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At Quanta Magazine: How Gödel’s Proof Works

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His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.

Natalie Wolchover writes in an article in Quanta Magazine:

In 1931, the Austrian logician Kurt Gödel pulled off arguably one of the most stunning intellectual achievements in history.

Mathematicians of the era sought a solid foundation for mathematics: a set of basic mathematical facts, or axioms, that was both consistent — never leading to contradictions — and complete, serving as the building blocks of all mathematical truths.

But Gödel’s shocking incompleteness theorems, published when he was just 25, crushed that dream. He proved that any set of axioms you could posit as a possible foundation for math will inevitably be incomplete; there will always be true facts about numbers that cannot be proved by those axioms. He also showed that no candidate set of axioms can ever prove its own consistency.

His incompleteness theorems meant there can be no mathematical theory of everything, no unification of what’s provable and what’s true. What mathematicians can prove depends on their starting assumptions, not on any fundamental ground truth from which all answers spring.

Undecidable questions have even arisen in physics, suggesting that Gödelian incompleteness afflicts not just math, but — in some ill-understood way — reality.

The article next outlines a “simplified, informal rundown of how Gödel proved his theorems.” What the results imply is discussed next.

No Proof of Consistency

We’ve learned that if a set of axioms is consistent, then it is incomplete. That’s Gödel’s first incompleteness theorem. The second — that no set of axioms can prove its own consistency — easily follows.

What would it mean if a set of axioms could prove it will never yield a contradiction? It would mean that there exists a sequence of formulas built from these axioms that proves the formula that means, metamathematically, “This set of axioms is consistent.” By the first theorem, this set of axioms would then necessarily be incomplete. But “The set of axioms is incomplete” is the same as saying, “There is a true formula that cannot be proved.”

Gödel’s proof killed the search for a consistent, complete mathematical system. The meaning of incompleteness “has not been fully fathomed,” Nagel and Newman wrote in 1958. It remains true today.

Full article available at Quanta Magazine.

Truth is bigger than proof.”

13 Replies to “At Quanta Magazine: How Gödel’s Proof Works

  1. 1
    PyrrhoManiac1 says:

    Good article. My only minor qualm is that Gödel’s proofs apply to axiomatic systems that are rich enough to capture arithmetic. Less rich axiomatic systems don’t have that problem. (I think Euclidean geometry is complete but I’m not sure.)

  2. 2
    bornagain77 says:

    As to: “Undecidable questions have even arisen in physics, suggesting that Gödelian incompleteness afflicts not just math, but — in some ill-understood way — reality.”

    How Gödel’s Proof Works – Natalie Wolchover -July 14, 2020
    His incompleteness theorems destroyed the search for a mathematical theory of everything. Nearly a century later, we’re still coming to grips with the consequences.
    Excerpt: In the 89 years since Gödel’s discovery, mathematicians have stumbled upon just the kinds of unanswerable questions his theorems foretold. For example, Gödel himself helped establish that the continuum hypothesis, which concerns the sizes of infinity, is undecidable, as is the halting problem, which asks whether a computer program fed with a random input will run forever or eventually halt. Undecidable questions have even arisen in physics, suggesting that Gödelian incompleteness afflicts not just math, but — in some ill-understood way — reality.
    https://www.quantamagazine.org/how-godels-incompleteness-theorems-work-20200714/

    Natalie Wolchover links to a paper which discusses the undecidability of the Spectral Gap,

    Paradox at the heart of mathematics makes physics problem unanswerable – Davide Castelvecchi – Nature (2015)
    Except: Spectral gap
    Cubitt and his collaborators focused on calculating the ‘spectral gap’: the gap between the lowest energy level that electrons can occupy in a material, and the next one up. This determines some of a material’s basic properties. In some materials, for example, lowering the temperature causes the gap to close, which leads the material to become a superconductor.
    The team started with a theoretical model of a material: an infinite 2D crystal lattice of atoms. The quantum states of the atoms in the lattice embody a Turing machine, containing the information for each step of a computation to find the material’s spectral gap.
    Cubitt and his colleagues showed that for an infinite lattice, it is impossible to know whether the computation ends, so that the question of whether the gap exists remains undecidable.
    For a finite chunk of 2D lattice, however, the computation always ends in a finite time, leading to a definite answer. At first sight, therefore, the result would seem to have little relation to the real world. Real materials are always finite, and their properties can be measured experimentally or simulated by computer.
    But the undecidability ‘at infinity’ means that even if the spectral gap is known for a certain finite-size lattice, it could change abruptly — from gapless to gapped or vice versa — when the size increases, even by just a single extra atom.,,,
    https://www.nature.com/articles/nature.2015.18983

    And although Natalie Wolchover characterized their finding as afflicting physical reality in “some ill-understood way”, in the following article they are quite clear as to how their finding ‘afflicts’ physical reality.

