of heaven and I able to see the same limitations in their descriptions and vocabulary that I see in my own.”
    Mary C. Neal, MD – To Heaven And Back pg. 71

    “Well, when I was taking geometry, they always told me there were only three dimensions, and I always just accepted that. But they were wrong. There are more… And that is why so hard for me to tell you this. I have to describe with words that are three-dimensional. That’s as close as I can get to it, but it’s really not adequate.”
    John Burke – Imagine Heaven pg. 51 – quoting a Near Death Experiencer

    That what we now know to be true from special relativity, (namely that it outlines a ‘timeless’, i.e. eternal, dimension that exists above this temporal dimension), would fit hand and glove with the personal testimonies of people who have had a deep heavenly NDEs is, needless to say, powerful evidence that their testimonies are, in fact, true and that they are accurately describing the ‘reality’ of a higher heavenly dimension, that they experienced first hand, and that they say exists above this temporal dimension.

    I would even go so far as to say that such corroboration from ‘non-physicists’, who, in all likelihood, know nothing about the intricacies of special relativity, is a complete scientific verification of the overall validity of their personal NDE testimonies.

    Matthew 6:33
    But seek first the kingdom of God and his righteousness, and all these things will be added to you.

    It is also interesting to point out that, although Special Relativity can be unified with Quantum Mechanics, that General Relativity simply refuses to ever be mathematically unified with quantum mechanics in any realistic way,

    Theories of the Universe: Quantum Mechanics vs. General Relativity
    Excerpt: The first attempt at unifying relativity and quantum mechanics took place when special relativity was merged with electromagnetism. This created the theory of quantum electrodynamics, or QED. It is an example of what has come to be known as relativistic quantum field theory, or just quantum field theory. QED is considered by most physicists to be the most precise theory of natural phenomena ever developed.
    In the 1960s and ’70s, the success of QED prompted other physicists to try an analogous approach to unifying the weak, the strong, and the gravitational forces. Out of these discoveries came another set of theories that merged the strong and weak forces called quantum chromodynamics, or QCD, and quantum electroweak theory, or simply the electroweak theory, which you’ve already been introduced to.
    If you examine the forces and particles that have been combined in the theories we just covered, you’ll notice that the obvious force missing is that of gravity (i.e. General Relativity).
    – Per info please

    In fact, mathematically speaking, there is found to be an ‘infinite divide’ between General Relativity and Quantum Mechanics that forever prevents them from being unified mathematically.

    Why Gravity Is Not Like the Other Forces
    We asked four physicists why gravity stands out among the forces of nature. We got four different answers.
    Excerpt: the quantum version of Einstein’s general relativity is “nonrenormalizable.”,,,
    In quantum theories, infinite terms appear when you try to calculate how very energetic particles scatter off each other and interact. In theories that are renormalizable — which include the theories describing all the forces of nature other than gravity — we can remove these infinities in a rigorous way by appropriately adding other quantities that effectively cancel them, so-called counterterms. This renormalization process leads to physically sensible answers that agree with experiments to a very high degree of accuracy.
    The problem with a quantum version of general relativity is that the calculations that would describe interactions of very energetic gravitons — the quantized units of gravity — would have infinitely many infinite terms. You would need to add infinitely many counterterms in a never-ending process. Renormalization would fail.,,,
    Sera Cremonini – theoretical physicist – Lehigh University
    https://www.quantamagazine.org/why-gravity-is-not-like-the-other-forces-20200615/

    Professor Jeremy Bernstein states the situation as such, “there remains an irremediable difficulty. Every order reveals new types of infinities, and no finite number of renormalizations renders all the terms in the series finite.”

    Quantum Leaps – Jeremy Bernstein – October 19, 2018
    Excerpt: Divergent series notwithstanding, quantum electrodynamics yielded results of remarkable accuracy. Consider the magnetic moment of the electron. This calculation, which has been calculated up to the fifth order in ?, agrees with experiment to ten parts in a billion. If one continued the calculation to higher and higher orders, at some point the series would begin to break down. There is no sign of that as yet. Why not carry out a similar program for gravitation? One can readily write down the Feynman graphs that represent the terms in the expansion. Yet there remains an irremediable difficulty. Every order reveals new types of infinities, and no finite number of renormalizations renders all the terms in the series finite.
    The theory is not renormalizable.
    https://inference-review.com/article/quantum-leaps
    Jeremy Bernstein is professor emeritus of physics at the Stevens Institute of Technology.

    Considering the ‘infinitely’ chaotic entropy associated with General Relativity, this mathematically ‘infinite divide’ between General Relativity and Quantum Mechanics reminds me very much of this quote from scripture concerning the rich man finding himself in hell and pleading with Abraham to get him out.

    Luke 16:26
    And besides all this, between us and you a great chasm has been set in place, so that those who want to go from here to you cannot, nor can anyone cross over from there to us.’

    But anyways, to continue on, the ‘zero/infinity’ conflict between General Relativity and Quantum Mechanics has some fairly disturbing theoretical implications. Specifically, when theorists try to combine the two theories, then the resulting theory predicts that spacetime, atoms, and even the universe itself should all be literally blown apart.
    https://uncommondescent.com/intelligent-design/at-quanta-how-gravity-differs-from-the-other-three-fundamental-forces/#comment-704725

    And yet, despite both theories contradicting each other to the point of literally blowing the universe apart, quantum mechanics and general relativity are both tested to extreme levels of precision, (in fact, both general relativity and quantum mechanics are consider to be our most successful theories ever in the history of science), as was referenced previously,,,

    The Most Precisely Tested Theory in the History of Science – May 5, 2011
    Excerpt: So, which of the two (general relativity or QED) is The Most Precisely Tested Theory in the History of Science?
    It’s a little tough to quantify a title like that, but I think relativity can claim to have tested the smallest effects. Things like the aluminum ion clock experiments showing shifts in the rate of a clock set moving at a few m/s, or raised by a foot, measure relativistic shifts of a few parts in 10^16. That is, if one clock ticks 10,000,000,000,000,000 times, the other ticks 9,999,999,999,999,999 times. That’s an impressively tiny effect, but the measured value is in good agreement with the predictions of relativity.
    In the end, though, I have to give the nod to QED, because while the absolute effects in relativity may be smaller, the precision of the measurements in QED is more impressive. Experimental tests of relativity measure tiny shifts, but to only a few decimal places. Experimental tests of QED measure small shifts, but to an absurd number of decimal places. The most impressive of these is the “anomalous magnetic moment of the electron,” expressed is terms of a number g whose best measured value is:
    g/2 = 1.001 159 652 180 73 (28)
    Depending on how you want to count it, that’s either 11 or 14 digits of precision (the value you would expect without QED is exactly 1, so in some sense, the shift really starts with the first non-zero decimal place), which is just incredible. And QED correctly predicts all those decimal places (at least to within the measurement uncertainty, given by the two digits in parentheses at the end of that).
    http://scienceblogs.com/princi.....sted-theo/

  171. 171
    bornagain77 says:

    And since quantum mechanics and general relativity are both tested to such an extreme level of precision, (and we can thus have a very high level of confidence that both theories are, in fact, true mathematical descriptions of reality), and since Godel’s incompleteness theorem itself requires something to be ‘outside the circle’ of mathematics,,,,

    “Gödel’s incompleteness theorem (1931), proves that there are limits to what can be ascertained by mathematics. Kurt Gödel halted the achievement of a unifying all-encompassing theory of everything in his theorem that: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove”.
    Stephen Hawking & Leonard Miodinow, The Grand Design (2010)

    ,,, then it is fairly safe to assume that there must be something very powerful that must be holding the universe together in order to keep it from blowing itself apart. ,,,

    For the Christian this theoretical finding from our very best theories in science, (i.e. that something very powerful must be ‘outside the universe’ that is holding this universe together), should not be all that surprising to find out. Christianity, a couple of millennium before the zero/infinity conflict between the two theories was even known about, predicted that Christ is before all things, and in him all things hold together,,,

    Colossians 1:17
    He is before all things, and in him all things hold together.

    Dr. William Dembski in this following comment, although he was not directly addressing the Zero/Infinity conflict between General Relativity and Quantum Mechanics, offers this insight into what the ‘unification’ of infinite God and finite man might look like mathematically:

    The End Of Christianity – Finding a Good God in an Evil World – Pg.31
    William Dembski PhDs. Mathematics and Theology
    Excerpt: “In mathematics there are two ways to go to infinity. One is to grow large without measure. The other is to form a fraction in which the denominator goes to zero. The Cross is a path of humility in which the infinite God becomes finite and then contracts to zero, only to resurrect and thereby unite a finite humanity within a newfound infinity.”
    http://www.designinference.com.....of_xty.pdf

    Philippians 2:8-9
    And being found in appearance as a man, He humbled Himself and became obedient to the point of death, even the death of the cross. Therefore God also has highly exalted Him and given Him the name which is above every name,

    Moreover, if we rightly let the Agent causality of God ‘back’ into the picture of modern physics, as the Christian founders of modern science originally envisioned,,,, (Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders of modern science),,, and as quantum mechanics itself now empirically demands (with the closing of the free will loophole by Anton Zeilinger and company), rightly allowing the Agent causality of God ‘back’ into physics provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead provides an empirically backed reconciliation, via the Shroud of Turin, between quantum mechanics and general relativity into the much sought after ‘Theory of Everything”. Here are a few posts where I lay out and defend some of the evidence for that claim:

    November 2019 – despite the fact that virtually everyone, including the vast majority of Christians, hold that the Copernican Principle is unquestionably true, the fact of the matter is that the Copernican Principle is now empirically shown, (via quantum mechanics and general relativity, etc..), to be a false assumption.
    https://uncommondescent.com/intelligent-design/so-then-maybe-we-are-privileged-observers/#comment-688855

    (February 19, 2019) To support Isabel Piczek’s claim that the Shroud of Turin does indeed reveal a true ‘event horizon’, the following study states that ‘The bottom part of the cloth (containing the dorsal image) would have born all the weight of the man’s supine body, yet the dorsal image is not encoded with a greater amount of intensity than the frontal image.’,,,
    Moreover, besides gravity being dealt with, the shroud also gives us evidence that Quantum Mechanics was dealt with. In the following paper, it was found that it was not possible to describe the image formation on the Shroud in classical terms but they found it necessary to describe the formation of the image on the Shroud in discrete quantum terms.
    https://uncommondescent.com/intelligent-design/experiment-quantum-particles-can-violate-the-mathematical-pigeonhole-principle/#comment-673178

    The evidence for the Shroud’s authenticity keeps growing. (Timeline of facts) – November 08, 2019
    What Is the Shroud of Turin? Facts & History Everyone Should Know – Myra Adams and Russ Breault
    https://www.christianity.com/wiki/jesus-christ/what-is-the-shroud-of-turin.html

    To give us a small glimpse of the power that was involved in Christ’s resurrection from the dead, the following recent article found that, ”it would take 34 Thousand Billion (trillion) Watts of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.”

    Astonishing discovery at Christ’s tomb supports Turin Shroud – NOV 26TH 2016
    Excerpt: The first attempts made to reproduce the face on the Shroud by radiation, used a CO2 laser which produced an image on a linen fabric that is similar at a macroscopic level. However, microscopic analysis showed a coloring that is too deep and many charred linen threads, features that are incompatible with the Shroud image. Instead, the results of ENEA “show that a short and intense burst of VUV directional radiation can color a linen cloth so as to reproduce many of the peculiar characteristics of the body image on the Shroud of Turin, including shades of color, the surface color of the fibrils of the outer linen fabric, and the absence of fluorescence”.
    ‘However, Enea scientists warn, “it should be noted that the total power of VUV radiations required to instantly color the surface of linen that corresponds to a human of average height, body surface area equal to = 2000 MW/cm2 17000 cm2 = 34 thousand billion watts makes it impractical today to reproduce the entire Shroud image using a single laser excimer, since this power cannot be produced by any VUV light source built to date (the most powerful available on the market come to several billion watts )”.
    Comment
    The ENEA study of the Holy Shroud of Turin concluded that it would take 34 Thousand Billion Watts of VUV radiations to make the image on the shroud. This output of electromagnetic energy remains beyond human technology.
    http://westvirginianews.blogsp.....in-is.html

    Verse:

    Colossians 1:15-20
    The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross.

  172. 172
    Retired Physicist says:

    @JVL 158 heavens to betsy there is a lot of jabbering where there is little substance.

  173. 173
    kairosfocus says:

    RP & JVL:

    As by direct import of reference, after a late intervention, I am being targetted for dismissal without serious examination of the substance (over years, an all too familiar tactic in dealing with design thinkers . . . ) I again point you to 85 above and to the onward linked note here and JB’s more popular level article here.

    I particularly clip from 85:

    >>Do you have an explanation of how math came to be?>>

    1: Yes, as you know I have examined a core of Mathematics [–> see the article], showing that once a distinct possible world is, a certain logically ordered structure linked to quantity obtains. Indeed, we then see that such core aspects necessarily extend to any possible world, i.e. all of them, securing universality and global relevance. Which in turn answers Wigner on the astonishing power of Mathematics.

    2: So, this is not a matter of clever rhetorical games dependent on whatever ideas, suggestions or gaps may obtain with particular interlocutors, but something established as a base for further thought.

    3: There is, however, a second order question: how are possible worlds just that, possible?

    4: To answer that, notice, that were there ever utter, genuine nothingness — utter non-being — then as such has no causal capability, such would forever obtain. Further, transfinite regress cannot be traversed in finite stage steps, i.e. an actual infinity of successive contingent worlds with finite duration [years, say] is also ruled out, as is retro-causation by which a not yet future state reaches back to generate the chain that leads to itself. That, too would be pulling a world out of a non-existent hat.

    5: That is, there is adequate, finitely remote root cause for the actual world we inhabit and others that may or do actually exist. Such, is a reality root, necessary being. Once a world is, something always was, a something of different order from ourselves. Something, capable of creating worlds.

    6: So, there are consequences to there being possible worlds.

    Clearly, the issue is NOT, whether one can propose an alternative arithmetic. We have on the table several frameworks that get us to Arithmetic, I usually favour von Neumann’s approach. No alternative axiomatic framework that is inconsistent with long known, pre-axiomatisation facts (a core of which are self evident of order || + ||| –> ||||| which we conveniently symbolise 2 + 3 = 5) would be generally accepted. Similarly, as I showed in my paper the answer to Wigner is that as there is a core of mathematics — logic of structure and quantity — that pivots on requisites of distinct identity of any PW W marked apart from a close neighbour W’, then there is a core trans-world applicability of that core, which embraces the structured sets . . . hence, many familiar key relationships, operations and functions . . . N, Z, Q, R, C etc. This structure, quantity and logic are a cluster of abstract necessary entities and structured relationships that lead to what Wigner marvelled at.

    However, that does not end the matter, as I just clipped: how do we get to possible worlds?

    Not from utter non-being, nor from a transfinite past succession of finite duration stages [years, for simple short], nor from circular retrocausality. That leaves a bill of requisites for the world root: independent being [so, necessary], causally adequate to worlds such as ours existing with freely thinking creatures capable of doing Math [i.e. rational, responsible, morally governed, significantly free], finitely remote.

    A familiar — but too often these days, unwelcome and/or unfashionable — figure looms as the only truly serious candidate. Which, is the real problem. Math and linked logic of being are pointing where many refuse to go.

    As at now, the two of you are in danger of slipping into the zero credibility, unserious carping, sneering commenter ilk. Do you really want to go there?

    Please, do better than that.

    KF

    PS: On traversal of the transfinite, there was a three years long series of exchanges here at UD. The matter is readily resolved once it is recognised that a lot of talk about number lines and continua makes better sense if we accept that people — such as HS Math teachers — are often implying the hyperreals not the reals, R*/*R being mileposted by the hyperintegers. It is then trivial to see that stepwise ascent from a transfinitely remote claimed actual past cannot span a transfinite intervening range. And there is no evading that the structure of Z mileposting R includes the direct import that it cannot be spanned in stepwise succession, hence the use of ellipses of continuation L-ward and R-ward: { . . . -2,-1,0,1,2 . . .}. Much of the debate, per fair comment, boiled down to refusal to admit the hyperreals and/or to accept that Z’s structure implies that spanning of the transfinite supertask.

  174. 174
    JVL says:

    What do you get when you cross an elephant with a grape? |elephant||grape|sin(theta).

    I am happy to let the whole matter drop. I’m just here to talk about the mathematics not the theology or philosophy. Discussing axiomatic systems is not theology or philosophy.

  175. 175
    kairosfocus says:

    JVL, you raised a question that goes beyond axiomatisation and raises the sorts of issues I addressed from 85. Perhaps, you have not seen that the Godel results relativised any axiomatisation of a reasonably complex body of mathematics? Axiomatisation is incomplete or incoherent, and there is no constructive process to build a known coherent axiomatisation. The grand axiomatisation agenda of 100+ years ago has long since been dead. As for links to logic of being and to reality roots, they are inherent in mathematics once the Wigner challenge of the bridge to physics is on the table. Indeed, historically a lot of mathematics arose from physics and to address physics. Logic of being issues include what accounts for a world involving rational, responsible, significantly free, thus morally governed creatures. KF

  176. 176
    JVL says:

    Kairosfocus: Axiomatisation is incomplete or incoherent, and there is no constructive process to build a known coherent axiomatisation.

    I don’t think that’s exactly what Godel’s incompleteness theorems say.

    Gödel published his incompleteness theorems in Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme (called in English “On Formally Undecidable Propositions of Principia Mathematica and Related Systems”). In that article, he proved for any computable axiomatic system that is powerful enough to describe the arithmetic of the natural numbers (e.g., the Peano axioms or Zermelo–Fraenkel set theory with the axiom of choice), that:

    If a (logical or axiomatic formal) system is consistent, it cannot be complete.

    The consistency of axioms cannot be proved within their own system.

    These theorems ended a half-century of attempts, beginning with the work of Frege and culminating in Principia Mathematica and Hilbert’s formalism, to find a set of axioms sufficient for all mathematics.

    In hindsight, the basic idea at the heart of the incompleteness theorem is rather simple. Gödel essentially constructed a formula that claims that it is unprovable in a given formal system. If it were provable, it would be false. Thus there will always be at least one true but unprovable statement. That is, for any computably enumerable set of axioms for arithmetic (that is, a set that can in principle be printed out by an idealized computer with unlimited resources), there is a formula that is true of arithmetic, but which is not provable in that system. To make this precise, however, Gödel needed to produce a method to encode (as natural numbers) statements, proofs, and the concept of provability; he did this using a process known as Gödel numbering.

    You seem to be using the word ‘coherent’ in place of the clearer word ‘consistent’. Neither theorem says axiomatisation is incomplete or inconsistent: the first theorem says that IF system is consistent then it will be incomplete but it does not say that a complete system will be incoherent. The second theorem says the consistency of axioms cannot be proved within their own system which is roughly consistent with your phrase that there is no constructive process to build a known consistent axiomatisation. Anyway, my point is that the subtle points matter. A lot of people ascribe things to Godel that aren’t the case so it’s important to get it right.

    Logic of being issues include what accounts for a world involving rational, responsible, significantly free, thus morally governed creatures.

    Nothing to do with mathematics so I won’t comment further.

  177. 177
    Retired Physicist says:

    “What do you get when you cross an elephant with a grape? |elephant||grape|sin(theta).”

    One of my very favorite math/physics jokes.

  178. 178
    ET says:

    I am sensing a bromance…

  179. 179
    kairosfocus says:

    JVL:

    I note from your clip:

    If a (logical or axiomatic formal) system is consistent, it cannot be complete.

    The consistency of axioms cannot be proved within their own system.

    These theorems ended a half-century of attempts, beginning with the work of Frege and culminating in Principia Mathematica and Hilbert’s formalism, to find a set of axioms sufficient for all mathematics

    With my addition that we speak of complex domains, that is essentially what I said. Inconsistency and incoherence here effectively mean the same. Note here, the principle of explosion. You are making up an objection out of nothing.

    And BTW, once we see that Mathematics is in effect substantially the logic of structure and quantity, logic of being has everything to do with Mathematics and its foundations, as well as with the existence of creatures able to do mathematics with some confidence that they are in fact rational. Those things then make issues of axiomatisation and what comes before such — to which axiomatisations answer — highly relevant. With Godel’s work a capital example.

    KF

  180. 180
    JVL says:

    Kairosfocus: With my addition that we speak of complex domains, that is essentially what I said. Inconsistency and incoherence here effectively mean the same. Note here, the principle of explosion. You are making up an objection out of nothing.

    I am insisting that correct and proper terminology is used. I don’t think that inconsistency and incoherence mean the same thing and I encourage you to use the accepted forms to avoid misunderstanding.

    Those things then make issues of axiomatisation and what comes before such — to which axiomatisations answer — highly relevant. With Godel’s work a capital example.

    Whatever. You would do better getting your points across if you wrote more plainly.

  181. 181
    bornagain77 says:

    Eugene Wigner, who rightly considered the applicability of mathematics to the universe to be a ‘miracle’, won a Nobel prize for his work in quantum mechanics in 1963,

    Eugene Wigner receives his Nobel Prize for Quantum Symmetries – video 1963?http://www.nobelprize.org/medi.....hp?id=1111

    Here is Wigner commenting on the key experiment that led Wigner to his Nobel Prize winning work on quantum symmetries,,, “As the observer is replaced by another observer (working elsewhere, looking at a different direction, using an other clock, perhaps being lefthanded), the state of the very same particle is described by another vector, obtained from the previous vector by multiplying it with a matrix. This matrix transfers from one observer to another.,,,”

    Eugene Wigner –
    Excerpt: This, (1925-26), is when Wigner’s interest started in symmetry. Let us listen to his recollection:
    — When I returned to Berlin, the excellent crystallographer Weissenberg asked me to study: why is it that in a crystal the atoms like to sit in a symmetry plane or symmetry axis. After a short time of thinking I understood: being on the symmetry axis ensures that the derivatives of the potential energy vanish in two directions perpendicular to the symmetry axis. (In case of a symmetry plane the derivative of the potential energy vanishes in one direction.) This is how I became interested in the role of symmetries in quantum mechanics. I spent the holidays — Christmastime and summertime — in Hungary, in Budapest and in Alsógöd, on the shore of the Danube. There I wrote the book on “Group Theory and its Application to the Quantum Mechanics of Atomic Spectra.” [To the author 1983.] — The intrusion of group theory into quantum mechanics was not received with applause. Wolfgang Pauli called the idea Gruppenpest. Albert Einstein and Erwin Schrödinger also expressed their uneasiness. Max Born and Max von Laue were more encouraging. John von Neumann and Leo Szilard enthusiastically encouraged Wigner’s efforts. It was worth to do so: these efforts later resulted in a Nobel Prize.
    If an experiment is repeated elsewhere in another laboratory under similar conditions, it will give identical result. The experiment today yields the very same result as it yielded yesterday. If we turn the whole equipment by 300, it will not influence the result. The outcome depends neither on the location and timing of the experiment, nor on the spacial orientation of the equipment. Even speed (e.g. that of the Earth) does not influence the way the laws of Nature work. To express this basic experience in a more direct way: the world does not have a privileged center, there is no absolute rest, preferred direction, unique origin of calendar time, even left and right seem to be rather symmetric.
    The interference of electrons, photons, neutrons has indicated that the state of a particle can be described by a vector. possessing a certain number of components. As the observer is replaced by another observer (working elsewhere, looking at a different direction, using an other clock, perhaps being lefthanded), the state of the very same particle is described by another vector, obtained from the previous vector by multiplying it with a matrix. This matrix transfers from one observer to another.,,,
    In 1930 Wigner showed the utmost power of these experienced symmetry properties of space and time in quantum mechanics. His book has become one of the most important classics of the new science, having been published in German, English, Japanese, and Hungarian. The author is convinced that the long-lasting essence of quantum mechanics has been understood by Eugene Wigner: the basic experiences of superposition and symmetry will serve as a lasting foundation; it will influence how this intellectual achievement of the 20th century with utmost importance will be taught in the schools of the 21st century. (When this was told to Wigner, he sharply disagreed. According to him only one person understood quantum mechanics: John von Neumann. )
    Wigner received the Nobel Prize in 1963 for his contribution to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles.
    http://oldweb.reak.bme.hu/Wign.....io/wb1.htm

    Wigner’s insights into the foundations of quantum mechanics, continue to drive breakthroughs,

    Eugene Wigner – A Gedanken Pioneer of the Second Quantum Revolution – Anton Zeilinger – Sept. 2014
    Conclusion
    It would be fascinating to know Eugene Wigner’s reaction to the fact that the gedanken experiments he discussed have not only become reality, but building on his gedanken experiments, new ideas have developed which on the one hand probe the foundations of quantum mechanics even deeper, and which on the other hand also provide the foundations to the new field of quantum information technology. All these experiments pay homage to the great insight Wigner expressed in developing these gedanken experiments and in his analyses of the foundations of quantum mechanics,
    http://epjwoc.epj.org/articles....._01010.pdf

    For instance of Wigner’s insights into the foundations of quantum mechanics continuing to drive breakthroughs, Wigner’s thought experiment, “Wigner’s friend’, was recently experimentally realized in 2019,

    More Than One Reality Exists (in Quantum Physics)
    By Mindy Weisberger – March 20, 2019
    Excerpt: “measurement results,, must be understood relative to the observer who performed the measurement”.
    https://www.livescience.com/65029-dueling-reality-photons.html

    “Wigner’s friend” thought experiment made its first appearance in this following 1961 paper where Wigner stated, “”It will remain remarkable, in whatever way our future concepts may develop, that the very study of the external world led to the scientific conclusion that the content of the consciousness is the ultimate universal reality” –

    Remarks on the mind-body question – E.P. Wigner (1961),
    Excerpt: “It will remain remarkable, in whatever way our future concepts may develop, that the very study of the external world led to the scientific conclusion that the content of the consciousness is the ultimate universal reality” –
    http://www.projects.science.uu.....wigner.pdf

    And in 1970 Wigner further stated that,,

    “It was not possible to formulate the laws (of quantum theory) in a fully consistent way without reference to consciousness.”
    – Eugene Wigner (1902 -1995) from his collection of essays “Symmetries and Reflections – Scientific Essays” – 1970;

    The experimental realization of Wigner’s claim that “the content of the consciousness is the ultimate universal reality”, was foreshadowed, ‘philosophically’, by other giants in quantum mechanics,

    “No, I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness.”
    Max Planck (1858–1947), – The Observer, London, January 25, 1931

    “Consciousness cannot be accounted for in physical terms. For consciousness is absolutely fundamental. It cannot be accounted for in terms of anything else.”
    – Schroedinger, Erwin. 1984. “General Scientific and Popular Papers,” in Collected Papers, Vol. 4. Vienna: Austrian Academy of Sciences. Friedr. Vieweg & Sohn, Braunschweig/Wiesbaden. p. 334.

