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Philip Cunningham argues: Jesus Christ is the correct Theory of Everything

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Here are the notes.

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He’s been a faithful commenter over the years.

Comments
In further solidifying Professor Wolf and company's claim that, via Godel and Turing, “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." - per physorg
,,, In further solidifying that claim, it is interesting to note how the microscopic descriptions of quantum mechanics have thus far failed to account macroscopic descriptions of the universe. In inflation theory it is held that "(inflation cosmology) explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe."
Inflation (cosmology) Excerpt: explains the origin of the large-scale structure of the cosmos. Quantum fluctuations in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe. - per wikipedia
Inflation theory was postulated to try to solve the The Monopole Problem, The Flatness Problem, and The Horizon Problem.
Inflation: Status Update - Sabine Hossenfelder - March 08, 2019 Excerpt: The currently most popular theory for the early universe is called “inflation”. According to inflation, the universe once underwent a phase in which volumes of space increased exponentially in time. This rapid expansion then stopped in an event called “reheating,” at which the particles of the standard model were produced. After this, particle physics continues the familiar way. Inflation was originally invented to solve several finetuning problems.,,, 1. The Monopole Problem Guth invented inflation to solve the “monopole problem.” If the early universe underwent a phase-transition, for example because the symmetry of grand unification was broken – then topological defects, like monopoles, should have been produced abundantly. We do not, however, see any of them. Inflation dilutes the density of monopoles (and other worries) so that it’s unlikely we’ll ever encounter one. But a plausible explanation for why we don’t see any monopoles is that there aren’t any. We don’t know there is any grand symmetry that was broken in the early universe, or if there is, we don’t know when it was broken, or if the breaking produced any defects. Indeed, all searchers for evidence of grand symmetry – mostly via proton decay – turned out negative.,,, 2. The Flatness Problem The flatness problem is a finetuning problem. The universe currently seems to be almost flat, or if it has curvature, then that curvature must be very small. The contribution of curvature to the dynamics of the universe however increases in relevance relative to that of matter. This means if the curvature density parameter is small today, it must have been even smaller in the past.,,, 3. The Horizon Problem The Cosmic Microwave Background (CMB) has almost at the same temperature in all directions. Problem is, if you trace back the origin the background radiation without inflation, then you find that the radiation that reached us from different directions was never in causal contact with each other. Why then does it have the same temperature in all directions?,,, Ever since the results of the Planck in 2013 it hasn’t looked good for inflation. After the results appeared, Anna Ijjas, Paul Steinhardt, and Avi Loeb argued in a series of papers that the models of inflation which are compatible with the data themselves require finetuning, and therefore bring back the problem they were meant to solve. They popularized their argument in a 2017 article in Scientific American, provocatively titled “Pop Goes the Universe.”,,, http://backreaction.blogspot.com/2017/10/is-inflationary-universe-scientific.html
Yet the "Quantum fluctuations in the microscopic inflationary region" predict none of these properties. As Paul Steinhardt of Princeton University, who helped develop inflationary theory but is now scathing of it, stated, "The deeper problem is that once inflation starts, it doesn't end the way these simplistic calculations suggest," he says. "Instead, due to quantum physics it leads to a multiverse where the universe breaks up into an infinite number of patches. The patches explore all conceivable properties as you go from patch to patch. So that means it doesn't make any sense to say what inflation predicts, except to say it predicts everything. If it's physically possible, then it happens in the multiverse someplace"
Cosmic inflation is dead, long live cosmic inflation - 25 September 2014 Excerpt: (Inflation) theory, the most widely held of cosmological ideas about the growth of our universe after the big bang, explains a number of mysteries, including why the universe is surprisingly flat and so smoothly distributed, or homogeneous,,, Paul Steinhardt of Princeton University, who helped develop inflationary theory but is now scathing of it, says this is potentially a blow for the theory, but that it pales in significance with inflation's other problems. Meet the multiverse Steinhardt says the idea that inflationary theory produces any observable predictions at all – even those potentially tested by BICEP2 – is based on a simplification of the theory that simply does not hold true. "The deeper problem is that once inflation starts, it doesn't end the way these simplistic calculations suggest," he says. "Instead, due to quantum physics it leads to a multiverse where the universe breaks up into an infinite number of patches. The patches explore all conceivable properties as you go from patch to patch. So that means it doesn't make any sense to say what inflation predicts, except to say it predicts everything. If it's physically possible, then it happens in the multiverse someplace Steinhardt says the point of inflation was to explain a remarkably simple universe. "So the last thing in the world you should be doing is introducing a multiverse of possibilities to explain such a simple thing," he says. "I think it's telling us in the clearest possible terms that we should be able to understand this and when we understand it it's going to come in a model that is extremely simple and compelling. And we thought inflation was it – but it isn't." http://www.newscientist.com/article/dn26272-cosmic-inflation-is-dead-long-live-cosmic-inflation.html?page=1#.VCajrGl0y00
And in 2017 Steinhardt and company further explained, “…inflation continues eternally, generating an infinite number of patches where inflation has ended, each creating a universe unto itself…(t)he worrisome implication is that the cosmological properties of each patch differ because of the inherent randomizing effect of quantum fluctuations…The result is what cosmologists call the multiverse. Because every patch can have any physically conceivable properties, the multiverse does not explain why our universe has the very special conditions that we observe—they are purely accidental features of our particular patch.”,,, the multimess does not predict the properties of our observable universe to be the likely outcome. A good scientific theory is supposed to explain why what we observe happens instead of something else. The multimess fails this fundamental test.”
