Eric Holloway: A philosopher explains why thinking matter is impossible

_{Denyse O'Leary

February 21, 2020

Artificial Intelligence, Intelligent Design, Mind}

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He’s right but Captain Kirk tumbled to it before him on Star Trek:

What’s there to do about lying liars who lie about their own lying?
Analytical philosopher Richard Johns’s recent paper in an analytical philosophy journal susses out the fact that if any such liars exist, then the lying part of them must be non-physical. That is, he offers an argument against physicalism, the popular philosophy that only physical things exist and that therefore, if humans exist, we are merely physical.
His argument is deeper version of Captain Kirk’s scheme to defeat enemy robots in I, Mudd, a 1967 episode of Star Trek. Kirk posed a paradox that led to circuit meltdown.
Eric Holloway, “A philosopher explains why thinking matter is impossible” at Mind Matters News

Comments

PS: This looks like a useful discussion https://fme.upc.edu/ca/arxius/butlleti-digital/riemann/071218_conferencia_atiyah-d_article.pdfkairosfocus_{February 29, 2020
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Groov, good to hear you. I used dual in a loose sense [mutual, conjugate functional domains accessible through a direct mapping relationship with corresponding results -- Wiki's 101 note is here]. The Laplace variable s or sometimes p is indeed complex, with the imaginary part associated with frequency and the real part with transient behaviour. Connexions with differential equations and dynamics lurk, through transfer functions that characterise system behaviour. My basic point is, there are structural and quantitative aspects of the logic of being involved, so that once those differential equations are in place that characterise dynamics, the frequency domain behaviour necessarily follows by force of those dynamics and relationships of structure and quantity. And yes, 1/time is indeed how frequency is dimensionalised, cycles of oscillation [phenomenon] per unit time [fundamental dimension]. Frequency domain behaviour is then bound up in the nature of dynamical systems with implications for phase behaviour too, in which context sinusoids and their properties of summing to form arbitrary waveforms or transients allows us to specify that we deal in frequency of sinusoids, one of two related characteristic functions, the other being the complex exponential. Where, sinusoidal motion is a natural result of simple harmonic motion, a dynamic case with a linear restoring force for disturbances around an equilibrium; it is also connected to circular motion, where uniform circular motion is superposition of sinusoids with orthogonal axes and quadrature phase. Which brings in complex numbers and the complex exponential as in effect a vector approach. The discrete case, leading into difference equation based approaches, is related. My overall key point is that mathematical properties are tied into the logic of being and associated dynamics. That is, it is not an arbitrary intellectual game, in relevant aspects. KFkairosfocus_{February 29, 2020
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KF: 55: nope. The frequency domain is very real, and dual to the time domain. Only, it is not so familiar to those who have not worked with it. Our hearing is a good example. I'm going to write as this is core to my livelihood. Integral transforms operate on conjugate domains the descriptor dual is a term unfamiliar to me. Something characteristic of conjugate domains is that their dimensional units are mutually inverse. In Joseph Fourier's application the conjugate dimensions were {length, 1/length}. The same is true in quantum mechanics when probability waves are described in space. In electrical engineering the classic application of Fourier analysis renders measure in terms of time and frequency whose dimensions are {t, 1/t} whether frequency is in Hz (dimensioned 1/sec) or rads/sec (still 1/sec since radians are dimensionless). Also to further indicate the possible confusion, with Fourier analysis, the conjugate pair of domains each have at least one codomain, i.e. the time domain has a codomain of amplitude, but the frequency domain has two codomains, those of amplitude and phase. However in recent decades EE's have delved into applied mathematics for imaging and image compression, with an important tool being the discrete cosine transform (DCT) whose conjugate dimensions are either {length, 1/length}. or {pixel, 1/pixel} Something that I see frequently on Quora and stackexchange is confusion regarding the Laplace transform and one of the conjugate domains itself (the variable s) is complex, so is two-dimensional. And its codomain is complex/two-dimensional, requiring a 4-d space to visualize. Many beginners cannot fathom how one of the domains can have units inverse to its conjugate and be 2-d and this is one of many difficult hurdles to visualizing the workings of these operations.groovamos_{February 28, 2020
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Kevin Moran, an optical engineer working on the mysterious ‘3D’ nature of the Shroud image, states the ‘quantum’ explanation this way, “This suggests a quantum event where a finite amount of energy transferred abruptly. The fact that there are images front and back suggests the radiating particles were released along the gravity vector.”
Optically Terminated Image Pixels Observed on Frei 1978 Samples – Kevin E. Moran – 1999 Discussion Pia’s negative photograph, from 1898, showed what looked to be a body that was glowing, but slightly submerged in a bath of cloudy water. This condition is more properly described as an image that is visible, at a distance, but by locally attenuated radiation. The unique front-and-back only image can be best described as gravitationally collimated. The radiation that made the image acted perfectly parallel to gravity. There is no side image. The radiation is parallel to gravity and, if moving at light speed, only lasted about 100 picoseconds. It is particulate in nature, colliding only with some of the fibers. It is not a continuum or spherical-front radiation that made the image, as visible or UV light. It is not the X-ray radiation that obeys the one over R squared law that we are so accustomed to in medicine. It is more unique,,, Theoretical model It is suggested that the image was formed when a high-energy particle struck the fiber and released radiation within the fiber at a speed greater that the local speed of light. Since the fiber acts as a light pipe, this energy moved out through the fiber until it encountered an optical discontinuity, then it slowed to the local speed of light and dispersed. Discussion The fact that the pixels don’t fluoresce suggests that the conversion to their now brittle dehydrated state occurred instantly and completely so no partial products remain to be activated by the ultraviolet light. This suggests a quantum event where a finite amount of energy transferred abruptly. The fact that there are images front and back suggests the radiating particles were released along the gravity vector. The radiation pressure may also help explain why the blood was “lifted cleanly” from the body as it transformed to a resurrected state.” https://www.shroud.com/pdfs/moran.pdf
Moreover, the following article found that it would take 34 Trillion Watts of what is termed VUV (directional) radiation to form the image on the shroud.