    Specifically they state, “even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behaviour.,,,” and that “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-q.....godel.html

    Moreover, per wikipedia, in 2020 they made their proof more robust,

    Spectral gap (physics)
    Excerpt: In quantum mechanics, the spectral gap of a system is the energy difference between its ground state and its first excited state.[1][2] The mass gap is the spectral gap between the vacuum and the lightest particle. A Hamiltonian with a spectral gap is called a gapped Hamiltonian, and those that do not are called gapless.
    In solid-state physics, the most important spectral gap is for the many-body system of electrons in a solid material, in which case it is often known as an energy gap.
    In quantum many-body systems, ground states of gapped Hamiltonians have exponential decay of correlations.[3][4][5]
    In 2015 it was shown that the problem of determining the existence of a spectral gap is undecidable in two or more dimensions.[6][7] The authors used an aperiodic tiling of quantum Turing machines and showed that this hypothetical material becomes gapped if and only if the machine halts.[8] The one-dimensional case was also proved undecidable in 2020 by constructing a chain of interacting qudits divided into blocks that gain energy if they represent a full computation by a Turing machine, and showing that this system becomes gapped if and only if the machine does not halt.[9]
    https://en.wikipedia.org/wiki/Spectral_gap_(physics)

    And since attempting to mathematically unify the macroscopic descriptions of General Relativity with the microscopic descriptions of Quantum Mechanics lies at the heart of all (failed) attempts to find a single overarching mathematical ‘theory of everything’,,,

    Theory of everything
    A theory of everything (TOE[1] or ToE), final theory, ultimate theory, or master theory is a hypothetical single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe.[2]:6 Finding a TOE is one of the major unsolved problems in physics.[3] String theory and M-theory have been proposed as theories of everything.
    Over the past few centuries, two theoretical frameworks have been developed that, together, most closely resemble a TOE. These two theories upon which all modern physics rests are general relativity and quantum mechanics.,,,
    General relativity is a theoretical framework that only focuses on gravity for understanding the universe in regions of both large scale and high mass: stars, galaxies, clusters of galaxies, etc. On the other hand, quantum mechanics is a theoretical framework that only focuses on three non-gravitational forces for understanding the universe in regions of both small scale and low mass: sub-atomic particles, atoms, molecules, etc. ,,,
    However, the two theories are considered incompatible in regions of extremely small scale – the Planck scale – such as those that exist within a black hole or during the beginning stages of the universe (i.e., the moment immediately following the Big Bang). To resolve the incompatibility, a theoretical framework revealing a deeper underlying reality, unifying gravity with the other three interactions, must be discovered to harmoniously integrate the realms of general relativity and quantum mechanics into a seamless whole: the TOE is a single theory that, in principle, is capable of describing all phenomena in the universe.
    https://en.wikipedia.org/wiki/Theory_of_everything

    ,,, then their proof clearly shows that the microscopic descriptions of quantum mechanics can never be successfully extended to the account for the macroscopic descriptions of General Relativity.

    Moreover, their finding should not really be all that surprising to find out. It is already known that an unbridgeable ‘infinite mathematical divide’ exists between General Relativity and Quantum Mechanics.

    But before we get into that it is necessary to clarify a few things.

    First off, as Gregory Chaitin has shown, there are an infinite number of mathematical theorems that could have described the universe, but don’t.

    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.
    https://www.cs.virginia.edu/~robins/The_Limits_of_Reason_Chaitin_2006.pdf

    This presents an irremediably difficult situation for those who hope to find a purely mathematical theory of everything that makes no reference to God. As the late Steven Weinberg, an atheist, confessed to Richard Dawkins, “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.”

    “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

  3. 3
    bornagain77 says:

    And although atheists are, self-admittedly, in a pretty bad ‘fix’, the Christian Theist has a ready explanation. As Bruce Gordon explains, “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.”

