Sabine Hossenfelder: Is math real?

_{Denyse O'Leary

July 31, 2021

Intelligent Design, Mathematics, Philosophy}

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It is a deeper question than some might suppose:

The idea has more recently been given a modern formulation by Max Tegmark who called it the Mathematical Universe Hypothesis.
Tegmark’s hypothesis is actually more, shall we say, grandiose. He doesn’t just claim that actually reality is math but that all math is real. Not just the math that we use in the theories that describe our observations, but all of it. The exponential function, Mandelbrot sets, the number 18, they’re all real as you and I. If you believe Tegmark.
But should you believe Tegmark? Well, as we have seen earlier, the justification we have for calling some mathematical structures real is that they describe what we observe. This means we have no rationale for talking about the reality of mathematics that does not describe what we observe, therefore the mathematical universe hypothesis isn’t scientific. This is generally the case for all types of the multiverse. The physicists who believe in this argue that unobservable universes are real because they are in their math. But just because you have math for something doesn’t mean it’s real. You can just assume it’s real, but this is unnecessary to describe what we observe and therefore unscientific.
Sabine Hossenfelder, “Are we made of math? Is math real?[article title]” at BackRe(Action)

There is mathematics to prove that the universe is shaped like a leprechaun’s hat.

All that said, a bigger question looms. We are able to understand mathematics but why are we? Something is missing from a discussion of whether math is real apart from that.