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 only to several billion watts)”. Comment The ENEA study of the Holy Shroud of Turin concluded that it would take 34 Thousand Billion (trillion) Watts of VUV radiation to make the image on the shroud. This output of electromagnetic energy remains beyond human technology. http://www.predatormastersforums.com/forums/ubbthreads.php?ubb=showflat&Number=3014106
To provide further plausibility to Christ’s resurrection from the dead providing the correct solution for the much sought after ‘Theory of Everything” it is also important to note that humans ‘naturally’ emit quantum light:
Photocount distribution of photons emitted from three sites of a human body – 2006 Excerpt: Signals from three representative sites of low, intermediate and high intensities are selected for further analysis. Fluctuations in these signals are measured by the probabilities of detecting different numbers of photons in a bin. The probabilities have non-classical features and are well described by the signal in a quantum squeezed state of photons. Measurements with bins of three sizes yield same values of three parameters of the squeezed state. http://www.ncbi.nlm.nih.gov/pubmed/16520060
And to add even more plausibility that Christ’s resurrection from the dead provides the correct solution for the much sought after ‘Theory of Everything” it is also important to note that both General Relativity and Quantum Mechanics have now themselves overturned the Copernican principle:
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
As well, another important fact to take note of is that the 'free will loophole' has now been closed by Anton Zeilinger and company.
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
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, 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: January 2020 https://uncommondescent.com/intelligent-design/welcome-to-the-brave-new-world-of-science/#comment-690569
As you can see from my above argument, the main linchpin in the success of my argument for Jesus Christ's ressurection from the dead providing the correct solution for the much sought after 'theory of everything' hinges on the authenticity of the Shroud of Turin. Of course atheists simply refuse to accept the authenticity of the Shroud of Turin since, if they accepted the fact that the Shroud is authentic then they, of course, will no longer be atheists but will be, well, Christians. :) But as with their refusal to accept the evidence for intelligent design itself, the empirical evidence for the authenticity of the Shroud of Turin itself could care less if atheists refuse to accept it or not. And as far as empirical evidence itself is concerned, the Shroud of Turin is most certainly authentic:
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 Shroud of Turin: From discovery of Photographic Negative, to 3D Information, to 3D Hologram https://youtu.be/F-TL4QOCiis
Thus in conclusion, the resolution of the fairly intense conflict between potential infinity and actual infinity is yet another line evidence that supports my claim that Christ's resurrection from the dead in the correct solution for the much sought after 'theory of everything' Verses:
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, 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.
bornagain77_{February 28, 2020
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As the preceding video clearly illustrated, the main conflict of reconciling General Relativity and Quantum Mechanics appears to arise from the inability of either theory to successfully deal with the Zero/Infinity conflict that crops up between each theory:
THE MYSTERIOUS ZERO/INFINITY Excerpt: The biggest challenge to today's physicists is how to reconcile general relativity and quantum mechanics. However, these two pillars of modern science were bound to be incompatible. "The universe of general relativity is a smooth rubber sheet. It is continuous and flowing, never sharp, never pointy. Quantum mechanics, on the other hand, describes a jerky and discontinuous universe. What the two theories have in common - and what they clash over - is zero.",, "The infinite zero of a black hole -- mass crammed into zero space, curving space infinitely -- punches a hole in the smooth rubber sheet. The equations of general relativity cannot deal with the sharpness of zero. In a black hole, space and time are meaningless.",, "Quantum mechanics has a similar problem, a problem related to the zero-point energy. The laws of quantum mechanics treat particles such as the electron as points; that is, they take up no space at all. The electron is a zero-dimensional object,,, According to the rules of quantum mechanics, the zero-dimensional electron has infinite mass and infinite charge. http://www.fmbr.org/editoral/edit01_02/edit6_mar02.htm
In short, by all appearances, it seems readily apparent that we are dealing with a 'actual infinity' instead of merely a 'potential infinity' in our endeavor to try to mathematically unify General Relativity with Quantum Mechanics.
Potential Infinity vs. Actual Infinity - June 7, 2012 by Ryan Excerpt: In a potential infinity, one can keep adding or subdividing without end, but one never actually reaches infinity. In a sense, a potential infinity is an endless process that at any point along the way is finite. By contrast, in an actual infinity, the infinite is viewed as a completed totality. http://www.numbersleuth.org/trends/potential-vs-actual-infinity/
Thus in order to achieve unification between General Relativity and Quantum Mechanics, it seems readily apparent that an 'actual infinity' would have to found to exist between the two theories. And this is where Christ's resurrection from the dead comes into play once again. Dr. William Dembski in this following comment, although he was not specifically addressing the Zero/Infinity conflict in General Relativity and Quantum Mechanics, offers insight into the fact that Christ's resurrection from the dead was the realization of an 'actual infinity' instead of merely being a realization of a 'potential infinity':
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/documents/2009.05.end_of_xty.pdf
I hold it to be fairly obvious that 'growing large without measure' is a merely a 'potential infinity', whereas I also hold it to be fairly obvious that a fraction in which the denominator goes to zero is an 'actual infinity'. In regards to growing large without measure, here are a few references that clearly illustrate the deficiencies of a 'potential infinite' when compared to an 'actual infinite'
Can We Have a 'Now' or a 'Today' if Time is Actually Infinite? - DrCraig video https://www.youtube.com/watch?v=Xg0pdUvQdi4 The dissolution of today - graph - May 21, 2014 Scenario A shows the actual situation of the arrow of time, running from left to right, from today to the future. If this arrow is infinite then we would have no last day. To scenario A we apply a shift according to a leftward vector of infinite length to get scenario B suggested by Carroll. Of course the arrow of time continues to run from left to right, but the shift produces a “little” problem: the “no last day” becomes “no today!”. Simply in Carroll’s wonderland the present disappears, and with the present ourselves disappear. :(Please give us back the Creator!) https://uncommondescent.com/physics/the-dissolution-of-today/
In short, "A collection formed by adding one member to another cannot be actually infinite,,,"
Can A "Beginning-less Universe" Exist? - William Lane Craig – video ,,"the impossiblity of forming an actually infinite number of things by adding one member after another.,,, 1. A collection formed by adding one member to another cannot be actually infinite,,," http://www.youtube.com/watch?v=K8YN0fwo5J4
Simply put, the reason why 'growing large without measure', i.e. a 'potential infinite', is a lesser quality infinity than 'a fraction in which the denominator goes to zero', i.e. an actual infinite, is because anything that begins to grow large without measure must necessarily have some sort of beginning. Whereas, on the other hand, to form a fraction in which the denominator goes to zero is to force a finite object into a type of infinity that can have no discernible beginning, no discernible end, no discernible anything. i.e. it is to force a finite object into a true infinity! But does Christ's resurrection from the dead provide us with the necessary 'actual infinity' that is apparently required in order to unify Quantum Mechanics and General Relativity? Well, according to evidence gleaned from the Shroud of Turin, Christ's resurrection from the dead DOES provide us with the necessary 'actual infinity' that is apparently required in order to satisfactorily unify Quantum Mechanics and General Relativity. As Isabel Piczek notes in the following video, the Shroud of Turin reveals a strange ‘event horizon’:
“When you look at the image of the shroud, the two bodies next to each other, you feel that it is a flat image. But if you create, for instance, a three dimensional object, as I did, the real body, then you realize that there is a strange dividing element. An interface from which the image is projected up and the image is projected down. The muscles of the body are absolutely not crushed against the stone of the tomb. They are perfect. It means the body is hovering between the two sides of the shroud. What does that mean? It means there is absolutely no gravity. Other strange you discover is that the image is absolutely undistorted. Now if you imagine the clothe was wrinkled, tied, wrapped around the body, and all of the sudden you see a perfect image, which is impossible unless the shroud was made absolutely taut, rigidly taut.” Isabel Piczek – Turin shroud – (Particle Physicist explains event horizon) – video https://www.youtube.com/watch?v=PIpdIz5Rp3I
And in support of Isabel Piczek's claim, the following study found 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.’