Pop Goes The Universe - Scientific American - January 2017 - Anna Ijjas, Paul J. Steinhardt and Abraham Loeb Excerpt: “If anything, the Planck data disfavored the simplest inflation models and exacerbated long-standing foundational problems with the theory, providing new reasons to consider competing ideas about the origin and evolution of the universe… (i)n the years since, more precise data gathered by the Planck satellite and other instruments have made the case only stronger……The Planck satellite results—a combination of an unexpectedly small (few percent) deviation from perfect scale invariance in the pattern of hot and colds spots in the CMB and the failure to detect cosmic gravitational waves—are stunning. For the first time in more than 30 years, the simplest inflationary models, including those described in standard textbooks, are strongly disfavored by observations.” “Two improbable criteria have to be satisfied for inflation to start. First, shortly after the big bang, there has to be a patch of space where the quantum fluctuations of spacetime have died down and the space is well described by Einstein’s classical equations of general relativity; second, the patch of space must be flat enough and have a smooth enough distribution of energy that the inflation energy can grow to dominate all other forms of energy. Several theoretical estimates of the probability of finding a patch with these characteristics just after the big bang suggest that it is more difficult than finding a snowy mountain equipped with a ski lift and well-maintained ski slopes in the middle of a desert.” “More important, if it were easy to find a patch emerging from the big bang that is flat and smooth enough to start inflation, then inflation would not be needed in the first place. Recall that the entire motivation for introducing it was to explain how the visible universe came to have these properties; if starting inflation requires those same properties, with the only difference being that a smaller patch of space is needed, that is hardly progress.” “…inflation continues eternally, generating an infinite number of patches where inflation has ended, each creating a universe unto itself…(t)he worrisome implication is that the cosmological properties of each patch differ because of the inherent randomizing effect of quantum fluctuations…The result is what cosmologists call the multiverse. Because every patch can have any physically conceivable properties, the multiverse does not explain why our universe has the very special conditions that we observe—they are purely accidental features of our particular patch.” “We would like to suggest “multimess” as a more apt term to describe the unresolved outcome of eternal inflation, whether it consists of an infinite multitude of patches with randomly distributed properties or a quantum mess. From our perspective, it makes no difference which description is correct. Either way, the multimess does not predict the properties of our observable universe to be the likely outcome. A good scientific theory is supposed to explain why what we observe happens instead of something else. The multimess fails this fundamental test.” https://www.cfa.harvard.edu/~loeb/sciam3.pdf
As should be obvious, the failure of inflation theory, (via 'quantum fluctuations' generating an infinitude of universes with differing properties), to predict the specific macroscopic properties of our observable universe is a fairly clear example that brings Wolf and company main point home, i.e. “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." And whereas inflation theory has utterly failed to predict exactly why our universe has the specific macroscopic properties that it does, namely, why the universe is as flat as it is and why the Cosmic Microwave Background (CMB) has almost at the same temperature in all directions,,, Whereas inflation theory has utterly failed in that endeavor, on the other hand Christian Theism 'predicted those exact macroscopic properties for our universe thousands of years before those macroscopic properties of our universe were even discovered by modern science. As to 'the flatness problem', the following quote gives us a clue as to just how bad the 'flatness problem' is for atheistic astrophysicists to try to 'explain away',
"The Universe today is actually very close to the most unlikely state of all, absolute flatness. And that means it must have been born in an even flatter state, as Dicke and Peebles, two of the Princeton astronomers involved in the discovery of the 3 K background radiation, pointed out in 1979. Finding the Universe in a state of even approximate flatness today is even less likely than finding a perfectly sharpened pencil balancing on its point for millions of years, for, as Dicke and Peebles pointed out, any deviation of the Universe from flatness in the Big Bang would have grown, and grown markedly, as the Universe expanded and aged. Like the pencil balanced on its point and given the tiniest nudges, the Universe soon shifts away from perfect flatness." - John Gribbin, In Search of the Big Bang
In fact, "for it (the universe) to maintain this level of flatness over 13.8 billion years of expansion, in kind of amazing. In fact, astronomers estimate that the universe must have been flat to 1 part within 1×10^57 parts. Which seems like an insane coincidence."
How do we know the universe is flat? Discovering the topology of the universe - by Fraser Cain - June 7, 2017 Excerpt: With the most sensitive space-based telescopes they have available, astronomers are able to detect tiny variations in the temperature of this background radiation. And here's the part that blows my mind every time I think about it. These tiny temperature variations correspond to the largest scale structures of the observable universe. A region that was a fraction of a degree warmer become a vast galaxy cluster, hundreds of millions of light-years across. The cosmic microwave background radiation just gives and gives, and when it comes to figuring out the topology of the universe, it has the answer we need. If the universe was curved in any way, these temperature variations would appear distorted compared to the actual size that we see these structures today. But they're not. To best of its ability, ESA's Planck space telescope, can't detect any distortion at all. The universe is flat.,,, We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,, Since the universe is flat now, it must have been flat in the past, when the universe was an incredibly dense singularity. And for it to maintain this level of flatness over 13.8 billion years of expansion, in kind of amazing. In fact, astronomers estimate that the universe must have been flat to 1 part within 1×10^57 parts. Which seems like an insane coincidence. - per physorg
And whereas this 'insane coincidence' of 1 in 10^57 flatness was not predicted by inflation theory, (indeed it is a thorn in the side of inflation theory), thousands of years before this exceptional flatness of the universe was discovered, the Bible, on the other hand, is on record as to 'predicting' this 'insane coincidence' of the universe being exceedingly flat:
Job 38:4-5 “Where were you when I laid the earth’s foundation??Tell me, if you understand.?Who marked off its dimensions? Surely you know!?Who stretched a measuring line across it?
Moreover, without some remarkable degree of exceptional, and stable, flatness for the universe, (as well as exceptional stability for all the other constants), Euclidean (3-Dimensional) geometry would not be applicable to our world. or to the universe at large, and this would make modern science, and engineering, for humans, for all practical purposes, all but impossible.