Comments

Of course the problem is the definitions of "real", and "exist". Depending on how you define those terms, things like mathematical concepts, unicorns, God, the past, quantum probability distribution, and many other things may or may not be "real". The past is not to be found anywhere, only in memories and records, which we assume relate to actual previous events. God is not a part of the universe so may not be considered to "exist" for some, even as he is quite "real" to others. My grand daughter has several unicorns, and I have read stories about unicorns, so they are apparently "real" in some sense. Numbers and other mathematical concepts and abstractions are not physical, but are very real to people who use them - even "imaginary" numbers. I expect that hard core philosophers have tried to delineate "reality" and "existence" to partly clarify these concepts, but clearly the language allows for a range of definitions and interpretations, so no one is allowed to decide definitively.Fasteddious_{August 3, 2021
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Are we made of math?
Since math is only a logical mental discipline and exist only in our heads and not the real world, we are not made of math. Again, math is an extremely useful discipline but it essentially exists only in our minds.jerry_{August 1, 2021
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As to Hossenfelder's first question, "Are we made of math?", she never really directly answers the question if she personally thinks that we ourselves are made of math or not. From the nearest I can tell, she basically just punts on the question, like she did the first question, and calls it "unscientific".
"Then what about the question whether we are made of math? Well, you can’t falsify this hypothesis. Suppose you had an observation that you can’t describe by math, it could always be that you just haven’t found the right math. So the idea that we’re made of math is also not wrong but unscientific. You can believe it if you want. There’s no evidence for or against it." - Hossenfelder
The reason she asked this question in the first place was because Max Tegmark himself did in fact claim that we are made of math.
Everything in the Universe Is Made of Math – Including You By Max Tegmark - Nov 3, 2013 https://www.discovermagazine.com/the-sciences/everything-in-the-universe-is-made-of-math-including-you
This claim was not received well by a few other leading theoretical physicists. Nobel Laureate Sheldon Glashow, professor of Mathematics and Physics at Boston University, was a bit harsh in his critique of Max Tegmark's claim that we ourselves are made of math and stated that “I may be a blockhead but I am certainly not a mathematical structure akin to a triangle.”
A Hand-Waving Exact Science - Sheldon Glashow Excerpt: And our ToE is just one among an infinity of mathematical structures, each of them its own universe. If Tegmark is correct, there must exist a slightly different mathematical structure, whose equations are emblazoned on another T-shirt, wherein I am Tegmark’s psychiatrist rather than a physicist. I do not believe a word of it. Paraphrasing Danny, I may be a blockhead but I am certainly not a mathematical structure akin to a triangle. - Sheldon Glashow Sheldon Glashow is professor of Mathematics and Physics at Boston University and professor emeritus of Physics at Harvard University. He received the Nobel Prize in Physics in 1979. https://inference-review.com/letter/a-hand-waving-exact-science
Likewise George Ellis, in a bit more understated tone, simply stated, “Tegmark has argued that every consistent mathematical structure exists in some disconnected universe. Tegmark also believes that nothing else exists beyond the consistent mathematical structures. Tegmark is himself nothing more than a consistent mathematical structure. This is a view that assigns to mathematical structures a degree of agency that they are not otherwise thought to possess.”
Physics on Edge - George Ellis - August 2017 Excerpt: Tegmark has argued that every consistent mathematical structure exists in some disconnected universe. Tegmark also believes that nothing else exists beyond the consistent mathematical structures. Tegmark is himself nothing more than a consistent mathematical structure. This is a view that assigns to mathematical structures a degree of agency that they are not otherwise thought to possess. http://inference-review.com/article/physics-on-edge
So where does Tegmark derive his belief that we ourselves are nothing but 'consistent mathematical structures'? Well it is derived from the belief that everything in the universe will eventually be describable by mathematics by a purely mathematical "Theory of Everything", (which is, despite the shunning of Tegmark, actually a widely held belief among naturalists)
A Hand-Waving Exact Science - Sheldon Glashow Excerpt: According to Tegmark, our universe is (rather than merely “is described by”) the long sought,,, “Theory of Everything, or ToE, from which all else can be derived… [S]uch a complete description must be devoid of any human baggage. This means that it must contain no concepts at all! In other words, it must be a purely mathematical theory… [An] infinitely intelligent mathematician should be able to derive the entire theory tree [including all of science, engineering, sociology, psychology etc.] from these equations alone, by deriving the properties of the physical reality that they describe, the properties of its inhabitants, their perceptions of the world, and even the words they invent. This purely mathematical theory of everything could potentially turn out to be simple enough to describe with equations that fit on a T-shirt.9” - Max Tegmark - Sheldon Glashow is professor of Mathematics and Physics at Boston University and professor emeritus of Physics at Harvard University. He received the Nobel Prize in Physics in 1979. https://inference-review.com/letter/a-hand-waving-exact-science