Particle Radiation from the Body – July 2012 – M. Antonacci, A. C. Lind Excerpt: The Shroud’s frontal and dorsal body images are encoded with the same amount of intensity, independent of any pressure or weight from the body. 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. Radiation coming from the body would not only explain this feature, but also the left/right and light/dark reversals found on the cloth’s frontal and dorsal body images. http://www.academicjournals.org/app/webroot/article/article1380798649_Antonacci.pdf
In other words, gravity was dealt with in Christ's Resurrection from the dead. 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.
The absorbed energy in the Shroud body image formation appears as contributed by discrete (quantum) values – Giovanni Fazio, Giuseppe Mandaglio – 2008 Excerpt: This result means that the optical density distribution,, can not be attributed at the absorbed energy described in the framework of the classical physics model. It is, in fact, necessary to hypothesize a absorption by discrete values of the energy where the ‘quantum’ is equal to the one necessary to yellow one fibril. http://cab.unime.it/mus/541/1/c1a0802004.pdf
bornagain77_{February 28, 2020
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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 Cantor, Gödel, & Turing: Incompleteness of Mathematics - video (excerpted from BBC's 'Dangerous Knowledge' documentary) https://www.facebook.com/philip.cunningham.73/videos/vb.100000088262100/1119397401406525/?type=2&theater
As the beginning of the preceding video made clear, this endeavor by Cantor to 'tame infinity' was very much a theological quest for Cantor. 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
I will touch upon the conflict between "potential and actual infinity" later on. 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
Although Cantor ultimately failed in his endeavor to 'tame infinity', never-the-less, Cantor pioneered some very useful tools in mathematics, useful tools which are useful today and which were 'probably' essential to Gödel in his work on bringing incompleteness to fruition,,
19TH CENTURY MATHEMATICS – CANTOR http://www.storyofmathematics.com/19th_cantor.html 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
Now back to the conflict between "potential and actual infinity". As was touched upon in post 49, General relativity simply refuses to be mathematically unified with quantum mechanics in any acceptable way. In technical terms, Gravity has yet to be successfully included into a theory of everything since the infinities that crop up in that attempt simply are not renormalizable as they were in Quantum-Electrodynamics. https://uncommondescent.com/intelligent-design/eric-holloway-a-philosopher-explains-why-thinking-matter-is-impossible/#comment-693691 As was referenced in post 49, "Yet there remains an irremediable difficulty, (in unifying gravitation with quantum mechanics). 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.
And at the 7:08 minute mark of the following video, Michio Kaku,, after going through some calculations trying to integrate Quantum Mechanics and Gravity at a black hole, goes on to state “And when you do this integral, you get something which makes no sense whatsoever. An infinity. Total nonsense. In fact, you get an infinite sequence of infinities. Infinitely worse than the divergences of Einstein's original theory.”
“And when you do this integral, you get something which makes no sense whatsoever. An infinity. Total nonsense. In fact, you get an infinite sequence of infinities. Infinitely worse than the divergences of Einstein's original theory.” Quantum Mechanics & Relativity – Michio Kaku - The Collapse Of Physics As We Know It ? - video http://www.dailymotion.com/video/x2jbd7x
bornagain77_{February 28, 2020
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JVL, time, length, mass, angle, temperature, electric current, luminous intensity and extensions thereof including number of cycles per second aka frequency are "just" measurements. They take a standardised amount of some Q and take a ratio P:Q as the value in some scheme of units. 1.98 metres or 610 kHz or 91.1 MHz is a measurement reflecting underlying structures and quantities of reality. These are not fictional. And above, I noted to BO'H on frequency response, transfer functions, poles and zeros. I guess that gets us into another issue, that complex numbers are real, with the j- or i- operator indicating rotation by a right angle anticlockwise, so j^2- is such rotation by two right angles implying that j is square root minus one. Nope, that is no more imaginary than reals are. Again, I point out that we are dealing with the logic of structure and quantity that in part constrains what may be in any possible world through logic of being and in part reflects the similar import of the framework of a particular world such as our own. Mathematics, so understood, is not an arbitrary game we can make up as we will. KF PS Note how the cochlea uses frequency sensitive hairs in an array to convert vibrations and transients in time to patterns in frequency. Hearing carries out in effect a fast fourier transform mechanically.kairosfocus_{February 28, 2020
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BO'H: I am actually going next door into Laplace and Z transforms. A classic picture is that the sigma axis captures transient behaviour and j omega behaviour frequency behaviour. Plot a Laplace transfer function's poles and zeros and imagine a heavy rubber sheet draped over the poles and nailed down at the zeros. The cut along the j omega axis gives frequency response, reflecting what one of my students called the shoulders of the poles. Of course as the differential operator amounts to multiply by s and the integral, divide by s, all of this goes to differential equations etc too. A familiar manifestation is the sort of bode plot, frequency response curves [in log form] shown in audio reviews. The pattern is far more general than that. KFkairosfocus_{February 28, 2020
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Yup, Fourier analysis is correct. Not sure what poles you are talking about.