Why We Need Cosmic Inflation By Paul Sutter, Astrophysicist | October 22, 2018 Excerpt: As best as we can measure, the geometry of our universe appears to be perfectly, totally, ever-so-boringly flat. On large, cosmic scales, parallel lines stay parallel forever, interior angles of triangles add up to 180 degrees, and so on. All the rules of Euclidean geometry that you learned in high school apply. But there’s no reason for our universe to be flat. At large scales it could’ve had any old curvature it wanted. Our cosmos could’ve been shaped like a giant, multidimensional beach ball, or a horse-riding saddle. But, no, it picked flat. https://www.space.com/42202-why-we-need-cosmic-inflation.html Scientists Question Nature’s Fundamental Laws – Michael Schirber – 2006 Excerpt: “There is absolutely no reason these constants should be constant,” says astronomer Michael Murphy of the University of Cambridge. “These are famous numbers in physics, but we have no real reason for why they are what they are.”?The observed differences are small-roughly a few parts in a million-but the implications are huge (if they hold up): The laws of physics would have to be rewritten, not to mention we might need to make room for six more spatial dimensions than the three that we are used to.”,,,?The speed of light, for instance, might be measured one day with a ruler and a clock. If the next day the same measurement gave a different answer, no one could tell if the speed of light changed, the ruler length changed, or the clock ticking changed. http://www.space.com/2613-scientists-question-nature-fundamental-laws.html
This is certainly very suggestive to the fact that the universe was specifically designed for intelligent creatures, such as ourselves, to be able to use and grow in their mathematical abilities. Likewise, the Horizon Problem, the fact that the Cosmic Microwave Background (CMB) has almost at the same temperature in all directions, a problem which inflation theory has failed to 'explain away' much less 'predict',,, as the following article explains, "“On the face of it, inflation is a totally bonkers idea – it replaces a coincidence with a completely nonsensical vision of what the early universe was like,”
Space is all the same temperature. Coincidence? Distant patches of the universe should never have come into contact. So how come they’re all just as hot as each other? - 26 October 2016 Excerpt: THE temperature of the cosmic microwave background – the radiation bathing all of space – is remarkably uniform. It varies by less than 0.001 degrees from a chilly 2.725 kelvin. But while that might seem natural enough, this consistency is a real puzzle. For two widely separated areas of the cosmos to reach thermal equilibrium, heat needs enough time to travel from one to the other. Even if this happens at the speed of light, the universe is just too young for this to have happened. Cosmologists try to explain this uniformity using the hypothesis known as inflation. It replaces the simple idea of a big bang with one in which there was also a moment of exponential expansion. This sudden, faster-than-light increase in the size of the universe allows it to have started off smaller than an atom, when it would have had plenty of time to equalise its temperature. “On the face of it, inflation is a totally bonkers idea – it replaces a coincidence with a completely nonsensical vision of what the early universe was like,” says Andrew Pontzen at University College London. https://www.newscientist.com/article/mg23230970-900-cosmic-coincidences-everythings-at-the-same-temperature/
While inflation theory has failed to explain exactly why the Cosmic Background radiation is "remarkably uniform" in all directions that we look, the Bible, on the other hand, thousands of years before it was discovered by modern science, predicted the universe to be "remarkably uniform" in all directions that we may look,
Proverbs 8:26-27 While as yet He had not made the earth or the fields, or the primeval dust of the world. When He prepared the heavens, I was there, when He drew a circle on the face of the deep,?? Job 26:10 He has inscribed a circle on the face of the waters at the boundary between light and darkness.
Thus, whereas cosmologist, (who try to explain why the universe is the way it is without any reference to God), have, at every turn, been stymied in their attempts to extrapolate the microscopic descriptions of quantum mechanics to explain the macroscopic structures of the universe, the Christian Theist, on the other hand, can take assurance in the fact that the Bible predicted these macroscopic structures of the universe thousands of years before these macroscopic structures were even discovered by modern science. I would call those some pretty amazing fulfilled predictions for modern science coming from a book that many atheists try to claim to be nothing but a book of myths. Quotes and Verse:
“My argument,” Dr. Penzias concluded, “is that the best data we have are exactly what I would have predicted, had I had nothing to go on but the five books of Moses, the Psalms, the Bible as a whole.” - Dr. Arno Penzias, Nobel Laureate in Physics – co-discoverer Cosmic Microwave Background Radiation – as stated to the New York Times on March 12, 1978 “Certainly there was something that set it all off,,, I can’t think of a better theory of the origin of the universe to match Genesis” - Robert Wilson – Nobel laureate – co-discoverer Cosmic Microwave Background Radiation - Fred Heeren, Show Me God (Wheeling, Ill.: Daystar, 2000), "The question of 'the beginning' is as inescapable for cosmologists as it is for theologians...there is no doubt that a parallel exists between the big bang as an event and the Christian notion of creation from nothing" - George Smoot and Keay Davidson, Wrinkles in Time, 1993, p.189., Nobel laureate in 2006 for his work on COBE "Now we see how the astronomical evidence supports the biblical view of the origin of the world. The details differ, but the essential elements in the astronomical and biblical accounts of Genesis are the same: the chain of events leading to man commenced suddenly and sharply at a definite moment in time, in a flash of light and energy."? - Robert Jastrow – Founder of NASA’s Goddard Institute – ‘God and the Astronomers’ - Pg.15 - 2000?? “The Bible is frequently dismissed as being anti-scientific because it makes no predictions. Oh no, that is incorrect. It makes a brilliant prediction. For centuries it has been saying there was a beginning. And if scientists had taken that a bit more seriously they might have discovered evidence for a beginning a lot earlier than they did.” John Lennox? - Science Is Impossible Without God - video? Genesis 1:1-3 In the beginning God created the heavens and the earth. Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters. And God said, “Let there be light,” and there was light.
bornagain77
February 1, 2021
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in 112 Viola Lee states that he does not believe the universe will explicable to mathematics because,
,, QM inherently involves probabilities, I don’t think a mathematical description will ever be able to fully model what is going to happen in all situations. To believe that is to believe the universe is completely deterministic, and I don’t believe that.