    In fact, Wigner himself considered the philosophical argument for the primacy of consciousness to be more powerful than the fact that materialism is experimentally found to be incompatible with quantum theory,

    “The principal argument against materialism is not that illustrated in the last two sections: that it is incompatible with quantum theory. The principal argument is that thought processes and consciousness are the primary concepts, that our knowledge of the external world is the content of our consciousness and that the consciousness, therefore, cannot be denied. On the contrary, logically, the external world could be denied—though it is not very practical to do so. In the words of Niels Bohr, “The word consciousness, applied to ourselves as well as to others, is indispensable when dealing with the human situation.” In view of all this, one may well wonder how materialism, the doctrine that “life could be explained by sophisticated combinations of physical and chemical laws,” could so long be accepted by the majority of scientists.”
    – Eugene Wigner, Remarks on the Mind-Body Question, pp 167-177.

    But anyways, in his 1960 paper where he considered that the applicability of mathematics to the universe to be a miracle, Wigner stated that, “We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity.,,, The two theories operate with different mathematical concepts: the four dimensional Riemann space and the infinite dimensional Hilbert space,?”

    The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner – 1960?Excerpt: We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity.,,, The two theories operate with different mathematical concepts: the four dimensional Riemann space and the infinite dimensional Hilbert space,
    http://www.dartmouth.edu/~matc.....igner.html

    Since I have already covered, in posts 168 through 170, how the “four dimensional Riemann space” of Relativity is very friendly to Christian presuppositions, I will now cover how the infinite dimensional Hilbert space is also very friendly to Christian presuppositions,

    In its ‘uncollapsed’ state, a particle, and/or a photon, is mathematically described as being in an infinite dimensional state,,,

    Wave function
    Excerpt “wave functions form an abstract vector space”,,, This vector space is infinite-dimensional, because there is no finite set of functions which can be added together in various combinations to create every possible function.
    http://en.wikipedia.org/wiki/W.....ctor_space

    Why do we need infinite-dimensional Hilbert spaces in physics?
    You need an infinite dimensional Hilbert space to represent a wavefunction of any continuous observable (like position for example).
    https://physics.stackexchange.com/questions/149786/why-do-we-need-infinite-dimensional-hilbert-spaces-in-physics

  182. 182
    bornagain77 says:

    ,, an infinite dimensional state that also takes an infinite amount of information to describe properly.

    Explaining Information Transfer in Quantum Teleportation: Armond Duwell †‡ University of Pittsburgh
    Excerpt: In contrast to a classical bit, the description of a (quantum) qubit requires an infinite amount of information. The amount of information is infinite because two real numbers are required in the expansion of the state vector of a two state quantum system (Jozsa 1997, 1)
    http://www.cas.umt.edu/phil/fa.....lPSA2K.pdf

    Quantum Computing – Stanford Encyclopedia
    Excerpt: Theoretically, a single qubit can store an infinite amount of information, yet when measured (and thus collapsing the superposition of the Quantum Wave state) it yields only the classical result (0 or 1),,,
    http://plato.stanford.edu/entr.....tcomp/#2.1

    WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT? Infinity – Max Tegmark
    Excerpt: real numbers with their infinitely many decimals have infested almost every nook and cranny of physics, from the strengths of electromagnetic fields to the wave functions of quantum mechanics: we describe even a single bit of quantum information (a qubit) using two real numbers involving infinitely many decimals.
    https://www.edge.org/response-detail/25344

    Now, saying something is in an infinite dimensional state to me, as a Christian Theist, certainly sounds very much like the theistic attribute of omnipresence to me.

    Psalm 139: 7-12
    Where can I go to escape Your Spirit?
    Where can I flee from Your presence?
    If I ascend to the heavens, You are there;
    if I make my bed in Sheol, You are there.
    If I rise on the wings of the dawn,
    if I settle by the farthest sea,
    even there Your hand will guide me;
    Your right hand will hold me fast.
    If I say, “Surely the darkness will hide me,
    and the light become night around me”—
    even the darkness is not dark to You,
    but the night shines like the day,
    for darkness is as light to You.

    Jeremiah 23:23-24
    “Am I only a God nearby,” declares the LORD, “and not a God far away?” “Can a man hide in secret places where I cannot see him?” declares the LORD. “Do I not fill the heavens and earth?” declares the LORD.…

    And then saying something takes an infinite amount of information to describe, as a Christian, certainly sounds very much like the Theistic attribute of Omniscience to me.

    Psalm 147:5
    Great is our Lord, and mighty in power; his understanding is infinite

    Colossians 2:3
    in whom are hidden all the treasures of wisdom and knowledge.

    Now all this is pretty much exactly what we would expect to see under Christian presuppositions. But, on the other hand, under Atheistic materialism and/or naturalism, and the presuppositions therein, there simply is no rational explanation for why we should find these infinite dimensional/infinite information mathematical definitions to be as they are.

    Moreover, the basics of quantum wave collapse dovetail perfectly into some of the oldest philosophical arguments that were made by Aristotle and Aquinas for the existence of God, and even offers empirical confirmation for those ancient philosophical arguments. Michael Egnor states that ‘Aristotle 2,300 years ago described the basics of collapse of the quantum waveform (reduction of potency to act),,,’

    Stephen Hawking: “Philosophy Is Dead” – Michael Egnor – August 3, 2015
    Excerpt: The metaphysics of Aristotle and Aquinas is far and away the most successful framework on which to understand modern science, especially quantum mechanics. Heisenberg knew this (Link on site). Aristotle 2,300 years ago described the basics of collapse of the quantum waveform (reduction of potency to act),,,
    http://www.evolutionnews.org/2.....98261.html

    Here is a technical explanation and video of Aquinas’ First way argument for God where you can, at your leisure, see just how well the argument from motion dovetails into what we are seeing in quantum mechanics

    Aquinas’ First Way
    1) Change in nature is elevation of potency to act.
    2) Potency cannot actualize itself, because it does not exist actually.
    3) Potency must be actualized by another, which is itself in act.
    4) Essentially ordered series of causes (elevations of potency to act) exist in nature.
    5) An essentially ordered series of elevations from potency to act cannot be in infinite regress, because the series must be actualized by something that is itself in act without the need for elevation from potency.
    6) The ground of an essentially ordered series of elevations from potency to act must be pure act with respect to the casual series.
    7) This Pure Act– Prime Mover– is what we call God.
    http://egnorance.blogspot.com/.....t-way.html

    Aquinas’ First Way – (The First Mover – Unmoved Mover) – video
    http://www.youtube.com/watch?v=Qmpw0_w27As

    Or to put Aquinas’ argument much more simply “The ‘First Mover’ is necessary for change occurring at each moment.”:

    “The ‘First Mover’ is necessary for change occurring at each moment.”
    Michael Egnor – Aquinas’ First Way
    http://www.evolutionnews.org/2.....first.html

    Again, all this fits hand in glove with Christian presuppositions about infinite and almighty God sustaining this universe in its continual existence,,,

    Acts 17:28
    for “‘In him we live and move and have our being’; as even some of your own poets have said, “‘For we are indeed his offspring.’

    Thus, Christians, despite what atheists may claim, certainly have no problem with the findings of modern science. In fact, despite their claims to the contrary, it is the atheist himself who finds his foundational beliefs about reality to be directly challenged by the findings of modern science.

    Why Atheists would fight tooth and nail against what is such a wonderful thing, i.e. that God is really real, I have no idea. Frankly, I find the basics of quantum mechanics much easier to understand than why atheists would fight so hard against what Is such a wonderful realization, i.e., that God is really real!

    Such irrational hatred of God, who they claim does not exist, is simply completely unreasonable.

    “I’ve shaken my fist in anger at stalled cars, storm clouds, and incompetent meteorologists. I’ve even, on one terrible day that included a dead alternator, a blaring blaring tornado-warning siren, and a horrifically wrong weather forecast, cursed all three at once. I’ve fumed at furniture, cussed at crossing guards, and held a grudge against Gun Barrel City, Texas. I’ve been mad at just about anything you can imagine.
    Except unicorns. I’ve never been angry at unicorns.
    It’s unlikely you’ve ever been angry at unicorns either. We can become incensed by objects and creatures both animate and inanimate. We can even, in a limited sense, be bothered by the fanciful characters in books and dreams. But creatures like unicorns that don’t exist—that we truly believe not to exist—tend not to raise our ire. We certainly don’t blame the one-horned creatures for our problems.
    The one social group that takes exception to this rule is atheists. They claim to believe that God does not exist and yet, according to empirical studies, tend to be the people most angry at him.”
    https://www.firstthings.com/web-exclusives/2011/01/when-atheists-are-angry-at-god

    John 15:25
    But this is to fulfill what is written in their Law: ‘They hated me without reason.’

  183. 183
    kairosfocus says:

    JVL, first, I gave a summary in a blog, not a detailed theorem statement. In that context, incoherence takes in inconsistency and its immediate corollary effects per principle of explosion. A “complete” axiom system for a complex enough domain will be inconsistent; immediately, per explosion, the system is incoherent and so unsafe; we for cause routinely use reductio ad absurdum as a means of disproof by contradiction. That is, we see here disintegration and disjointedness of a system. Your tangent game is duly noted as making mountains out of nothing. And, it is clear enough that you refuse to look at the logic of being issues that directly connect to the mathematics, once we recognise that substantially, Math is the logic of structure and quantity. A Possible Worlds approach, as I linked, is fruitful on that, drawing out necessary facts of math that are antecedent to axiomatisation. As a human endeavour, it is again fruitful: the study of the substance. This instantly leads to how do we get to creatures capable of freely reasoning so they can credibly, confidently explore and study that substance. That again points to roots of reality and matters ontological. KF

    PS: Statements

    First Incompleteness Theorem: “Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.” (Raatikainen 2015)

    Second Incompleteness Theorem: “Assume F is a consistent formalized system which contains elementary arithmetic. Then F [stroke-entail] Cons ( F ) .” (Raatikainen 2015)

  184. 184
    JVL says:

    Kairosfocus: first, I gave a summary in a blog, not a detailed theorem statement. In that context, incoherence takes in inconsistency and its immediate corollary effects per principle of explosion.

    Principle of explosion? What is that?

    A “complete” axiom system for a complex enough domain will be inconsistent; immediately, per explosion, the system is incoherent and so unsafe; we for cause routinely use reductio ad absurdum as a means of disproof by contradiction.

    The first incompleteness theorem DOES NOT say that any complete system will be inconsistent. It just doesn’t. It says: If a (logical or axiomatic formal) system is consistent, it cannot be complete.

    The second incompleteness theorem says, roughly: The consistency of axioms cannot be proved within their own system. That doesn’t mean the system is complete or inconsistent.

    Proof by contradiction doesn’t work that way. If, according to the first theorem: C (consistent) -> -K (not complete) . You can attempt to prove that by contradiction but you then have to demonstrate that K -> -C. If that’s what you’re trying to say then please make things clearer instead of like this:

    Then F [stroke-entail] Cons ( F )

    Your tangent game is duly noted as making mountains out of nothing.

    I am trying to make sure the mathematics is represented correctly. If I think you’ve misrepresented it then I will say so. It’s nothing person. You do the same when I say something you find incorrect.

    And, it is clear enough that you refuse to look at the logic of being issues that directly connect to the mathematics, once we recognise that substantially, Math is the logic of structure and quantity. A Possible Worlds approach, as I linked, is fruitful on that, drawing out necessary facts of math that are antecedent to axiomatisation. As a human endeavour, it is again fruitful: the study of the substance. This instantly leads to how do we get to creatures capable of freely reasoning so they can credibly, confidently explore and study that substance. That again points to roots of reality and matters ontological

    I think I’ll just stick to what the established mathematics actually says if that’s okay.

  185. 185
    bornagain77 says:

    JVL states:

    I think I’ll just stick to what the established mathematics actually says if that’s okay.

    Save, of course, for when ‘established mathematics’ says that the origin of life, and subsequent evolution of life, by unguided processes is mathematically impossible, Then, of course, ‘established mathematics’ can be safely ignored by JVL.

    DID LIFE START BY CHANCE? ?
    Excerpt: Molecular biophysicist, Horold Morowitz (Yale University), calculated the odds of life beginning under natural conditions (spontaneous generation). He calculated, if one were to take the simplest living cell and break every chemical bond within it, the odds that the cell would reassemble under ideal natural conditions (the best possible chemical environment) would be one chance in 10^100,000,000,000. You will have probably have trouble imagining a number so large, so Hugh Ross provides us with the following example. If all the matter in the Universe was converted into building blocks of life, and if assembly of these building blocks were attempted once a microsecond for the entire age of the universe. Then instead of the odds being 1 in 10^100,000,000,000, they would be 1 in 10^99,999,999,916 (also of note: 1 with 100 billion zeros following would fill approx. 20,000 encyclopedias)?http://members.tripod.com/~Black_J/chance.html

    Claim: New Proteins Evolve Very Easily – Cornelius Hunter – April 25, 2017
    Excerpt:  It is now clear that for a given protein, only a few changes to its amino acid sequence can be sustained before the protein function is all but eliminated. Here is how one paper explained it:
    “The accepted paradigm that proteins can tolerate nearly any amino acid substitution has been replaced by the view that the deleterious effects of mutations, and especially their tendency to undermine the thermodynamic and kinetic stability of protein, is a major constraint on protein evolvability—the ability of proteins to acquire changes in sequence and function.”
    In other words, protein function precipitously drops off with only a tiny fraction of its amino acids altered. It is not a gradual fitness landscape. Another paper described the protein fitness landscape as rugged.
    Therefore it is not surprising that various studies on evolving proteins have failed to show a viable mechanism. One study concluded that 10^63 attempts would be required to evolve a relatively short protein. And a similar result (10^65 attempts required) was obtained by comparing protein sequences. Another study found that 10^64 to 10^77 attempts are required, and another study concluded that 10^70 attempts would be required.
    So something like 10^70 attempts are required yet evolutionists estimate that only 10^43 attempts are possible. In other words, there is a shortfall of 27 orders of magnitude.
    But it gets worse. The estimate that 10^43 attempts are possible is utterly unrealistic. For it assumes billions of years are available, and that for that entire time the Earth is covered with bacteria, constantly churning out mutations and new protein experiments. Aside from the fact that these assumptions are entirely unrealistic, the estimate also suffers from the rather inconvenient fact that those bacteria are, err, full of proteins. In other word, for evolution to evolve proteins, they must already exist in the first place.
    This is absurd. And yet, even with these overly optimistic assumptions, evolution falls short by 27 orders of magnitude.
    https://www.evolutionnews.org/2017/04/claim-new-proteins-evolve-very-easily/

    The waiting time problem in a model hominin population – 2015 Sep 17
    John Sanford, Wesley Brewer, Franzine Smith, and John Baumgardner
    Excerpt: the waiting time for the fixation of a “string-of-one” is by itself problematic (Table 2). Waiting a minimum of 1.5 million years (realistically, much longer), for a single point mutation is not timely adaptation in the face of any type of pressing evolutionary challenge. This is especially problematic when we consider that it is estimated that it only took six million years for the chimp and human genomes to diverge by over 5 % [1]. ,,,
    While fixing one point mutation is problematic, our simulations show that the fixation of two co-dependent mutations is extremely problematic – requiring at least 84 million years (Table 2). This is ten-fold longer than the estimated time required for ape-to-man evolution.,,, Certainly the creation and fixation of a string of three (requiring at least 380 million years) would be extremely untimely (and trivial in effect), in terms of the evolution of modern man.
    ,,, When we increase the hominin population from 10,000 to 1 million (our current upper limit for these types of experiments), the waiting time for creating a string of five is only reduced from two billion to 482 million years.
    http://www.ncbi.nlm.nih.gov/pm.....MC4573302/

  186. 186
    kairosfocus says:

    JVL, your grudging retreat tells us the balance on merits. You and those in the penumbra of attack sites cannot evade the issue of where possibility of worlds comes from, especially worlds with creatures with rational, thus morally governed, freedom to confidently do Mathematics. That tells us a lot. KF

  187. 187
    JVL says:

    Bornagain77: Save, of course, for when ‘established mathematics’ says that the origin of life, and subsequent evolution of life, by unguided processes is mathematically impossible, Then, of course, ‘established mathematics’ can be safely ignored by JVL.

    That’s someone applying mathematics to a particular situation. They may or may nt be doing so correctly. Personally I don’t think evolution via unguided processes has been ruled out and certainly not by some mathematical argument.

    Kairosfocus: your grudging retreat tells us the balance on merits. You and those in the penumbra of attack sites cannot evade the issue of where possibility of worlds comes from, especially worlds with creatures with rational, thus morally governed, freedom to confidently do Mathematics. That tells us a lot.

    Oddly enough, I wasn’t even addressing that issue. I was just talking about the mathematics.

  188. 188
    ET says:

    JVL:

    Personally I don’t think evolution via unguided processes has been ruled out and certainly not by some mathematical argument.

    Great. We await your refutation of “Waiting for TWO Mutations”. Because that paper definitely rules out unguided processes ability to account for the diversity of life via a mathematical argument.

  189. 189
    bornagain77 says:

    JVL,
    “Personally I don’t think evolution via unguided processes has been ruled out and certainly not by some mathematical argument.”

    Of course you don’t because, as I pointed out, you believe math can be safely ignored whenever it conflicts with your atheistic worldview.

    i.e. When the ontology of math points to God, you ignore it. Likewise, when the implications of math point to God, you also ignore them.

    Such denial of facts is rampant throughout arguments from Darwinian atheists.

    Such a mindset is called ‘denialism’, i.e. the denial of reality, and the denial of reality is certainly not a coherent argument, as you seem to think that it is, but is instead considered a mental illness.

    Denialism
    In the psychology of human behavior, denialism is a person’s choice to deny reality as a way to avoid a psychologically uncomfortable truth.[1]
    https://en.wikipedia.org/wiki/Denialism

  190. 190
    JVL says:

    ET: Great. We await your refutation of “Waiting for TWO Mutations”. Because that paper definitely rules out unguided processes ability to account for the diversity of life via a mathematical argument.

    There have been plenty of discussions of that paper and its ramifications; I don’t think I can add anything significant. I do note, however, that mainstream biologists are not fleeing the ship of unguided evolution because of that paper. Food for though eh?

  191. 191
    JVL says:

    Bornagain77: Of course you don’t because, as I pointed out, you believe math can be safely ignored whenever it conflicts with your atheistic worldview.

    Or, it’s because I disagree with your use and interpretation of the mathematics.

    i.e. When the ontology of math points to God, you ignore it. Likewise, when the implications of math point to God, you also ignore them.

    I’m not ignoring anything; I simply disagree with your interpretation of the mathematics.

    Such denial of facts is rampant throughout arguments from Darwinian atheists.

    And they would say you’re mistinterpreting the mathematics.

    Such a mindset is called ‘denialism’, i.e. the denial of reality, and the denial of reality is certainly not a coherent argument, as you seem to think that it is, but is instead considered a mental illness.

    It’s not denialism if I am right is it?

    Why does it bother you so much that I disagree with you? Who cares? I don’t particularly care if you agree with me or not. I find it interesting to know how you see the data and the math but I don’t expect (nor am I trying) to change you or your view.

  192. 192
    kairosfocus says:

    JVL,

    The evasiveness continues, so let’s roll the tape to part of why I intervened, your comment at 79 above:

    79
    JVL
    July 8, 2020 at 2:08 pm

    ET: How do you think mathematics came to be, then, JVL? Your turn- your “math just is” is a cop out.

    [JVL response:] How did your designer come to be?

    I think mathematics is just part of the fabric of reality. No being had to design it or create it.

    H’mm, it looks a whole lot like at that point you were interested in logic of being and reality root issues, once you could assert confidently that Math stands independent of any world-designer.

    So, your retreat from that assertion once challenged on those subjects you are suddenly no longer interested in is as Mr Spock says, “interesting.”

    As, once a serious logic of being challenge was put up in response to your attempt to imply that those who suggested above that God is responsible for the Mathematical framework of reality run into the roadblock of core Mathematics having independent necessary character you retreated to a fallback of only being interested in the Math.

    Only, the tape sez different.

    (From 85 on I first rebalanced the exchange, as there are structural and quantitative aspects of reality framework to any/all worlds and particular fine-tuned aspects relevant to a viable world amenable to C-chem, aqueous medium, terrestrial planet in galactic and circumstellar habitable zone life. With further constraints to get to significantly free, rational — thus, morally governed — creatures capable of credibly, confidently doing Mathematics and similar intellectual endeavours.)

    You were asking also for a different Arithmetic, presumably a completely alien axiomatised framework.

    I showed, by pointing and summarising from published work, that there are Math realities antecedent to any axiomatisation (which, since Godel, has had a bit of the shine taken off the new ball) and that such things . . . e.g. N,Z,Q,R,C etc with linked relationships, structures, properties . . . are tied to what it takes per logic of being for there to be a distinct possible world.

    Thus, the directly tied — so, highly relevant and even decisive — logical issue is, how are such PW’s possible? How does the P get there? That, takes us to reality root, and in particular, we see how on logic of being:

    1: a world from utter non-being is absurdly implausible,

    2: a world by circular retro-cause of a not yet future state is again trying to get a world out of utter non-being,

    3: a beginningless succession of finite stages [years for simplicity] cannot be traversed to get to now, it implies a cross the transfinite in finite steps supertask.

    (This last is best seen by using the hyperreals mileposted by hyperintegers. Where, say HS Math teachers and the like . . . Engineers, Physicists in many cases [from Newton etc on], etc . . . using the intuitive number line on balance, are better understood as speaking intuitively in the hyperreals context. Such even arguably rehabilitates a good part of Euler’s thinking etc. Infinitesimals, suitably tamed, are back. Arguably, as part of the framework structure-quantity infrastructure for all PW’s. Where, once an infinitesimals cloud surrounds 0, *0*, we then can infinitestimally alter any r in R by vector displacement of the cloud *0* to superimpose on r yielding *r*, an infrastructure closer to r than a similarly shifted 1/n for any n in N and its negative -1/n. This is tied to nonstandard analysis and the ubiquity of Calculus in physics, including our habitual treatment of infinitesimals as a valid meaning of dr. This is of course directly connected to Wigner’s marvelling, as what is in any PW applies to our world, and extends to any coherent suggested framework for a world.)

    Such leaves one serious candidate in the room: the P in PW gets there through a finitely remote, causally independent — thus necessary — reality root being framework to any world. Mathematical entities framework to any PW are not independent of there being a reality root.

    In that context, your retreat into of you are just interested in the Math, is an interesting result. Indeed, on the just rolled tape, it is a disguised retreat.

    Of course, with implications for your credibility in arguments you have been making here at UD.

    KF

  193. 193
    bornagain77 says:

    JVL, and disagreeing for the sake of disagreeing, minus any coherent argument to the contrary, and being nonchalant about the fact that your belief is not rooted in reality, i.e. “Who cares?”,,, is suppose to be different from the mental illness of denialism how exactly?

    As mentioned previously, denialism, i.e. the denial of reality, is rampant in the arguments used by Darwinian atheists.

    Although the Darwinian atheist firmly believes he is on the terra firma of science, (in his appeal, even demand, for methodological naturalism), the fact of the matter is that Darwinists are adrift in an ocean of fantasy and imagination with no discernible anchor for reality to grab on to:

    Basically, because of reductive materialism (and/or methodological naturalism), the atheistic materialist is forced to claim that he is merely a ‘neuronal illusion’ (Coyne, Dennett, etc..), who has the illusion of free will (Harris), who has unreliable, (i.e. illusory), beliefs about reality (Plantinga), who has illusory perceptions of reality (Hoffman), who, since he has no real time empirical evidence substantiating his grandiose claims, must make up illusory “just so stories” with the illusory, and impotent, ‘designer substitute’ of natural selection (Behe, Gould, Sternberg), so as to ‘explain away’ the appearance (i.e. illusion) of design (Crick, Dawkins), and who must make up illusory meanings and purposes for his life since the reality of the nihilism inherent in his atheistic worldview is too much for him to bear (Weikart), and who must also hold morality to be subjective and illusory since he has rejected God (Craig, Kreeft). Who, since beauty cannot be grounded within his materialistic worldview, must hold beauty itself to be illusory (Darwin).
    Bottom line, nothing is truly real in the atheist’s worldview, least of all, beauty, morality, meaning and purposes for life.,,,
    Darwinian Materialism and/or Methodological Naturalism vs. Reality – video
    https://www.youtube.com/watch?v=CaksmYceRXM

    Thus, although the Darwinian Atheist firmly believes he is on the terra firma of science (in his appeal, even demand, for methodological naturalism), it would be hard to fathom a worldview more antagonistic to modern science, indeed more antagonistic to reality itself, than Atheistic materialism and/or methodological naturalism have turned out to be.

    2 Corinthians 10:5
    Casting down imaginations, and every high thing that exalteth itself against the knowledge of God, and bringing into captivity every thought to the obedience of Christ;

  194. 194
    kairosfocus says:

    BA77, you ask an excellent question which ties in with the bold assertions as just tape-rolled, then suddenly retreated from once challenged. Mental illness is maybe too strong, worldview induced blind spots is more specific. KF

  195. 195
    Retired Physicist says:

    @JVL The only math I’ve seen on this website is ET’s horrendous misunderstanding of set theory.

  196. 196
    bornagain77 says:

    Kf, “Mental illness is maybe too strong, worldview induced blind spots is more specific.”

    Nope, not too strong at all. To point out the obvious fact that Darwinian atheists are in the grip of the mental illness of Denialism is to hit the nail squarely on the head.