Poles and zeroes means complex analysis. Poles are when a function becomes infinity, zeroes are when it becomes zero. I haven't done enough Fourier analysis to know if poles crop up a lot there. I'd imagine it's preferable if they don't.Bob O'H_{February 28, 2020
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BA77, 59: But alas, Godel forces us to confront the ontology of mathematics and the question of what provides its ultimate foundation. The atheist simply has no answer to that question, and therefore, like you are doing right now, the atheist chooses to ignore or to not seriously engage the question (of note: I’m not calling you an atheist), Thanks for the disclaimer! And you may be right about the implications of Gödel's work. I know if I participate in that conversation I will look like a complete fool and so, rather than confirm I AM a complete fool, I'm going to attempt to maintain my ambiguity and keep quiet!JVL_{February 27, 2020
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KF, 58:There is no good reason to think that a frequency of a vibration is fictional as opposed to the time domain pattern. I would hope no one would suggest it's fictional! But that is just a measurement made with regard to basic units. Extending, our hearing responds to frequency components, cf the cochlea. The superposition of sinusoids works as advertised. A frequency response, linked transient response [Laplace etc enter here] and effects of poles and zeros are all significant. Yup, Fourier analysis is correct. Not sure what poles you are talking about. And there usually are a lot of zeroes about! :-)JVL_{February 27, 2020
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JVL, as to:
I’m not ignoring your arguments in post 54, I’m choosing not to engage with them. I think you’re delving into theology and that is something I am hideously poorly equipped to contribute to.
But alas, Godel forces us to confront the ontology of mathematics and the question of what provides its ultimate foundation. The atheist simply has no answer to that question, and therefore, like you are doing right now, the atheist chooses to ignore or to not seriously engage the question (of note: I'm not calling you an atheist),
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/article/2010/08/the-god-of-the-mathematicians
Berlinski went even further and stated, "There is no argument against religion that is not also an argument against mathematics. Mathematicians are capable of grasping a world of objects that lies beyond space and time…."
An Interview with David Berlinski - Jonathan Witt Berlinski: There is no argument against religion that is not also an argument against mathematics. Mathematicians are capable of grasping a world of objects that lies beyond space and time…. Interviewer:… Come again(?) … Berlinski: No need to come again: I got to where I was going the first time. The number four, after all, did not come into existence at a particular time, and it is not going to go out of existence at another time. It is neither here nor there. Nonetheless we are in some sense able to grasp the number by a faculty of our minds. Mathematical intuition is utterly mysterious. So for that matter is the fact that mathematical objects such as a Lie Group or a differentiable manifold have the power to interact with elementary particles or accelerating forces. But these are precisely the claims that theologians have always made as well – that human beings are capable by an exercise of their devotional abilities to come to some understanding of the deity; and the deity, although beyond space and time, is capable of interacting with material objects. http://tofspot.blogspot.com/2013/10/found-upon-web-and-reprinted-here.html
Indeed mathematics itself is immaterial. That is to say, mathematics itself exists in a transcendent, beyond space and time realm, a realm which simply is not reducible any possible material explanation. This transcendent mathematical realm has been referred to as a Platonic mathematical world.
Platonic mathematical world - image http://abyss.uoregon.edu/~js/images/platonic_physical.gif
In the following article, Dr. Michael Egnor does an excellent job of highlighting the sheer poverty that naturalism has in regards to ever providing an coherent explanation for 'immaterial' mathematics
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/
Likewise M. Anthony Mills explains, “And yet — here’s the rub — these “abstract (mathematical) 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.”
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
The predicament that Darwinian naturalists find themselves in regards to denying the reality of this transcendent, immaterial, world of mathematics, and yet needing validation from this transcendent, immaterial, world of mathematics in order for their materialistic theory to even be considered scientific in the first place, should be the very definition of a scientifically self-refuting worldview. Moreover, as should be obvious by now, the fact that man himself has access to, and can use, this transcendent, beyond space and time, immaterial world of mathematics, offers fairly compelling evidence that man in not a purely material being but that man must also possess a transcendent, beyond space and time, immaterial mind and/or soul.
Dr. Ed Feser – The Immateriality of the Intellect – video Excerpt: 1: Formal thought processes can have an exact or unambiguous conceptual content. However, 2: Nothing material can have an exact or unambiguous conceptual content. So, 3: Formal thought processes are not material. https://www.youtube.com/watch?v=fNi0j19ZSpo
As Charles Darwin’s contemporary, Alfred Russel 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.”
“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 https://evolutionnews.org/2010/08/alfred_russel_wallace_co-disco/
Verse:
Mark 8:37 Is anything worth more than your soul?