    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.....arguments/

    And it is not as if ID proponents do not already have sufficient reason to believe that free will must be involved in choosing among an “infinite variety of mathematical descriptions and bring(ing) into existence a reality that corresponds to a consistent subset of them.”

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

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

    In fact, modern science was born out of the belief that any mathematics that might describe this universe are ‘God’s thoughts’.

    As Johannes Kepler stated shortly after discovering the third law of planetary motion,

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

    God In Mathematics – 2016
    Jerry Bowyer – Interview with Vern Poythress
    Excerpt: The standard modern culture-war revolves around God vs. the mathematical sciences. Take your choice: Faith or physics. Then there are the voices of mutual toleration, which attempt to leave room for science among the faithful and for faith among the scientific. Poythress, though, taps into a different tradition entirely, one which is seldom heard in modern debate: That God and science are neither enemies, nor partners, but rather that God is the necessary foundation for mathematics and therefore of every science which uses it.
    The argument is that mathematical laws, in order to be properly relied upon, must have attributes which indicate an origin in God. They are true everywhere (omnipresent), true always (eternal), cannot be defied or defeated (omnipotent), and are rational and have language characteristics (which makes them personal). Omnipresent, omnipotent, eternal, personal… Sounds like God. Math is an expression of the mind of God. Sound strange? It isn’t. Modern natural science was created by people who said that they were trying to “think God’s thoughts after Him.”
    https://www.forbes.com/sites/jerrybowyer/2016/04/19/where-does-math-come-from-a-mathematiciantheologian-talks-about-the-limits-of-numbers/

    And as Edward Feser explains, “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.”

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

    And you don’t have to take Kepler, Poythress, and Feser’s word for it, Eugene Wigner, (who’s insights into quantum mechanics continue to drive breakthroughs into quantum mechanics; per A. Zeilinger), and Albert Einstein, (who needs no introduction), are both on record as to regarding it as a ‘miracle’ that math should even be applicable to the universe in the first place.

    Moreover, Wigner questioned Darwinism in his process of calling it a miracle. Whereas Einstein went so far as to chastise ‘professional atheists’ in his process of calling it a miracle.

    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.
    https://web.njit.edu/~akansu/PAPERS/The%20Unreasonable%20Effectiveness%20of%20Mathematics%20(EP%20Wigner).pdf

    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

    And the last time I checked, a miracle is considered to be the sole province of God,

    mir·a·cle
    noun
    a surprising and welcome event that is not explicable by natural or scientific laws and is therefore considered to be the work of a divine agency.

    Thus, (before we even get into the ‘infinite mathematical divide’ that exists between General Relativity and Quantum Mechanics), the fact that mathematics should even be applicable to the universe in the first place is, (in spite of any a-priori philosophical biases that atheists may have against it), by all rights, already to be considered a miracle of God.

    Now to the ‘infinite mathematical divide’ that exists between General Relativity and Quantum Mechanics.

    Professor Jeremy Bernstein states the ‘infinite mathematical divide’ between the two theories 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.

  4. 4
    bornagain77 says:

    And as theoretical physicist Sera Cremonini 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/

    And as Michio Kaku stated in the following video, when you try to combine General Relativity with Quantum Mechanics, “you get an infinite sequence of infinities, (which is) infinitely worse than the divergences of Einstein’s original theory (i.e. General Relativity).”

    “Here is the problem (with black holes), right there, when ‘r’ (radius) is equal to zero, The point at which physics itself breaks down. So 1 over ‘r’ equals 1 over 0 equals infinity. To a mathematician infinity is simply a number without limit. To a physicist it is a monstrosity. It means first of all that gravity is infinite at the center of a black hole. That time stops. And what does that mean? Space makes no sense. It means the collapse of everything we know about the physical universe. In the real world there is no such thing as infinity. Therefore there is a fundamental flaw in the formulation of Einstein’s theory.”
    (And Michio Kaku then notes, when you try to combine General Relativity with Quantum Mechanics) “In fact, you get an infinite sequence of infinities, (which is) infinitely worse than the divergences of Einstein’s original theory (i.e. General Relativity).”
    Quantum Mechanics & Relativity – Michio Kaku – The Collapse Of Physics As We Know It ? – video
    Science vs God Its The Collapse Of Physics As We Know it – video
    https://www.dailymotion.com/video/x2jbd7x