Yet Viola hedges his bet a bit with this,
The fact that all mathematical descriptions of the world are necessarily incomplete because of quantum probabilities doesn’t mean that there can’t be, at some point, a mathematical description that ties together the general fundamentals of QM and general relativity.
And just in case anyone has missed the inherent hostility that VL has towards Christianity, Viola Lee then states this,
But whatever the case, the conclusion “therefore Jesus” is the imposition of a religious belief system that is really not relevant to the situation at all.
Well, that's a lot to unpack. So to get started let's start with VL's claim that there will never be a 'theory of everything, (not because of the insurmountable limitation imposed by Godel that was elucidated by Wolf and company mind you), but because in VL's view 'QM inherently involves probabilities' Well,,, since probabilities are indeed amendable to mathematical analysis, (i.e. to talk about probabilities is to in fact talk about math), I don't necessarily see that, in and of itself, as necessarily being a insurmountable roadblock to there ever being a purely mathematical 'theory of everything. But what I do see as being an insurmountable roadblock to there ever being a purely mathematical 'theory of everything is how the probabilities themselves get into quantum mechanics.. As Steven Weinberg stated, "In quantum mechanics these probabilities do not exist until people choose what to measure,,,"
The_Trouble_with_Quantum_Mechanics__by_Steven_Weinberg Excerpt: The introduction of probability into the principles of physics was disturbing to past physicists, but the trouble with quantum mechanics is not that it involves probabilities. We can live with that. The trouble is that in quantum mechanics the way that wave functions change with time is governed by an equation, the Schrödinger equation, that does not involve probabilities. It is just as deterministic as Newton’s equations of motion and gravitation. That is, given the wave function at any moment, the Schrödinger equation will tell you precisely what the wave function will be at any future time. There is not even the possibility of chaos, the extreme sensitivity to initial conditions that is possible in Newtonian mechanics. So if we regard the whole process of measurement as being governed by the equations of quantum mechanics, and these equations are perfectly deterministic, how do probabilities get into quantum mechanics?,,, The instrumentalist approach is a descendant of the Copenhagen interpretation, but instead of imagining a boundary beyond which reality is not described by quantum mechanics, it rejects quantum mechanics altogether as a description of reality. There is still a wave function, but it is not real like a particle or a ?eld. Instead it is merely an instrument that provides predictions of the probabilities of various outcomes when measurements are made. It seems to me that the trouble with this approach is not only that it gives up on an ancient aim of science: to say what is really going on out there. It is a surrender of a particularly unfortunate kind. In the instrumentalist approach, we have to assume, as fundamental laws of nature, the rules (such as the Born rule I mentioned earlier) for using the wave function to calculate the probabilities of various results when humans make measurements. Thus 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, but I think not yet. 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, because in quantum mechanics not everything can be simultaneously measured. As Werner Heisenberg realized, a particle cannot have, at the same time, both a definite position and a definite velocity. The measuring of one precludes the measuring of the other. Likewise, if we know the wave function that describes the spin of an electron we can calculate the probability that the electron would have a positive spin in the north direction if 4/8 that were measured, or the probability that the electron would have a positive spin in the east direction if that were measured, but we cannot ask about the probability of the spins being found positive in both directions because there is no state in which an electron has a definite spin in two different directions. https://www.coursehero.com/file/78050243/The-Trouble-with-Quantum-Mechanics-by-Steven-Weinberg-The-New-York-Review-of-Bookspdf/
And as I pointed out in my video, Weinberg, an atheist, rejected the instrumentalist approach precisely because “humans are brought into the laws of nature at the most fundamental level” and precisely because it undermined the Darwinian worldview from within. Yet, regardless of how he and other atheists may prefer the world to behave, quantum mechanics itself could care less how atheists prefer the world to behave. As leading experimentalist Anton Zeilinger states in the following video, “what we perceive as reality now depends on our earlier decision what to measure. Which is a very, very, deep message about the nature of reality and our part in the whole universe. We are not just passive observers.”
“The Kochen-Speckter Theorem talks about properties of one system only. So we know that we cannot assume – to put it precisely, we know that it is wrong to assume that the features of a system, which we observe in a measurement exist prior to measurement. Not always. I mean in certain cases. So in a sense, what we perceive as reality now depends on our earlier decision what to measure. Which is a very, very, deep message about the nature of reality and our part in the whole universe. We are not just passive observers.” Anton Zeilinger – Quantum Physics Debunks Materialism – video (7:17 minute mark) https://www.youtube.com/watch?feature=player_detailpage&v=4C5pq7W5yRM#t=437
And as I further pointed out in my video, Zeilinger and company, as of 2018, closed the last remaining 'free will loop hole' in quantum mechanics,
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
Thus regardless of how Steven Weinberg and other atheists may prefer the universe to behave, with the closing of the last remaining free will loophole in quantum mechanics, “humans are indeed brought into the laws of nature at the most fundamental level”, and thus these recent findings from quantum mechanics directly undermine, as Weinberg himself stated, the “vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else.” Moreover, besides undermining the Darwinian worldview from within, with human observers, via their free will, now being brought into the laws of nature at their most fundamental level then it now becomes, at least, theoretically plausible for God, via his son Jesus Christ, to bridge the infinite mathematical divide that exists between General Relativity and Quantum Mechanics.
John 6:38 because I came down from heaven not to do my own will but the will of the one who sent me.