Supplemental note that you may like JVL
11. The Argument from Truth Excerpt: 1. Our limited minds can discover eternal truths about being. 2. Truth properly resides in a mind. 3. But the human mind is not eternal. 4. Therefore there must exist an eternal mind in which these truths reside. https://www.peterkreeft.com/topics-more/20_arguments-gods-existence.htm#11
bornagain77_{February 27, 2020
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JVL, structure and quantity are aspects of logic of being. There is no good reason to think that a frequency of a vibration is fictional as opposed to the time domain pattern. Extending, our hearing responds to frequency components, cf the cochlea. The superposition of sinusoids works as advertised. A frequency response, linked transient response [Laplace etc enter here] and effects of poles and zeros are all significant. KFkairosfocus_{February 27, 2020
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KF, 55: nope. The frequency domain is very real, and dual to the time domain. Only, it is not so familiar to those who have not worked with it. Our hearing is a good example. The frequency domain . . . in a mathematical sense? Domain would mean possible inputs to a function. What does 'dual to the time domain' mean? The same as? Or ? I'm not trying to trip you up, I'm just trying to figure out what you're saying. And I'm probably being a bit stupid for which I apologise. if you don't think it's worth the time that's okay but I would like to know.JVL_{February 27, 2020
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John_a_designer, 53: For example, I don’t think that his theorem leads to total agnosticism or nihilism nor does it prove or refute metaphysical positions like materialism or theism etc., Agreed! My point is that in logic as in mathematics there ARE propositions whose truth and falsity CANNOT be determined. However, it does not follow that there are NO propositions whose truth and falsity CAN be determined. Or that unsolved problems in logic or mathematics are unsolvable. In other words, the existence of logical paradoxes does not undermine the foundations of logic itself any more than Gödel’s theorem undermines the foundations of mathematics. Lovely! Yes, yes, yes!! For example, “the Goldbach Conjecture is a yet unproven conjecture stating that every even integer greater than two is the sum of two prime numbers… [It] is one of the oldest unsolved problems in number theory.” However, it does not follow that because it is unsolved that it is unsolvable. In other words, even though Gödel was able to prove that there are undecidable theorems in mathematics it does not prove that the Goldbach Conjecture is undecidable or unprovable. Again, lovely. I think you've summed it all up beautifully. I think the Goldbach Conjecture is definitely true . . . or false. But it's not one of those statements which may be better thought of as axioms. Like Zorn's Lemma. Which, just to dive down that rabbit's hole a bit further, has been shown to be equivalent to The Axiom of Choice and The Well Ordering Principle. IF you accept The Axiom of Choice you get one kind of mathematics. If you don't accept it then things change. There is a lot and a lot and a lot of mathematics that is proven, that is true beyond any sensible argument. In fact, just about everything taught in undergraduate classes. But there are swathes of grey areas. Along with whole classes of problems like NP-Complete ones that defy certain kinds of solutions. Mathematics is huge, really huge. Seriously, Calculus is just the beginning. BA77, 54: I'm not ignoring your arguments in post 54, I'm choosing not to engage with them. I think you're delving into theology and that is something I am hideously poorly equipped to contribute to. I might be wrong about that but I do not want to pretend I understand something which I have no sound knowledge of. We agreed on the math part and that's good with me.JVL_{February 27, 2020
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JVL, nope. The frequency domain is very real, and dual to the time domain. Only, it is not so familiar to those who have not worked with it. Our hearing is a good example. KFkairosfocus_{February 27, 2020
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John_a_designer as to this claim,
I don’t think that his theorem leads to total agnosticism or nihilism nor does it prove or refute metaphysical positions like materialism or theism etc.
Well, here are a few people who disagree with you, (although I don't think they would use the words 'prove' or 'refute',,, let's just stick with the term 'strongly indicates' OK?)
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.org/articles/am/v7/n1/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/a-biblical-view-of-mathematics/
i.e. Without God, Atheists can't even 'intuitively know' that 2+2=4. Of related interest to that embarrassing little fact, Godel's incompleteness theorem was born out of the fact that mathematicians could not actually 'prove' that 1+1=2. You can pick up some of the details of that fact at 10:00 minute mark of the following video
BBC-Dangerous Knowledge – Part 3 of 5 https://www.dailymotion.com/video/xdoj7y
bornagain77_{February 27, 2020
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Gödel was able to prove that there are self-referential propositions in mathematics that are undecidable. Of course, there is a long ongoing debate as how widely his incompleteness theory can be applied outside of mathematics. I am not going to go off on that tangent here (I am neither a mathematician nor a logician) though I do think we need to be cautious about being over reaching with the implications. For example, I don’t think that his theorem leads to total agnosticism or nihilism nor does it prove or refute metaphysical positions like materialism or theism etc. However, I do think it does have some things to say about basic logic. Indeed, Gödel in his paper does allude to these problems that have been known since ancient times. For example, there are some logical paradoxes that can be stated in plain English (or if you were living in ancient Greece, in “plain Greek.”) Gödel, for example, mentions the so-called liar’s paradox. Here is one version of that paradox that I think is the clearest. Consider the following proposition: *1: This sentence contains six words. Notice there are two things we can say about this sentence. First, it is self-referential. It’s referring to itself. Second, it’s making a truth claim about itself. But furthermore, we can determine whether it really is true or false by just counting the words. In this case it’s false. So its truth or falsity can be established or decided. Now consider a second sentence. *2: This sentence is false. This is also a self-referential sentence. So is it true or false? Can anyone determine whether it’s true or false? If you think you can, go ahead and try to prove that you can arrive at an answer. My point is that in logic as in mathematics there ARE propositions whose truth and falsity CANNOT be determined. However, it does not follow that there are NO propositions whose truth and falsity CAN be determined. Or that unsolved problems in logic or mathematics are unsolvable. In other words, the existence of logical paradoxes does not undermine the foundations of logic itself any more than Gödel’s theorem undermines the foundations of mathematics. For example, “the Goldbach Conjecture is a yet unproven conjecture stating that every even integer greater than two is the sum of two prime numbers… [It] is one of the oldest unsolved problems in number theory.” However, it does not follow that because it is unsolved that it is unsolvable. In other words, even though Gödel was able to prove that there are undecidable theorems in mathematics it does not prove that the Goldbach Conjecture is undecidable or unprovable.john_a_designer_{February 27, 2020
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"Why ’77’" Well because both bornagain, and bornagain7 were taken when I first set up my e-mail account way back in the mid 1990s. I had to settle for bornagain77. :)bornagain77_{February 27, 2020
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BA77, 49: You are right, the author of that article choose his words very poorly. Yeah, you have to be really careful when talking about this kind of stuff. Why '77' by the way? Just curious. It's a year I remember well. But anyways, regardless of the fact that mathematics itself is now shown to be incomplete, which you yourself agree that you “have to rationalise from outside a given set of axioms”, mathematicians and physicists today still act as if ‘the truth’, i.e. the ‘theory of everything’, can be reached by mathematics and observation alone. Not a view I share. But I'll stay out of the philosophical aspects; I know so little I can't even be wrong, just moronic.JVL_{February 27, 2020
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All hope for a coherent 'theory of everything' is not lost though. A major problem that crops up in trying to unify quantum mechanics and general relativity is that when theorists try to combine the two theories, then the resulting theory predicts that spacetime, atoms, and the universe itself should all be literally torn apart. Here are a few references that get this point across.