    Denialism
    In the psychology of human behavior, denialism is a person’s choice to deny reality as a way to avoid a psychologically uncomfortable truth.[1]
    https://en.wikipedia.org/wiki/Denialism

    As alcoholics and drug addicts must come to grips with their own denialism, their own mental illness, that leads to their destructive lifestyles, in order to make a successful recovery, so to atheists, in order to ‘make a recovery’, must come to grips with their own denialism. i.e. their own mental illness that has destructive effects in their own personal lives, (and on society at large, i.e. abortion and the horrors of socialist/atheist ‘utopias’, i.e. Hitler, Stalin, Mao, etc.. etc..),

    Of snakebites and suicide – February 18, 2014
    RESULTS: Religiously unaffiliated subjects had significantly more lifetime suicide attempts and more first-degree relatives who committed suicide than subjects who endorsed a religious affiliation.
    http://www.uncommondescent.com.....d-suicide/

    “I maintain that whatever else faith may be, it cannot be a delusion.
    The advantageous effect of religious belief and spirituality on mental and physical health is one of the best-kept secrets in psychiatry and medicine generally. If the findings of the huge volume of research on this topic had gone in the opposite direction and it had been found that religion damages your mental health, it would have been front-page news in every newspaper in the land.”
    – Professor Andrew Sims former President of the Royal College of Psychiatrists – Is Faith Delusion?: Why religion is good for your health – preface

    “In the majority of studies, religious involvement is correlated with well-being, happiness and life satisfaction; hope and optimism; purpose and meaning in life; higher self-esteem; better adaptation to bereavement; greater social support and less loneliness; lower rates of depression and faster recovery from depression; lower rates of suicide and fewer positive attitudes towards suicide; less anxiety; less psychosis and fewer psychotic tendencies; lower rates of alcohol and drug use and abuse; less delinquency and criminal activity; greater marital stability and satisfaction… We concluded that for the vast majority of people the apparent benefits of devout belief and practice probably outweigh the risks.”
    – Professor Andrew Sims former President of the Royal College of Psychiatrists – Is Faith Delusion?: Why religion is good for your health – page 100
    https://books.google.com/books?id=PREdCgAAQBAJ&pg=PA100#v=onepage&q&f=false

    Can attending church really help you live longer? This study says yes – June 1, 2017
    Excerpt: Specifically, the study says those middle-aged adults who go to church, synagogues, mosques or other houses of worship reduce their mortality risk by 55%. The Plos One journal published the “Church Attendance, Allostatic Load and Mortality in Middle Aged Adults” study May 16.
    “For those who did not attend church at all, they were twice as likely to die prematurely than those who did who attended church at some point over the last year,” Bruce said.
    https://www.usatoday.com/story/news/nation-now/2017/06/02/can-attending-church-really-help-you-live-longer-study-says-yes/364375001/

    Study: Religiously affiliated people live “9.45 and 5.64 years longer…”
    July 1, 2018
    Excerpt: Self-reported religious service attendance has been linked with longevity. However, previous work has largely relied on self-report data and volunteer samples. Here, mention of a religious affiliation in obituaries was analyzed as an alternative measure of religiosity. In two samples (N = 505 from Des Moines, IA, and N = 1,096 from 42 U.S. cities), the religiously affiliated lived 9.45 and 5.64 years longer, respectively, than the nonreligiously affiliated. Additionally, social integration and volunteerism partially mediated the religion–longevity relation.
    https://uncommondescent.com/intelligent-design/study-religiously-affiliated-people-lived-religiously-affiliated-lived-9-45-and-5-64-years-longer/

    Can Religion Extend Your Life? – By Chuck Dinerstein — June 16, 2018
    Excerpt: The researcher’s regression analysis suggested that the effect of volunteering and participation accounted for 20% or 1 year of the impact, while religious affiliation accounted for the remaining four years or 80%.
    https://www.acsh.org/news/2018/06/16/can-religion-extend-your-life-13092

    Of related interest, Thomas Nagel, who recognized the devastating implications of the hard problem of consciousness for Darwinism,,,,

    “I have argued patiently against the prevailing form of naturalism, a reductive materialism that purports to capture life and mind through its neo-Darwinian extension.” “…, I find this view antecedently unbelievable—a heroic triumph of ideological theory over common sense”.?
    – Thomas Nagel – “Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature Is Almost Certainly False” – pg.128

    ,,,, although Nagel knew Darwinism must be false because of the ‘hard problem’ of consciousness, none-the-less, rejected God simply because God was a “a psychologically uncomfortable truth” for him. i.e. full blown Denialism!

    “I want atheism to be true and am made uneasy by the fact that some of the most intelligent and well-informed people I know are religious believers. It isn’t just that I don’t believe in God and, naturally, hope that I’m right in my belief. It’s that I hope there is no God! I don’t want there to be a God; I don’t want the universe to be like that.
    – ”(”The Last Word” by Thomas Nagel, Oxford University Press: 1997)”

    Might I be so bold as to further suggest that Nagel’s guilty conscious is what compels him to try to hide from God?

    Genesis 3:8
    Then the man and his wife heard the sound of the LORD God as he was walking in the garden in the cool of the day, and they hid from the LORD God among the trees of the garden.
    But the LORD God called out to the man, “Where are you?”
    “I heard Your voice in the garden,” he replied, “and I was afraid because I was naked; so I hid myself.”

  197. 197
  198. 198
    kairosfocus says:

    RP, first, you have obviously not monitored years of mathematical discussions here at UD. Second, on fair comment you have given half truth in order to belittle and denigrate; on the contrary to your suggestions in this thread, there is summary discussion and there are links to elsewhere where summary can be filled in, as I just exemplified again. Further to this the mention of hyperreals, infinitesimals and infinitesimally altered reals is an allusion to model theory and to linked nonstandard analysis. This includes how that brings the calculus firmly into the embrace of algebra, as JB has argued in these pages and elsewhere. Also, the intuitive number line, arguably is about the hyperreals not the reals, I have gone so far as to suggest these are more relevant to general math than the reals, at minimum as setting conceptual context in which we work, including habitual usage of Physicists that looks really sloppy without that context; well do I recall the dichotomy between routine use of dr, curly dr and improper d-bar [think d’q in thermodynamics] in Physics and the repeated R-driven, limits and epsilon-delta formulation in math that dr was not a number, worse dr/dt is not a ratio but a limit as abbreviated, only it LOOKS like it can be treated like algebraic fractions etc. I suspect also that you wish to dismiss cosmological fine tuning, which would be ill advised. KF

  199. 199
    kairosfocus says:

    RP, you have posed a tangent, again one suggestive of the notorious Dawkins theme, ignorant, stupid, insane or wicked. In fact, it is notorious that the cognitively challenged can often be resistant to change (especially change where in a few weeks to a couple of months there was major flip-flopping and this tied to evidence of lying by medical authorities . . . undermining their credibility across the board). I note, personally, as one with asthma, prolonged wearing of masks is a struggle that is debilitating. Far more robust people than I am, speak of how it wears them down as they do heavy physical work. Then, there are the debates over just how effective such are at filtering in praxis, with what mechanisms. I favour electrostatic and van der Waals type forces so passing through a microfibre-forest raises odds of sticking to a fibre . . . with the “fuzz” on cloth threads or felted matrices highly significant . . . then being bound more tightly through polarisation, native or induced. On which, washing with detergent pulls out the trapped particles, also breaking up bilipid layers and perhaps hydrolysing proteins etc. Distancing at 6 feet was subject to a debate and raises issues that goggles are necessary, recall sneezes can entrain a spreading cloud up to the whole nine yards, including going over supermarket shelves and the issue of long suspended particles. Think, on modern split unit air conditioning, too. KF

  200. 200
    ET says:

    RP:

    The only math I’ve seen on this website is ET’s horrendous misunderstanding of set theory.

    And another coward who doesn’t understand infinity.

  201. 201
    ET says:

    JVL:

    There have been plenty of discussions of that paper and its ramifications; I don’t think I can add anything significant. I do note, however, that mainstream biologists are not fleeing the ship of unguided evolution because of that paper.

    Willful ignorance is rampant with evolutionary biologists. They don’t even know how to test the claims of their own position! No one uses unguided evolution for anything. It is a useless heuristic.

    Mainstream biologists don’t even know what makes an organism what it is! How pathetic is that?

    Food for thought, indeed…

  202. 202
    ET says:

    Unguided evolution is untestable nonsense. The only reason probability arguments exist is because there isn’t any way to test its claims. Evolutionists just lie, bluff and equivocate their way through life. Theirs is the most pathetic existence.

    It is very telling that evos are afraid to compare to see which side has the science an which side has the nonsense. I offered a $10,000 challenge @ the swamp. At first it was taken and then the coward ran away when the debate terms were laid out

  203. 203
    ET says:

    KF:

    RP, first, you have obviously not monitored years of mathematical discussions here at UD.

    RP is just another insipid troll. He is just like all of the others who can only spew false accusations and innuendos but never support its trope. RP will definitely never even try to support the claim that I have a “horrendous misunderstanding of set theory”. That’s because RP is an ignorant coward who thinks false accusations are enough.

  204. 204
    kairosfocus says:

    F/N: Just for emphasis, the von Neumann construction of the Naturals, with order type w:

    {} –> 0
    {0} –> 1
    {0,1} –> 2
    {0,1,2} –> 3
    . . .

    {0,1,2 . . . } –> w

    w is first transfinite ordinal, of cardinality aleph null. beyond as copiously discussed previously, we can construct the hyperreals and the surreals.

    DV, I will be looking at some interesting issues that give a very different view on what the Greeks esp Pythagoreans and Platonists etc were up to. Number patterns and how they connect to deep structures and phenomena of reality.

    KF

  205. 205
    Seversky says:

    Retired Physicist @ 197

    I mean, you could’ve guessed this

    I could.

    And, continuing the ‘why am I not surprised’ theme:

    New study identifies a psychological factor linked to Trump supporters’ vindictiveness.

  206. 206
    jerry says:

    Two things

    First, guessing is often ignorance

    I mean, you could’ve guessed this

    Hans Rosling showed that the more educated one was the more ignorant one was. So I would not use polls of behavior of anything as proof of something especially about the wisdom of the so called educated. Apparently chimpanzees give more accurate guesses about our world than do the educated. So what is one person’s guess is often ignorance. Read Factfulness. http://bit.ly/2HQZCS4

    For example, is this evaluation of mask usage accurate? Seems pretty damning of the use of masks, not so much for face shields. https://bit.ly/2CvpJ0l

    Second, I reiterate mathematics exist only in our heads and is essentially logic. The only numbers that exist in our world are possitive integers and even this concept requires an abstraction from the real world. Enumeration or quantity are so essential to our existence that we fail to realize it. You can point to a tree or a river but you can not point to any number.

    QED Is so natural to us that we don’t understand it is all in our minds. So when we use the term infinity either as a large analogy or an extremely small analogy it is just that. an analogy to something large or small. Not something that actually exists.

    When this is done mathematics is better understood and why logic is built into us and so important for our existence.

  207. 207
    bornagain77 says:

    RP and Seversky, linked to articles that have nothing to do with the topic at hand. That is called evasion.

    Moreover, Seversky linked to an article whose headline reads,”New study identifies a psychological factor linked to Trump supporters’ vindictiveness”,,,

    All I have to say after 3 years of the false Russian Collusion narrative, is that “YOU HAVE GOT TO BE KIDDING ME” Democrats, simply because they lost the 2016 election, turned into the most vindictive spoiled brats they could possibly be. Falsely targeting President Trump and a host of people associated with President Trump. i.e. Flynn, Stone, etc.. etc.., Besides using the CIA and FBI to illegally spy on resident Trump, they literally turned Congress, which use to be one of the most respected bodies in America, into a circus because of their antics. Republicans have been overly restrained to an absurd degree in not punishing the Democrats to the full extent of the law that were responsible for orchestrating such antics.

    Myself, since integrity is apparently scarce to non-existent among the Democrats who brought this on the nation, I wish they would hold the Democrats who orchestrated this farce of a circus responsible for their crimes, to the full extent of the law, so that Democrats in the future would seriously think twice before putting the nation through such antics again.

  208. 208
    JVL says:

    Kairosfocus: As, once a serious logic of being challenge was put up in response to your attempt to imply that those who suggested above that God is responsible for the Mathematical framework of reality run into the roadblock of core Mathematics having independent necessary character you retreated to a fallback of only being interested in the Math.

    That’s because I want to be polite and not get into an argument about your beliefs wHich I don’t share. I don’t feel the need to dissuade you of your view. I’ve stated mine and that’s enough.

    Thus, the directly tied — so, highly relevant and even decisive — logical issue is, how are such PW’s possible? How does the P get there? That, takes us to reality root, and in particular, we see how on logic of being:

    What are PWs anyway?

    (This last is best seen by using the hyperreals mileposted by hyperintegers. Where, say HS Math teachers and the like . . . Engineers, Physicists in many cases [from Newton etc on], etc . . . using the intuitive number line on balance, are better understood as speaking intuitively in the hyperreals context. Such even arguably rehabilitates a good part of Euler’s thinking etc. Infinitesimals, suitably tamed, are back. Arguably, as part of the framework structure-quantity infrastructure for all PW’s. Where, once an infinitesimals cloud surrounds 0, *0*, we then can infinitestimally alter any r in R by vector displacement of the cloud *0* to superimpose on r yielding *r*, an infrastructure closer to r than a similarly shifted 1/n for any n in N and its negative -1/n. This is tied to nonstandard analysis and the ubiquity of Calculus in physics, including our habitual treatment of infinitesimals as a valid meaning of dr. This is of course directly connected to Wigner’s marvelling, as what is in any PW applies to our world, and extends to any coherent suggested framework for a world.)

    I do not see what any of the above has to do with theology but I guess it does for you.

  209. 209
    JVL says:

    Bornagain77: JVL, and disagreeing for the sake of disagreeing, minus any coherent argument to the contrary, and being nonchalant about the fact that your belief is not rooted in reality, i.e. “Who cares?”,,, is suppose to be different from the mental illness of denialism how exactly?

    I’m not inclined to get involved with something I consider to be a theological argument which you find comforting and supportive. I’m not here to dissuade you of your long held and deeply rooted beliefs.

  210. 210
    JVL says:

    Retired Physicist: The only math I’ve seen on this website is ET’s horrendous misunderstanding of set theory.

    You might very well think so, I couldn’t possibly comment.

  211. 211
    JVL says:

    Nope, not too strong at all. To point out the obvious fact that Darwinian atheists are in the grip of the mental illness of Denialism is to hit the nail squarely on the head.

    I guess poisoning the well of discourse is okay if you agree with the sentiments expressed.

    you have posed a tangent, again one suggestive of the notorious Dawkins theme, ignorant, stupid, insane or wicked.

    As opposed to openly calling your opponents insane?

  212. 212
    ET says:

    So now the truth = poisoning the well. You have to be in denial if you think that nature can produce coded information processing systems. And that is a hallmark of Darwinian atheists.

  213. 213
    ET says:

    So RP ran away instead of trying to support its cowardly accusation. Vey telling, that

  214. 214
    JVL says:

    ET: Willful ignorance is rampant with evolutionary biologists. They don’t even know how to test the claims of their own position! No one uses unguided evolution for anything. It is a useless heuristic

    Unguided evolution is untestable nonsense. The only reason probability arguments exist is because there isn’t any way to test its claims. Evolutionists just lie, bluff and equivocate their way through life. Theirs is the most pathetic existence..

    No indication of how organisms are ‘designed’ to evolve -> no design. No design -> it’s all down to unguided processes.

    Since you claimed there is a mechanism, some kind of programming the guides organisms to evolve, can you point to that mechanism and explain how it works, where it is stored and how it’s encoded in organisms?

    RP is just another insipid troll. He is just like all of the others who can only spew false accusations and innuendos but never support its trope. RP will definitely never even try to support the claim that I have a “horrendous misunderstanding of set theory”. That’s because RP is an ignorant coward who thinks false accusations are enough.

    There is no need to support what you’ve already clearly demonstrated with your own comments and statements

  215. 215
    JVL says:

    ET: So now the truth = poisoning the well. You have to be in denial if you think that nature can produce coded information processing systems. And that is a hallmark of Darwinian atheists.

    That is your opinion. But that’s all it is. For some reason, thousands, if not millions, of working biologists disagree with you.

  216. 216
    ET says:

    It’s a fact, not an opinion. And not one working biologist can refute what I said. Not one can demonstrate nature can produce coded information processing systems. They don’t even know how to test the claim.

  217. 217
    bornagain77 says:

    JVL, you still failed to provide a coherent argument, and thus your ‘disagreeing’ is no more than ‘denialism’ by a different name.

  218. 218
    ET says:

    JVL:

    No indication of how organisms are ‘designed’ to evolve -> no design.

    Read “Not By Chance” and “the Evolution Revolution”. Your ignorance is not an argument.

    No design -> it’s all down to unguided processes.

    That is the “logic” of a moron.

    There is no need to support what you’ve already clearly demonstrated with your own comments and statements

    I proved that you don’t understand infinity and you don’t grasp the implications of set subtraction.

    Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.

  219. 219
    JVL says:

    ET: It’s a fact, not an opinion. And not one working biologist can refute what I said. Not one can demonstrate nature can produce coded information processing systems. They don’t even know how to test the claim.

    I wonder why your opinion is not the one promulgated in millions of research papers and seminar presentations let alone thousands of books both technical and for the general public. Weird that. I guess almost everyone who actually studies biology professionally disagrees with you. Oh well.

  220. 220
    JVL says:

    Bornagain77: you still failed to provide a coherent argument, and thus your ‘disagreeing’ is no more than ‘denialism’ in a different name.

    I am under no obligation to get involved in what I consider a theological argument. I disagree with you and for some reason that bothers you immensely. Why not just leave it?

  221. 221
    ET says:

    Strange that out of all those alleged working biologists no one can come up with a scientific theory of evolution! And again, they don’t even know what determines form. How pathetic is that?

  222. 222
    ET says:

    JVL:

    I wonder why your opinion is not the one promulgated in millions of research papers and seminar presentations let alone thousands of books both technical and for the general public.

    And yet there isn’t any support for blind watchmaker evolution, anywhere. Your working biologists appear to be a bunch of dolts. They don’t even use unguided evolution for anything

  223. 223
    Seversky says:

    Bornagain77 @ 196

    As alcoholics and drug addicts must come to grips with their own denialism, their own mental illness, that leads to their destructive lifestyles, in order to make a successful recovery, so to atheists, in order to ‘make a recovery’, must come to grips with their own denialism. i.e. their own mental illness that has destructive effects in their own personal lives,

    Atheism is nowhere classified as an addictive disorder and there is no evidence that it leads to destructive lifestyles. There is plenty of evidence, however, that absolutist beliefs, such as those of religions or political ideologies, can lead to destructive effects on many personal lives.

    And disagreeing with your religious beliefs does not indicate pathological denialism. By that logic I could, with equal justification, argue that your persistence with your religious beliefs in the face of contradictory argument and evidence is also denialism. However, my position is that, while I may disagree with them, your religious beliefs are your own and we are both free to express our respective views.

  224. 224
    ET says:

    Evos always try to bluff their way through any discussion. JVL isn’t any different. It must suck to be such a desperate fool.

  225. 225
    JVL says:

    Et: Read “Not By Chance” and “the Evolution Revolution”. Your ignorance is not an argument.

    You can’t explain the basic precepts? Why is that? Everyone else brings their evidence to the table.

    I proved that you don’t understand infinity and you don’t grasp the implications of set subtraction.

    You didn’t ‘prove’ anything except that you don’t understand real set theory.

    Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.

    You’re really funny when you double and triple down on something that is clearly incorrect based on over a century of published and well established mathematics as can be easily verified by anyone willing to have a look.

    Strange that out of all those alleged working biologists no one can come up with a scientific theory of evolution! And again, they don’t even know what determines form. How pathetic is that?

    Even Dr Behe admits there is a theory of unguided evolution. Did someone say denialism?

    And yet there isn’t any support for blind watchmaker evolution, anywhere. Your working biologists appear to be a bunch of dolts. They don’t even use unguided evolution for anything

    Again, if you can’t establish your claim that organisms are ‘designed’ to evolve then it must all be down to unguided processes. So, can you support your claim? Where is the designed programming in organisms? How does it interact with development? How is it encoded?

    Evos always try to bluff their way through any discussion. JVL isn’t any different. It must suck to be such a desperate fool.

    I’m asking you if you can support your own claim that organisms are ‘designed’ to evolve. So far, you can’t.

    Oh well.

    Atheism is incoherent desperation.

    Too funny, change the topic instead of defending your own claims.

  226. 226
    ET says:

    Atheism is incoherent desperation.

  227. 227
    bornagain77 says:

    JVL, when you defend atheism, as you have done in this thread, you are, by default, making a Theological argument.

    For you to deny that you are doing so is just more proof that you are in the grip of denialism.

  228. 228
    ET says:

    JVL:

    You can’t explain the basic precepts?

    I have. Your willful ignorance gets in the way, every time.

    You didn’t ‘prove’ anything except that you don’t understand real set theory.

    Like a punk you are a liar.

    Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.

    I made my case. JVL ignored it and tried to use the very thing being debated to win the debate. You can’t be any more ignorant than that.

  229. 229
    ET says:

    Why is it that no one can link to this alleged scientific theory of unguided evolution? Why can’t anyone say when it was published and who the authors were?

    Why do I always get evos lying about the theory as if their lies mean something? How pathetic are you, JVL?

  230. 230
    bornagain77 says:

    Seversky at 223, after I listed these studies,

    Of snakebites and suicide – February 18, 2014
    RESULTS: Religiously unaffiliated subjects had significantly more lifetime suicide attempts and more first-degree relatives who committed suicide than subjects who endorsed a religious affiliation.
    – per UD

    “I maintain that whatever else faith may be, it cannot be a delusion.
    The advantageous effect of religious belief and spirituality on mental and physical health is one of the best-kept secrets in psychiatry and medicine generally. If the findings of the huge volume of research on this topic had gone in the opposite direction and it had been found that religion damages your mental health, it would have been front-page news in every newspaper in the land.”
    – Professor Andrew Sims former President of the Royal College of Psychiatrists – Is Faith Delusion?: Why religion is good for your health – preface

    “In the majority of studies, religious involvement is correlated with well-being, happiness and life satisfaction; hope and optimism; purpose and meaning in life; higher self-esteem; better adaptation to bereavement; greater social support and less loneliness; lower rates of depression and faster recovery from depression; lower rates of suicide and fewer positive attitudes towards suicide; less anxiety; less psychosis and fewer psychotic tendencies; lower rates of alcohol and drug use and abuse; less delinquency and criminal activity; greater marital stability and satisfaction… We concluded that for the vast majority of people the apparent benefits of devout belief and practice probably outweigh the risks.”
    – Professor Andrew Sims former President of the Royal College of Psychiatrists – Is Faith Delusion?: Why religion is good for your health – page 100
    https://books.google.com/books?id=PREdCgAAQBAJ&pg=PA100#v=onepage&q&f=false

    Can attending church really help you live longer? This study says yes – June 1, 2017
    Excerpt: Specifically, the study says those middle-aged adults who go to church, synagogues, mosques or other houses of worship reduce their mortality risk by 55%. The Plos One journal published the “Church Attendance, Allostatic Load and Mortality in Middle Aged Adults” study May 16.
    “For those who did not attend church at all, they were twice as likely to die prematurely than those who did who attended church at some point over the last year,” Bruce said.
    https://www.usatoday.com/story/news/nation-now/2017/06/02/can-attending-church-really-help-you-live-longer-study-says-yes/364375001/

    Study: Religiously affiliated people live “9.45 and 5.64 years longer…”
    July 1, 2018
    Excerpt: Self-reported religious service attendance has been linked with longevity. However, previous work has largely relied on self-report data and volunteer samples. Here, mention of a religious affiliation in obituaries was analyzed as an alternative measure of religiosity. In two samples (N = 505 from Des Moines, IA, and N = 1,096 from 42 U.S. cities), the religiously affiliated lived 9.45 and 5.64 years longer, respectively, than the nonreligiously affiliated. Additionally, social integration and volunteerism partially mediated the religion–longevity relation.
    https://uncommondescent.com/intelligent-design/study-religiously-affiliated-people-lived-religiously-affiliated-lived-9-45-and-5-64-years-longer/

    Can Religion Extend Your Life? – By Chuck Dinerstein — June 16, 2018
    Excerpt: The researcher’s regression analysis suggested that the effect of volunteering and participation accounted for 20% or 1 year of the impact, while religious affiliation accounted for the remaining four years or 80%.

    After I listed those studies, Seversky has the audacity to state, “there is no evidence that it (Atheism) leads to destructive lifestyles.”

    And there you have it folks, the mental illness of denialism displayed in an atheist in all its full blown glory. 🙂

  231. 231
    ET says:

    JVL:

    I’m asking you if you can support your own claim that organisms are ‘designed’ to evolve.

    I have. And when compared to what you spew my side is by far more coherent.

  232. 232
    JVL says:

    Bornagain77: When you defend atheism, as you have done in this thread, you are, by default, making a Theological argument.

    Not in the course of a discussion about mathematics. Math has NOTHING to do with theism. Nothing.

  233. 233
    bornagain77 says:

    ^^^^ Pathetic, for you to claim that math has nothing to with God, you must, by necessity, show that math can exist independently of God. It is, by default, a theological argument that you making. Denying it, just proves my point about you suffering from the mental affliction of denialism.

    Moreover, contrary to what you want to believe, you are VERY far from ever proving that math can exist independently of God:

    A BIBLICAL VIEW OF MATHEMATICS
    Vern Poythress – Doctorate in theology, PhD in Mathematics (Harvard)
    15. Implications of Gödel’s proof
    B. Metaphysical problems of anti-theistic mathematics: unity and plurality
    Excerpt: Because of the above difficulties, anti-theistic philosophy of mathematics is condemned to oscillate, much as we have done in our argument, between the poles of a priori knowledge and a posteriori knowledge. Why? It will not acknowledge the true God, wise Creator of both the human mind with its mathematical intuition and the external world with its mathematical properties. In sections 22-23 we shall see how the Biblical view furnishes us with a real solution to the problem of “knowing” that 2 + 2 = 4 and knowing that S is true.
    http://www.frame-poythress.org.....athematics

    Taking God Out of the Equation – Biblical Worldview – by Ron Tagliapietra – January 1, 2012
    Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties.
    1. Validity … all conclusions are reached by valid reasoning.
    2. Consistency … no conclusions contradict any other conclusions.
    3. Completeness … all statements made in the system are either true or false.
    The details filled a book, but the basic concept was simple and elegant. He (Godel) summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem.
    Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation.
    Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3).
    http://www.answersingenesis.or...../equation#

  234. 234
    ET says:

    Again, the ONLY reason probability arguments exist with respect to unguided evolution, is because there isn’t any way to actually test its claims. That means unguided evolution is outside of science. And that is why there isn’t any scientific theory of unguided evolution.