And as I also pointed out in the video, the Shroud of Turin does indeed give us empirical evidence that both quantum mechanics and General Relativity were dealt with in Christ's resurrection from the dead. Thus regardless of whatever bias against Christianity Viola Lee, and other people who are hostile to Christianity, may personally have, the resurrection of Jesus Christ from the dead, especially with the closing of the last remaining free will loop hole in quantum mechanics, is indeed very much a viable option for solving the long standing mystery of the 'theory of everything'. As Zeilinger noted, “the fact that some of the brightest minds in physics have been working on this issue, (i.e. The unification of General Relativity and Quantum Mechanics), for 80 years now at least, and have not found a solution means that the solution will be extremely deep. It will be extremely significant if somebody found it, and it will probably be in a direction where nobody expected it.,,,”
Anton Zeilinger interviewed about Quantum Mechanics – video – 2018 (The essence of Quantum Physics for a general audience) https://www.youtube.com/watch?v=z82XCvgnpmA 15:45 min:,,, the fact that some of the brightest minds in physics have been working on this issue, (i.e. The unification of General Relativity and Quantum Mechanics), for 80 years now at least, and have not found a solution means that the solution will be extremely deep. It will be extremely significant if somebody found it, and it will probably be in a direction where nobody expected it.,,,
And Jesus Christ rising from the dead is definitely a direction where nobody expected it. But regardless of whether people were looking in that direction or not, that still does not take away from the fact that Jesus' resurrection from the dead is still very much a live option and is very much a plausible solution for the much sought after 'theory of everything. That such a solution for the 'theory of everything' would even be a live option as to providing a viable solution should definitely be more than enough to raise quite a few eyebrows. i.e. How is it even remotely possible that a supposed 'ancient myth' of a man rising from the dead could find itself as a serious candidate to solving the most perplexing scientific problem of our day? And although many scientists of today, who are totally committed to the doctrine of methodological naturalism, may find this to be quite a unacceptable state of affairs in science, I am fairly certain that the many of the Christian founders of modern science themselves would be quite pleased to see that Christ's resurrection from the dead provides a very plausible solution for the much sought after 'theory of everything'.
“Since we astronomers are priests of the highest God in regard to the book of nature, it befits us to be thoughtful, not of the glory of our minds, but rather, above all else, of the glory of God.” (Kepler, as cited in Morris 1982, 11; see also Graves 1996, 51). “I think men of science as well as other men need to learn from Christ, and I think Christians whose minds are scientific are bound to study science that their view of the glory of God may be as extensive as their being is capable of.” (Maxwell, as cited in Campbell and Garnett 1882, 404-405) - James_Clerk_Maxwell “Overpoweringly strong proofs of intelligent and benevolent design lie all around us; and if ever perplexities, whether metaphysical or scientific, turn us away from them for a time, they come back upon us with irresistible force, showing to us through Nature the influence of a free will, and teaching us that all living things depend on one ever-acting Creator and Ruler.” (Kelvin 1871; see also Seeger 1985a, 100-101)
Verse:
Colossians 1:15-20 The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him. He is before all things, and in him all things hold together. And he is the head of the body, the church; he is the beginning and the firstborn from among the dead, so that in everything he might have the supremacy. For God was pleased to have all his fullness dwell in him, and through him to reconcile to himself all things, whether things on earth or things in heaven, by making peace through his blood, shed on the cross.
bornagain77
January 31, 2021
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Kairosfocus and Bornagain77, Thanks for your cogent replies and excellent quotes! I'm now able to belatedly post replies again (woohoo). Viola Lee, It seems like you're not considering a lot of relevant points in these posts--something that I'm admittedly guilty of as well. Perhaps it's at least partly due to the sheer length of some of the posts, again something I'm guilty of creating. It might seem more productive to consider one point at a time, but the resulting downside is the proliferation of threads that are 1,000+ posts long. Thus, this dilemma reinforces my conviction that we're experiencing a manifestation of the dendritic hierarchy of the levels of abstraction that's inherent in Information. From this statement, one might recognize an analogy between the Mandelbrot set emerging from observable nature and from intellectual information. I think it's worth thinking about. An emergent phenomenon is that ALL non-trivial true-false questions on tests are False at a sufficiently detailed level of abstraction. In 108, you make the following point:
So I don’t think BA is correct when he says “the halting problem itself is proof that Godel’s incompleteness can be applied to physical systems.” A computer is a physical manifestation of a logical axiomatic system, to which Godel’s proofs apply, but that is different than saying Godel’s proofs apply to our attempts to create a mathematical model of real-world phenomena.
I have four issues with your assertion: 1. I don't think it's consistent with your previous assertions. 2. Your assertions are unsupported in the sense that you don't often include reasons why you believe as you do. 3. There's a false dichotomy between "mathematics" (which serves as models of the Logos) and "the real world." The real world IS fundamentally Information together with Conscious Measurement approximated by mathematical abstractions from a QM perspective. Heisenberg, Vedral, and others have famously noted (a) that atoms and molecules don't actually exist unless they're observed, and (b) Reality is fundamentally Information and the processes in which information interacts. Are you familiar with Finite Element Analysis? 4. Turing machines are easily created both in software (electrons acting as bits in an electronic device) and macro/physically. For example, in high school, I created a macro/physical Turing machine in cardboard that followed several rules and yes, it inevitably did "run off the tape." In software, there are different types of bugs. One pernicious type of bug that's hard to identify obeys all the rules but falls through the code into an unexpected error condition. These are often encountered as "occasional" or "non-reproducible" (sic) under most conditions. -QQuerius
January 31, 2021
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Thanks KF, it appears that not only have they successfully defended their 2015 proof, but, as of 2020, they have now made it more robust. per wikipedia,
Spectral gap (physics) 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)
bornagain77
January 31, 2021
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P. 7 in the 2020 version: >>A short version of this paper – including a statement of the main result, dis- cussion of its implications, an outline of the main ideas behind the proof, together with a sketch of the argument – was published recently in Nature [CPW15]. We encourage the reader to consult it in order to gain some high-level intuition about the full, rigorous proof given in this work.>>kairosfocus
January 31, 2021
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I see that one of the issues in this discussion is the difference between the mathematical statement of general "laws of nature" as are expressed in QM and general relativity (GR), which are generalizations, and the application of those laws to exactly predict events in the real world. The former is a map and the latter is the territory. These are not the same. Wigner, in his famous essay "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", has some interesting things to say about this.