“There are serious problems with the traditional view that the world is a space-time continuum. Quantum field theory and general relativity contradict each other. The notion of space-time breaks down at very small distances, because extremely massive quantum fluctuations (virtual particle/antiparticle pairs) should provoke black holes and space-time should be torn apart, which doesn’t actually happen.” – Gregory J. Chaitin , Francisco A. Doria, and Newton C. a. Da Costa – Goedel’s Way: Exploits into an Undecidable World “In order for quantum mechanics and relativity theory to be internally self-consistent [Seeking consistency between quantum mechanics and relativity theory is the major task theoretical physicists have been grappling with since quantum mechanics emerged], the physical vacuum has to contain 10^94 grams equivalent of energy per cubic centimeter. What that means is, if you take just a single hydrogen atom, which is one proton and one electron and all the rest of the atom is ‘empty space,’ if you take just that volume of empty space, … you find that you end up with a trillion times as much vacuum energy as all the electromagnetic energy in all the planets, all the stars, and all the cosmic dust in a sphere of radius 15 billion light-years.” To summarize, the subtle energy in the vacuum space of a single hydrogen atom is as great as all the electromagnetic energy found in everything within 15 billion light-years of our space-time cosmos.” ,,, Dr. William Tiller – Human Intention Cosmic coincidence spotted – Philip Ball – 2008 Excerpt: One interpretation of dark energy is that it results from the energy of empty space, called vacuum energy. The laws of quantum physics imply that empty space is not empty at all, but filled with particles popping in and out of existence. This particle ‘fizz’ should push objects apart, just as dark energy seems to require. But the theoretical value of this energy is immense — so huge that it should blow atoms apart, rather than just causing the Universe to accelerate. Physicists think that some unknown force nearly perfectly cancels out the vacuum energy, leaving only the amount seen as dark energy to push things apart. This cancellation is imperfect to an absurdly fine margin: the unknown ‘energy’ differs from the vacuum energy by just one part in 10^122. It seems incredible that any physical mechanism could be so finely poised as to reduce the vacuum energy to within a whisker of zero, but it seems to be so. http://www.nature.com/news/2008/080219/full/news.2008.610.html The 2 most dangerous numbers in the universe are threatening the end of physics – Jessica Orwig – Jan. 14, 2016 Excerpt: Dangerous No. 2: The strength of dark energy ,,, you should be able to sum up all the energy of empty space to get a value representing the strength of dark energy. And although theoretical physicists have done so, there’s one gigantic problem with their answer: “Dark energy should be 10^120 times stronger than the value we observe from astronomy,” Cliff said. “This is a number so mind-boggling huge that it’s impossible to get your head around … this number is bigger than any number in astronomy — it’s a thousand-trillion-trillion-trillion times bigger than the number of atoms in the universe. That’s a pretty bad prediction.” On the bright side, we’re lucky that dark energy is smaller than theorists predict. If it followed our theoretical models, then the repulsive force of dark energy would be so huge that it would literally rip our universe apart. The fundamental forces that bind atoms together would be powerless against it and nothing could ever form — galaxies, stars, planets, and life as we know it would not exist. http://finance.yahoo.com/news/two-most-dangerous-numbers-universe-194557366.html
And yet, despite both theories contradicting each other to the point of 'blowing up the universe', never-the-less quantum mechanics and general relativity are both tested to extreme levels of precision, so we can have extreme confidence that both theories are true. And herein is where our reasoning outside 'the circle of mathematics' becomes necessary. Since quantum mechanics and general relativity are both tested to extreme levels of precision, and we can thus have a very high level of confidence that both theories are in fact true, and since Godel’s incompleteness theorem requires that 'something' must be assumed to be ‘outside the circle’ of mathematics, then it is safe to assume that something very powerful must be holding the universe together. ,,, After all we do not see the universe blowing up do we? Atheists have nothing to appeal to, whereas Christianity predicts that Christ is before all things, and in him all things hold together, and also that He upholds the universe by the word of his power.
Colossians 1:17 He is before all things, and in him all things hold together. Hebrews 1:3 He is the radiance of the glory of God and the exact imprint of his nature, and he upholds the universe by the word of his power.
Further note to Christ, particularly the resurrection of Jesus Christ from the dead, being the correct 'theory of everything':
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: January 2020 https://uncommondescent.com/intelligent-design/welcome-to-the-brave-new-world-of-science/#comment-690569
bornagain77_{February 27, 2020
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JVL, i agree completely with you that Gödel's critique applies to mathematics and not to logic itself. After all, Gödel himself used logic to develop his proof against the belief that mathematics was complete. You are right, the author of that article choose his words very poorly. The main reason I cited that particular article was because of this comment in particular from the article
The second was the Undecidability Theorem, which proves that logic cannot be used to decide the truth or falsity of certain statements. One famous example is Euclid’s Parallel Postulate. Whether it is true or false is a matter of choice, not logic. If we choose to deny this postulate, we create a non-Euclidean geometry which has its own valid and useful insights, quite different from the Euclidean world we studied in school.
Moreover, I also laid out the fact that we know that the parallel postulate does not hold for the non-Euclidean geometries of special relativity and general relativity, geometries in which parallel lines do not stay parallel and 90-degree turns do not behave as true 90-degree turns. But anyways, regardless of the fact that mathematics itself is now shown to be incomplete, which you yourself agree that you "have to rationalise from outside a given set of axioms", mathematicians and physicists today still act as if 'the truth', i.e. the 'theory of everything', can be reached by mathematics and observation alone. The search for the ultimate truth about reality in science today takes the form of trying to find the hypothetical final mathematical ‘theory of everything’. Indeed much money and research has been dedicated to this particular endeavor. In its present form this search entails trying to mathematically unify general relativity and quantum field theory (QED), (which is the unification quantum mechanics and special relativity), into a single mathematical ‘theory of everything’. It is hoped that this hypothetical final ‘theory of everything’ will be ‘capable of describing all phenomena in the universe.’