  235. 235
    JVL says:

    ET: I have. Your willful ignorance gets in the way, every time.

    Not everyone on this thread will have seen your defence. Better go over it again.

    Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.

    Repeating something in bold doesn’t make it true.

    I made my case. JVL ignored it and tried to use the very thing being debated to win the debate. You can’t be any more ignorant than that.

    It’s not under debate because it’s proven mathematics. And you never found a fault with the proof. QED.

    Why is it that no one can link to this alleged scientific theory of unguided evolution? Why can’t anyone say when it was published and who the authors were?

    We don’t bother any more because every time someone tries you just deny what is said.

    Why do I always get evos lying about the theory as if their lies mean something? How pathetic are you, JVL?

    No one is lying. You just don’t like the cases being presented. But that doesn’t mean the cases weren’t presented. Nor does it mean the cases are false.

    I have. And when compared to what you spew my side is by far more coherent.

    Go on, let’s see it again. Remember the questions: where is the ‘designed’ evolution encouraging programming stored? How is it encoded? How does it affect development and affect mutations?

    Again, the ONLY reason probability arguments exist with respect to unguided evolution, is because there isn’t any way to actually test its claims. That means unguided evolution is outside of science. And that is why there isn’t any scientific theory of unguided evolution.

    Gosh, I don’t think anyone else brought up probability arguments just now? I wonder what ET is thinking . . . . first he says that paper, Waiting for Two Mutations (which is a probability argument) shows something about unguided evolutionary theory. Then he says probability arguments are rubbish. You know, I wonder why ET believes that paper anyway since the authors were testing unguided evolutionary processes which ET thinks you can’t test. It’s all kind of convoluted and weird.

  236. 236
    JVL says:

    Bornagain77: ^^^^ Pathetic, for you to claim that math has nothing to with God, you must, by necessity, show that math can exist indepently of God. It is, by default, a theological argument that you making. Denying it, just proves my point about you suffering from the mental affliction of denialism.

    Sorry I disagree with you and that I don’t want to get caught up in a Bible-quoting argument. It is NOT a theological argument. You just want it to be.

    Moreover, contrary to what you want to believe, you are VERY far from ever proving that math can exist independently of God:

    If there is no God then math came from someplace else.

  237. 237
    ET says:

    JVL:

    Repeating something in bold doesn’t make it true.

    What I said is true. Clearly you are just a pathetic loser.

    Evos are lying. Anyone who says that nature produced the genetic code is a liar. No one has presented any cases in that regard. You are lying.

    I never said probability arguments are rubbish. What’s wrong with you?

    Clearly you are just a pathetic liar and troll

    Good luck with that

  238. 238
    bornagain77 says:

    To repeat,’ Moreover, contrary to what you want to believe, you are VERY far from ever proving that math can exist independently of God:

    A BIBLICAL VIEW OF MATHEMATICS
    Vern Poythress – Doctorate in theology, PhD in Mathematics (Harvard)
    15. Implications of Gödel’s proof
    B. Metaphysical problems of anti-theistic mathematics: unity and plurality
    Excerpt: Because of the above difficulties, anti-theistic philosophy of mathematics is condemned to oscillate, much as we have done in our argument, between the poles of a priori knowledge and a posteriori knowledge. Why? It will not acknowledge the true God, wise Creator of both the human mind with its mathematical intuition and the external world with its mathematical properties. In sections 22-23 we shall see how the Biblical view furnishes us with a real solution to the problem of “knowing” that 2 + 2 = 4 and knowing that S is true.
    http://www.frame-poythress.org.....athematics

    Taking God Out of the Equation – Biblical Worldview – by Ron Tagliapietra – January 1, 2012
    Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties.
    1. Validity … all conclusions are reached by valid reasoning.
    2. Consistency … no conclusions contradict any other conclusions.
    3. Completeness … all statements made in the system are either true or false.
    The details filled a book, but the basic concept was simple and elegant. He (Godel) summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem.
    Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation.
    Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3).
    http://www.answersingenesis.or...../equation#

  239. 239
    ET says:

    Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.

    I challenge anyone to make the case that I have a horrendous misunderstanding of set theory. If no one steps up to even try then they should be banned for being pathological liars and losers

  240. 240
    kairosfocus says:

    JVL, your own words at 79 speak for themselves. Also, that you did not follow enough above to see that PW is possible worlds. That may also explain why you failed to see that Mathematics, substantially, being logic of structure and quantity would tie to how necessary mathematical entities will be framework to PWs, thus universally applicable. Thence, how do we get the P in PW, i.e. a logic of being, ontological question. Ontology being a subdiscipline of metaphysics, one of the main foci of philosophy. BTW, so is logic. And yes, meta questions raised by Mathematics and other disciplines are by definition matters of philosophy. It is unsurprising that you would mislabel meta issues of Mathematics as “theology,” that palpably being a dismissive sneer on “beliefs.” BTW, every worldview option — the stuff of metaphysics — necessarily has core first plausible beliefs that are antecedent to proofs, they are how you get to proofs. The issue is comparative difficulties and strengths and it so happens that PW framing allows a powerful answer to the Wigner challenge. KF

  241. 241
    bornagain77 says:

    Of related interest, to JVL statement: “If there is no God then math came from someplace else.”

    Not only would math not have a basis if God did not exist, but, since the entire concept of ‘personhood’ itself is immaterial and therefore must be based in the personhood of God, then JVL himself would not exist as a real person if God did not really exist:

    What Does It Mean to Say That Science & Religion Conflict? – M. Anthony Mills – April 16, 2018
    Excerpt: Barr rightly observes that scientific atheists often unwittingly assume not just metaphysical naturalism but an even more controversial philosophical position: reductive materialism, which says all that exists is or is reducible to the material constituents postulated by our most fundamental physical theories.
    As Barr points out, this implies not only that God does not exist — because God is not material — but that you do not exist. For you are not a material constituent postulated by any of our most fundamental physical theories; at best, you are an aggregate of those constituents, arranged in a particular way. Not just you, but tables, chairs, countries, countrymen, symphonies, jokes, legal contracts, moral judgments, and acts of courage or cowardice — all of these must be fully explicable in terms of those more fundamental, material constituents.
    In fact, more problematic for the materialist than the non-existence of persons is the existence of mathematics. Why? Although a committed materialist might be perfectly willing to accept that you do not really exist, he will have a harder time accepting that numbers do not exist. The trouble is that numbers — along with other mathematical entities such as classes, sets, and functions — are indispensable for modern science. And yet — here’s the rub — these “abstract objects” are not material. Thus, one cannot take science as the only sure guide to reality and at the same time discount disbelief in all immaterial realities.
    https://www.realclearreligion.org/articles/2018/04/16/what_does_it_mean_to_say_that_science_and_religion_conflict.html

    But hey, don’t take M. Anthony Mills’ word for it, here are leading atheists themselves denying that they really exist as real persons,

    “You are robots made out of meat. Which is what I am going to try to convince you of today”
    Jerry Coyne – No, You’re Not a Robot Made Out of Meat (Science Uprising 02) – video
    https://youtu.be/rQo6SWjwQIk?list=PLR8eQzfCOiS1OmYcqv_yQSpje4p7rAE7-&t=20

    “(Daniel) Dennett concludes, ‘nobody is conscious … we are all zombies’.”
    J.W. SCHOOLER & C.A. SCHREIBER – Experience, Meta-consciousness, and the Paradox of Introspection – 2004

    The Brain: The Mystery of Consciousness – STEVEN PINKER – Monday, Jan. 29, 2007
    Part II THE ILLUSION OF CONTROL
    Another startling conclusion from the science of consciousness is that the intuitive feeling we have that there’s an executive “I” that sits in a control room of our brain, scanning the screens of the senses and pushing the buttons of the muscles, is an illusion.
    http://www.academia.edu/279485.....sciousness

    The Consciousness Deniers – Galen Strawson – March 13, 2018
    Excerpt: What is the silliest claim ever made? The competition is fierce, but I think the answer is easy. Some people have denied the existence of consciousness: conscious experience, the subjective character of experience, the “what-it-is-like” of experience.,,,
    Who are the Deniers?,,, Few have been fully explicit in their denial, but among those who have been, we find Brian Farrell, Paul Feyerabend, Richard Rorty, and the generally admirable Daniel Dennett.,,,
    http://www.nybooks.com/daily/2.....s-deniers/

    “that “You”, your joys and your sorrows, your memories and your ambitions, your sense of personal identity and free will, are in fact no more than the behaviour of a vast assembly of nerve cells and their associated molecules. As Lewis Carroll’s Alice might have phrased: “You’re nothing but a pack of neurons.” This hypothesis is so alien to the ideas of most people today that it can truly be called astonishing.”
    Francis Crick – “The Astonishing Hypothesis” 1994

    At the 23:33 minute mark of the following video, Richard Dawkins agrees with materialistic philosophers who say that:
    “consciousness is an illusion”
    A few minutes later Rowan Williams asks Dawkins ”If consciousness is an illusion…what isn’t?”.
    https://www.youtube.com/watch?v=HWN4cfh1Fac&t=22m57s

    Atheistic Materialism – Does Richard Dawkins Exist? – video 37:51 minute mark
    Quote: “It turns out that if every part of you, down to sub-atomic parts, are still what they were when they weren’t in you, in other words every ion,,, every single atom that was in the universe, that has now become part of your living body, is still what is was originally. It hasn’t undergone what metaphysicians call a ‘substantial change’. So you aren’t Richard Dawkins. You are just carbon and neon and sulfur and oxygen and all these individual atoms still.
    You can spout a philosophy that says scientific materialism, but there aren’t any scientific materialists to pronounce it.,,, That’s why I think they find it kind of embarrassing to talk that way. Nobody wants to stand up there and say, “You know, I’m not really here”.
    https://www.youtube.com/watch?v=rVCnzq2yTCg&t=37m51s

    “There is no self in, around, or as part of anyone’s body. There can’t be. So there really isn’t any enduring self that ever could wake up morning after morning worrying about why it should bother getting out of bed. The self is just another illusion, like the illusion that thought is about stuff or that we carry around plans and purposes that give meaning to what our body does. Every morning’s introspectively fantasized self is a new one, remarkably similar to the one that consciousness ceased fantasizing when we fell sleep sometime the night before. Whatever purpose yesterday’s self thought it contrived to set the alarm last night, today’s newly fictionalized self is not identical to yesterday’s. It’s on its own, having to deal with the whole problem of why to bother getting out of bed all over again.”
    – Alex Rosenberg, The Atheist’s Guide to Reality, ch.10

    The claim that our sense of self, that is to say, our conscious experience, is just a neuronal illusion is simply insane. As David Bentley Hart states in the following article, “Simply enough, you cannot suffer the illusion that you are conscious because illusions are possible only for conscious minds. This is so incandescently obvious that it is almost embarrassing to have to state it.”

    The Illusionist – Daniel Dennett’s latest book marks five decades of majestic failure to explain consciousness. – 2017
    Excerpt: “Simply enough, you cannot suffer the illusion that you are conscious because illusions are possible only for conscious minds. This is so incandescently obvious that it is almost embarrassing to have to state it.”
    – David Bentley Hart
    https://www.thenewatlantis.com/publications/the-illusionist

  242. 242
    kairosfocus says:

    BA77 (& attn RP et al):

    The claim that our sense of self, that is to say, our conscious experience, is just a neuronal illusion is simply insane.

    The direct import of such a claim of our being under grand delusion is to discredit rationality itself. This definitely rises above mere gaps or blind spots in worldviews and is patently, manifestly self-falsifyingly absurd. To cling to such rather than recoiling in abject defeat implies that one finds the consequences of a sounder view unacceptable. So, one clings to the absurd, like a security blanket.

    And that is indeed seriously irrational.

    Worse, it is but one of many ways in which atheistical materialism is absurdly self-referentially incoherent.

    In this context “insane” may be a bit over the top but it is fair comment,once the homework behind it has been done.

    KF

  243. 243
    bornagain77 says:

    Kf as to ““insane” may be a bit over the top”,,

    And yet from the horse’s mouth,

    “You are robots made out of meat. Which is what I am going to try to convince you of today”
    Jerry Coyne – No, You’re Not a Robot Made Out of Meat (Science Uprising 02) – video
    https://youtu.be/rQo6SWjwQIk?list=PLR8eQzfCOiS1OmYcqv_yQSpje4p7rAE7-&t=20

    Nope, the word ‘insane’ fits exactly. Just because Coyne is a professor doesn’t change just how insane that statement actually is.

  244. 244

    .

    If there is no God then math came from someplace else.

    Mathematics is the product of measurement and expression, i.e. something must become specified among alternatives. You know this, but ignore it.

  245. 245
    Retired Physicist says:

    BornAgain are you capable of doing any level of math?

    Calculus 2? Ordinary differential equations? Partial differential equations?

  246. 246

    .

    BornAgain are you capable of doing any level of math?

    That’s a silly question, and you know it.

    RP can you do any level of mathematics without measurement and symbolic expression; can you do any level of mathematics without specifying something among alternatives?

  247. 247
    Retired Physicist says:

    @upright biped i’m guessing the answer is no.

  248. 248
    ET says:

    RP, can you make a coherent argument? I am very sure the answer is no.

  249. 249

    .
    Are you actually unsure if you can do mathematics without specifying something among alternatives, or is “guessing” just a rhetorical maneuver to depreciate the obvious answer?

  250. 250
    JVL says:

    ET: What I said is true. Clearly you are just a pathetic loser.

    Evos are lying. Anyone who says that nature produced the genetic code is a liar. No one has presented any cases in that regard. You are lying.

    So, given the evidence you just say the thousands of researchers are lying? That’s your counter-argument?

    Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.

    I challenge anyone to make the case that I have a horrendous misunderstanding of set theory. If no one steps up to even try then they should be banned for being pathological liars and losers

    You disagree with one of the most basic precepts of modern set theory.

  251. 251
    JVL says:

    Bornagain77: To repeat,’ Moreover, contrary to what you want to believe, you are VERY far from ever proving that math can exist independently of God:

    Okay. I’ll leave it then.

    Not only would math not have a basis if God did not exist, but, since the entire concept of ‘personhood’ itself is immaterial and therefore must be based in the personhood of God, then JVL himself would not exist as a real person if God did not really exist:

    But you just can’t leave it alone can you? Me disagreeing with you, that you just cannont tolerate.

  252. 252
    JVL says:

    Kairosfocus: your own words at 79 speak for themselves. Also, that you did not follow enough above to see that PW is possible worlds.

    Why can’t you just speak plainly?

    That may also explain why you failed to see that Mathematics, substantially, being logic of structure and quantity would tie to how necessary mathematical entities will be framework to PWs, thus universally applicable. Thence, how do we get the P in PW, i.e. a logic of being, ontological question. Ontology being a subdiscipline of metaphysics, one of the main foci of philosophy. BTW, so is logic. And yes, meta questions raised by Mathematics and other disciplines are by definition matters of philosophy. It is unsurprising that you would mislabel meta issues of Mathematics as “theology,” that palpably being a dismissive sneer on “beliefs.” BTW, every worldview option — the stuff of metaphysics — necessarily has core first plausible beliefs that are antecedent to proofs, they are how you get to proofs. The issue is comparative difficulties and strengths and it so happens that PW framing allows a powerful answer to the Wigner challenge

    Just repeating yourself over and over again doesn’t make you right. Or, I’m afraid, coherent.

  253. 253
    kairosfocus says:

    RP, you have ignored the substantive issue on the table to play at credentials. That tells us something, and not to your advantage. From 79 a challenge was issued which bridges mathematics and ontology. A response was on the table since 85 (see onward here), which you have evaded, while trying to belittle. I would suggest that as Math proper a reasonable senior high school or freshman exposure to core math would be adequate to follow the substantive math of the von Neumann construction and cascade N,Z,Q,R,C, R* and it is easy enough to pick up on the possible worlds context, including how logic of structure and quantity emerges from the principle of distinct identity of a PW. Thus we see how an answer to Wigner’s wonder emerges: necessary, framework entities obtain in any PW, so will be relevant through logical necessity not cause-effect bonds. Beyond, the attempt to infer to Math independent of a causal root of reality runs into: where do possible worlds come from. Non-being fails, circular retrocausality fails, infinite descent from an unbounded past is a supertask. That leaves one serious candidate: finitely remote, causally capable, necessary being reality root. KF

  254. 254
    JVL says:

    Upright BiPed: Mathematics is the product of measurement and expression, i.e. something must become specified among alternatives. You know this, but ignore it.

    I don’t ignore that but that has nothing to do with theology.

  255. 255
    bornagain77 says:

    RP, I most likely have far more experience working with math and applying it to the real world than you do.

    I worked as a technician helping build Chemical factories in the Texas area.

    This is the math that I had to be familiar with in order to qualify for, and do, that job:

    PID math demystified, part 1
    https://www.controleng.com/articles/pid-math-demystified-part-1/
    PID math demystified, part 2
    https://www.controleng.com/articles/pid-math-demystified-part-2/

    In fact, in college, I was required to build a PID controller from scratch, i.e. from the component level up. It was either pass or fail. In other words, you did not graduate from that college until you successfully built that PID controller. It was the most challenging, and nerve wracking, class that I have ever taken.

    And even though you probably know the math RP, I still don’t think you could have done my job. Besides the math, I had to be extremely knowledgeable in troubleshooting many other areas, i.e. electronics, chemistry, hydraulics, pneumatics, etc.. etc..

    Frankly, I would not have given two cents for anyone who tooted their own horn as being smarter than everyone else as you do, but the respect that I received and gave to others in that job was every bit earned. Book learning could only get you so far in that job, but in the field, in the real world of applied science, it was the common sense solutions to extremely complicated problems that most often earned you the most respect from others in that job.

    Do you have that required common sense to do that job? The only way to find out is to throw you in the water and see if you can swim, i.e. can do the job. I doubt it. I’ve seen many people fail at trying to do that job after they got out of college. There is something about being in the field that just can’t be learned in the classroom. That something is common sense. And in that area of having common sense, I have not seen much coming from you.

  256. 256
    JVL says:

    Retired Physicist: BornAgain are you capable of doing any level of math? Calculus 2? Ordinary differential equations? Partial differential equations?

    In my experience: BornAgain77 hasn’t actually shown any experience with mathematics above the basic level. He’s good at copying and pasting references. For lots of different things.

    Bornagain77: In fact, in college, I was required to build a PID controller from scratch, i.e. from the component level up. It was either pass or fail. In other words, you did not graduate from that college until you successfully built that PID controller. It was the most challenging, and nerve wracking, class that I have ever taken.

    Okay, I stand corrected. Always happy to revise my stance with the addition of new data.

    ET likes to think he’s good at math and, a few times when I’ve pushed him, has come up with some good answers. After quite a few proddings. As you’ve noted, his understanding of set theory is severely flawed; but there is no way he’s ever going to back down from that stance as he’s decided to die on that hill a long time ago.

    Upright Biped is quite good on philosophical discussions and topics but mathematics . . . .I’m not so sure.

    Kairosfocus certainly does has some good basic mathematical knowledge but he’s prone to throw out tons of jargon and irrelevant comments; I think maybe he was taught in a very old and out dated fashion and that has affected his approach to communicated mathematical ideas.

    I could be very wrong but those are my impressions.

  257. 257
    ET says:

    JVL:

    So, given the evidence you just say the thousands of researchers are lying?

    What evidence? Stop bluffing.

    What evidence is there that unguided, blind and mindless processes can produce a ribosome? How can we test for such a thing?

    You disagree with one of the most basic precepts of modern set theory.

    Liar. I disagree with something that no one uses for anything. And the reason I disagree is because basic set subtraction warrants my disagreement. You are just too dim to grasp what I post.

    Again, I only disagree with an insignificant and useless part of set theory. To say otherwise is a blatant lie. JVL has steadfastly refused to answer my challenges and can only falsely accuse, as cowards are want to do.

  258. 258
    kairosfocus says:

    F/N: Normal math level to work with PID controllers, familiarity with Laplace Transforms and associated s-domain block diagram algebra [z-domain is related, for the discrete time case], poles and zeros of a rational, complex frequency domain function, the transfer function. Even with tricks and tools such as the heavy rubber sheet model, you need to understand transient behaviour, circular frequency and cycle frequency as well as frequency response. The transfer function is of course the image of unit area impulse response; this can be used to draw it out of noise and responses thereto. Generally, do not hit a system in a real world situation with an impulse . Familiarity with ODE’s is a given, indeed that is what you are manipulating . . . that auxiliary equation or D operator is a thinly disguised Laplace Transform. Way back the get the idea concept was, sophisticated logarithms. Someone with that background and required basic intelligence will be able to access and appreciate the mathematical thinking in baseline special relativity and quantum mechanics. With persistence and good references, should be able to appreciate more advanced topics. Of course, such an autodidact will have limitations, but such will not be relevant to what is on the table substantially from 85 on, which answers the challenge in 79. KF

  259. 259
    ET says:

    Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.

    I challenge anyone to make the case that I have a horrendous misunderstanding of set theory. If no one steps up to even try then they should be banned for being pathological liars and losers

    Still waiting. More nonsensical accusations just prove that JVL is a coward, liar and bluffing loser.

  260. 260
    bornagain77 says:

    JVL, and again, disagreeing without presenting a coherent argument defending your position is no different than straight up ‘denialism’, i.e. a mental illness!

  261. 261
    JVL says:

    ET: What evidence? Stop bluffing.

    What evidence is there that unguided, blind and mindless processes can produce a ribosome? How can we test for such a thing?

    As you like to say: your ignorence of the evidence is not an argument.

    Liar. I disagree with something that no one uses for anything. And the reason I disagree is because basic set subtraction warrants my disagreement. You are just too dim to grasp what I post.

    You are in stark contrast with every single math publication produced in the last century. No one takes your view seriously. Why you bother I just can’t fathom.

    Again, I only disagree with an insignificant and useless part of set theory. To say otherwise is a blatant lie. JVL has steadfastly refused to answer my challenges and can only falsely accuse, as cowards are want to do.

    Welcome to obscurity. No one takes you seriously or uses your system. No one.

    Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.

    It doesn’t matter what you think. You are incorrect.

    I challenge anyone to make the case that I have a horrendous misunderstanding of set theory. If no one steps up to even try then they should be banned for being pathological liars and losers

    You have already made the case yourself and NO ONE has come to your defence. No one.

    Still waiting. More nonsensical accusations just prove that JVL is a coward, liar and bluffing loser.

    I’m good being correct.

  262. 262
    JVL says:

    Kairosfocus: Normal math level to work with PID controllers, familiarity with Laplace Transforms and associated s-domain block diagram algebra [z-domain is related, for the discrete time case], poles and zeros of a rational, complex frequency domain function, the transfer function. Even with tricks and tools such as the heavy rubber sheet model, you need to understand transient behaviour, circular frequency and cycle frequency as well as frequency response. The transfer function is of course the image of unit area impulse response; this can be used to draw it out of noise and responses thereto. Generally, do not hit a system in a real world situation with an impulse . Familiarity with ODE’s is a given, indeed that is what you are manipulating . . . that auxiliary equation or D operator is a thinly disguised Laplace Transform. Way back the get the idea concept was, sophisticated logarithms. Someone with that background and required basic intelligence will be able to access and appreciate the mathematical thinking in baseline special relativity and quantum mechanics.

    You really do not make sense. I can’t even parse most of what you write. Just speak clearly and plainly.

  263. 263
    kairosfocus says:

    ET, I appreciate that you take a heterodox view of set theory. There are difficulties with that view, but they do not substantially alter the key point in 85 above. Though, it is much harder to hammer home to the determined, that finite stage step traversal of the transfinite is impossible, a supertask, as we saw four years ago. That is what needs to be answered. Of course, I see that tamed infinitesimals thus transfinite hyperreals and infinitesimally altered reals are very useful. For concepts, surreals. Likewise, there is transfinite induction that goes beyond limits of induction on N. KF

  264. 264

    .

    I don’t ignore that but that has nothing to do with theology.

    I made no comment about theology; my issue with you (among others) is your claim that math exists outside of an observer. Mathematics requires the specification of something among alternatives (i.e. measurement and symbolic expression), so do have an argument that supports this assertion? You tell us that mankind learned mathematics by counting – i.e. matching our symbolic expressions to the quantity of objects in a set. Additionally you seem to suggest that if that scenario were repeated elsewhere, the symbolic expressions might certainly be different, but the math itself would be the same. Whatever else that argument may be, it is not an argument that math exists outside the measurement and expression of an observer.

  265. 265
    ET says:

    JVL:

    As you like to say: your ignorence of the evidence is not an argument.

    You coward. The ignorance is all yours.
    Liar. I disagree with something that no one uses for anything. And the reason I disagree is because basic set subtraction warrants my disagreement. You are just too dim to grasp what I post.

    You are in stark contrast with every single math publication produced in the last century.

    Liar. Again, I only disagree with an insignificant and useless part of set theory. To say otherwise is a blatant lie. JVL has steadfastly refused to answer my challenges and can only falsely accuse, as cowards are want to do.

    No one takes you seriously or uses your system. No one.

    No one uses what I am disputing for anything. No one.

    Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.

    It doesn’t matter what you think.

    I don’t care what you say. All you can do is use the thing being disputed to try to settle the dispute. How stupid is that?

    I challenge anyone to make the case that I have a horrendous misunderstanding of set theory. If no one steps up to even try then they should be banned for being pathological liars and losers

    I only dispute an insignificant and useless part of set theory. And at least I understand the implications of set subtraction. All JVL has is its cowardly accusations and ignorance when it comes to debate tactics.