Please note that implicit in Tegmark's assumption that everything, including people, are reducible to purely mathematical explanations is a deterministic view of reality. A deterministic view of reality in which not only we ourselves, but all our actions are reducible to some mathematical equation. i.e. "You" do not really choose to do anything but some mathematical equation determines everything that you have done and that you will do. Hence George Ellis's remark to Tegmark, "This is a view that assigns to mathematical structures a degree of agency that they are not otherwise thought to possess.” The problem for Tegmark, (and for all other Naturalists, such as Hossenfelder herself, who believe in determinism), is that Quantum Mechanics itself, which is arguably our most powerful mathematical theory in science, (edging out General Relativity for that honor), has empirically falsified determinism. Specifically, Zeilinger and company, have closed the 'freedom of choice' loophole, thus falsifying all 'local' deterministic models:
Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars – Anton Zeilinger – 14 June 2018 Excerpt: This experiment pushes back to at least 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
In quantum mechanics, as the late Steven Weinberg explains, "In the instrumentalist approach (in quantum mechanics) humans are brought into the laws of nature at the most fundamental level.,,, the instrumentalist approach turns its back on a vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else.,,, In quantum mechanics these probabilities do not exist until people choose what to measure,,, Unlike the case of classical physics, a choice must be made,,,"
The Trouble with Quantum Mechanics – Steven Weinberg – January 19, 2017 Excerpt: The instrumentalist approach,, (the) wave function,, is merely an instrument that provides predictions of the probabilities of various outcomes when measurements are made.,, In the instrumentalist approach,,, humans are brought into the laws of nature at the most fundamental level. According to Eugene Wigner, a pioneer of quantum mechanics, “it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness.”11 Thus the instrumentalist approach turns its back on a vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else. It is not that we object to thinking about humans. Rather, we want to understand the relation of humans to nature, not just assuming the character of this relation by incorporating it in what we suppose are nature’s fundamental laws, but rather by deduction from laws that make no explicit reference to humans. We may in the end have to give up this goal,,, Some physicists who adopt an instrumentalist approach argue that the probabilities we infer from the wave function are objective probabilities, independent of whether humans are making a measurement. I don’t find this tenable. In quantum mechanics these probabilities do not exist until people choose what to measure, such as the spin in one or another direction. Unlike the case of classical physics, a choice must be made,,, http://quantum.phys.unm.edu/466-17/QuantumMechanicsWeinberg.pdf
In other words, the mathematical probabilities of quantum mechanics don't even come into play until AFTER we choose what to measure. Which is to say, that although mathematics can describe what happens after we, via our free will, choose what to measure, mathematics can never determine what, how, or when, we may choose to measure. i.e. In short, our free will choices are irreducible to mathematics! Needless to say, that throws a big ole monkey wrench in Tegmark's entire argument that we are made of math. We, (whatever we may really be made of), are simply not reducible to purely mathematical explanations as Tegmark believes. Quote, Video, and Verse
“You don’t have a soul. You are a soul. You have a body.” George MacDonald - Annals of a Quiet Neighborhood - 1892 Darwinian Materialism vs. Quantum Biology – Part II - video https://www.youtube.com/watch?v=oSig2CsjKbg Mark 8:37 Is anything worth more than your soul?
bornagain77_{August 1, 2021
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Corrected link:
Jesus Christ as the correct “Theory of Everything” – video https://www.youtube.com/watch?v=Vpn2Vu8--eE
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(and to reiterate what I stated last week) The main, irresolvable, problem for theoretical physicists in finding a purely mathematical theory of everything is the problem of mathematically unifying General Relativity with Quantum Mechanics. Mathematically speaking, General Relativity and Quantum Mechanics are separated by an unbridgeable ‘infinite mathematical divide’. Professor Jeremy Bernstein states the situation between General Relativity and Quantum Mechanics as such, “there remains an irremediable difficulty. Every order reveals new types of infinities, and no finite number of renormalizations renders all the terms in the series finite. The theory is not renormalizable.”
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 as the following theoretical physicist noted, “You would need to add infinitely many counterterms in a never-ending process. Renormalization would fail.,,,”
Why Gravity Is Not Like the Other Forces We asked four physicists why gravity stands out among the forces of nature. We got four different answers. Excerpt: the quantum version of Einstein’s general relativity is “nonrenormalizable.”,,, In quantum theories, infinite terms appear when you try to calculate how very energetic particles scatter off each other and interact. In theories that are renormalizable — which include the theories describing all the forces of nature other than gravity — we can remove these infinities in a rigorous way by appropriately adding other quantities that effectively cancel them, so-called counterterms. This renormalization process leads to physically sensible answers that agree with experiments to a very high degree of accuracy. The problem with a quantum version of general relativity is that the calculations that would describe interactions of very energetic gravitons — the quantized units of gravity — would have infinitely many infinite terms. You would need to add infinitely many counterterms in a never-ending process. Renormalization would fail.,,, Sera Cremonini – theoretical physicist – Lehigh University https://www.quantamagazine.org/why-gravity-is-not-like-the-other-forces-20200615/
So the burning question becomes, “how can we possibly bridge this ‘infinite mathematical divide’ that exists between General Relativity and Quantum Mechanics?” Dr. William Dembski in this following comment, although he was not directly addressing the ‘infinite mathematical divide’ that exists between General Relativity and Quantum Mechanics, offers this insight into what the ‘unification’ of infinite God with finite man might look like mathematically:, Specifically he states, “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.”
