Mysterious link between physics and math?

_{Denyse O'Leary

February 26, 2020

Cosmology, Intelligent Design, Mathematics, Physics}

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In an enormously complicated 165-page paper, computer scientist Zhengfeng Ji and colleagues present a result that penetrates to the heart of deep questions about math, computing and their connection to reality. It’s about a procedure for verifying the solutions to very complex mathematical propositions, even some that are believed to be impossible to solve. In essence, the new finding boils down to demonstrating a vast gulf between infinite and almost infinite, with huge implications for certain high-profile math problems. Seeing into that gulf, it turns out, requires the mysterious power of quantum physics.
Tom Siegfried, “How a quantum technique highlights math’s mysterious link to physics” at ScienceNews

It’s not entirely clear why a link between physics and math should be mysterious. If mathematics underlies the universe, we ought to expect such links.

Of course, some people may believe that mathematics is an illusion generated by the human brain to aid survival and reproduction. But that is their lookout.

Comments

Pav, you might appreciate this as well
“I’m not an atheist and I don’t think I can call myself a pantheist. We are in the position of a little child entering a huge library filled with books in many languages. The child knows someone must have written those books. It does not know how. It does not understand the languages in which they are written. The child dimly suspects a mysterious order in the arrangement of the books but it doesn’t know what it is. That it seems to me, is that attitude of even the most intelligent human being toward God. We see the universe marvelously arranged and obeying certain laws but only dimly understand these laws. Our limited minds cannot grasp the mysterious force that moves the constellations.” - Einstein “In the view of such harmony in the cosmos which I, with my limited human mind, am able to recognize, there are yet people who says there is no God. But what makes me really angry is that they quote me for support of such views. “ (The Expanded Quotable Einstein, Princeton University, page 214)”
bornagain77_{February 27, 2020
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BA77: Well done. I'm particularly delighted with your quotes from 'latter-day' Einstein. Einstein was, of course, very religious as a youth, but later much influenced by positivists. He outgrew them, apparently.PaV_{February 27, 2020
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In essence, the new finding boils down to demonstrating a vast gulf between infinite and almost infinite "Almost infinite", eh? This is a new one for me but I can't bring myself to read the full article. I never believed in the crackpottery of infinity but "almost infinite" has crushed any faith I might have had. This is embarrassing for a science writer.FourFaces_{February 26, 2020
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as to this comment from the article,
But the new work isn’t likely to make any immediate impact in the everyday world. For one thing, all-knowing provers do not exist, and if they did they would probably have to be future super-AI quantum computers with unlimited computing capability (not to mention an unfathomable supply of energy). Nobody knows how to do that in even Star Trek’s century.
Actually, Godel's incompleteness plays into that as well,
A Mono-Theism Theorem: Gödelian Consistency in the Hierarchy of Inference - Winston Ewert and Robert J. Marks II - June 2014 Abstract: Logic is foundational in the assessment of philosophy and the validation of theology. In 1931 Kurt Gödel derailed Russell and Whitehead’s Principia Mathematica by showing logically that any set of consistent axioms will eventually yield unknowable propositions. Gödel did so by showing that, otherwise, the formal system would be inconsistent. Turing, in the first celebrated application of Gödelian ideas, demonstrated the impossibility of writing a computer program capable of examining another arbitrary program and announcing whether or not that program would halt or run forever. He did so by showing that the existence of a halting program can lead to self-refuting propositions. We propose that, through application of Gödelian reasoning, there can be, at most, one being in the universe omniscient over all other beings. This Supreme Being must by necessity exist or have existed outside of time and space. The conclusion results simply from the requirement of a logical consistency of one being having the ability to answer questions about another. The existence of any question that generates a self refuting response is assumed to invalidate the ability of a being to be all-knowing about the being who was the subject of the question. http://robertmarks.org/REPRINTS/2014_AMonoTheismTheorem.pdf
bornagain77_{February 26, 2020
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>One expert, upon hearing the news, compared his feces to bricks. Why were they asking a mason about math problems?EDTA_{February 26, 2020
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As to these comments from the article,