    So to claim anything else about my knowledge of set theory is a cowardly lie.

  266. 266
    JVL says:

    Bornagain77: JVL, again, disagreeing without presenting a coherent argument defending your position is no different than straight up ‘denialism’, i.e. a mental illness!

    How do you know the laws of mathematics are mutable at all? You don’t. That’s all just a supposition on your part because your conception of the ‘creator’ of the universe dictates that they have control over all things.

    I think mathematics is invariant. God or no God we have to work with the mathematical structures. And that means that ‘God’ did not create them. I may be wrong but I see not evidence to contradict that belief.

    Show me an example of God affecting mathematics. Just one. And not something that you just find ‘amazing’ or ‘beautiful’. I mean something really clearly divinely influenced.

  267. 267
    ET says:

    KF, set subtraction proves there are difficulties with Cantor’s view. If all people have is to Jedi hand-wave away the implications of set subtraction, then they have left mathematics behind.

    And the fact that no one uses the concept that all countably infinite sets have the same cardinality for anything, tells me all I need to know about that Jedi hand-wave. Arguments from authority don’t stand a chance in the octagon.

  268. 268
    JVL says:

    Upright Biped: I made no comment about theology; my issue with you (among others) is your claim that math exists outside of an observer.

    Show me a counter example.

  269. 269
    ET says:

    JVL:

    God or no God we have to work with the mathematical structures. And that means that ‘God’ did not create them.

    That doesn’t follow. This is the problem, JVL. Your posts prove that you don’t understand logic and reasoning.

  270. 270
    JVL says:

    ET: Liar. I disagree with something that no one uses for anything. And the reason I disagree is because basic set subtraction warrants my disagreement. You are just too dim to grasp what I post.

    Your basic set subtraction is not used by anyone, ever, for infinite sets. Why do you keep embarrassing yourself with this futile line or argumentation?

    Liar. Again, I only disagree with an insignificant and useless part of set theory. To say otherwise is a blatant lie. JVL has steadfastly refused to answer my challenges and can only falsely accuse, as cowards are want to do.

    I have and you just deny anything that runs counter to your view.

    No one uses what I am disputing for anything. No one.

    Now who’s a denialist?

    Only a total loser would say that I have horrendous misunderstandings of set theory just because I disagree with one insignificant claim Cantor made. And here you two are- desperate moron twins.

    No one is going to agree with you just because you type it in bold.

    I don’t care what you say. All you can do is use the thing being disputed to try to settle the dispute. How stupid is that?

    Find a fault in a proof. Can you do that? If you can’t then there is no dispute.

    I challenge anyone to make the case that I have a horrendous misunderstanding of set theory. If no one steps up to even try then they should be banned for being pathological liars and losers

    Find a fault in a proof. Can you do that?

    I only dispute an insignificant and useless part of set theory. And at least I understand the implications of set subtraction. All JVL has is its cowardly accusations and ignorance when it comes to debate tactics.

    Find a fault in a proof. Can you do that?

    So to claim anything else about my knowledge of set theory is a cowardly lie.

    You can’t find a fault in the proofs which establish what you dispute. You lose.

  271. 271

    .

    UB: my issue with you (among others) is your claim that math exists outside of an observer.

    JVL: Show me a counter example.

    You want “counter examples” to mathematics existing outside of an observer? Hello?

    Instead of incoherence, let’s try out what you actually do say as an argument instead. Let’s match our symbols with the quantity of objects in a set, as you suggested upthread.

    How many moons are in our sky at night?

    Answer: One

    Okay … explain to me how mathematics exists outside of measurement and expression here. Surely you are not arguing that math exist merely because a single moon exist in the night’s sky?!?

  272. 272
    ET says:

    JVL:

    Your basic set subtraction is not used by anyone, ever, for infinite sets.

    Wow, what a devastating refutation- not.

    I have and you just deny anything that runs counter to your view.

    More lies. I have challenged you to show that the concept is useful and you have failed.

    No one uses what I am disputing for anything. No one.

    Now who’s a denialist?

    YOU. YOU have FAILED to demonstrate that the concept under dispute is used or useful. Clearly you are just a punk.

    Set subtraction proves there is fault with the inferences from the proof. JVL is still too dim to grasp what that means.

    There isn’t anything in set theory that prevents set subtraction from being used with infinite sets. You have to be a special type of coward to even try that BS argument.

  273. 273
    ET says:

    The only thing I dispute is the concept that all countably infinite sets have the same cardinality. And no one uses the concept that all countably infinite sets have the same cardinality for anything. No one.

    For years I have asked JVL to produce something showing the concept is used and useful. For years JVL has been the typical coward, refusing the challenge.

  274. 274
    JVL says:

    Upright Biped: Okay … explain to me how mathematics exists outside of measurement and expression here. Surely you are not arguing that math exist merely because a single moon exist in the night’s sky?!?

    Of course not. That would be incredibly stupid.

    Why don’t you show me a consistent system of mathematics that works for basic problems like arithmetic that is significantly different from ours. Are you sure one exists?

  275. 275
    JVL says:

    ET: Wow, what a devastating refutation- not.

    It’s quite true though.

    More lies. I have challenged you to show that the concept is useful and you have failed.

    Deny, deny, deny. Strange that no one is coming to your defence on this. I wonder why?

    No one uses what I am disputing for anything. No one.

    Your ignorance is not an argument.

    YOU. YOU have FAILED to demonstrate that the concept under dispute is used or useful. Clearly you are just a punk.

    Your ignorance is not an argument.

    Set subtraction proves there is fault with the inferences from the proof. JVL is still too dim to grasp what that means.

    You never found a fault with any of Cantor’s proofs. You lose.

    There isn’t anything in set theory that prevents set subtraction from being used with infinite sets. You have to be a special type of coward to even try that BS argument.

    You never found a fault with any of Cantor’s proofs. You lose.

    The only thing I dispute is the concept that all countably infinite sets have the same cardinality. And no one uses the concept that all countably infinite sets have the same cardinality for anything. No one.

    Your ignorance is not an argument.

    For years I have asked JVL to produce something showing the concept is used and useful. For years JVL has been the typical coward, refusing the challenge.

    Deny, deny, deny. Oh hey, listen . . . . do you hear that? That stark silence? That’s the silence of NO ONE coming to your defence on this issue. Not Kairosfocus, not Bornagain77, not Upright Biped. NO ONE. They’re leaving you to twist in the wind. Being wrong.

    Welcome to reality.

    Oh, and by the way . . .

    Are you going to provide evidence, as in hard physical evidence, that organisms are ‘designed’ to evolve? As in evidence of where such programming exists.. How it’s encoded. How it affect development. People want to know if you can uphold your claim. So far, there’s a lot of disappointment.

  276. 276

    .

    UB: Okay … explain to me how mathematics exists outside of measurement and expression here. Surely you are not arguing that math exist merely because a single moon exist in the night’s sky?!?

    JVL: Of course not. That would be incredibly stupid.

    Why don’t you show me a consistent system of mathematics that works for basic problems like arithmetic that is significantly different from ours. Are you sure one exists?

    And how would that relieve you of the fact that mathematics requires measurement and symbolic expression?

    – – – – – – – – – – – – – – – –

    EDIT … unless of course, you are simply arguing that mathematics exists because there is a single moon in the night’s sky – a position you’ve summed up as “incredibly stupid”.

  277. 277
    JVL says:

    Upright Biped: And how would that relieve you of the fact that mathematics requires measurement and symbolic expression?

    What? Sigh. What does that have to do with the question of whether or not math is independent of any possible creator?

    You keep arguing on some odd fringe of mathematics. I hope you enjoy it. But the real fun is actually doing the work. As well you know.

  278. 278

    .
    lol

    Just for the fun of it, I did a word search on this page for the phrase “any possible creator”. I found it only appears on this page once, in comment #277.

    Your argument, JVL, is that mathematics exists outside any mind, any observer, any intelligent agent whatsoever — “it just is” as you say.

    For that to be so, it would require math to exist without the need to specify something among alternatives, without measurement, and without expression. You are now down to arguing that math exist because a single moon orbits in the night sky. Surprise surprise.

    – – – – – – – – – – – – – –

    Your argument is not only incoherent but pointless, JVL, and has been since the start of this conversation. The problem here is that you’ve already proven yourself incapable of doing an “about face” — i.e. you are are unwilling to admit mistakes to those who point them out to you (certainly not uncommon) but most unfortunate of all, you are equally unwilling to just walk away.

  279. 279
    ET says:

    The only thing I dispute is the concept that all countably infinite sets have the same cardinality. And no one uses the concept that all countably infinite sets have the same cardinality for anything. No one.

    Your ignorance is not an argument.

    YOU are the ignorant one here, JVL. I noticed no one has come to your defense. No one. Stark silence, you loser.

    Are you going to provide evidence, as in hard physical evidence, that organisms are ‘designed’ to evolve?

    According to the paper “Waiting for TWO Mutations” that is the only thing that can explain the diversity of life. But you are too stupid to understand that. And that is not my problem.

  280. 280
    ET says:

    The only thing I dispute is the concept that all countably infinite sets have the same cardinality. And no one uses the concept that all countably infinite sets have the same cardinality for anything. No one.

    For years I have asked JVL to produce something showing the concept is used and useful. For years JVL has been the typical coward, refusing the challenge.

    To refute that claim all JVL had to do was show us how it is used. So it is very telling that he bailed like a coward

  281. 281
    bornagain77 says:

    Earlier in the thread Jerry stated,

    ‘math is in our heads’ and “I made the point above that the only numbers that exist are positive integers and in reality they are in our head too. They are not in nature though we can certainly count but for that we have to have a concept of what is meant by number. In our universe there are no negative numbers, no pi, no e, no rational or irrational numbers, nothing infinite nor anything infinitely small.”

    Later in the thread at post 264 Upright Biped states:

    “my issue with you (JVL) (among others) is your claim that math exists outside of an observer.”

    The fact that math is immaterial, and that it takes an immaterial mind to even think about immaterial mathematics in the first place, is certainly not that hard to understand. As Dr. Egnor once commented, “What is the physics behind the Pythagorean theorem? After all, no actual triangle is perfect, and thus no actual triangle in nature has sides such that the Pythagorean theorem holds. There is no real triangle in which the sum of the squares of the sides exactly equals the square of the hypotenuse. That holds true for all of geometry. Geometry is about concepts, not about anything in the natural world or about anything that can be described by physics. What is the “physics” of the fact that the area of a circle is pi multiplied by the square of the radius? And of course what is natural and physical about imaginary numbers, infinite series, irrational numbers, and the mathematics of more than three spatial dimensions? ”

    Naturalism and Self-Refutation – Michael Egnor – January 31, 2018
    Excerpt: Mathematics is certainly something we do. Is mathematics “included in the space-time continuum [with] basic elements … described by physics”?,,, What is the physics behind the Pythagorean theorem? After all, no actual triangle is perfect, and thus no actual triangle in nature has sides such that the Pythagorean theorem holds. There is no real triangle in which the sum of the squares of the sides exactly equals the square of the hypotenuse. That holds true for all of geometry. Geometry is about concepts, not about anything in the natural world or about anything that can be described by physics. What is the “physics” of the fact that the area of a circle is pi multiplied by the square of the radius? And of course what is natural and physical about imaginary numbers, infinite series, irrational numbers, and the mathematics of more than three spatial dimensions? Mathematics is entirely about concepts, which have no precise instantiation in nature,,,
    Furthermore, the very framework of Clark’s argument — logic — is neither material nor natural. Logic, after all, doesn’t exist “in the space-time continuum” and isn’t described by physics. What is the location of modus ponens? How much does Gödel’s incompleteness theorem weigh? What is the physics of non-contradiction? How many millimeters long is Clark’s argument for naturalism? Ironically the very logic that Clark employs to argue for naturalism is outside of any naturalistic frame.
    The strength of Clark’s defense of naturalism is that it is an attempt to present naturalism’s tenets clearly and logically. That is its weakness as well, because it exposes naturalism to scrutiny, and naturalism cannot withstand even minimal scrutiny. Even to define naturalism is to refute it.
    https://evolutionnews.org/2018/01/naturalism-and-self-refutation/

    And as Eugene Wigner once commented, “thought processes and consciousness are the primary concepts, that our knowledge of the external world is the content of our consciousness and that the consciousness, therefore, cannot be denied.”

    “The principal argument against materialism is not that illustrated in the last two sections: that it is incompatible with quantum theory. The principal argument is that thought processes and consciousness are the primary concepts, that our knowledge of the external world is the content of our consciousness and that the consciousness, therefore, cannot be denied. On the contrary, logically, the external world could be denied—though it is not very practical to do so. In the words of Niels Bohr, “The word consciousness, applied to ourselves as well as to others, is indispensable when dealing with the human situation.” In view of all this, one may well wonder how materialism, the doctrine that “life could be explained by sophisticated combinations of physical and chemical laws,” could so long be accepted by the majority of scientists.”
    – Eugene Wigner, Remarks on the Mind-Body Question, pp 167-177.

    In short, consciousness is the primary prerequisite of all possible prerequisites for any coherent ‘mathematical’ model of reality to be put forth. To postulate anything other than consciousness as the primary substratum of reality is self-negating, As William J Murray once stated, “Mind must be postulated as the unobserved observer, the uncaused cause simply to avoid a self-negating, self-conflicting worldview. It is the necessary postulate of all necessary postulates, because nothing else can come first. To say anything else comes first requires mind to consider and argue that case and then believe it to be true, demonstrating that without mind, you could not believe that mind is not primary in the first place.”?

    “In any philosophy of reality that is not ultimately self-defeating or internally contradictory, mind – unlabeled as anything else, matter or spiritual – must be primary. What is “matter” and what is “conceptual” and what is “spiritual” can only be organized from mind. Mind controls what is perceived, how it is perceived, and how those percepts are labeled and organized. Mind must be postulated as the unobserved observer, the uncaused cause simply to avoid a self-negating, self-conflicting worldview. It is the necessary postulate of all necessary postulates, because nothing else can come first. To say anything else comes first requires mind to consider and argue that case and then believe it to be true, demonstrating that without mind, you could not believe that mind is not primary in the first place.”
    – William J. Murray

    Moreover, we no longer have to rely solely on these powerful philosophical arguments that immaterial Mind must precede immaterial math itself, but we can now support the fact that Mind must be primary by appealing to advances in quantum mechanics, Specifically, numerous experiments have all concluded that “Material reality does not exist without an observer”

    The Death of Materialism – InspiringPhilosophy – (Material reality does not exist without an observer) video
    https://www.youtube.com/watch?v=wM0IKLv7KrE
    Materialism has been dead for decades and recent research only reconfirms this, as this video will show. This video was reviewed by physicist Fred Kuttner and Richard Conn Henry. A few other physicists reviewed this but asked to remain anonymous for privacy reasons.

    Quantum physics says goodbye to reality – Apr 20, 2007 ?Excerpt: Many realizations of the thought experiment have indeed verified the violation of Bell’s inequality. These have ruled out all hidden-variables theories based on joint assumptions of realism, meaning that reality exists when we are not observing it; and locality, meaning that separated events cannot influence one another instantaneously. But a violation of Bell’s inequality does not tell specifically which assumption – realism, locality or both – is discordant with quantum mechanics.?Markus Aspelmeyer, Anton Zeilinger and colleagues from the University of Vienna, however, have now shown that realism is more of a problem than locality in the quantum world. They devised an experiment that violates a different inequality proposed by physicist Anthony Leggett in 2003 that relies only on realism, and relaxes the reliance on locality. To do this, rather than taking measurements along just one plane of polarization, the Austrian team took measurements in additional, perpendicular planes to check for elliptical polarization.?They found that, just as in the realizations of Bell’s thought experiment, Leggett’s inequality is violated – thus stressing the quantum-mechanical assertion that reality does not exist when we’re not observing it. “Our study shows that ‘just’ giving up the concept of locality would not be enough to obtain a more complete description of quantum mechanics,” Aspelmeyer told Physics Web. “You would also have to give up certain intuitive features of realism.”?http://physicsworld.com/cws/article/news/27640

    New Mind-blowing Experiment Confirms That Reality Doesn’t Exist If You Are Not Looking at It – June 3, 2015
    Excerpt: Some particles, such as photons or electrons, can behave both as particles and as waves. Here comes a question of what exactly makes a photon or an electron act either as a particle or a wave. This is what Wheeler’s experiment asks: at what point does an object ‘decide’?
    The results of the Australian scientists’ experiment, which were published in the journal Nature Physics, show that this choice is determined by the way the object is measured, which is in accordance with what quantum theory predicts.
    “It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,” said lead researcher Dr. Andrew Truscott in a press release.,,,
    “The atoms did not travel from A to B. It was only when they were measured at the end of the journey that their wave-like or particle-like behavior was brought into existence,” he said.
    Thus, this experiment adds to the validity of the quantum theory and provides new evidence to the idea that reality doesn’t exist without an observer.
    http://themindunleashed.org/20.....at-it.html

    “The concept of the objective reality of the elementary particles has thus evaporated…”,,,; “The idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them,,, is impossible.,,, We can no longer speak of the behavior of the particle independently of the process of observation”
    – W. Heisenberg, Physics and Philosophy, Harper and Row, New York (1958)

    Moreover, the math of quantum mechanics requires for us to make a choice in what we will measure before reality can be said to be brought into existence. As Stephen Weinberg, an atheist, stated, “In quantum mechanics these probabilities do not exist until people choose what to measure,,, Unlike the case of classical physics, a choice must be made,,,”

    The Trouble with Quantum Mechanics – Steven Weinberg – January 19, 2017
    Excerpt: The instrumentalist approach,, (the) wave function,, is merely an instrument that provides predictions of the probabilities of various outcomes when measurements are made.,,
    In the instrumentalist approach,,, humans are brought into the laws of nature at the most fundamental level. According to Eugene Wigner, a pioneer of quantum mechanics, “it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness.”11
    Thus the instrumentalist approach turns its back on a vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else. It is not that we object to thinking about humans. Rather, we want to understand the relation of humans to nature, not just assuming the character of this relation by incorporating it in what we suppose are nature’s fundamental laws, but rather by deduction from laws that make no explicit reference to humans. We may in the end have to give up this goal,,,
    Some physicists who adopt an instrumentalist approach argue that the probabilities we infer from the wave function are objective probabilities, independent of whether humans are making a measurement. I don’t find this tenable. In quantum mechanics these probabilities do not exist until people choose what to measure, such as the spin in one or another direction. Unlike the case of classical physics, a choice must be made,,,
    http://quantum.phys.unm.edu/46.....inberg.pdf

    In fact Weinberg, again an atheist, rejected the instrumentalist approach precisely because “humans are brought into the laws of nature at the most fundamental level” and because it undermined the Darwinian worldview from within. Yet, regardless of how he and other atheists may prefer the world to behave, quantum mechanics itself could care less how atheists prefer the world to behave.

    For instance, this recent 2019 experimental confirmation of the “Wigner’s Friend” thought experiment established that “measurement results,, must be understood relative to the observer who performed the measurement”.

    More Than One Reality Exists (in Quantum Physics) By Mindy Weisberger – March 20, 2019
    Excerpt: “measurement results,, must be understood relative to the observer who performed the measurement”.
    https://www.livescience.com/65029-dueling-reality-photons.html

    My question for JVL and RP is this, “why in blue blazes does a supposedly deterministic mathematical equation even care what I, as a person, choose to measure?” Mathematical equations, by definition, can’t care about people, Only a person can care about another person. Thus, it follows from logical necessity, that the Mind of God must be behind the mathematics of quantum mechanics.

    As the Bible said thousands of years before quantum mechanics was even discovered,

    Colossians 1:17
    He is before all things, and in him all things hold together.

    Supplemental note:

    Eight intersecting lines of experimental evidence from quantum mechanics that shows that consciousness must precede material reality (Double Slit experiment, Wigner’s Quantum Symmetries, as well as the recent confirmation of the Wigner’s friend thought experiment, Wheeler’s Delayed Choice, Leggett’s Inequalities, Quantum Zeno effect, Quantum Information theory, and the recent closing of the Free Will loophole.)
    Although each of those (eight) experiments are very interesting in their own right as to proving that the Mind of God must precede material reality, my favorite evidences out of that group, for proving that the Mind of God must be behind the creation of the universe itself, is the Quantum Zeno effect and Quantum Information theory. This is because the Quantum Zeno effect and Quantum Information theory deal directly with entropy. And, entropy is, by a VERY wide margin, the most finely tuned of the initial conditions of the Big Bang. Finely tuned to an almost incomprehensible degree of precision, 1 part in 10 to the 10 to the 123rd power. As Roger Penrose himself stated that, “This now tells us how precise the Creator’s aim must have been: namely to an accuracy of one part in 10^10^123.”
    https://uncommondescent.com/big-bang/sabine-hossenfelder-physicists-theories-of-how-the-universe-began-arent-any-better-than-traditional-tales-of-creation/#comment-690210

  282. 282
    kairosfocus says:

    JVL, if you cannot understand what I summed up about ET, then you are unfamiliar with instrumentation and control, and perhaps with linked Mathematics. Though, I am surprised if you are unfamiliar with Laplace Transforms (close cousins of both Fourier Transforms and Z-transforms), all of which are connected to the complex frequency domains. For years, I lived more in that domain than in our day-to-day time domain (and yes, there are t-domain techniques too). As an applied physicist who played both sides of the street (and an educator), I took time to draw up some conceptual bridges. KF

    PS: I am also quite confident that what I wrote here and summarised then augmented above is both coherent and well warranted. However, it may well cut across your own worldview first plausibles. Let me clip — nope real mess, just read it there and respond on points. Otherwise for cause we call your dismissive bluff.

  283. 283
    kairosfocus says:

    ET, kindly turn down rhetorical voltage. KF

  284. 284
    ET says:

    If JVL is going to get away with lying what choice do I have?

    Can you tell me what the concept of all countably infinite sets have the same cardinality is used for?

  285. 285
    kairosfocus says:

    UB, core structure and quantity connected to logic of being will exist in any possible world. The question then is how possible gets there; what makes a PW possible. That connects to logic of being and the root of reality. JVL, here, confuses ontology with theology. S/he also seems to imagine a power of blind chance and mechanical necessity that is patently unwarranted. Conveniently, twice over. Of course the study requires a rational, free observer. KF

  286. 286
    kairosfocus says:

    UB, 276:

    unless of course, you are simply arguing that mathematics exists because there is a single moon in the night’s sky

    This actually does show how a PW embeds the substance of structure and quantity, here first a countable discrete object and it s being of a definite size, shape and location for starters. We then find out that what is must be compatible with everything else that is, and that to be distinct and identifiable there must be core characteristics of distinction. This brings out logic through the principle of distinct identity.

    No PW is possible, then, without embedding a logic of structure and quantity that in part is trans-world, i.e. necessary and framework to any world. This includes N,Z,Q,R,C,R* etc. Where, already at abstract level vectors are present from Z on, with invitation to spaces.

    Does that suggest that Mathematics is an independent realm of necessary entities? No, it is a consequence of being a possible world that core structures and quantities will be present, as key abstracta. The issue pivots on what I pointed out from 85 on: what makes a world possible?

    JVL et al refuse to go there but we may freely do so: utter non-being has no causal capacity, circular retrocausation is the same from a different angle, traversing a beginningless past of “years” is an infeasible supertask. That leaves on the table just one serious option: a finitely remote root of reality, where in any world with creatures sufficiently rationally and responsibly free to do math, they will be governed morally by first duties of reason. Even objectors, to argue are forced to appeal to same. That is, they are self evident.

    That further constrains the root, as we are such creatures, i.e. our existence implies the root is inherently good and so too utterly wise. That is philosophy, and it naturally arises from asking about what it means to be rational. It is interesting that the objectors here, at this npoint, tend to support views that undermine credibility of rationality required to do math.

    No wonder berlinski suggested there are no arguments against God that are not arguments against math.

    KF

  287. 287
    kairosfocus says:

    ET, it is part of the coherence of Mathematics, inter alia it connects to the further implication of different transfinite cardinalities such as continuum. That connects to any number of properties in NZQRC etc. And BTW, cardinality of a number is a scaling metric, countability meaning, can be put in 1:1 correspondence with N or a subset thereof. Transfiniteness emerges from the endless continuation property of N as a structured set. So, if N and another set S can be endlessly matched, S has the same cardinality and can be transformed into N, it is N in another form so to speak, insofar as this property is concerned. For example: {0,1,2 . . . } x2 element by element is {0,2,4 . . .}. This means, we have to broaden our understanding of cardinality once sets become transfinite. And the transfinite opens up the world of the infinitesimal, thus calculus. And arguably the epsilon delta limit approach simply manages the infinitesimal by exploiting its scale. Continuum and limits are inextricably tied to the transfinite. Just, it is hard to manage. KF

  288. 288
    ET says:

    No, it isn’t part of any coherence and no it doesn’t connect anything.

    Again, no one uses the concept that all countably infinite sets have the same cardinality. The concept is useless. And no one can demonstrate otherwise. Notice I am NOT saying infinity is useless.

    Cantor’s diagonal just shows that two sets are countably infinite. It says nothing about the cardinality. Set subtraction can prove the cardinalities are not the same.

  289. 289
    kairosfocus says:

    ET, I have summarised uncontroversial facts. KF

  290. 290
    JVL says:

    ET: Cantor’s diagonal just shows that two sets are countably infinite. It says nothing about the cardinality.

    Countably infinite sets all have the same infinite cardinality; aleph-nought.

    Set subtraction can prove the cardinalities are not the same.

    Nope. Find a mistake in a proof that the set of all even integers has the same cardinality as the set of all integers. If you can’t find a mistake then the proof holds. QED

  291. 291
    JVL says:

    Kairosfocus: I have summarised uncontroversial facts

    Thank you!!

  292. 292
    Retired Physicist says:

    ET, if you have made a massive breakthrough in infinite set theory, you are due for a Fields medal and the accompanying $15,000. So can you tell us what mathematicians you have contacted or publications you have prepared to publish in? Because if the answer is zero that suggests you know you’re full of it.

  293. 293
    ET says:

    RP, why do you think your cowardly comments mean something? The fact that the concept I am disputing is useless says it all, really. But then again you are clearly too dim to grasp that fact.

