Fields medalist says math really exists

_{Denyse O'Leary

September 29, 2019

Intelligent Design, Mathematics}

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Presumably, that means medalist Alain Connes was never drafted into the current war on math.

Among a number of mathematicians who think that math really exists we find him quoted:

Alain Connes, Fields Medalist 1982:
“Two extreme viewpoints are opposed in relation to mathematical activity. The first, to which I completely subscribe, is of Platonic inspiration: it postulates that there exists a mathematical reality, raw, primitive, which predates its discovery. A world which exploration requires the creation of tools, as it was necessary to invent vessels to cross the oceans. The second viewpoint is the one of the formalists; they deny any preexistence to mathematics, believing that they are a formal game, based on axioms and logical deductions, thus a pure human creation.”
Then he adds,
“This viewpoint seems more natural to the non-mathematician, who refuses to postulate an unknown world of which he has no perception. People understand that mathematics is a language, but not that it is a reality external to the human spirit. The great discoveries of the twentieth century, especially the works of Gödel, have shown that the formalist viewpoint is not tenable. Whatever the exploratory medium, the formal system used, there will always be mathematical truths that will elude it, and mathematical reality cannot be reduced to the logical consequences of a formal system.”
Antoine Bret, “ I’d say math exist” at Antoine’s Blog

Bret, who describes himself as a Christian and a physicist, offers a number of other quotable quotes on the reality of math.

The “formalist” idea that math doesn’t really exist helps account for Big Brother’s world in which 2+2=5 if the Party says so.

So okay, if math really exists, it undermines a great deal of the nonsense barked about consciousness as an evolved illusion. That is, if consciousness enables us to apprehend what really exists, there is good reason for believing that consciousness itself exists.

Ridiculous theories about consciousness also exist but, like unicorns, they are abstractions that do not coincide with reality.