All these laws of nature contain, in even their remotest consequences, only a small part of our knowledge of the inanimate world. All the laws of nature are conditional statements which permit a prediction of some future events on the basis of the knowledge of the present, except that some aspects of the present state of the world, in practice the overwhelming majority of the determinants of the present state of the world, are irrelevant from the point of view of the prediction. It is in consonance with this, first, that the laws of nature can be used to predict future events only under exceptional circumstances when all the relevant determinants of the present state of the world are known. It is also in consonance with this that the construction of machines, the functioning of which he can foresee, constitutes the most spectacular accomplishment of the physicist. In these machines, the physicist creates a situation in which all the relevant coordinates are known so that the behavior of the machine can be predicted. The principal purpose of the preceding discussion is to point out that the laws of nature are all conditional statements and they relate only to a very small part of our knowledge of the world. ... It should be mentioned, for the sake of accuracy, that we discovered about thirty years ago that even the conditional statements cannot be entirely precise: that the conditional statements are probability laws which enable us only to place intelligent bets on future properties of the inanimate world, based on the knowledge of the present state. They do not allow us to make categorical statements, not even categorical statements conditional on the present state of the world.
This is the point I am making about the difference between pure mathematics and real-world phenomena. A machine, in the theoretical sense, can manifest a purely mathematical axiomatic system to the extent that "all the relevant coordinates are known so that the behavior of the machine can be predicted." In this sense, the machine, or the laws of nature that it might model, are subject to Godel's conclusions. But the real-world is not a machine, and our knowledge about it is, and can never be, comprehensive. Mathematical laws of nature, as manifestations of axiomatic systems, can never model all the relevant initial conditions of an actual situation in the real world, and thus are only abstract approximations of reality. Given that "the conditional statements (of QM) are probability laws which enable us only to place intelligent bets on future properties of the inanimate world", the real world does not behave deterministically like a machine, so Godel's conclusions do not apply. Things in the real world, at the level of individual quantum events, can be undecideable because the relevant initial conditions are probabilistic, not because the generalized mathematical laws of nature which we use to describe them are subject to Godel's limitations.Viola Lee
January 31, 2021
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Thanks KF, I note that the date on the pdf is June 16, 2020, so apparently they are still going strong, and have not been refuted, 5 years since they first published their results in Nature in 2015 Undecidability of the Spectral Gap - June 16, 2020 Toby Cubitt, David Perez-Garcia, and Michael M. Wolf https://arxiv.org/pdf/1502.04573.pdfbornagain77
January 31, 2021
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VL (attn BA77 & Q): The actual abstract:
. . . These and other problems are particular cases of the general spectral gap problem: given the Hamiltonian of a quantum many-body system, is it gapped or gapless? [--> A Hamiltonian Operator expression is "a function that is used to describe a dynamic system (such as the motion of a particle) in terms of components of momentum and coordinates of space and time and that is equal to the total energy of the system when time is not explicitly part of the function " . . . it is one of the original keys that opened up Q-theory, it is central] Here we prove that this is an undecidable problem [--> tie to Turing and Godel]. Specifically, we construct families of quantum spin systems on a two-dimensional lattice with translationally invariant, nearest-neighbour interactions, for which the spectral gap problem is undecidable. This result extends to undecidability of other low-energy properties, such as the existence of algebraically decaying ground-state correlations. The proof combines Hamiltonian complexity techniques with aperiodic tilings, to construct a Hamiltonian whose ground state encodes the evolution of a quantum phase-estimation algorithm followed by a universal Turing machine. The spectral gap depends on the outcome of the corresponding ‘halting problem’. Our result implies that there exists no algorithm to determine whether an arbitrary model is gapped or gapless, and that there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics.
2020 full version at Arxiv https://arxiv.org/pdf/1502.04573.pdf KFkairosfocus
January 31, 2021
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BA writes, "So does Viola believe that the universe is fully explicable to mathematics or does he believe there will always be “properties or indeterminacies not included in our (mathematical) model”?" Given that QM inherently involves probabilities, I don't think a mathematical description will ever be able to fully model what is going to happen in all situations. To believe that is to believe the universe is completely deterministic, and I don't believe that. BA writes, "If the universe is not fully explicable to mathematics then there, obviously, can never be a purely mathematical ‘theory of everything. And that is precisely my point!" The fact that all mathematical descriptions of the world are necessarily incomplete because of quantum probabilities doesn't mean that there can't be, at some point, a mathematical description that ties together the general fundamentals of QM and general relativity. However, it may be that such a formulation will never be developed because the two phenomena aren't in fact related in such a fashion. I don't think that it a necessary truth that the universe can be modelled by a one single mathematical theory of everything. Maybe it can't be. But whatever the case, the conclusion "therefore Jesus" is the imposition of a religious belief system that is really not relevant to the situation at all. Also BA writes, "As an atheist, Viola Lee simply has no reason to presuppose the universe should be fully explicable to mathematics." As I have pointed out several times, which BA seems to not get, there are metaphysical positions that fully accept the inherent mathematical nature of reality without there being a personal god, much less one that human beings are capable of knowing details about, much less the Christian God upon which BA builds all his beliefs. I'm pretty sure that BA has never displayed any curiosity about what I in fact do believe, and I'm pretty sure he actually has no interest in views others than his own. But I do object, not that it will do any good, to his simple black-and-white stereotyped dichotomies about the range of people's religious and philosophical beliefs.Viola Lee
January 31, 2021
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Although the invention of the computer itself is directly linked to Turing’s desire to make Godel’s incompleteness theorem clearer and simpler, i.e. more ‘concrete’, to understand, i.e. less abstract, this is still not good enough for Viola Lee to accept the broad applicability of Godel's proof to the physical universe at large and so he objects thusly,
,,, This is different than describing a real-world phenomena in which we are modeling the system mathematically to see if we have a good model, but which itself may have (almost certainly does have) properties or indeterminacies not included in our model.