  294. 294
    ET says:

    JVL:

    Countably infinite sets all have the same infinite cardinality;

    Repeating your trope isn’t going to make it so.

    Set subtraction can prove the cardinalities are not the same.

    JVL:

    Nope.

    Yes, it can. And no amount of your whining and handwaving will ever change that fact.

  295. 295
    ET says:

    Kairosfocus- You have failed to show how the concept that I am disputing is used. Your “summary” is pure double-talk

  296. 296
    ET says:

    Again, no one uses the concept that all countably infinite sets have the same cardinality. The concept is useless. And no one can demonstrate otherwise. Notice I am NOT saying infinity is useless.

    Cantor’s diagonal just shows that two sets are countably infinite. It says nothing about the cardinality. Set subtraction can prove the cardinalities are not the same.

    Everyone can see that no one has refuted my claim that the concept is useless

  297. 297
    JVL says:

    ET: Repeating your trope isn’t going to make it so.

    It is true. And will stay that way unless you can find a fault in a pertinent proof.

    Set subtraction can prove the cardinalities are not the same.

    Find a mistake in a proof.

    Yes, it can. And no amount of your whining and handwaving will ever change that fact.

    If you can’t find a mistake you lose.

    Welcome to real mathematics. It’s not a spectator sport. Kairosfocus agrees with me.

    Everyone can see that no one has refuted my claim that the concept is useless

    Everyone can see you can’t find a mistake in a proof that says you’re wrong. And I and Kairosfocs have told you how it is used and is fundamental in mathematics. You just deny, deny, deny.

  298. 298
    ET says:

    My example of two different counters refutes the notion that all countably infinite sets have the same cardinality. And all anyone can do is demonstrate they do not understand infinity.

    I know JVL doesn’t understand infinity. KF thinks that a set with infinite elements can be handed in all at once- hint, it cannot.

    So perhaps we need to start with the concept of infinity…

  299. 299
    ET says:

    Earth to JVL- how many times do I have to explain the proof to you? Why do you think that your willful ignorance is an argument? And why do you think you can use the very thing being debated to try to settle the debate? Are you really that daft?

  300. 300
    ET says:

    JVL:

    And I and Kairosfocs have told you how it is used and is fundamental in mathematics.

    No, he did no such thing. Clearly you are just a desperate fool.

  301. 301
    ET says:

    Again: Let A = {1,2,3,4,5,…}; Let B = {2,4,6,8,10,…}; Let C = {1,3,5,7,9,…}

    A – B = C. If A and B had the same cardinality A – B would = {}

  302. 302
    Retired Physicist says:

    So, ET, you have contacted zero mathematicians to tell them about your amazing breakthrough. And there are intelligent design leaning mathematicians like Edward Grandville Sewell that we can talk to.

    What does Dr. Sewell think of your math?

  303. 303
    daveS says:

    ET,

    I’m late to the party, so you might have already answered this question. Given two _arbitrary_ sets A and B (not necessarily integers or what have you), how do you decide whether they are equinumerous? (that is, whether they have the same cardinality).

    Of course you can make sense of statements such as “{2, 4, 6, …} is half the size of {1, 2, 3, …}”, and that’s sometimes useful, but I think the others are talking about the absolute “sizes” of arbitrary sets where B may not be a subset of A and vice-versa.

  304. 304
    ET says:

    Hi DaveS- A system would have a standard that everything is relative to.

  305. 305
    ET says:

    Earth to RP, what part of “it’s a useless concept” are you too dim to understand?

  306. 306
    JVL says:

    ET: Earth to JVL- how many times do I have to explain the proof to you? Why do you think that your willful ignorance is an argument? And why do you think you can use the very thing being debated to try to settle the debate? Are you really that daft?

    Hey, I’m not the one that denies well over a century of well established and used mathematics. For those who haven’t seen the proof:

    Let A = {1, 2, 3, 4, . . . . } Let B = {2, 4, 6, 8 ,. . . . }

    Match the first element of A with the first element of B: 1 (in A) 2 (in B)
    Match the second element of A with the second element of B: 2 (in A) 4 (in B)
    Match the third element of A with the third element of B: 3 (in A) 6 (in B)
    And so on.

    Every element of A has a match with one and only one element of B. Every element of B has a match with one and only one element of A. You tell me an element of A and I can tell you what element of B it’s matched with. You tell me an element of B and I can tell you what element of A it’s matched with. It’s called a one-to-one correspondence.

    No element of either set is unmatched. They only way two sets can have complete one-to-one correspondence is if they have the same number of elements. Sets A and B are clearly infinite and we’ve just seen that they are the same size. Any infinite set that can be put into a one-to-one correspondence with A (the set of positive integers is said to be countably infinite with cardinality aleph-nought.

    Everyone on the planet except ET accepts this as proof sets A and B (and C) are countably infinite with cardinality aleph-nought. It can also be shown that the rational numbers are likewise countably infinite. But not the reals. The reals cannot be put into a one-to-one correspondence with the positive integers (set A).

    IF ET is right and Set A and set B are NOT the same size then he should be able to find at least one element in either set that doesn’t have a match in the other set. But he can’t find such an element. Thats’ why his ‘set subtraction’ doesn’t work. It’s not consistent with the rest of set theory.

  307. 307
    ET says:

    LoL! @ JVL:

    Hey, I’m not the one that denies well over a century of well established and used mathematics.

    If it isn’t used it isn’t established. Cantor is not infallible. Ser subtraction works. Your cowardice doesn’t change that.

    With set subtraction I found infinite unmatched elements. You lose.

  308. 308
    ET says:

    And most people would agree with me. Only the people who think they are math experts disagree.

  309. 309
    JVL says:

    DaveS: I’m late to the party, so you might have already answered this question. Given two _arbitrary_ sets A and B (not necessarily integers or what have you), how do you decide whether they are equinumerous? (that is, whether they have the same cardinality).

    Technically speaking: they are the same size if their elements can be matched up one-to-one. But think ot it like counting. When you’re trying to see how big a set of things is you count them. That’s putting the elements of the set into a one-to-one correspondence with a subset of the positive integers.

    1 the first element of the set
    2 the second element of the set
    3 the third element of the set
    And so on.

    When you run out of elements of the mystery set you know how many elements it has because the last elements is matched with your count.

    When working with infinite sets you have to be more careful to make sure your matching is tight with nothing left out before deciding if the sets have the same size.

    Of course you can make sense of statements such as “{2, 4, 6, …} is half the size of {1, 2, 3, …}”, and that’s sometimes useful, but I think the others are talking about the absolute “sizes” of arbitrary sets where B may not be a subset of A and vice-versa.

    Yes. Another reason ET;s ‘set subtraction’ doesn’t work is because he can’t compare the sizes of sets B and C. In fact, he can’t compare lots of sets. His ‘method’ only works for two sets where one is a subset of the other. But how does that work when comparing the positive integers with the polynomials with rational coefficients? You can’t ‘subtract’ one set from another. So you have to use element matching to see if those two sets are the same size.

    Like I said, well established and well used mathematics. You couldn’t do power series without it.

  310. 310
    ET says:

    Two counters- A and B. Counter A counts every second. Counter B counts every other second. Both counters start at the same time. Counter A will ALWAYS AND FOREVER have more counts, ie elements, than counter B. At EVERY finite point in time- meaning for infinity. Counter B will NEVER equal counter A.

    Now watch as JVL bastardizes the English language or just ignores it

  311. 311
    JVL says:

    ET: With set subtraction I found infinite unmatched elements. You lose.

    Using your set A and B and my matching tell me an element of either set with is unmatched. Support your claim.

  312. 312
    JVL says:

    ET: Now watch as JVL bastardizes the English language or just ignores it

    You can’t find an unmatched element of set A or B using my matching. That means the sets are the same size. They have to be.

    It’s not a counter or a time thing. It’s just a question of lining up both sets to see if they match up, one-to-one all the way down the line.

  313. 313
    JVL says:

    ET: And most people would agree with me. Only the people who think they are math experts disagree.

    Most people don’t understand the mathematics. I’m not an expert but I know basic axiomatic set theory. This stuff is in chapter one of any real set theory book. Go check it out. Look it up on Wikipedia. It’s everywhere and easy to find.

  314. 314
    ET says:

    As predicted, JVL ignores the refuting post. How typical and cowardly of you, JVL.

    Why would I use JVL’s matching when it is then very thing that I am disputing? How much of a desperate fool are you JVL?

  315. 315
    ET says:

    Again, I know what set theory says. And I also know that I am well within my rights to dispute it. Especially since I can refute it. Just because JVL can ignore my refutations just makes my case.

  316. 316
    ET says:

    Two counters- A and B. Counter A counts every second. Counter B counts every other second. Both counters start at the same time. Counter A will ALWAYS AND FOREVER have more counts, ie elements, than counter B. At EVERY finite point in time- meaning for infinity. Counter B will NEVER equal counter A.

    Cantor did not understand relativity. Cantor was not infallible.

  317. 317
    JVL says:

    ET will not be able to find an unmatched element of set A or B using my matching no matter what he says. But he won’t back down or admit he’s in disagreement with any mathematician you ask.

    Anyone can check this stuff out by going to your local University library and looking at a book on set theory. A proper, university textbook not some primary school thing. Or you can read all about it on Wikipedia. It’s easy to find and see.

    For those who have taken Calculus you might recall doing Taylor and MacLaurin power series. Remember how you had to match the index with the coefficients and come up with a formula? You were setting up a one-to-one correspondence with the positive integers. And any electrical or acoustical will tell you that power series are incredibly pervasive.

    This is all well established, well used and absolutely non-controversial mathematics. When Cantor first starting mucking about with such things lots of people did think he was a bit wrong in the head. But not any more. Now he is lauded as on of the seminal mathematicians of all time.

    And ET can’t find an unmatched element or an error in any proof done by Cantor or anyone else working in this area.

  318. 318
    daveS says:

    ET,

    Hi DaveS- A system would have a standard that everything is relative to.

    Then I think you’re talking about something very different from JVL, KF, RP, etc.

    Do you agree that it’s reasonable to say that {1, 2, 3, …} and {10, 20, 30, …} have the “same number of elements” in _some_ sense? Those two sets obviously have a striking similarity. You could obtain the second set by simply adding a “0” each element of the first set. And this trivial alteration of symbols should not change the total number of elements involved.

    Similarly, {a, aa, aaa, …} and {xxx, xxxx, xxxxx, …} also have the same number of elements according to the same reasoning.

  319. 319
    ET says:

    Wow, all JVL can do is repeat his oft-refuted trope.

  320. 320
    JVL says:

    Why would I use JVL’s matching when it is then very thing that I am disputing? How much of a desperate fool are you JVL?

    You can dispute it by finding an element of either set that is unmatched. Can you find such an element, yes or no?

    Again, I know what set theory says. And I also know that I am well within my rights to dispute it. Especially since I can refute it. Just because JVL can ignore my refutations just makes my case.

    You always have to righ to look foolish when you can’t support your own claims and methods.

    Again, can you find an unmatched element, yes or no?

    Cantor did not understand relativity. Cantor was not infallible.

    This has nothing to do with relativity.

    Can you find an unmatched element, yes or no?

    Wow, all JVL can do is repeat his oft-refuted trope.

    It’s not my fault you cannot find an unmatched element in my scheme. That means the sets are the same size. QED

    JVL YOU are looking foolish by ignoring my example that refutes you:

    I addressed your example by saying this has nothing to do with time or counters running at different speeds.

    Can you find an unmatched element, yes or no? You said you found some, let’s see them.

    Your ignorance is not an argument.

    This has nothing to do with relativity. This has to do with set theory. And proving that two sets have the same number of elements which I have done. And you can’t find a mistake in my proof. You can’t find an unmatched element. But you continue to whine and moan and declare you are right.

    Keep digging your hole deeper and deeper if you so choose. But don’t blame others because you look a fool.

    Two counters- A and B. Counter A counts every second. Counter B counts every other second. Both counters start at the same time. Counter A will ALWAYS AND FOREVER have more counts, ie elements, than counter B. At EVERY finite point in time- meaning for infinity. Counter B will NEVER equal counter A.

    This has nothing to do with how fast something is happening, the time something happens or any of that stuff. This has to do with taking two sets and lining them up one-to-one. Which I have done.

  321. 321
    ET says:

    Yes, daves, I know I am talking about something different. Look @ my example in 316.

  322. 322
    ET says:

    JVL YOU are looking foolish by ignoring my example that refutes you:

    Two counters- A and B. Counter A counts every second. Counter B counts every other second. Both counters start at the same time. Counter A will ALWAYS AND FOREVER have more counts, ie elements, than counter B. At EVERY finite point in time- meaning for infinity. Counter B will NEVER equal counter A.

    You lose

  323. 323
    ET says:

    JVL:

    This has nothing to do with relativity.

    Your ignorance is not an argument.

  324. 324
    JVL says:

    DaveS: Do you agree that it’s reasonable to say that {1, 2, 3, …} and {10, 20, 30, …} have the “same number of elements” in _some_ sense? Those two sets obviously have a striking similarity. You could obtain the second set by simply adding a “0” each element of the first set. And this trivial alteration of symbols should not change the total number of symbols involved.

    That is correct. DaveS gets it. ET just denies, denies, denies.

  325. 325
    ET says:

    daves:

    Do you agree that it’s reasonable to say that {1, 2, 3, …} and {10, 20, 30, …} have the “same number of elements” in _some_ sense? Those two sets obviously have a striking similarity.

    And set subtraction demonstrates the differences.

  326. 326
    daveS says:

    ET,

    It would then seem that there isn’t so much a disagreement here, but rather that the interlocutors are talking past each other?

  327. 327
    ET says:

    JVL, why do you think your ignorance and cowardice mean something? Why can’t you nor anyone else show us how the concept of all countably infinite sets have the same cardinality is used?

  328. 328
    ET says:

    Yes, daves. That JVL ignores what I post and prattles on, is evidence of that.

  329. 329
    daveS says:

    ET,

    I will say that when people talk about “cardinality” of sets, they always understand it in the way JVL explained.

    Your concept of the two “counters” makes sense, but people don’t use the term “cardinality” in connection with it.

    Therefore your usage is non-standard.

  330. 330
    JVL says:

    ET: JVL, why do you think your ignorance and cowardice mean something? Why can’t you nor anyone else show us how the concept of all countably infinite sets have the same cardinality is used?

    I and Kairosfocus have told you that it’s fundamental to the foundations of set theory and therefore modern mathematics. But you ignore that.

    I mentioned, in passing, that it underlies and puts on a firm foundation the ability to work with infinite series including power series which lead on to Laplace transforms and Fourier transforms. But you dill deny that as well no doubt.

    And, finally, it doesn’t matter if it’s used or not. It’s still true. You don’t get to say it’s rubbish just because you don’t know how it’s used.

    Does any use Fermat’s last theorem? Or the Four Colour theorem? No one used Topology for quite a while until physics caught up. Lots and lots of Number Theory is pure mathematics with no real world applications whatsoever.

    You can’t find an unmatched element in my matching between sets A and B. Therefore they must have the same number of elements. It doesn’t matter how fast you count them or any of that. All that matters when you’re talking about size is how many elements there are. Your example is not pertinent. But you cry and whine that I haven’t addressed it. How many times do you have to have it explained?

    Deny, deny, deny. You can’t be wrong so everyone else, over a century of mathematicians, textbooks, papers, etc got it wrong. But you got it right. Uh huh.

  331. 331
    JVL says:

    DaveS: I will say that when people talk about “cardinality” of sets, they always understand it in the way JVL explained.

    Your concept of the two “counters” makes sense, but people don’t use the term “cardinality” in connection with it.

    Therefore your usage is non-standard.

    See, DaveS gets it. Didn’t take long either. Not years and years like ET.

  332. 332
    ET says:

    Yes, daves, I know my usage is non-standard. I never said that it wasn’t. Both my counter example and set subtraction support my point of view. All anyone else can do is repeat the very thing that I am disputing. “People” don’t use cardinality at all. Go out on the street and take a poll.

  333. 333
    ET says:

    JVL:

    I and Kairosfocus have told you that it’s fundamental to the foundations of set theory and therefore modern mathematics.

    Your words are HOLLOW and meaningless.

    I mentioned, in passing, that it underlies and puts on a firm foundation the ability to work with infinite series including power series which lead on to Laplace transforms and Fourier transforms.

    And you are full of it.

    That JVL has to ignore my counter example says it all, really.

  334. 334
    daveS says:

    ET,

    Then why not state your point using standard vocabulary? That would help others to understand it.

  335. 335
    JVL says:

    ET: All anyone else can do is repeat the very thing that I am disputing.

    In mathematics people ‘dispute’ things by finding mistakes not just stomping their feet and claiming they’re right. Can you find a mistake? Can you find an unmatched element? If you can’t then how can sets A and B have different sizes?

    “People” don’t use cardinality at all. Go out on the street and take a poll.

    You don’t use it so it’s not true? How does that follow?

    Your words are HOLLOW and meaningless.

    So you whine and complain that no one has explained to you how the concepts are used and then when someone explains it to you you deny what’s been said?

    And you are full of it.

    It’s not my fault you don’t understand the applications within mathematics.

    That JVL has to ignore my counter example says it all, really.

    I didn’t ignore it. I told you determine the size of sets has NOTHING to do with counters clicking at different speeds. That’s stupid. It has to do with seeing if two sets can be put into a one-to-one correspondence. But you’ll claim I ignored it again because you can not admit you can’t find an unmatched element in set A or B in my matching EVEN THOUGH you said you had found loads. Can’t name one though can you?

    Use your set subtraction to compare the cardinalities of the positive integers and the polynomials with rational coefficients. What, you can’t do that. Gosh, I guess ‘set subtraction’ is pretty useless isn’t it. I wonder if anyone actually uses it when comparing sets that are infinite and where one is not a subset of the other . . .. gosh, nope, they don’t!! I guess it doesn’t work. What a shame.

  336. 336
    ET says:

    daves- I have beaten this to death. My point is that there are different densities of infinity with respect to a set’s elements. Set subtraction and the counter example demonstrate this. Different densities is the very reason why Cantor said there are different infinities- one for the countably infinite and one for the non countably infinite.

    There are and have been objections to Cantor’s axiom of infinity: https://en.wikipedia.org/wiki/Controversy_over_Cantor%27s_theory

  337. 337
    ET says:

    JVL:

    In mathematics people ‘dispute’ things by finding mistakes not just stomping their feet and claiming they’re right.

    And yet all YOU do is stomp your feet and claim that you are right.

  338. 338
    ET says:

    JVL:

    I told you determine the size of sets has NOTHING to do with counters clicking at different speeds.

    That is just stupid. As I said, you do not understand infinity.

  339. 339
    ET says:

    Jvl:

    So you whine and complain that no one has explained to you how the concepts are used and then when someone explains it to you you deny what’s been said?

    You did NOT explain anything. You just spewed gibberish.

  340. 340
    JVL says:

    ET: And yet all YOU do is stomp your feet and claim that you are right.

    Still can’t find a mistake or an unmatched element in set A or B can you? And too afraid to admit it.

    My point is that there are different densities of infinity with respect to a set’s elements.

    Great, compare the ‘densities’ of the positive integers and the positive primes and show us how it works.

    Set subtraction and the counter example demonstrate this. Different densities is the very reason why Cantor said there are different infinities- one for the countably infinite and one for the non countably infinite.

    There’s a lot more than two! Which is also easy to find.

    ET has been shown the proof that the cardinality of the reals is NOT the same as the cardinality of the counting numbers. That proof takes off from the proof that the rational numbers DO have the same cardinality of the counting numbers (aleph-nought). ET has also been shown a proof that any infinite subset of a countably infinite set is also countably infinite. And he cannont find a mistake in that proof or any proof.

    He can ‘dispute’ all he wants. But if he can’t find a mistake then the proofs stand. That’s how it works.

    There are and have been objections to Cantor’s axiom of infinity:

    Go on, explain what the objection are, in your own words.

    And yet all YOU do is stomp your feet and claim that you are right.

    I am right. I’ve demonstrated it over and over again. I’ve shown you the proofs. You cannot find a mistake in any of the proofs AND, more pertinently, you cannot find an unmatched element of set A or B. But you won’t admit that you can’t find an unmatched elements so you keep trying to deflect attention away from that question.

    So, again, can you find an unmatched element in set A or B in my matching scheme? Yes or no?

    That is just stupid. As I said, you do not understand infinity.

    Everyone else agrees with me.

    You did NOT explain anything. You just spewed gibberish.

    If you think I’ve ‘spewed gibberish’ then you have demonstrated that you don’t understand the mathematics.

    Keep digging the hole you’re standing in. It’s very amusing. I suspect there are some people laughing at you as we speak.

  341. 341
    kairosfocus says:

    ET, I note that the key problem in every case has been the structural importance of the ellipsis. Countable endlessness has cardinality aleph null, which is a degree of transfiniteness, not the same as 5 or 3. I am sure x –> 2*x –> 2x is uncontroversial, so take N:

    {0,1,2 . . .}

    x*2 for all elements:

    {0,2,4 . . .}.

    These two sets have the same cardinality

    now do 2*x +1:

    {1,3,5 . . .}

    Again, the same cardinality.

    The property/structure of endless continuation makes the key difference from a finite chain.

    In effect, thanks to never running out on the series, the evens and the odds are transmuted forms of N.

    Similarly, and relevant to earlier debates strike off k elements:

    {k,k+1,k+2 . . .}

    is again a transmuted form, shifted right to k on, take away k from each element and we have {0,1,2 . . .}

    And more.

    From this, we see that the properties are inherent.

    This is why one definition of a transfinite set is that a proper subset can be placed in full correspondence with it.

    KF

    PS, you can construct an abstract, logic model world on different premises but where it goes is a problem, and whether it is as useful is another.

  342. 342
    daveS says:

    ET,

    If you clarify that you are talking about densities, and not claiming that {1, 2, 3,…} and {2, 4, 6, …} have different cardinalities, then everything would be fine.

  343. 343
    JVL says:

    Kairosfocus: Countable endlessness has cardinality aleph null, which is a degree of transfiniteness, not the same as 5 or 3. I am sure x –> 2*x –> 2x is uncontroversial, so take N:

    {0,1,2 . . .}

    x*2 for all elements:

    {0,2,4 . . .}.

    These two sets have the same cardinality

    now do 2*x +1:

    {1,3,5 . . .}

    Again, the same cardinality.

    Yup, yup. Thank you.

    This is why one definition of a transfinite set is that a proper subset can be placed in full correspondence with it.

    See, Kairosfocus gets it.

  344. 344
    JVL says:

    DaveS: If you clarify that you are talking about densities, and not claiming that {1, 2, 3,…} and {2, 4, 6, …} have different cardinalities, then everything would be fine.

    In fact, there is a way to handle the ‘densities’ of infinite sets. But I’m afraid the math is beyond ET‘s capabilities.

  345. 345
    ET says:

    Again, set subtraction proves there is something wrong with then INFERENCE from Cantor’s proof. That JVL cannot grasp that is on him, not me.

  346. 346
    ET says:

    Nothing in what KF said has anything to do with using the concept that all countably infinite sets have the same cardinality. He is just repeating Cantor

  347. 347
    ET says:

    daves:

    If you clarify that you are talking about densities, and not claiming that {1, 2, 3,…} and {2, 4, 6, …} have different cardinalities, then everything would be fine.

    They are the same thing. Set subtraction demonstrates there is a difference in the number of elements, ie cardinality.

  348. 348
    ET says:

    JVL:

    There’s a lot more than two!

    I know. I was just providing an example. But clearly that, too, is over your head

    ET has been shown the proof that the cardinality of the reals is NOT the same as the cardinality of the counting numbers.

    Yes, I was shown that decades ago. And I understand it. It is the very basis of my claim.

    No one can show us anyone using the concept for anything. No one can present an example of how to use the concept that all countably infinite sets have the same cardinality. No one

  349. 349
    ET says:

    JVL, if you really want to make this personal I suggest meeting me and getting it over with. YOU are NO ONE to challenge me. YOU have proven to be ignorant of logic and reasoning.

    So stuff it

  350. 350
    ET says:

    If someone wants to believe that one set (A) has ALL of the elements in another set (B), PLUS set A has infinite elements B does NOT have, yet they have the same cardinality, ie the same number of elements, I don’t care. Just don’t try to get me to drink your BS.

  351. 351
    JVL says:

    ET: Again, set subtraction proves there is something wrong with then INFERENCE from Cantor’s proof. That JVL cannot grasp that is on him, not me.

    You’ve proved nothing and you haven’t been able to find a fault in anyone’s proof or find an unmatched element of set A or B under my scheme.

    Nothing in what KF said has anything to do with using the concept that all countably infinite sets have the same cardinality. He is just repeating Cantor

    Because it’s correct. And you haven’t been able to prove otherwise.

    They are the same thing. Set subtraction demonstrates there is a difference in the number of elements, ie cardinality.

    Nope, as established by proofs you have failed to disprove.

    Yes, I was shown that decades ago. And I understand it. It is the very basis of my claim.

    Not true at all. You don’t even understand what you’ve claimed. Too funny.

    No one can show us anyone using the concept for anything. No one can present an example of how to use the concept that all countably infinite sets have the same cardinality. No one

    It has been shown, you just deny, deny, deny. AND the truth of it doesn’t depend on an application. You lose, twice over.

    JVL, if you really want to make this personal I suggest meeting me and getting it over with. YOU are NO ONE to challenge me. YOU have proven to be ignorant of logic and reasoning.

    Ooo, I’m scared now! Physical threats, that’s how you do mathematics. Too funny. You have been shown to be ignorant of well established and used mathematics and you think you can win with fisticuffs? What a buffoon.

    If someone wants to believe that one set (A) has ALL of the elements in another set (B), PLUS set A has infinite elements B does NOT have, yet they have the same cardinality, ie the same number of elements, I don’t care. Just don’t try to get me to drink your BS.

    You’re very welcome to NOT be able to get your head around well established, well used and (mostly) non-controversial mathematics. Knock yourself out.

    AND, let’s say it again:

    You have NOT found a fault with any proof that establishes the results you dispute.

    You have NOT found an unmatched element in either set A or set B under my matching even though you said you had found unmatched elements. I guess that was just bluffing and hoping no one would call you on it.