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 Philippians 2:8-9 And being found in appearance as a man, He humbled Himself and became obedient to the point of death, even the death of the cross. Therefore God also has highly exalted Him and given Him the name which is above every name,
Moreover, when we rightly allow the Agent Causality of God ‘back’ into physics, as the Christian founders of modern science originally envisioned, and as quantum mechanics itself now empirically demands with the closing of the free will loophole by Anton Zeilinger and company,
Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars – Anton Zeilinger – 14 June 2018 Excerpt: This experiment pushes back to at least 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
,, then that VERY reasonable concession on our part, to rightly allow God ‘back’ into physics, as the Christian founders of physics originally envisioned, 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”. In short, the Shroud of Turin, (which is THE most scientifically scrutinized artifact ever from ancient history), provides evidence that both General Relativity and Quantum Mechanics were successfully dealt with in Christ’s resurrection from the dead. Here are a few notes to that effect: Kevin Moran, an optical engineer, describes the Shroud Image in this way, “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,,,”
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 rather astonishing study on the Shroud, 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
So thus in conclusion, when we rightly allow the Agent Causality of God back into physics then a very plausible solution to the number one unsolved mystery in science today, of finding a reconciliation between General Relativity and Quantum Mechanics, readily pops out for us in that, as the Shroud of Turin gives witness to, both Gravity and Quantum Mechanics were successfully dealt, (and the ‘infinite mathematical divide’ between the two theories was bridged), with Christ’s resurrection from the dead.
Matthew 28:18 Then Jesus came to them and said, “All authority in heaven and on earth has been given to me,” 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.
Supplemental note:
Jesus Christ as the correct “Theory of Everything” – video https://youtu.be/Vpn2Vu8–eE
bornagain77_{August 1, 2021
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In the title of her article, Hossenfelder asks two questions, "Are we made of math?" and "Is math real?" To her last question first, "Is math real?" (I will leave her first question “Are we made of math?” for a later post) Math is not "real" in the sense that we can pick up, say, Pythagoras's theorem, hold it in our hands, smell it, taste it, etc...,, We can make physical objects that approximate 'real' triangles fairly closely, but that is not Pythagoras's theorem in and of itself. Which is to say, we grasp the "real essence" of Pythagoras's theorem solely by faculty of our immaterial minds, not by any physical objects that exist in nature, nor by any objects that we may make to approximate Pythagoras's theorem. As Michael Egnor stated, "Mathematics is entirely about concepts, which have no precise instantiation in nature,,,"
Naturalism and Self-Refutation – Michael Egnor – January 31, 2018 Excerpt: Mathematics is certainly something we do. Is mathematics “included in the space-time continuum [with] basic elements … described by physics”?,,, What is the physics behind the Pythagorean theorem? After all, no actual triangle is perfect, and thus no actual triangle in nature has sides such that the Pythagorean theorem holds. There is no real triangle in which the sum of the squares of the sides exactly equals the square of the hypotenuse. That holds true for all of geometry. Geometry is about concepts, not about anything in the natural world or about anything that can be described by physics. What is the “physics” of the fact that the area of a circle is pi multiplied by the square of the radius? And of course what is natural and physical about imaginary numbers, infinite series, irrational numbers, and the mathematics of more than three spatial dimensions? Mathematics is entirely about concepts, which have no precise instantiation in nature,,, Furthermore, the very framework of Clark’s argument — logic — is neither material nor natural. Logic, after all, doesn’t exist “in the space-time continuum” and isn’t described by physics. What is the location of modus ponens? How much does Gödel’s incompleteness theorem weigh? What is the physics of non-contradiction? How many millimeters long is Clark’s argument for naturalism? Ironically the very logic that Clark employs to argue for naturalism is outside of any naturalistic frame. The strength of Clark’s defense of naturalism is that it is an attempt to present naturalism’s tenets clearly and logically. That is its weakness as well, because it exposes naturalism to scrutiny, and naturalism cannot withstand even minimal scrutiny. Even to define naturalism is to refute it. https://evolutionnews.org/2018/01/naturalism-and-self-refutation/
And although, (since we can find no experimental deviation from the mathematical descriptions of General Relativity, Quantum Electrodynamics, and/or the Amplituhedron), I would politely disagree with Dr. Egnor's overall claim that no mathematical object has a "precise instantiation in nature", never-the-less, Dr. Egnor's main point about Mathematics being entirely about concepts of the immaterial mind is spot on. To further solidify the fact that 'immaterial' mathematics must be a product of the immaterial mind, it is important to note that, "the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information.,"
Algorithmic Information Theory, Free Will and the Turing Test - Douglas S. Robertson Excerpt: Chaitin’s Algorithmic Information Theory shows that information is conserved under formal mathematical operations and, equivalently, under computer operations. This conservation law puts a new perspective on many familiar problems related to artificial intelligence. For example, the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information.? http://cires.colorado.edu/~doug/philosophy/info8.pdf?
And as James Franklin challenged Atheistic Naturalists, "the intellect (is) immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.,,"