How a quantum technique highlights math’s mysterious link to physics - FEBRUARY 17, 2020 Verifying proofs to very hard math problems is possible with infinite quantum entanglement Tom Siegfried Excerpt: "Refuting the Connes conjecture, and showing that MIP (multiprover interactive proof) plus entanglement could be used to verify immensely complicated proofs, stunned many in the mathematical community. (One expert, upon hearing the news, compared his feces to bricks.) ,,, On another level, the new work raises an interesting point about the relationship between math and the physical world. The existence of quantum entanglement, a (surprising) physical phenomenon, somehow allows mathematicians to solve problems that seem to be strictly mathematical. Wondering why physics helps out math might be just as entertaining as contemplating math’s unreasonable effectiveness in helping out physics. Maybe even one will someday explain the other." https://www.sciencenews.org/article/how-quantum-technique-highlights-math-mysterious-link-physics
Well sorry to disappoint you Tom Siegfried but your belief that "Maybe even one (physics) will someday explain the other (mathematics)" is simply out of the question. As Alexander Vilenkin noted, at one time the physical universe itself did not exist and thus we are stuck with the question of "where did the laws of quantum theory come from?" Vilenken even dares to ask, "Does this mean that the laws are not mere descriptions of reality and can have an independent existence of their own? In the absence of space, time, and matter, what tablets could they be written upon? The laws are expressed in the form of mathematical equations. If the medium of mathematics is the mind, does this mean that mind should predate universe?,,,"
In the Beginning was Quantum Mechanics? - NOVEMBER 30, 2012 - WALLACE G. SMITH Excerpt: “If the universe owes its origins to quantum theory, then quantum theory must have existed before the universe. So the next question is surely: where did the laws of quantum theory come from?”,,, "Does this mean that the laws are not mere descriptions of reality and can have an independent existence of their own? In the absence of space, time, and matter, what tablets could they be written upon? The laws are expressed in the form of mathematical equations. If the medium of mathematics is the mind, does this mean that mind should predate universe?,,," - Alexander Vilenkin https://wallacegsmith.wordpress.com/tag/alex-vilenkin/
In fact, besides the physical universe itself, (i.e. all space, time, and matter), having a beginning, and therefore the physical universe itself being causally incomplete, mathematics itself is also incomplete,
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
Thus since the physical universe and mathematics itself are both 'incomplete', then it necessarily follows that ,, "the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.”
BRUCE GORDON: Hawking’s irrational arguments – October 2010 Excerpt: ,,,The physical universe is causally incomplete and therefore neither self-originating nor self-sustaining. The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,, Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.” Anything else invokes random miracles as an explanatory principle and spells the end of scientific rationality. http://www.washingtontimes.com/news/2010/oct/1/hawking-irrational-arguments/
I also note that Tom Siegfried backed off using the word 'miracle' from Wigner's essay on 'the unreasonable effectiveness of Mathematics', and instead opted to highlight the word 'mysterious' from the essay,
Nobel laureate physicist Eugene Wigner alluded to math’s mysterious power as the “unreasonable effectiveness of mathematics in the natural sciences.” Somehow, Wigner said, math devised to explain known phenomena contains clues to phenomena not yet experienced — the math gives more out than was put in. “The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and … there is no rational explanation for it,”
Myself, I prefer to highlight the word 'miracle' that Wigner used, several times, in his essay.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences - Eugene Wigner - 1960 Excerpt: ,,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
Einstein himself did not hesitate to use the "Miracle" word, and Einstein even went so far as to chastise 'professional atheists' in the process of using the 'Miracle' word..
On the Rational Order of the World: a Letter to Maurice Solovine - Albert Einstein - March 30, 1952 Excerpt: "You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such a comprehensibility) as a miracle or as an eternal mystery. Well, a priori, one should expect a chaotic world, which cannot be grasped by the mind in any way .. the kind of order created by Newton's theory of gravitation, for example, is wholly different. Even if a man proposes the axioms of the theory, the success of such a project presupposes a high degree of ordering of the objective world, and this could not be expected a priori. That is the 'miracle' which is constantly reinforced as our knowledge expands. There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods but “bared the miracles." -Albert Einstein http://inters.org/Einstein-Letter-Solovine
I will conclude with a quote from mathematician John Lennox
“Our answer to the question of why the universe is rationally intelligible will in fact depend, not on whether we are scientists or not, but on whether we are theists or naturalists. Theists will say that the intelligibility of the universe is grounded in the nature of the ultimate rationality of God: both the real world and the mathematics are traceable to the Mind of God who created both the universe and the human mind. It is therefore, not surprising when the mathematical theories spun by human minds created in the image of God’s Mind, find ready application in a universe whose architect was that same creative mind.” - John Lennox http://www.logosapologia.org/?p=2874
bornagain77_{February 26, 2020
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