Theory of everything Excerpt: a theoretical framework revealing a deeper underlying reality,,,, a single theory that, in principle, is capable of describing all phenomena in the universe. https://en.wikipedia.org/wiki/Theory_of_everything
As the following article states, “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.”
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). http://www.infoplease.com/cig/theories-universe/quantum-mechanics-vs-general-relativity.html Quantum field theory – History Excerpt: ,,, (Quantum field theory) QFT is an unavoidable consequence of the reconciliation of quantum mechanics with special relativity (Weinberg (1995)),,, The first achievement of quantum field theory, namely quantum electrodynamics (QED), is “still the paradigmatic example of a successful quantum field theory” (Weinberg (1995)). per wikipedia
Interestingly, “Although quantum field theory is fully compatible with the special theory of relativity, a relativistic treatment of quantum measurement has yet to be formulated.”, i.e. conscious observation was dropped by the wayside in QFT!
Not So Real – Sheldon Lee Glashow – Oct. 2018 Review of: “What Is Real? The Unfinished Quest for the Meaning of Quantum Physics” by Adam Becker Excerpt: Heisenberg, Schrödinger, and their contemporaries knew well that the theory they devised could not be made compatible with Einstein’s special theory of relativity. First order in time, but second order in space, Schrödinger’s equation is nonrelativistic. Although quantum field theory is fully compatible with the special theory of relativity, a relativistic treatment of quantum measurement has yet to be formulated. https://inference-review.com/article/not-so-real
In what should be needless to say, since ‘conscious observation’ itself was dropped by the wayside in QFT , then that necessarily precludes QFT from being the correct step towards the final ‘theory of everything’ that supposedly “is capable of describing all phenomena in the universe". But anyways, Richard Feynman (and others) were only able to unify special relativity and quantum mechanics into Quantum Electrodynamics by quote unquote “brushing infinity under the rug” with a technique called Renormalization.
THE INFINITY PUZZLE: Quantum Field Theory and the Hunt for an Orderly Universe Excerpt: In quantum electrodynamics, which applies quantum mechanics to the electromagnetic field and its interactions with matter, the equations led to infinite results for the self-energy or mass of the electron. After nearly two decades of effort, this problem was solved after World War II by a procedure called renormalization, in which the infinities are rolled up into the electron’s observed mass and charge, and are thereafter conveniently ignored. Richard Feynman, who shared the 1965 Nobel Prize with Julian Schwinger and Sin-Itiro Tomonaga for this breakthrough, referred to this sleight of hand as “brushing infinity under the rug.” http://www.americanscientist.org/bookshelf/pub/tackling-infinity
And whereas special relativity, by ‘brushing infinity under the rug’, has been semi-successfully unified, (i.e. save of course for quantum measurement), with quantum theory to produce Quantum Electrodynamics and/or Quantum Field Theory, no such mathematical ‘sleight of hand’ exists for unifying general relativity with quantum mechanics. General relativity, as the following articles show, simply refuses to be mathematically unified with quantum mechanics in any acceptable way. In technical terms, Gravity has yet to be successfully included into a theory of everything since the infinities that crop up in that attempt simply are not renormalizable as they were in Quantum-Electrodynamics.
Does quantum mechanics contradict the theory of relativity? Sanjay Sood, Microchip Design Engineer, Theoretical and Applied Physicist – Feb 14, 2016 Excerpt: quantum mechanics was first integrated with special theory of relativity by Dirac in 1928 just 3 years after quantum mechanics was discovered. Dirac produced an equation that describes the behavior of a quantum particle (electron). In this equation the space and time enter on the same footing – equation is first order in all 4 coordinates. One startling by product of this equation was the prediction of anti matter. It also gave the correct explanation for the electron’s spin. Dirac’s equation treats an electron as a particle with only a finite degrees of freedom. In 1940s Dirac’s equation was incorporated into the relativistic quantum field theory that’s knowns as quantum electrodynamics (QED) independently by Feynman, Schwinger and Tomonaga. This is the theory that describes the behavior of electrons and photons and their interactions with each other in terms of relativistic quantum fields that have infinite degrees of freedom. QED allowed extremely precise calculation of anomalous magnetic dipole moment of an electron. This calculated value matches the experimentally measured value to an astonishing precision of 12 decimal places! The integration of Einstein’s general theory of relativity and quantum mechanics has proved to be far more difficult. Such an integration would give a quantum theory of gravity. Even after a sustained effort lasting more than half a century, no renormalized quantum field theory of gravity has ever been produced. Renormalization means a theory that’s free of infinities at zero distance or infinite energy because 2 point particles can interact with each other at zero distance. A non renormalizable theory has no predictive value because it contains an infinite number of singular coefficients. https://www.quora.com/Does-quantum-mechanics-contradict-the-theory-of-relativity Unified field theory Excerpt: Gravity has yet to be successfully included in a theory of everything. Simply trying to combine the graviton with the strong and electroweak interactions runs into fundamental difficulties since the resulting theory is not renormalizable. Theoretical physicists have not yet formulated a widely accepted, consistent theory that combines general relativity and quantum mechanics. The incompatibility of the two theories remains an outstanding problem in the field of physics. Some theoretical physicists currently believe that a quantum theory of general relativity may require frameworks other than field theory itself, such as string theory or loop quantum gravity. https://en.wikipedia.org/wiki/Unified_field_theory#Current_status 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.
This mathematically ‘infinite’ divide to there ever being a purely mathematical ‘theory of everything’ should have, somewhat, been foreseen. Godel’s incompleteness theorem implies exactly that. There simply never will be a purely mathematical ‘theory of everything’. As Hawking himself conceded, “Kurt Gödel halted the achievement of a unifying all-encompassing theory of everything” and,, “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)
In fact, Gödel’s incompleteness theorem has now been extended to physics and is not just some abstract mathematical limit that prevents there from ever being a purely mathematical ‘theory of everything’ but is now shown to be, in actuality, a defining feature of reality: In the following article entitled ‘Quantum physics problem proved unsolvable: Gödel and Turing enter quantum physics’, which studied the derivation of macroscopic properties from a complete microscopic description, the researchers remark that even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behaviour.,,, The researchers further commented that their findings challenge the reductionists’ point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description.”