    Your ideas run counter to what has been published in hundreds, thousands of paper, textbooks, etc over the last century. Kairosfocus agrees with me as well, DaveS got the issue easily. You just can’t admit you have been wrong for several years. And when it’s been shown to you over and over and over again you make physical threats. What a great example of doing mathematics you present.

    Can you find an unmatched element in set A or B? Yes or no?

    Can you find a mistake in any of the proofs that have established the mathematics you dispute? Yes or no?

  352. 352
    daveS says:

    ET,

    They are the same thing. Set subtraction demonstrates there is a difference in the number of elements, ie cardinality.

    You seemed to agree above that they are not the same.

    By one way of reckoning, {10, 20, 30, …} has density 1/10 that of {1, 2, 3, …}, while the operation of adding a zero, which associates 1 to 10, 2 to 20, etc., preserves the number of elements, so that the cardinalities of {1, 2, 3, …} and {10, 20, 30, …} are equal.

    Now you are saying that your “counter” method is the only valid way to do this.

  353. 353
    ET says:

    DaveS- The densities and the cardinality are directly linked. If the cardinalities are equal then set subtraction should verify an validate that claim. It doesn’t.

    The set {1,2,3,4,5,…} has EVERY element in the set {10,20,30,40,50,…} PLUS it has infinitely more elements. If you want to believe that they have the same cardinality, I don’t care. The reason what you believe is counter-intuitive is because it is nonsense

  354. 354
    ET says:

    Earth to JVL- You have no clue. You request that I use my own words to describe something and yet all YOU can do is parrot a dead guy stuck in the 19th century. You are a sick person.

  355. 355
    ET says:

    You’re very welcome to NOT be able to get your head around well established, well used and (mostly) non-controversial mathematics.

    And you are welcome to believe something that is patently false. I will gladly join the over 6 BILLION people who agree with me

  356. 356
    ET says:

    daves:

    Now you are saying that your “counter” method is the only valid way to do this.

    ‘The counter method is just a clear example that demonstrates an inference from Cantor’s proof is incorrect. In mathematics all it takes is ONE example that goes counter to the claim to ruin the claim

  357. 357
    daveS says:

    ET,

    But now you have to swallow some very counterintuitive consequences yourself. Tacking a zero onto the end of each numeral decreases the number of elements by a factor of 10. Also, placing decimal points to the left of each zero, as in 5 -> 50 -> 5.0, increases the number of elements by a factor of 10, and we’re back to where we started. That’s too magical for my tastes.

  358. 358
    ET says:

    What? How is it too magical to end up where you started if your process takes you there? There isn’t anything counterintuitive about ending up where you start if that is the path you take. Tack a zero on and then take it away. Where did you think you would end up? It would be very magical to not end up where you started.

    All I am saying, daves, is the bijective function that maps the one-to-one correspondence becomes the relative cardinality.

  359. 359
    daveS says:

    ET,

    The rest of us are not talking about “relative” cardinality. The cardinality of a set, as we understand it, is absolute. The notion that simply adding a dot to each numeral changes the cardinality of the set is just unacceptable.

  360. 360
    ET says:

    Major Face Palm- come in major face palm.

    The cardinality of a set, as we understand it, is absolute.

    I agree. However, cardinality refers to a number. Infinity isn’t a number, it’s a journey. That is where relativity comes in.

    The notion that simply adding a dot to each numeral changes the cardinality of the set is just unacceptable.

    That “dot” is a decimal point and has meaning in mathematics. It actually does something. The notion that one set has all of the elements contained in another, PLUS elements the other doesn’t, and still have the same number of elements, is lunacy. And lunacy is unacceptable.

    But that is moot as you think it’s magical to add a zero, take it away and end up where you started. That is unacceptable.

  361. 361
    daveS says:

    Infinity isn’t a number, it’s a journey. That is where relativity comes in.

    🤦

    Edit: The number we are presently discussing is ℵ0.

  362. 362
    asauber says:

    ET is right.

    Infinity is not a number. Its an absurdity.

    Andrew

  363. 363
    JVL says:

    ET: Earth to JVL- You have no clue. You request that I use my own words to describe something and yet all YOU can do is parrot a dead guy stuck in the 19th century. You are a sick person.

    It doesn’t matter to me if you can’t explain something you support. It doesn’t matter to me if you can’t find an unmatched element in sets A or B under my matching. It’ doesn’t matter to me if you can’t find a mistake in the proofs of theorems which contradict your statements.

    And you are welcome to believe something that is patently false. I will gladly join the over 6 BILLION people who agree with me

    Welcome to the losers’ club.

    ‘The counter method is just a clear example that demonstrates an inference from Cantor’s proof is incorrect. In mathematics all it takes is ONE example that goes counter to the claim to ruin the claim

    But you haven’t found the counter example because you THINK the rate at which the counters tick means something. It doesn’t. That is not the issue.

    What? How is it too magical to end up where you started if your process takes you there? There isn’t anything counterintuitive about ending up where you start if that is the path you take. Tack a zero on and then take it away. Where did you think you would end up? It would be very magical to not end up where you started.

    Pure gibberish.

    All I am saying, daves, is the bijective function that maps the one-to-one correspondence becomes the relative cardinality.

    What’s the relative cardinality of the prime numbers then? Go on tell us.

    That “dot” is a decimal point and has meaning in mathematics. It actually does something. The notion that one set has all of the elements contained in another, PLUS elements the other doesn’t, and still have the same number of elements, is lunacy. And lunacy is unacceptable.

    Speaking of lunacy.

    Let’s recap:

    You haven’t been able to find an unmatched element in sets A or B under my matching.

    You haven’t found a fault in any proof supporting the accepted mathematics.

    You cannot specify the ‘relative’ cardinality of the prime numbers.

    Have I forgotten something?

  364. 364
    ET says:

    That isn’t a number, daves. It’s a contrivance.

  365. 365
    JVL says:

    Asauber: ET is right.

    Infinity is not a number. Its an absurdity.

    Welcome to the mathematics deniers’ club.

  366. 366
    asauber says:

    “Welcome to the mathematics deniers’ club.”

    JVL,

    Hey, I think rearranging symbols is very, very real.

    Andrew

  367. 367
    ET says:

    I am claiming that your “matching” is bogus. I have explained ad nauseum why your “matching” is bogus. That you still refuse to grasp that says it all.

    And no, I will never be a member of your club, loser.

  368. 368
    JVL says:

    Asauber: Hey, I think rearranging symbols is very, very real.

    As long as you don’t expect anyone to take you seriously.

  369. 369
    ET says:

    What? How is it too magical to end up where you started if your process takes you there? There isn’t anything counterintuitive about ending up where you start if that is the path you take. Tack a zero on and then take it away. Where did you think you would end up? It would be very magical to not end up where you started.

    JVL:

    Pure gibberish.

    Only to an imbecile.

  370. 370
    asauber says:

    “As long as you don’t expect anyone to take you seriously.”

    JVL,

    I don’t take you seriously, either, so we are even steven.

    Andrew

  371. 371
    JVL says:

    ET: I am claiming that your “matching” is bogus. I have explained ad nauseum why your “matching” is bogus. That you still refuse to grasp that says it all.

    It’s not ‘bogus’. It works. It does what it claims. It contradicts your assertions and claims. Let’s recap, again:

    You claimed to have found lots of unmatched elements under my matching between sets A and B but you haven’t specified a single unmatched element.

    You haven’t found a single fault in any proof of any mathematical theorem. At all.

    You proposed the idea of ‘relative cardinality’ but you cannot specify the relative cardinality of the primes.

  372. 372
    JVL says:

    ET: What? How is it too magical to end up where you started if your process takes you there? There isn’t anything counterintuitive about ending up where you start if that is the path you take. Tack a zero on and then take it away. Where did you think you would end up? It would be very magical to not end up where you started.

    More gibberish. And, it doesn’t address the issues on the table:

    What is the relative cardinality of the primes?

    Can you find a fault in any of the mathematical proofs which contradict your claims?

    Can you find an unmatched element in sets A or B under my matching scheme?

  373. 373
    bornagain77 says:

    As to infinity in mathematics, Gödel’s incompleteness theorems were ultimately a cumulation of the work of Georg Cantor in trying to bring a systematic understanding of infinity into mathematics. In short, Georg Cantor was trying to ‘tame infinity’ so as to make it mathematically useful.

    Dangerous Knowledge (part 1 of 5) – video
    https://vimeo.com/122917065

    As the beginning of the preceding video made clear, this endeavor by Cantor to ‘tame infinity’ was very much a theological quest for Cantor.

    GEORG CANTOR – His Mathematics and Philosophy of the Infinite – Joseph Warren Dauben
    Excerpt: It is also significant that Cantor believed in the absolute truth of his set theory because it had been revealed to him. Thus he may have seen himself not only as God’s messenger, accurately recording, reporting, and transmitting the newly revealed theory of the transfinite numbers but as God’s ambassador as well.
    https://math.dartmouth.edu/~matc/Readers/HowManyAngels/Cantor/Cantor.html

    In fact, in the following article Cantor is quoted as saying that, “From me Christian philosophy will be offered for the first time the true theory of the infinite.”

    God and Mathematical Infinity – Brendan Kneale
    Excerpt: What came from analyzing these difficulties was the key distinction between potential and actual infinity. The counting numbers are readily seen to be potentially infinite in the sense that no matter how large an integer you name, there is a larger one. It is not so clear that, taken as a whole, the set of integers is actually infinite.,,,
    These kinds of reasoning about infinite sets, we know today, can be carried out with logical consistency, though it requires us to take great care not to confuse our intuitions about the finite with the counterintuitive rules about the infinite. I believe such analytical efforts to be salutary exercises for all people interested in the philosophy or theology of the Infinite. Mathematicians learn to treat the actually infinite with great respect, a respect that seems to me readily transferable to a reverence for God.,,,
    Cantor, in particular, felt that his work had theological value. He is quoted as writing in 1896, “From me Christian philosophy will be offered for the first time the true theory of the infinite.” He got in touch with prominent theologians in order to be of service to them in this matter.
    Of course, his work provoked vigorous opposition.,,,
    Today, the opponents of Cantor and Dedekind are very few. The rigor and care with which infinite or “transcendental” numbers are treated have persuaded almost everyone that they constitute proper objects of study. Graduate students are routinely taught Cantor and Dedekind’s methods and results. Paradoxes and antinomies are taken seriously and are handled with appropriate definitions and axioms.,,,
    The least that can be said is that the infinity of the mathematicians supplies us with a useful metaphor: many of the assertions we make about God and about a mathematical infinity are similar.,,,
    Another insight is that the infinity of God requires the divinity of Christ, since the only possible atonement for sins committed against the Infinite is by way of an infinite redeemer.,,,
    https://www.asa3.org/ASA/PSCF/1998/PSCF3-98Kneale.html

    As the preceding video also touched upon, Cantor ultimately failed in his endeavor to ‘tame infinity’. In fact, the preceding video is also not too subtle in its hint that Cantor’s mental illness in his later life was directly associated with his endeavor to try to ‘tame infinity’.

    As the following article states, “Cantor spent the last thirty-five years of his life in a vain effort to prove this., (i.e. that all the possible orders of infinity could be counted,), He died in 1918 in a mental hospital.”

    The God of the Mathematicians – by David P. Goldman – 2010
    The religious beliefs that guided Kurt Gödel’s revolutionary ideas
    Excerpt: That is Cantor’s “continuum hypothesis,” which attempts to identify a first and second transfinite cardinal number. From there, he believed, all the possible orders of infinity could be counted, the same way the integers count groups of one, two, three, and so forth. He not only recognized, but was driven by, the ontological implications of this assertion: If the continuum hypothesis turned out to be true, Spinoza would be vindicated because God’s infinity could be packaged into a neat series of numbers. Cantor spent the last thirty-five years of his life in a vain effort to prove this. He died in 1918 in a mental hospital.
    It was Gödel and, later, Paul Cohen who demonstrated respectively that Cantor’s continuum hypothesis could be neither proved nor disproved within existing set theory. Indeed, Cantor’s hypothesis remains maddeningly undecidable.,,,
    God’s infinitude remains safe in heaven. Mathematicians have proven that an infinite number of transfinite numbers exist but cannot tell what they are or in what order they should be arranged.
    https://www.firstthings.com/article/2010/08/the-god-of-the-mathematicians

    And although Cantor failed to in his effort to completely ‘tame infinity’, none-the-less, he developed some very useful tools in mathematics which later proved to be very useful to Gödel in his work on bringing incompleteness to fruition,,

    Naming and Diagonalization, from Cantor to Gödel to Kleene – 2006
    Excerpt: The first part of the paper is a historical reconstruction of the way Godel probably derived his proof from Cantor’s diagonalization, through the semantic version of Richard. The incompleteness proof-including the fixed point construction-result from a natural line of thought, thereby dispelling the appearance of a “magic trick”. The analysis goes on to show how Kleene’s recursion theorem is obtained along the same lines.
    https://www.researchgate.net/publication/220245183_Naming_and_Diagonalization_from_Cantor_to_Godel_to_Kleene

    Cantor would have been very pleased with Gödel’s results. As to following article states, “Gödel demonstrated that mathematics was intrinsically incomplete. Gödel was reportedly concerned that he might have inadvertently proved the existence of God, a faux pas in his Viennese and Princeton circle.”

    “In an elegant mathematical proof, introduced to the world by the great mathematician and computer scientist John von Neumann in September 1930, Gödel demonstrated that mathematics was intrinsically incomplete. Gödel was reportedly concerned that he might have inadvertently proved the existence of God, a faux pas in his Viennese and Princeton circle. It was one of the famously paranoid Gödel’s more reasonable fears.”
    George Gilder, in Knowledge and Power : The Information Theory of Capitalism and How it is Revolutionizing our World (2013), Ch. 10: Romer’s Recipes and Their Limits

    Indeed Cantor would be very pleased with Gödel’s work. The Theistic, even Christian, implications of incompleteness are obvious,,,, as mentioned previously in this thread in these following articles,,,

    Taking God Out of the Equation – Biblical Worldview – by Ron Tagliapietra – January 1, 2012
    Excerpt: Kurt Gödel (1906–1978) proved that no logical systems (if they include the counting numbers) can have all three of the following properties.
    1. Validity … all conclusions are reached by valid reasoning.
    2. Consistency … no conclusions contradict any other conclusions.
    3. Completeness … all statements made in the system are either true or false.
    The details filled a book, but the basic concept was simple and elegant. He (Godel) summed it up this way: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove.” For this reason, his proof is also called the Incompleteness Theorem.
    Kurt Gödel had dropped a bomb on the foundations of mathematics. Math could not play the role of God as infinite and autonomous. It was shocking, though, that logic could prove that mathematics could not be its own ultimate foundation.
    Christians should not have been surprised. The first two conditions are true about math: it is valid and consistent. But only God fulfills the third condition. Only He is complete and therefore self-dependent (autonomous). God alone is “all in all” (1 Corinthians 15:28), “the beginning and the end” (Revelation 22:13). God is the ultimate authority (Hebrews 6:13), and in Christ are hidden all the treasures of wisdom and knowledge (Colossians 2:3).
    http://www.answersingenesis.or.....1/equation

    A BIBLICAL VIEW OF MATHEMATICS
    Vern Poythress – Doctorate in theology, PhD in Mathematics (Harvard)
    15. Implications of Gödel’s proof
    B. Metaphysical problems of anti-theistic mathematics: unity and plurality
    Excerpt: Because of the above difficulties, anti-theistic philosophy of mathematics is condemned to oscillate, much as we have done in our argument, between the poles of a priori knowledge and a posteriori knowledge. Why? It will not acknowledge the true God, wise Creator of both the human mind with its mathematical intuition and the external world with its mathematical properties. In sections 22-23 we shall see how the Biblical view furnishes us with a real solution to the problem of “knowing” that 2 + 2 = 4 and knowing that S is true.
    http://www.frame-poythress.org.....thematics/

    THE GOD OF THE MATHEMATICIANS – DAVID P. GOLDMAN – August 2010
    Excerpt: we cannot construct an ontology that makes God dispensable. Secularists can dismiss this as a mere exercise within predefined rules of the game of mathematical logic, but that is sour grapes, for it was the secular side that hoped to substitute logic for God in the first place. Gödel’s critique of the continuum hypothesis has the same implication as his incompleteness theorems: Mathematics never will create the sort of closed system that sorts reality into neat boxes.
    http://www.firstthings.com/art.....ematicians

    Of supplemental note, Gödel’s work was recently extended to Quantum Physics and “challenge the reductionists’ point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description.” (i.e. the reductive materialism of Darwinian evolution is, via the extension of incompleteness to quantum physics, proven to be false!)

    Quantum physics problem proved unsolvable: Gödel and Turing enter quantum physics – December 9, 2015
    Excerpt: A mathematical problem underlying fundamental questions in particle and quantum physics is provably unsolvable,,,
    It is the first major problem in physics for which such a fundamental limitation could be proven. The findings are important because they show that even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behaviour.,,,
    A small spectral gap – the energy needed to transfer an electron from a low-energy state to an excited state – is the central property of semiconductors. In a similar way, the spectral gap plays an important role for many other materials.,,,
    Using sophisticated mathematics, the authors proved that, even with a complete microscopic description of a quantum material, determining whether it has a spectral gap is, in fact, an undecidable question.,,,
    “We knew about the possibility of problems that are undecidable in principle since the works of Turing and Gödel in the 1930s,” added Co-author Professor Michael Wolf from Technical University of Munich. “So far, however, this only concerned the very abstract corners of theoretical computer science and mathematical logic. No one had seriously contemplated this as a possibility right in the heart of theoretical physics before. But our results change this picture. From a more philosophical perspective, they also challenge the reductionists’ point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description.”
    per physorg

    Also of supplemental note, Kurt Gödel, like Cantor, was also an adamant Christian. Specifically, a ‘baptized Lutheran’. Moreover, Gödel was convinced that there must be an afterlife by pure reasoning, A belief in the afterlife that he said was derived independently of any theology.

    Kurt Gödel
    Religious views
    Gödel was a convinced theist, in the Christian tradition.[28] He held the notion that God was personal.
    He believed firmly in an afterlife, stating: “Of course this supposes that there are many relationships which today’s science and received wisdom haven’t any inkling of. But I am convinced of this [the afterlife], independently of any theology.” It is “possible today to perceive, by pure reasoning” that it “is entirely consistent with known facts.” “If the world is rationally constructed and has meaning, then there must be such a thing [as an afterlife].”[29]
    In an unmailed answer to a questionnaire, Gödel described his religion as “baptized Lutheran (but not member of any religious congregation). My belief is theistic, not pantheistic, following Leibniz rather than Spinoza.”[30],,,
    According to his wife Adele, “Gödel, although he did not go to church, was religious and read the Bible in bed every Sunday morning”,[32]
    per wikipedia

    “If the world is rationally constructed and has meaning, then there must be such a thing [as an afterlife].”
    Kurt Gödel – Hao Wang, “A Logical Journey: From Gödel to Philosophy”, 1996, pp. 104–105.

  374. 374
    ET says:

    JVL:

    You claimed to have found lots of unmatched elements under my matching between sets A and B but you haven’t specified a single unmatched element.

    Between A and B the set C is unmatched.

    You proposed the idea of ‘relative cardinality’ but you cannot specify the relative cardinality of the primes.

    How much do you want to ante up? It has to be at least $10,000 US.

    Does anyone else think it is impossible to find the relative position of the primes as compared to the naturals? The squares is easy enough. The cubes. The cubes relative to the squares and the naturals. The cubes relative to the primes. The primes relative to the squares.

    It all can be one.

  375. 375
    ET says:

    JVL’s matching is bogus because in the case of the naturals vs the evens, you are forcing a 1 to be “matched” with a 2. The way I call it we have the natural matching. The 2’s match. The 4’s match. And so on. That is the SAME matching used throughout set theory to determine if one set is a subset of another. Or if there is a union between two sets.

    At least with me we get consistency from bottom to the top.

  376. 376
    daveS says:

    ET,

    How much do you want to ante up? It has to be at least $10,000 US.

    I believe this “relative cardinality” of the primes (to {1, 2, 3, …}) has already been computed. It’s available on a number of wikipedia pages (for much less than $10,000).

  377. 377
    ET says:

    Thanks daves. JVL just wants to make this personal. For that I charge $10,000 US.

  378. 378
    JVL says:

    ET: Between A and B the set C is unmatched.

    This is just dumb. We’re not talking about set C at all. Now, if you mean the odd numbers in set A then I showed you how they are matched to elements in set B. I guess I have to show the scheme again because some people just can’t understand it.

    A = {1, 2, 3, 4, 5, 6, 7 . . . . . .} B = {2, 4, 6, 8, 10, 12, 14 . . . . }

    1 (in A) 2 (in B)
    2 (in A) 4 (in B)
    3 (in A) 6 (in B)
    4 (in A) 8 (in B)
    5 (in A) 10 (in B)
    6 (in A) 12 (in B)
    7 (in A) 14 (in B)
    And so on.

    CLEARLY all the elements of A have a partner in B, even and odd numbers.

    How much do you want to ante up? It has to be at least $10,000 US.

    Just do it if you can.

    Does anyone else think it is impossible to find the relative position of the primes as compared to the naturals? The squares is easy enough. The cubes. The cubes relative to the squares and the naturals. The cubes relative to the primes. The primes relative to the squares.

    Do it then. (“relative position of the primes”?)

    It all can be one.

    We’re waiting to see you do it.

    JVL’s matching is bogus because in the case of the naturals vs the evens, you are forcing a 1 to be “matched” with a 2. The way I call it we have the natural matching. The 2’s match. The 4’s match. And so on. That is the SAME matching used throughout set theory to determine if one set is a subset of another. Or if there is a union between two sets.

    We’re not checking to see if one set is a subset of the other! We’re seeing if they’re the same size? And there is no preference or rules on how the matching is done. If you can come up with a scheme and it works then you’re done.

    At least with me we get consistency from bottom to the top.

    And you can’t handle a bunch of cases. What’s the cardinality of the polynomials with rational coefficients? What’s the cardinality of the primes?

    And you still haven’t found any unmatched elements in my scheme between A and B.

  379. 379
    JVL says:

    DaveS: I believe this “relative cardinality” of the primes (to {1, 2, 3, …}) has already been computed. It’s available on a number of wikipedia pages (for much less than $10,000).

    Well, link to it then!

    HInt: the primes have the same cardinality as the positive integers, that being aleph-nought. They are both countably infinite sets. AND there is an easy to find theorem which says any infinite subset of any countably infinite set is also countably infinite, i.e. with cardinality aleph-nought.

    Can I have my $10,000 please as my answer is correct and can be verified on many websites and textbooks. Or just phone up your local mathematics department at a university. I take checks.

  380. 380
    kairosfocus says:

    ET,

    I am not merely blindly quoting (esp. without attribution!), I am showing that once one defines an exhaustive 1:1 mapping between sets P and Q one defines a function . . . and yes this stuff connects to what a function is . . . so one can transform one set into another.

    The key with transfinite sets is that the ellipsis [and things beyond such as continuum] imply inexhaustibility of any case by case process.

    So, we TRANSFORM N into the evens and the odds or even k on continuation thereby showing these have the same scale as N, Aleph null, first order, inexhaustible countability.

    Power sets come in and there is a debate as to pinning c, continuum to a member of that chain. Using ordinals — there we go on how pervasive the influence of this work was — we can get a chain of transfinite integers and can go on to fill in a continuum, in principle. The infinitesimal cloud around 0 — I have represented *0* — can be transferred to any hyper-integer and that then extends to [0,1) and its mirror (-1,0]. Infinitesimally altered numbers are everywhere and are utterly dense. Indeed, there are vastly more densely packed in infinitesimally altered numbers than real numbers, as the transfinite extension of the reals will show.

    That is, we can translate from the intuitive but wrong sense of greater cardinality of sets as a whole to greater densities in sampled intervals. That is the density idea is that some types of numbers are far more common in a given interval than other types. Integers are less dense than reals but more dense than evens or odds or squares etc. But because of inexhaustibility, the cardinalities can be the same, here, first order countable but inexhaustible values.

    Could that be a way forward?

    In which context, we can speak of “subtraction” in set theoretic terms as say, the evens are the complement to the intersection of the naturals and the odds. But this does not do away with countability or inexhaustibility so we can make a 1:1 match betwen naturals and evens, or even transform the naturals into the evens.

    So, we have a counterintuitive but valid result.

    KF

  381. 381
    kairosfocus says:

    AS, infinity is indeed not a number, but a concept, beyond finite bound. Immensus in the Athanasian creed, beyond bounding finite measure. Indeed, in + finite means not finitely bounded. God is infinite, his powers and attributes are maximally great, confined only by the logic of compossibility i.e. they are all so together so are coherent. And God is not absurd. Infinity is not absurd with numbers either, we can properly conceive, construct and represent then manipulate transfinite quantities and structures, then use the 1/x catapult to get infinitesimals and by shifting the cloud around 0 –*0* for convenience — we infinitesimally alter any number. This points to calculus. And ultimately it is the infinitesimals and infinitesimally altered numbers that are the most densely present, indeed, they are the most familiar form of the transfinite at work, from Calculus. Which is always a main goal. Newton’s h, dx, dt, dr and onward extensions are absolutely vital to any number of disciplines, even when disguised under epsilon delta limit approaches. Nonstandard analysis is truly liberating. KF

  382. 382
    kairosfocus says:

    AS, infinity is indeed not a number, but a concept, beyond finite bound. Immensus in the Athanasian creed, beyond bounding finite measure. Indeed, in + finite means not finitely bounded. God is infinite, his powers and attributes are maximally great, confined only by the logic of compossibility i.e. they are all so together so are coherent. And God is not absurd. Infinity is not absurd with numbers either, we can properly conceive, construct and represent then manipulate transfinite quantities and structures, then use the 1/x catapult to get infinitesimals and by shifting the cloud around 0 –*0* for convenience — we infinitesimally alter any number. This points to calculus. And ultimately it is the infinitesimals and infinitesimally altered numbers that are the most densely present, indeed, they are the most familiar form of the transfinite at work, from Calculus. Which is always a main goal. Newton’s h, dx, dt, dr and onward extensions are absolutely vital to any number of disciplines, even when disguised under epsilon delta limit approaches. Nonstandard analysis is truly liberating. KF

    PS: Do not overlook the ubiquity of sequences and series in modern mathematics, which involve running indices, often from N.