Hat tip: Philip Cunningham

See also: The progressive war on science takes dead aim at math

Comments

BA77's #8 '‘What is referred to as M-theory isn’t even a theory. It’s a collection of ideas, hopes, aspirations.' ROFL. Really. Truly. Well, not literally physically. But some truths are just riotously comical to read ; and brevity being the soul of wit, the more economically expressed, the more hilarious. At last, I can see myself as a scientist ! Science for drop-outs. In another connection : 'This statement is just fascinating! Why in blue blazes should the finely tuned entropic actions of the universe, entropic actions which happen to explain time itself, even care if I am, via the quantum zeno effect and quantum information theory, consciously observing them unless “an observer who describes a system” really is more foundational to this universe than the finely tuned 1 in 10^10^123 entropy of the universe is?' Shades of my notion that we each live in a little, divinely-created world of our own, integrated and coordinated by the Almighty to appear seamless at the mechanistic level. I mentioned that it seemed to be implied by the remark of a rabbi in the Talmud, a very mixed source of wisdom, admittedly, when he asserted that when a person dies, a whole world dies with him. However, it also seems to be implied by the whole primacy of the Observer discovery at the quantum level. Or does it ? Somebody was kind enough to actually provide the 'chapter and verse' in the Talmud - though I was too disorganised to record it.Axel_{September 30, 2019
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In the following paper, the researchers 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
And to further drive this point home, the following study ‘concluded that it would take 34 Thousand Billion Watts of VUV radiations to make 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 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. https://www.ewtn.co.uk/news/latest/astonishing-discovery-at-christ-s-tomb-supports-turin-shroud
Moreover, the overturning of the Copernican principle by both General Relativity and Quantum Mechanics adds considerable weight to my claim that Jesus’s resurrection from the dead is the correct ‘theory of everything’
July 2019 – Overturning of the Copernican Principle by both General Relativity and Quantum Mechanics https://uncommondescent.com/intelligent-design/we-are-invited-to-consider-a-simpler-perspective-on-the-laws-of-physics/#comment-680427
And thus in conclusion, if 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 of modern science),,, and as quantum mechanics itself now empirically demands (with the confirmation of the Maxwell Demon thought experiment that empirically demonstrated that 'entropy is a property of an observer who describes the system', as well as with the closing of the free will loophole by Anton Zeilinger and company in 2018), if 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”. Verse and video:
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. Turin Shroud Hologram Reveals The Words “The Lamb” – Petrus Soons – video https://www.youtube.com/watch?v=4Tmka1l8GAQ
bornagain77_{September 30, 2019
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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/
This statement is just fascinating! Why in blue blazes should the finely tuned entropic actions of the universe, entropic actions which happen to explain time itself, even care if I am, via the quantum zeno effect and quantum information theory, consciously observing them unless "an observer who describes a system” really is more foundational to this universe than the finely tuned 1 in 10^10^123 entropy of the universe is? To state the obvious, this empirical 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 and adds considerable empirical weight to the already powerful philosophical and/or logical proofs that the Christian Theist already has that God must be behind the "miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics" Moreover, unlike atheistic materialism which predicted none of this, Christianity predicted that the Mind of God is behind entropy of the universe thousands of years ago before empirical science even came along. 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.
Of supplemental note, 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/article/info%3Adoi/10.1371/journal.pgen.0030220 Dr. John Sanford Lecture at NIH (National Institute of Health): Genetic Entropy - Can Genome Degradation be Stopped? https://www.youtube.com/watch?v=2Mfn2upw-O8
As well it is interesting to note that the primary source for increasing entropy in the universe are Black holes:
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
Kip Thorne describes the extremely destructive power inherent in black holes in this following quote:
“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
i.e. Black Holes are found to be ‘timeless’, i.e. ‘eternal’, singularities of destruction and disorder rather than being singularities of creation and order such as the extreme order we see at the creation event of the Big Bang.
“But why was the big bang so precisely organized, 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 - How Special Was The Big Bang?
Needless to say, the implications of this ‘eternity of destruction’ should be fairly disturbing for those of us who are of a. shall we say, ‘spiritually minded’ persuasion!
Quantum Mechanics, Special Relativity, General Relativity and Christianity (USA) (Special and General Relativity compared to Heavenly and Hellish Near Death Experiences) https://www.youtube.com/watch?v=h4QDy1Soolo
Thus in order to deal with the entropy associated with death itself it necessarily follows that gravity itself must somehow be dealt with. And again, unlike atheists who, with string theory and its red step child M-theory, are basically in mathematical fantasy-land,
‘What is referred to as M-theory isn’t even a theory. It’s a collection of ideas, hopes, aspirations. It’s not even a theory and I think the book is a bit misleading in that respect. It gives you the impression that here is this new theory which is going to explain everything. It is nothing of the sort. It is not even a theory and certainly has no observational (evidence),,, I think the book suffers rather more strongly than many (other books). It’s not a uncommon thing in popular descriptions of science to latch onto some idea, particularly things to do with string theory, which have absolutely no support from observations.,,, They are very far from any kind of observational (testability). Yes, they (the ideas of M-theory) are hardly science.” – Roger Penrose – former close colleague of Stephen Hawking – in critique of Hawking’s new book ‘The Grand Design’ the exact quote is in the following video clip: Roger Penrose Debunks Stephen Hawking’s New Book ‘The Grand Design’ – video https://www.youtube.com/watch?v=Dg_95wZZFr4
And again, unlike atheists who, with string theory and its red step child M-theory, are basically in mathematical fantasy-land, the Christian Theist can appeal directly to empirical evidence, via the Shroud of Turin, to support his claim that Jesus Christ dealt with gravity, and thus defeated death itself, in his resurrection from the dead. In the following video Isabel Piczek states,,, 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.