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.,,, “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.” http://phys.org/news/2015-12-quantum-physics-problem-unsolvable-godel.html
Simply put, despite how much mathematicians and physicists may believe that there simply must be a purely mathematical ‘theory of everything’ that exist out there somewhere, there, in fact, never will be a purely mathematical theory of everything that links the microscopic world of quantum mechanics to the macroscopic world of General Relativity.bornagain77_{February 27, 2020
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BA77, 45: This means that the ‘whole’ truth about numbers will forever remain outside the grasp of logical reasoning. No, it means that you cannot discover everything that is true about a system with a brick-by-brick construction of theorems. You may have to rationalise from outside a given set of axioms. Not outside the grasp of logical reasoning just outside a particular built-up structure. Godel proved what poets have always known, that transcendental truths are beyond the reach of reason: Again, Gödel was making statements about mathematics, that's it. And, by the way, there are 'transcendental' numbers like ? and e. Okay, that's just by definition but there's a reason that term was picked. If you think there are things that reason cannot touch then how could reason prove that that is the case?JVL_{February 27, 2020
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From the Wikipedia article on Kurt Gödel:
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." Describing religion(s) in general, Gödel said: "Religions are, for the most part, bad—but religion is not". According to his wife Adele, "Gödel, although he did not go to church, was religious and read the Bible in bed every Sunday morning", while of Islam, he said, "I like Islam: it is a consistent [or consequential] idea of religion and open-minded."
He sounds like a pretty interesting person!JVL_{February 27, 2020
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"MATERIALISM IS FALSE” – KURT GÖDEL
"Although Kurt Gödel has not become a household name like Albert Einstein, he was one of the greatest logicians in history, a towering intellectual giant who was also a close companion of Einstein and John von Neumann at the Institute for Advanced Study in Princeton." "What on earth (or in the heavens) could have prompted Gödel to reject materialism?" [... ]"One is left wondering: was Plato correct in referring to materialists as ‘terrible men’ and ‘very stubborn and perverse mortals’?" Dr. John H. Spencer
https://drjohnhspencer.com/materialism-is-false-kurt-godel/Truthfreedom_{February 27, 2020
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In response to Vivid and JVL at 40 and 41
Godel’s theorems & the limits of reason Dr Asad Zaman - April 12, 2015 German logician Kurt Godel finally achieved spectacular and entirely unexpected results in this area. His first result was the Incompleteness Theorem. This showed that no matter how we formulate the axiomatic-deductive machinery, there will always exist true statements about numbers which this machinery cannot prove. This means that the ‘whole’ truth about numbers will forever remain outside the grasp of logical reasoning. The second was the Undecidability Theorem, which proves that logic cannot be used to decide the truth or falsity of certain statements. One famous example is Euclid’s Parallel Postulate. Whether it is true or false is a matter of choice, not logic. If we choose to deny this postulate, we create a non-Euclidean geometry which has its own valid and useful insights, quite different from the Euclidean world we studied in school. The Enlightenment hopes that man could reach truth purely by observations and logic, cannot be fulfilled even in the limited domain of mathematics. Godel proved what poets have always known, that transcendental truths are beyond the reach of reason: https://tribune.com.pk/story/868779/godels-theorems-the-limits-of-reason/?
In fact, the non-Euclidean geometries of special relativity and general relativity, geometries in which parallel lines do not stay parallel and 90-degree turns do not behave as true 90-degree turns, are found to be the actual geometries that describe the space-time of this universe. https://uncommondescent.com/intelligent-design/faith-even-mathematics-depends-on-some-unprovable-assumptions/#comment-690689 In fact, in so far as measurement accuracy will allow, the non-Euclidean geometries of special relativity and general relativity are found to be the 'platonically perfect' mathematical descriptions of the non-Euclidean geometries of this universe
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. Copernicus, (who was heavily influenced by Platonic thinking), imagined (incorrectly) that the planets move in perfect circles (rather than ellipses). Later, Newton, for allowing God could adjust the orbits of the planets, was chastised by Leibniz, (and Laplace) for having a “very narrow ideas about the wisdom and the power of God.”.. i.e. For having a narrow view of the perfection of God.... Normally, as mentioned previously by Dr. Michael Egnor, and as Ethan Siegel himself alluded to in his article, “Mathematics is entirely about concepts, which have no precise instantiation in nature,,”... 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
bornagain77_{February 27, 2020
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KF, 43: For me Fourier analysis (transforms and series) are just mathematical procedures that make doing some other things easier. They're just mathematical analytic tools, not haunting at all! I guess you're thinking of how they point out how complicated things are built up of simpler pieces? I'm not sure why there is a particular significance in hearing and vision. If you'd like to elucidate that would be great but if you're not bothered that's okay too!JVL_{February 27, 2020
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JVL, Fourier series and integral analysis with related things like Laplace and Z transforms surfaces the frequency-phase domain as a dual to our time domain experience of dynamical processes. Along the way, integrals and differentials get absorbed, leading to a complex frequency perspective. In that context we enrich the digital-analogue divide. As an entry point, ponder how hearing effects a translation to the frequency domain using the cochlea. Similarly ponder our colour vision system. KFkairosfocus_{February 27, 2020
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KF, 33: as A/D and D/A exist and do so in a Fourier haunted world. I just notice this statement. What do you mean by "Fourier haunted world"? Fourier analysis?JVL_{February 27, 2020
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Vividbleau, 46: According to Gödel in what sense can we say mathematical propositions are true when they are not provable? If they are not provable then the truth or falsity rests on certain propositions and beliefs. That's not quite what Gödel actually showed. From Wikipedia:
Gödel published his two incompleteness theorems in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.
and
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.
Most of the mathematics that most of us are familiar with can be proved. Think of the Pythagorean Theorem. That is incontrovertibly true to the point that trying to disprove it is predictably a waste of time. Now the Axiom of Choice . . . that's a much more slippery concept.JVL_{February 26, 2020
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