  383. 383
    kairosfocus says:

    Weird a double post.

  384. 384
    asauber says:

    KF,

    I respectfully disagree. God is beyond human understanding, other than what He has revealed to us. So Because God doesn’t work to fix infinity. It’s still an absurdity.

    Andrew

  385. 385
    asauber says:

    KF,

    Introducing infinity into ideas like the progression of time causes paradoxes, doesn’t it? Why do you think that is?

    Andrew

  386. 386
    daveS says:

    JVL,

    Sorry, I should have used the standard term, density. I believe that by “relative cardinality” ET means a type of density, and this density of the primes in {1, 2, 3, …} is zero by the Prime Number Theorem. I do agree that the cardinality of the primes is aleph-0.

  387. 387
    JVL says:

    Kairosfocus: Weird a double post.

    You ARE special! Even the website thinks what you have to say is worth repeating!! 🙂

  388. 388
    JVL says:

    DaveS: Sorry, I should have used the standard term, density.

    Ah yes, that is something completely different! And has nothing to do with the size of the sets.

    I believe that by “relative cardinality” ET means a type of density, and this density of the primes in {1, 2, 3, …} is zero by the Prime Number Theorem.

    I agree with that result, obviously ’cause it’s correct. And no, that’s not what ET is thinking. He’s been saying the same thing for years.

    I do agree that the cardinality of the primes is aleph-0.

    DaveS: 2 points.

  389. 389
    ET says:

    KF:

    I am not merely blindly quoting (esp. without attribution!), I am showing that once one defines an exhaustive 1:1 mappin Sorry that’s not mathematicsg between sets P and Q one defines a function . . . and yes this stuff connects to what a function is . . . so one can transform one set into another.

    Wow, transform one set into another- like alchemy or magic? That isn’t mathematics

  390. 390
    ET says:

    Earth to JVL a “1” does NOT match a “2”. A “2” matches a “2”.

    No wonder you are ignorant of science.

  391. 391
    ET says:

    JVL:

    And you can’t handle a bunch of cases.

    YOU can’t because you are too dim to think beyond your own arse. And if you want to make this personal then I suggest we meet and get it over with. How desperate of a coward are you?

  392. 392
    daveS says:

    ET,

    The idea is that these transformations should not affect the cardinality of the set itself. We take this as axiomatic.

    Suppose you have a large jar full of marbles. Take each marble out and draw a dot on it with a Sharpie, and place the “dotted” marbles in a new jar. The total number of marbles does not change.

    Any theory of cardinality where this principle is violated is going to have problems.

    Edit:

    To continue the analogy, suppose you have a large (infinite) jar containing tickets labeled 1, 2, 3, and so on. Remove the tickets one at a time, cross out the original number, and write 2 times the original number minus 1. Then place the renumbered tickets in a new jar.

    Does the number of tickets change? Obviously not.

    Edit 2:

    This is a concrete illustration, and we are really talking about abstract concepts which do not occupy space. Therefore there is nothing stopping us from considering a jar with infinitely many “marbles” or tickets inside.

  393. 393
    ET says:

    Again, cardinality refers to the number of elements. Infinity is not a number, it’s a journey.

    The number of marbles in the jar is finite.

    If you want to believe that one set that has ALL of the elements of another, PLUS infinite elements NOT in the other set but still they both have same number of elements, I don’t care. I am not going to drink that BS. Cantor’s diagonal just proves both sets are countable. That some people take it to mean they also have the same cardinality is their wrong inference.

  394. 394
    ET says:

    Infinity is NOT magic, it’s a journey. That is why the counter example is relevant- it exemplifies the journey. And that is also why relativity is also relevant.- it looks at the journey from a proper perspective.

  395. 395
    daveS says:

    ET,

    Regarding Cantor’s diagonalization argument, it shows that the set of real numbers cannot be put in one-to-one correspondence with {1, 2, 3, …}. Hence the real numbers and {1, 2, 3, …} do not have the same cardinality. I would have assumed you agreed with this because your two-counter method also shows the set of real numbers is much larger than the set of natural numbers.

    PS to my #392: In the ticket/jar illustration, all the renumbered tickets have distinct numbers on them; if there were some “collisions”, then my analogy would break down.

  396. 396
    Retired Physicist says:

    Small technical note here, dx, dt, etc are Leibniz’s notation, not Newton. Newton used apostrophes. f’(x), f’’(x) etc.

  397. 397
    JVL says:

    ET: Earth to JVL a “1” does NOT match a “2”. A “2” matches a “2”. No wonder you are ignorant of science.

    The values or labels of the elements do not matter. If you don’t like those two sets then try these:

    A = {1, 2, 3, 4, 5 . .. . . } and B2 = {-2, -4, -6, -8, -10 . . . . }

    Clearly B and B2 are the same size. And here’s my new matching:

    1 -2
    2 -4
    3 -6
    4 -8
    etc.

    Same result: both sets are the same size, both are countably infinite, both have cardinality aleph-0.

    OU can’t because you are too dim to think beyond your own arse. And if you want to make this personal then I suggest we meet and get it over with. How desperate of a coward are you?

    You can’t handle some cases I have presented to you. You’re childish bully-boy threats are laughable and not the way mathematics is done.

    If you want to believe that one set that has ALL of the elements of another, PLUS infinite elements NOT in the other set but still they both have same number of elements, I don’t care. I am not going to drink that BS. Cantor’s diagonal just proves both sets are countable. That some people take it to mean they also have the same cardinality is their wrong inference.

    There is, in fact, a theorem which proves that any infinite subset of a countably infinite set is also countably infinite with the cardinality aleph-0. You can not find a fault with the proof of that theorem so it stands as truth.

    Infinity is NOT magic, it’s a journey. That is why the counter example is relevant- it exemplifies the journey. And that is also why relativity is also relevant.- it looks at the journey from a proper perspective.

    It’s not magic, the ways to deal with it were elucidated by Cantor and others. Relativity has to do with physics not mathematics.

    All your questions have been considered and answered. You just keep denying the truth.

    You’ve been asked to find some unmatched elements in my scheme for sets A and B, you haven’t been able to do so. You seem to think that only your matching is valid which is clearly not the case if you looked in any university level set theory book or just checked with the tons of online resources that confirm what I am saying. You just keep denying.

    You’ve been asked to apply your method of relative cardinalities to the prime numbers which you have failed to do. You have been asked to apply your method to the set of all polynomials with rational coefficients which you have failed to do. Your method barely works AND every mathematician in the world disagrees with you. But you just keep denying.

    You have been asked over and over and over again to find a fault or mistake in the proofs of the pertinent theorems and you have not been able to do so. But you just keep denying.

  398. 398
    JVL says:

    DaveS: Regarding Cantor’s diagonalization argument, it shows that the set of real numbers cannot be put in one-to-one correspondence with {1, 2, 3, …}. Hence the real numbers and {1, 2, 3, …} do not have the same cardinality. I would have assumed you agreed with this because your two-counter method also shows the set of real numbers is much larger than the set of natural numbers.

    DaveS gets it. It’s pretty straightforward. But ET will just keep denying.

  399. 399
    JVL says:

    ET: Infinity is NOT magic, it’s a journey. That is why the counter example is relevant- it exemplifies the journey. And that is also why relativity is also relevant.- it looks at the journey from a proper perspective.

    Put the integers in a box in ascending order. Put the evens in a box in ascending order. Take one out of each box at a time and match them together. Repeat. You have to count the elements of both sets at the same speed. As has been explained over and over and over again. But you just keep on denying.

  400. 400
    Retired Physicist says:

    I think ET just gets off on arguing with people, nobody would pursue this silly nonsense for years without contacting mathematicians. He knows he’s wrong he’s just getting some kind of kick out of it.

  401. 401
    JVL says:

    Retired Physicis: I think ET just gets off on arguing with people, nobody would pursue this silly nonsense for years without contacting mathematicians. He knows he’s wrong he’s just getting some kind of kick out of it.

    Maybe, but why all the threats and abuse? He’s much worse on his own site where there are no moderators except himself.

  402. 402
    Retired Physicist says:

    I didn’t know he had his own site, I can’t imagine why anybody would go there.

    But hey, there are people who have sexual interests that involve them getting dominated and abused, I don’t understand those people but I suppose you have to be wired that way to understand it. Maybe he gets off on some kind of public humiliation, he certainly seems to seek it out.

  403. 403
    Retired Physicist says:

    If he actually believed he was correct he would seek out mathematicians so that he could be awarded his Fields medal and recognized as a world-class mathematician. The fact that he doesn’t seek out mathematicians and doesn’t care what they think suggests that he knows he’s full of it.

  404. 404
    daveS says:

    RP,

    I suspect ET is beyond the age limit (40 years) for a Fields Medal.

  405. 405
    ET says:

    Why don’t you transform a set of infinite integers into food and feed the world!

    What? You can’t? Go figure…

  406. 406
    ET says:

    daves:

    Regarding Cantor’s diagonalization argument, it shows that the set of real numbers cannot be put in one-to-one correspondence with {1, 2, 3, …}.

    That’s because the reals are NOT countably infinite.

  407. 407
    ET says:

    JVL:

    The values or labels of the elements do not matter.

    Values matter in mathematics. Only a dolt would think otherwise.

  408. 408
    Retired Physicist says:

    DaveS 20 years ago I knew a Swedish guy who was one of the codiscoverers of wavelets, and unfortunately those math people are super arrogant, despite being super dumb with the ageism. What’s the deal with 40 years? At 41 you shouldn’t be recognized for an amazing discovery? So stupid.

  409. 409
    ET says:

    If you want to believe that one set that has ALL of the elements of another, PLUS infinite elements NOT in the other set but still they both have same number of elements, I don’t care. I am not going to drink that BS. Cantor’s diagonal just proves both sets are countable. That some people take it to mean they also have the same cardinality is their wrong inference.

    I have nothing else to say about this matter.

  410. 410
    daveS says:

    Eh? I thought you don’t accept that Cantor’s diagonalization argument is a valid proof?

  411. 411
    daveS says:

    RP,

    Yeah, I think it’s an odd requirement in this day and age. I guess that’s what Fields wanted, and apparently there hasn’t been pressure to remove it.

  412. 412
    ET says:

    WTF daves? I said Cantor’s diagonal is proof the sets are countable.

    You guys don’t even know how to read for comprehension. Why should anyone believe your asinine math?

  413. 413
    Retired Physicist says:

    @DaveS I was consulting for an engineering company in North Carolina about 15 years ago, and a guy said oh you’re in physics, my son said he went into math because the physics people are the people who are too stupid to be mathematicians. I responded something to him like OK that’s great, because they were paying me more than anybody’s ever paid me in my life. All I wanted to say was ‘Albert Einstein was in physics, and he figured out the photoelectric effect, Brownian motion, special relativity, and general relativity, he could have legit won 4 Nobel prizes, and you think everybody who is in math is smarter than that guy?’

    People who believe in conspiracy theories do so because they are intellectually insecure, but I’m starting to think there are some math people in that group too.

  414. 414
    ET says:

    RP:

    If he actually believed he was correct he would seek out mathematicians …

    That doesn’t follow. I am not on your asinine agenda. And seeing that the concept I am disputing is not used and is useless, why bother?

  415. 415
    ET says:

    Still waiting for the transformation of infinite integers into food….

  416. 416
    Retired Physicist says:

    Holy moly This all got me thinking about my friend Susan who works at a UF hospital and so I messaged her and she just messaged me that the hospital she works at in Gainesville is at 100% capacity.

  417. 417
    daveS says:

    ET @ 412,

    Well, it isn’t. How do you know the set of real numbers is not countably infinite? That’s what the diagonalization proof shows.

  418. 418
    ET says:

    daves:

    How do you know the set of real numbers is not countably infinite? That’s what the diagonalization proof shows.

    That’s what I said. Again, if you cannot read for comprehension there is no way I would trust your math.

  419. 419
    JVL says:

    Why don’t you transform a set of infinite integers into food and feed the world!

    Oh oh, starting off not making sense is bad.

    Values matter in mathematics. Only a dolt would think otherwise.

    NOT when you’re just counting how many things are in a set. Then, the only thing that matters is how many there are. But, this has been explained to you over and over again and you just keep denying.

    If you want to believe that one set that has ALL of the elements of another, PLUS infinite elements NOT in the other set but still they both have same number of elements, I don’t care. I am not going to drink that BS. Cantor’s diagonal just proves both sets are countable. That some people take it to mean they also have the same cardinality is their wrong inference.

    I’m okay with you being completely and utterly wrong, provably wrong. I can live with that.

    WTF daves? I said Cantor’s diagonal is proof the sets are countable.

    You guys don’t even know how to read for comprehension. Why should anyone believe your asinine math?

    Countably infinite. And all countably infinite sets have the same cardinality. If they didn’t you could find an unmatched element in my matching scheme, which you cannot do. But you just keep on denying.

    That doesn’t follow. I am not on your asinine agenda. And seeing that the concept I am disputing is not used and is useless, why bother?

    Unsuccessfully disputed. You never found a mistake or a counter-example. You lose. But you keep on denying.

    Still waiting for the transformation of infinite integers into food….

    I’m still waiting for you to find even one single unmatched element of sets A and B (or sets A and B2) under my scheme.

    I’m still waiting for you fo find the relative cardinality of the primes. I’m still waiting for you to find the cardinality of all polynomials with rational coefficients.

    I’m still waiting for you to find a fault with the proof that an infinite subset of a countably infinite set is also countably infinite and therefore has the same cardinality, aleph-0.

    Instead you just deny, deny, deny. Over and over and over again.

  420. 420
    daveS says:

    ET,

    WTF daves? I said Cantor’s diagonal is proof the sets are countable.

    daves:

    How do you know the set of real numbers is not countably infinite? That’s what the diagonalization proof shows.

    That’s what I said. Again, if you cannot read for comprehension there is no way I would trust your math.

    I don’t see how these can be reconciled. You first say the proof shows “the sets” are countable, then you say it shows the set of real numbers is not countable.

  421. 421
    ET says:

    Oh my- the proof can only show that the sets are countable or not.

  422. 422
    Retired Physicist says:

    Wow, my friend Susan is an administrator, and she just told me this

    I have tried to stay away from the ICU. They have converted and dedicated an entire closed unit ICU TO COVID.

    Don’t get sick right now friends.

  423. 423
    ET says:

    JVL- it is NOT YOUR scheme. YOU can only parrot the work of others. You cannot find a fault with set subtraction. You lose.

  424. 424
    ET says:

    JVL:

    NOT when you’re just counting how many things are in a set.

    OK then. Start counting then elements in {1,2,3,4,5,…} and let us know when you are finished.

    JVL still doesn’t understand infinity

  425. 425
    Retired Physicist says:

    JC 112 deaths here in Florida from it and it’s noon.

    One good thing that has happened is two months ago nobody here was wearing a mask except doctors and nurses, and now everybody’s wearing a mask.

  426. 426
    daveS says:

    ET,

    And it shows that the set of real numbers is uncountable. It doesn’t show that some set is countable.

    Anyway, apparently you believe that Cantor successfuly showed that R is uncountable (which is a positive thing).

    Edit: In particular, it doesn’t show that “all countably infinite sets have the same cardinality”—that’s an elementary consequence of the definitions.

  427. 427
    JVL says:

    ET: JVL- it is NOT YOUR scheme. YOU can only parrot the work of others. You cannot find a fault with set subtraction. You lose.

    I’m happy to use the correct work of others. I like the truth.

    I’ve found fault after fault. It can’t address lots of situations. It disagrees with proven results, proofs for which you can find no fault. And it’s not used for infinite sets for determining cardinality. It’s the wrong tool for the job.

    But you just keep on denying. Over and over and over again.

    OK then. Start counting then elements in {1,2,3,4,5,…} and let us know when you are finished.

    JVL still doesn’t understand infinity

    Still can’t find a mistake in any proofs. Still can’t find an unmatched element. Still can’t find some ‘relative cardinalities’.

    JVL- the only fault with set subtraction is YOU. Good luck with that.

    Funny you can’t use it to answer a couple of my questions then. Funny that NO ONE uses it to check the cardinality of infinite sets. Except for you. Funny that it gives contradictory answers to proven mathematics, proofs which you cannot find fault with.

    Deny, deny, deny.

    The only fault with my counter example is also JVL.

    It doesn’t work! It runs counter to proven mathematics, proofs which you cannot find fault with.

    Deny, deny, deny, deny.

  428. 428
    ET says:

    I never doubted that. You guys have serious issues.

  429. 429
    ET says:

    JVL- the only fault with set subtraction is YOU. Good luck with that.

  430. 430
    ET says:

    The only fault with my counter example is also JVL.

  431. 431
    ET says:

    daves:

    Edit: In particular, it doesn’t show that “all countably infinite sets have the same cardinality”—that’s an elementary consequence of the definitions.

    Or an elementary misunderstanding.

  432. 432
    JVL says:

    ET: Or an elementary misunderstanding.

    Deny, deny, deny. Deny well established and proven mathematics without being able to find a fault with any theorem you disagree with. Deny, deny, deny.

    Still waiting to see if you can:

    Find an unmatched element between sets A and B using my perfectly acceptable scheme.

    Find a mistake in any theorem in set theory.

    Find the ‘relative cardinality’ of the prime numbers.

    Find the cardinality of the set of all polynomials with rational coefficients.

    Here’s another one: find the cardinality of the roots of unity.

    Or this: find the cardinality of the complex numbers whose modulus is less than one.

    Go on, prove us wrong. Our views are falsifiable but so far you haven’t been able to falsify them. You just deny, deny, deny.

  433. 433
    daveS says:

    ET,

    Let’s assume that A and B are both countably infinite sets. Then there exist bijections f: A -> N and g: B -> N (where N = {1, 2, 3, …}). The function g^{-1} ∘ f (the composition of g inverse and f) is a bijection between A and B, so A and B have the same cardinality.

  434. 434
    ET says:

    daves- the bijective function would be/ represent the relative cardinality. The fact said function exists tells us there is a difference between the two sets.

  435. 435
    ET says:

    Is JVL saying that mathematicians are too stupid to be able to determine the relative cardinality of the primes with respect to all positive integers?

    Wow

  436. 436
    JVL says:

    ET: daves- the bijective function would be/ represent the relative cardinality. The fact said function exists tells us there is a difference between the two sets.

    Doesn’t have a clue about the mathematics. Not a clue.

    Is JVL saying that mathematicians are too stupid to be able to determine the relative cardinality of the primes with respect to all positive integers?

    I KNOW what the cardinality of the primes is. YOU made up the notion of ‘relative cardinality’ so it’s ups to you to show you can use it not the people who think it’s rubbish.

    And, guess what? You can’t find the relative cardinality of the primes. You can’t even support your own idea.

    I didn’t make the claim, you did. I don’t have to prop up your rubbish idea, you do. Can you? Looks pretty clear that you can’t. But you’ll keep avoiding admitting you can’t.

    You’re going to deny, deny, deny. As usual.

  437. 437
    daveS says:

    ET,

    It looks like you’re following Rudy Guiliani’s strategy now.

  438. 438
    Querius says:

    Is {deny, deny, deny, . . . } an infinitely countable set? What about a nested set of denials?

    Sorry, just couldn’t resist. 😉

    -Q

  439. 439
    kairosfocus says:

    ET, functions routinely transform one set into another. KF

  440. 440
    kairosfocus says:

    AS, I was quoting the Athanasian creed, the most technical of the three commonly referenced creeds. As for scripture, start with Isa 40 on independence of being and the common declaration of eternality. God is necessary thus eternal being himself. Among other cases, consider the point, nothing shall be impossible with God or the question, is there anything too hard for the Lord. Further, in fact the Scriptures do talk of testimonies to God in us and in the world, noting that those who dismiss God do so in the teeth of evidence, cf Rom 1. We can know and should acknowledge some things about God and ourselves in relation to him from reason and sound conscience reflecting on our inner morally governed rationality and the wonders of the world without; note here, Ac 17. But that is of course limited. Authentic scripture and the living edition of God’s word himself, teach us much more. KF

  441. 441
    kairosfocus says:

    Q, at simple level, a set is a collection of distinct objects that are such that we can determine what’s in and what’s not. A key set is the empty one. What’s in is nada, of course. Chaining collecting that set and successors gives us the counting numbers. This specifically excludes cases where that decision cannot be made. For Mathematics, an axiomatised framework was built up from contemplation of set facts and results after being duly chastened by certain challenges. Insofar as the strings are distinguishable and collected, that is a set, and the ellipsis says endless repetition. KF

  442. 442
    asauber says:

    “nothing shall be impossible with God”

    KF,

    Which is my point. Unicorns are not impossible with God. But is it reasonable to think they exist and have magical properties on top of that?

    Andrew

  443. 443
    kairosfocus says:

    ET, that sets may have the like cardinality does not imply having the same elements and only the same elements. It means they can somehow be matched 1:1, member by member, and of course with countable sets, to N or a subset of N. You have already seen what happens with N, the evens and the odds. Endless continuation is a key factor. And that is tied to the point that a transfinite set can be matched 1:1 with a proper subset, without exhaustion. That is a conceptual hurdle similar to understanding complex unity, the nature of a system, quantization or relativity. A paradigm shift is called for. KF

  444. 444
    ET says:

    KF:

    ET, functions routinely transform one set into another.

    And those functions demonstrate the differences between the two sets.

  445. 445
    kairosfocus says:

    AS, I suspect within 100 years unicorns will exist, through genetic engineering; the market is obvious. Magical properties, no. That nothing is impossible with God implies, nothing compossible with his character. KF

  446. 446
    ET says:

    daves:

    It looks like you’re following Rudy Guiliani’s strategy now.

    Make your case. Or admit that your “strategy” is bald assertions and false accusations

  447. 447
    kairosfocus says:

    ET, naturals, odds and evens etc are different in membership though there is overlap. All three share the same cardinality, first, countable, inexhaustible. Where O UNION E = N. KF

  448. 448
    ET says:

    JVL:

    Doesn’t have a clue about the mathematics.

    Says the loser who cannot read for comprehension.

    Why do all cowards just think they can falsely accuse someone as if it means something?

  449. 449
    asauber says:

    “I suspect within 100 years unicorns will exist’

    KF,

    Great. I’m glad you have a vivid imagination. Nothing to do with whether or not infinity is absurd.

    Andrew

    P.S. And you didn’t answer this question I asked above: “Introducing infinity into ideas like the progression of time causes paradoxes, doesn’t it? Why do you think that is?”

  450. 450
    kairosfocus says:

    AS, not imagination, marketing. The genes can doubtless be manipulated, to grow a horn. Rhinos already have such, though technically a hair IIRC. KF

    PS: And infinity is not absurd, it means, beyond finite limit. With the hyperreals we have the infinitely large and the infinitely small, quite readily. E.g. any number we can count to k can be exceeded, so we see that the set N has no identifiable upper limit. There is no last k so k+1 is infinity. The infinitesimals are v useful in workaday math. They have been since the days of the ancient Greeks actually.

  451. 451
    ET says:

    Yes, KF, I know what mainstream says. Just repeating it isn’t going to change anything.

  452. 452
    daveS says:

    ET,

    I have been making my case. You just haven’t engaged with my posts.

  453. 453
    kairosfocus says:

    ET, I didn’t merely repeat, i showed why I hold what views I do. But, we can leave it at that. KF

  454. 454
    ET says:

    daves, how can I be making your case seeing that I have agreed with much of what you have said?

  455. 455
    ET says:

    Yes, KF, I understand why you hold the views that you do. I also held them @ one time in my life. Then I came to a better understanding of infinity.

  456. 456
    asauber says:

    “k+1 is infinity”

    Sorry KF. k+1 is not infinity. It’s some number +1.

    Andrew

  457. 457
    JVL says:

    ET: Says the loser who cannot read for comprehension. Why do all cowards just think they can falsely accuse someone as if it means something?

    Hey, it’s not my fault you have demonstrated your misunderstanding of mathematics over and over and over again. I’ve told the truth and I’ve told you how you can properly dispute it. But you haven’t managed to do that.

    Yes, KF, I know what mainstream says. Just repeating it isn’t going to change anything.

    But you haven’t been able to refute any proof of any theorem. But you just keep denying over and over and over again.

  458. 458
    JVL says:

    ET:

    Okay, let’s try this:

    I’ve told you how you can falsify the standard mathematical views on infinity. You just have to find a fault or flaw in one of the many proofs of the theorems supporting that view. If you can do that, you win.

    Now, how can someone falsify your view of relative cardinalities? Something that is possible and not just you spouting off some impossible task. What would it take to get you to admit your view is incorrect?

  459. 459
    JVL says:

    Asauber: Sorry KF. k+1 is not infinity. It’s some number +1.

    It depends on what ‘k’ is doesn’t it? What did Kairosfocus say ‘k’ represented?

  460. 460
    asauber says:

    JVL,

    “any number we can count to k can be exceeded”

    He said k is a number.

    Andrew

  461. 461
    jerry says:

    There is a number k in our universe that has meaning but for which k+1 does not have meaning and therefore does not refer to anything that exists. It is a very large number and would be probably impossible to determine. Maybe a range could be made.

    Because the universe is finite, infinity has no real meaning. Infinity whether big or small is only in one’s mind not in reality. Extremely useful but not real.

    Positive integers also don’t exist, only the things associated with these integers. The positive integers are abstract concepts only in our minds. Extremely, extremely useful. That is they are “extremely” squared useful. But definitely not “extremely” to the kth power useful.

  462. 462
    ET says:

    JVL:

    Now, how can someone falsify your view of relative cardinalities?

    Demonstrate that A – B does not equal C, where A is the set of all positive integers; B is the set of all even integers and C is the set of all odd integers. Meaning demonstrate that A- B = {}

  463. 463
    ET says:

    JVL:

    Hey, it’s not my fault you have demonstrated your misunderstanding of mathematics over and over and over again.

    It’s your fault that you are a pathological liar

  464. 464
    ET says:

    And I say that set subtraction is enough to show fault with your understanding of the proofs. I have NO problem with the proofs. I have an issue with people’s misuse of them.

    That JVL still refuses to grasp that says it all, really.