    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.....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,

    And indeed, when rightly allow the Agent causality of God ‘back’ into physics as the Christian founders of modern science, such as Sir Isaac Newton, originally envisioned,

    ‘Without all doubt this world…could arise from nothing but the perfectly free will of God… From this fountain (what) we call the laws of nature have flowed, in which there appear many traces indeed of the most wise contrivance, but not the least shadow of necessity. These therefore we must not seek from uncertain conjectures, but learn them from observations and experiments.”,,,
    – Sir Isaac Newton – (Cited from Religion and the Rise of Modern Science by Hooykaas page 49).
    https://thirdspace.org.au/comment/237

    And when we rightly allow the agent causality of God ‘back’ into physics as is now empirically demanded by the closing of the ‘freedom of choice’ 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 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

    ,,, then that very reasonable concession on our part to rightly allow 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 bridges that infinite mathematical divide that exists between General Relativity and Quantum Mechanics and provides us with an empirically backed reconciliation, (via the Shroud of Turin), between Quantum Mechanics and General Relativity into the much sought after ‘Theory of Everything”

    Oct. 2022 – When scrutinizing some of the many fascinating details of the Shroud of Turin, we find that both General Relativity, i.e. gravity, and Quantum Mechanics were both dealt with in Christ’s resurrection from the dead.
    https://uncommondescent.com/cosmology/from-iai-news-how-infinity-threatens-cosmology/#comment-766384

    Thus in conclusion, and to repeat, when we rightly allow the Agent causality of God ‘back’ into physics, (as the Christian founders of modern science originally envisioned, Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders,,,, and as quantum mechanics itself now empirically demands with the closing of the ‘freedom of choice’ loophole by Anton Zeilinger and company), then 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 bridges the infinite mathematical divide that exists between General Relativity and Quantum Mechanics and provides us with a very plausible, empirically backed, reconciliation, (via the Shroud of Turin), between Quantum Mechanics and General Relativity into the much sought after ‘Theory of Everything”.

    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.

  5. 5
    Viola Lee says:

    Wow, BA sure knows how to overwhelm a potential discussion!

  6. 6
    relatd says:

    Ba77,

    I think gravity is very well understood. The so-called “strong force” and “weak force” in atoms is well understood. The various subatomic particles like quarks and leptons are well understood. Over the decades, the distances between various electron states, or levels, has become well understood. The quantum world is being mapped out and put to practical use at the same time.

    I propose that a Theory of Everything exists at this moment. And that it is being put to use already in various experiments. Even though the math has not been all worked out, a series of trial and error experiments are revealing more and more pieces of the puzzle. The end result will be new techniques for doing certain things and for use in new propulsion systems.

    God did create a universe that is rational and intelligible and given us the creativity to make discoveries about it. The same is true of the quantum world. However, if such knowledge exists, and I think it does, it will be kept highly secret by whoever has it.

  7. 7
    Viola Lee says:

    The OP doesn’t seem to have a link to the article that is quoted from. I’d like to see it.

  8. 8
    PyrrhoManiac1 says:

    @7:

    Here it is: How Gödel’s Proof Works.

  9. 9
    Viola Lee says:

    Thanks. What you typed doesn’t work as a link, but I found it by googling her name and the title.

  10. 10
    PyrrhoManiac1 says:

    Whoops! My bad. Anyway, here it is — correctly this time — for anyone who wants it:

    How Gödel’s Proof Works.

  11. 11
    Querius says:

    Relatd @6,

    I think gravity is very well understood. The so-called “strong force” and “weak force” in atoms is well understood. The various subatomic particles like quarks and leptons are well understood. Over the decades, the distances between various electron states, or levels, has become well understood. The quantum world is being mapped out and put to practical use at the same time.

    These are pretty ambitious assertions. Do you have any references?

    Consider just gravity, for example.

    -Q

  12. 12
    relatd says:

    Querius at 11,

    What do you want to know about gravity? There is the macro version that we all experience, and the subatomic version.

  13. 13
    Querius says:

    Relatd,

    Please understand, I’m not asking for your explanation. I’m simply asking about your references from where you’re getting your information.

    Thanks,
    -Q

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