The mathematical world - James Franklin - 7 April 2014 Excerpt: the intellect (is) immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.,,, James Franklin is professor of mathematics at the University of New South Wales in Sydney. http://aeon.co/magazine/world-views/what-is-left-for-mathematics-to-be-about/
The fact that 'immaterial' mathematics must be a product of the immaterial mind puts Darwinian materialists and/or Darwinian naturalists in quite the bind. Hossenfelder herself, (when Zeilinger closed the 'freedom of choice' loophole in quantum mechanics and she, in contradiction to the empirical evidence itself, opted to believe in super-determinism over and above believing in her own free will), proved that she does not believe in the reality of her own immaterial mind. Yet without an immaterial mind of her own, Hossenfelder simply has no explanation for how she herself is able to contemplate this immaterial world of mathematics, much less is she able to explain why this immaterial world of mathematics is able to describe the universe. Both Wigner and Einstein held it to be a 'miracle' that mathematics should be applicable to the universe. Yet, in her article Hossenfelder, for a theoretical physicist, seems surprisingly uninterested in the question of, "Exactly why does the universe lend itself to be described by some mathematical structures, but leaves itself undescribed by other mathematical structures? Hossenfelder seems content to sit back, throw her hands up in the air, and just say, Oh well, "we have no rationale for talking about the reality of mathematics that does not describe what we observe", because it isn't, quote unquote, "scientific"
,,, the justification we have for calling some mathematical structures real is that they describe what we observe. This means we have no rationale for talking about the reality of mathematics that does not describe what we observe, therefore the (i.e. Tegmark's) mathematical universe hypothesis isn’t scientific.
Might it be to obvious to point out the fact that until theoretical physicists actually do grapple with the question of "Exactly why do some mathematical structures describe the universe, and others don't?", then they will NEVER make headway towards finding a purely mathematical 'theory of everything"? And/or understanding why there is not, and can never be, a purely mathematical 'theory of everything"? To just say, as Hossenfelder does, that grappling with such a question isn't 'scientific' seems like a huge cop out for her, i.e. a theoretical physicist. Steven Weinberg, who recently passed away, certainly recognized the importance of such questions. As Steven Weinberg himself pointed out, “I don’t think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don’t describe the world as we know it. And we will always be left with a question ‘why are the laws nature what they are rather than some other laws?’. And I don’t see any way out of that.”
Quote: “I don’t think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don’t describe the world as we know it. And we will always be left with a question ‘why are the laws nature what they are rather than some other laws?’. And I don’t see any way out of that. The fact that the constants of nature are suitable for life, which is clearly true, we observe,,,” (Weinberg then comments on the multiverse conjecture of atheists) “No one has constructed a theory in which that is true. I mean,, the (multiverse) theory would be speculative, but we don’t even have a theory in which that speculation is mathematically realized. But it is a possibility.” Steven Weinberg – as stated to Richard Dawkins at the 8:15 minute mark of the following video – Leonard Susskind – Richard Dawkins and Steven Weinberg – 1 in 10^120 – Cosmological Constant points to intelligent design – video https://youtu.be/z4E_bT4ecgk?t=495
In fact, there are an infinite number of mathematical theorems that could have described the universe, but don't. Gregory Chaitin has found that “an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms.”
The Limits Of Reason – Gregory Chaitin – 2006 Excerpt: Unlike Gödel’s approach, mine is based on measuring information and showing that some mathematical facts cannot be compressed into a theory because they are too complicated. This new approach suggests that what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms. http://www.umcs.maine.edu/~chaitin/sciamer3.pdf
Of course the correct solution to Weinberg's question of ‘why are the laws nature what they are rather than some other laws?’ is, as Bruce Gordon succinctly explained, “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/
And to add further weight to Dr. Gordon's claim, I reference this following very informative article by Edward Feser where he states, "Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect."
Keep it Simple – Edward Feser Mathematics appears to describe a realm of entities with quasi-divine attributes. The series of natural numbers is infinite. That one and one equal two and two and two equal four could not have been otherwise. Such mathematical truths never begin being true or cease being true; they hold eternally and immutably. The lines, planes, and figures studied by the geometer have a kind of perfection that the objects of our experience lack. Mathematical objects seem immaterial and known by pure reason rather than through the senses. Given the centrality of mathematics to scientific explanation, it seems in some way to be a cause of the natural world and its order. How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect. https://www.firstthings.com/article/2020/04/keep-it-simple
bornagain77_{August 1, 2021
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You can just assume it’s real, but this is unnecessary to describe what we observe and therefore unscientific.
Unnecessary to describe what who observes and experiences? Does he have a mouse in his pocket? This is the same fallacy that KF falls prey to when he refers to "common experience;" the projection of one's own set of experiences as inclusive and definitive for everyone by using the word "we." Many, many people directly, fully experience other "universes," other "realities." These arrogant proclamations of "we" are absurdly egoic.William J Murray_{August 1, 2021
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