“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 – 2:20 mark Turin shroud – (Particle Physicist explains event horizon) – video https://www.youtube.com/watch?v=HHVUGK6UFK8 A Quantum Hologram of Christ’s Resurrection? by Chuck Missler Excerpt: “You can read the science of the Shroud, such as total lack of gravity, lack of entropy (without gravitational collapse), no time, no space—it conforms to no known law of physics.” The phenomenon of the image brings us to a true event horizon, a moment when all of the laws of physics change drastically. Dame Piczek created a one-fourth size sculpture of the man in the Shroud. When viewed from the side, it appears as if the man is suspended in mid air (see graphic, below), indicating that the image defies previously accepted science. The phenomenon of the image brings us to a true event horizon, a moment when all of the laws of physics change drastically. Per khouse
The following article, (which is behind a paywall), 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.’
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/sre/PDF/pdf2012/30JulSpeIss/Antonacci.pdf
Kevin Moran, who is an optical engineer who worked on the mysterious ‘3-Dimensional’ nature of the Shroud image, states that,, ,,, “The radiation that made the image acted perfectly parallel to gravity. There is no side image.,,, 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,,, 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
bornagain77_{September 30, 2019
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As to:
“The great discoveries of the twentieth century, especially the works of Gödel, have shown that the formalist viewpoint is not tenable. Whatever the exploratory medium, the formal system used, there will always be mathematical truths that will elude it, and mathematical reality cannot be reduced to the logical consequences of a formal system.”
And although the Christian Theist indeed has very powerful philosophical and/or logical proofs that God must be behind the "miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics",,,.
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/MathDrama/reading/Wigner.html 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/ 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# etc.. etc.. etc..
And although the Christian Theist indeed has very powerful philosophical and/or logical proofs that God must be behind the "miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics", the Christian Theist can now also appeal to empirical science itself in order to further ‘scientifically’ prove that God must behind the "miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics". In laying this empirical proof out, I will appeal to the ‘Quantum Zeno Effect’ and also to the recent experimental realization of the Maxwell demon thought experiment.. 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
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. 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/2015/150414/ncomms7811/full/ncomms7811.html?WT.ec_id=NCOMMS-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 possible materialistic explanation. And thus the statement of “an unstable particle, if observed continuously, will never decay”, stands as being a true statement. Moreover, on top of that, in quantum information theory, through experimental realiztion of the Maxwell demon thought experiment, it is now shown that entropy is not a property of a system, but "a property of an observer who describes a system.” 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/
Again to repeat that last sentence,“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 reason why I am very impressed with these developments in quantum information theory which empirically demonstrate that entropy is "a property of an observer who describes a system.”, is that the second law of thermodynamics, entropy, is VERY foundational in its explanatory role in science. 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/shining-light-on-dark-energy/
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? http://irafs.org/irafs_1/cd_irafs02/texts/penrose.pdf
In the following video, Dr, Bruce Gordon touches upon just how jaw droppingly 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
bornagain77_{September 30, 2019
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The clip is obviously from a longer speech, but I, along with the science teacher, always talked about accuracy and significant digits at the start of the year. We stressed that measured quantities are never exact, and in the real world use of math you had to pay attention to that. The science teacher taught that a distance of 5 cm, for instance is 5 ± 0.5, 5.0 is 5 ± 0.05, 5.00 is 5 ± 0.005, etc. I think that is Krauss' point. This has nothing to do with News' statement.hazel_{September 30, 2019
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BA77, Krause plays equivocation. What is perhaps arguable is that ~ 2 + ~ 2 = ~ (3 to 5) That is 1.5 + 1.5 = 3 and 2.5 + 2.5 = 5 where those are outer limits for roughly 2, represented as ~2. KFkairosfocus_{September 30, 2019
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Folks, Connes has a money-shot point pivoting on the irreducible complexity of describable structure and quantity:
The great discoveries of the twentieth century, especially the works of Gödel, have shown that the formalist viewpoint is not tenable. Whatever the exploratory medium, the formal system used, there will always be mathematical truths that will elude it, and mathematical reality cannot be reduced to the logical consequences of a formal system.
KFkairosfocus_{September 30, 2019
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Lawrence Krauss - 2+2=5 https://www.youtube.com/watch?v=NOrlIOm6eGMbornagain77_{September 29, 2019
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News say; "The “formalist” idea that math doesn’t really exist helps account for Big Brother’s world in which 2+2=5 if the Party says so." Hogwash. I'm not getting into this again, but News ought to at least not say ridiculous things that conflates a serious viewpoint in mathematical philosophy with Orwellian brainwashing.hazel_{September 29, 2019
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Well, it depends on the definition of math. Many math-style functions are intrinsic to life. Exp, log, tanh, counting, adding, subtracting, inequalities and comparisons, several levels of derivatives and integrals. All living things perform these functions all the time. Other math-style rules are NOT intrinsic to life. The commutative and associative properties never work in living math. Proofs aren't part of math at all. Proofs are just a peculiar hobby that academics enjoy, like arguing about citations or competing for grants. The above discussion about Godel has no connection to math.polistra_{September 29, 2019
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