And yet Godel's proof applies, not just to any mathematics that does not describe the universe, but also to any mathematics that may describe the universe. As Hawking himself reluctantly conceded,
“Gödel’s incompleteness theorem (1931), proves that there are limits to what can be ascertained by mathematics. Kurt Gödel halted the achievement of a unifying all-encompassing theory of everything in his theorem that: “Anything you can draw a circle around cannot explain itself without referring to something outside the circle—something you have to assume but cannot prove”. - Stephen Hawking & Leonard Miodinow, The Grand Design (2010)
In short, for Viola Lee to hold that Godel's proof is not applicable to the universe at large is for Viola Lee to, basically, claim that the universe itself is not fully explicable to mathematics.,,, i.e. "a real-world phenomena in which we are modeling the system mathematically to see if we have a good model, but which itself may have (almost certainly does have) properties or indeterminacies not included in our model." So does Viola believe that the universe is fully explicable to mathematics or does he believe there will always be "properties or indeterminacies not included in our (mathematical) model"? Either way, it is 'damned if you do, damned if you don't' for Viola Lee. If the universe is fully explicable to mathematics then Godel's proof necessarily applies. If the universe is not fully explicable to mathematics then there, obviously, can never be a purely mathematical 'theory of everything. And that is precisely my point! Apparently, unbeknownst to Viola Lee, Viola Lee's objection that Godel's proof can't be applied to the universe at large is making my point for me that I made in the video. i.e. 'There will never be a purely mathematical 'theory of everything' that describes all the phenomena of the universe.' Of course I made my point in my video because of Godel's proof and Viola Lee is, apparently, trying to make his point in spite of Godel's proof. But to the same conclusion is apparently being reached by both of us. i.e. There will never be a purely mathematical 'theory of everything' that describes all the phenomena of the universe. I'll leave it to Viola Lee to straighten out exactly where he stands on the question of whether the universe is fully explicable to mathematics or not. But if it is, then Godel's proof necessarily applies, and if not, then the nearly 100 year quest for a purely mathematical theory of everything has been in vain. It is also interesting to point out that, as an atheist, Viola Lee simply has no reason to presuppose the universe should be fully explicable to mathematics. Both Einstein, who discovered General Relativity, and Eugene Wigner, who's insights into quantum mechanics continue to drive breakthroughs in quantum mechanics,,,,
"When the province of physical theory was extended to encompass microscopic phenomena, through the creation of quantum mechanics, the concept of consciousness came to the fore again: it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness." - Eugene Wigner - "Remarks on the Mind-Body Question," in Symmetries and Reflections, p.171
,,, Both Einstein and Wigner are on record as to regarding it as a miracle that mathematics is applicable to the universe. (Einstein even chastised 'professional atheist' in the process of calling it a miracle.
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 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
And the last time I checked, miracles were the sole province of God.
mir·a·cle noun miracle; plural noun: miracles 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. "the miracle of rising from the grave"
So does Viola Lee believe the universe is fully and 'miraculously' explicable to mathematics or not? If so, then Godel's proof necessarily applies and, as the proof in the paper I cited found, “the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description.", and hence the conclusion that there never will be a purely mathematical theory of everything that bridges the 'infinite infinities' that separate the microscopic descriptions of Quantum Mechanics to the macroscopic descriptions of General Relativity is a straight forward reading of the paper I cited. And since Viola Lee apparently disagrees with the conclusion of the paper that I cited from Nature, then I suggest that he write one of the authors of the paper, such as Professor Wolf of Munich, and tell him exactly where he went wrong In his analysis so that Professor Wolf and his colleagues can have a chance to retract their paper from Nature. Or perhaps Viola Lee can just submit his own paper to Nature showing exactly where they went wrong in applying Godel's proof to Quantum Mechanics? Elsewise, it is basically just Viola Lee's word, (an internet atheist who rails against Christianity, and who self admittedly is not very well versed on Godel's proof), against the word of a Professor's, and his colleagues, published work in Nature. Viola Lee, seems, if you truly want to thoroughly refute their paper in Nature, instead of just throwing stuff on the wall on a blog to see if it sticks, then you have really got your intellectual work cut out for you. :) Verse:
Romans 1:22 Professing themselves to be wise, they became fools,
bornagain77
January 31, 2021
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F/N: JB of UD on axioms ant theorems (on the way to oracle machines): https://mindmatters.ai/2019/02/why-i-doubt-that-ai-can-match-the-human-mind/ >> cognitive ability is only one aspect of intelligence. Those who think that artificial intelligence will eventually equal human intelligence face many hurdles, including problems of consciousness, emotion, etc. Here, we are looking at only one problem—cognitive ability. Consider the difference between axioms and theorems. An axiom is a foundational truth, which cannot be proven within the system in which it operates. A theorem is a derivative truth, whose truth value we can know based on axioms. Computers are exclusively theorem generators, while humans appear to be axiom generators. Computers are much better than humans at processing theorems—by several orders of magnitude. However, they are limited by the fact that they cannot establish axioms. They are entirely boxed into their own axiomatic rules. You can see this in several aspects of computer science. The Halting Problem is probably the best known. In essence, you cannot create a computer program that will tell if another arbitrarily chosen program will ever finish. In fact, the problem is deeper than that: While the Halting Problem itself comes with a handy proof (which is why it is so often cited), we also find that absent outside information, computers have trouble telling if practically any program with loops will complete without directly running the program to completion. That is, I can program a computer to recognize certain traits of halters and/or non-halters. But without that programming, it cannot tell the difference. I have to add axioms to the program in order to process the information. Given a set of axioms, computers can produce theorems very swiftly. But no increase in speed allows them to jump the theorem/axiom gap. AI research identifies the axioms needed to solve certain types of problems and then lets the computer loose to calculate theorems that depend on them. AI research also creates more and more powerful axioms. That is, a previous generation may have started with axioms A, B, and C, but current generations have found more fundamental axioms, D, E, and F which reduce A, B, and C to theorems. A question now appears: Is there a super-axiom that allows all of these axioms to be reduced to theorems? The answer is no. The same logic that shows that the Halting Problem can’t be solved can be used to show why the super-axiom does not exist. This distinction is essentially the same as the one between first-order and second-order logic. Computers cannot process second-order logical statements in the same way as first-order logical statements. Some systems are described as second-order logic processors but they work is by picking out a subset of second order propositions, reducing them to first-order propositions, and then processing them as first-order logic. This is identical to the process I mentioned with respect to the Halting Problem. Humans can identify specific traits that will/will not halt and have the computer identify those traits but the computer itself cannot generate them on its own. In fact, if I were to hazard a guess, I would say that the point where computers break down is infinity. The halting problem deals with identifying programs that will have infinite states and second-order logic deals with propositions that require an infinite number of comparisons. As I mentioned, after humans discover truths about them, we can encode these specific truths as new axioms into the system. But computers cannot discover the truths by themselves. For instance, try to imagine how a computer program (AI or otherwise) could establish the well-ordering property of the natural numbers without using any other second-order logic operation (or even try to do so!).>> KF PS: I think the issue is, WP likely has done an update. I am not sure that such can be easily rolled back without losses. There is a whole -- relevant! -- theory out there that bugs are ineradicable in a sufficiently complex computational entity. Indeed there is a tradeoff where fixing bug A may create at least one other bug B and so forth. Where also, the low hanging fruit get picked first, so onward bugs tend to be increasingly intractable.kairosfocus
January 31, 2021
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VL, you will note that I have frequently suggested that mathematical axiomatisations, model frameworks and scientific theory frameworks alike compose abstract, logic model worlds, essentially defining start points, rules of computation, elements [suitably symbolised] that are structural-quantitative, and thus set up a core with a definable process to advance to particular states or statements in an abstract space. Those rules are obviously constrained by core logic and core mathematics ties to N,Z,Q,R,C,R* etc and structures built up from them. The fact that N and its extensions will be built in carries with it Godel's result, once we move beyond toy examples. These logic model worlds are amenable to analysis on computational theory [simple survey here], and yield to the standard result: many valid states in the world cannot be reached by finite length sequences of computation from a given start-point. Worse, given our actual atomic-material and temporal constraints on computability and observability [one has to spot and recognise a solution as valid per some criterion to guide reporting and halting on success], blind mechanical succession and/or chance processes cannot be reasonably expected to discover intelligent signals of greater than 500 - 1,000 bits of functionally specific complex information. Where, recall, existence of Autocad etc demonstrates that arbitrary 3-d functional elements and combinations are reducible to coded binary strings in some description language or other. Where, too, if the direct blind search for a satisfactory target zone in a complex space of n possibilities is challenging, the search space for a golden search on the space, is the collection of subsets, which is directly known to be the exponentially harder search in a space of scale 2^n, the power set. Put in another frame, powerful creative intelligence is not a manifestation of blindly mechanical and/or dynamic-stochastic computational trajectories. Our creative intelligence is itself evidence of a realm that exceeds computational limits. Mind space, we may term it. That is, Turing's analysis (which was about theory of numbers) propagates through other problems reducible to a similar framework. Effectively equivalently, Godel's analysis blows up any sufficiently complex universal calculation scheme. Including, the proposition that there is a grand continent of effective, evolutionarily ascending functions just waiting for blind physics and chemistry to assemble some first cell based life. Islands of complex function deeply isolated in and not computable by blind search are what we should expect. Starting from the domains for functional proteins in AA sequence space, such islands are also what we observe. And yes, the design inference challenge lurks here too. It is not about to go away. The config space for 1,000 elements is 1.07*10^301 and bigger spaces can be reduced to chaining sequences from such. But already the first space swamps any computation machine within the material and temporal resources of our observed cosmos. This problem is not going away, it actually comes from statistical mechanics:
In physics, particularly in statistical mechanics, we base many of our calculations on the assumption of metric transitivity, which asserts that a system’s trajectory will eventually [--> given "enough time and search resources"] explore the entirety of its state space – thus everything that is phys-ically possible will eventually happen. It should then be trivially true that one could choose an arbitrary “final state” (e.g., a living organism) and “explain” it by evolving the system backwards in time choosing an appropriate state at some ’start’ time t_0 (fine-tuning the initial state). In the case of a chaotic system the initial state must be specified to arbitrarily high precision. But this account amounts to no more than saying that the world is as it is because it was as it was, and our current narrative therefore scarcely constitutes an explanation in the true scientific sense. We are left in a bit of a conundrum with respect to the problem of specifying the initial conditions necessary to explain our world. A key point is that if we require specialness in our initial state (such that we observe the current state of the world and not any other state) metric transitivity cannot hold true, as it blurs any dependency on initial conditions – that is, it makes little sense for us to single out any particular state as special by calling it the ’initial’ state. If we instead relax the assumption of metric transitivity (which seems more realistic for many real world physical systems – including life), then our phase space will consist of isolated pocket regions and it is not necessarily possible to get to any other physically possible state (see e.g. Fig. 1 for a cellular automata example).
[--> or, there may not be "enough" time and/or resources for the relevant exploration, i.e. we see the 500 - 1,000 bit complexity threshold at work vs 10^57 - 10^80 atoms with fast rxn rates at about 10^-13 to 10^-15 s leading to inability to explore more than a vanishingly small fraction on the gamut of Sol system or observed cosmos . . . the only actually, credibly observed cosmos]
Thus the initial state must be tuned to be in the region of phase space in which we find ourselves [--> notice, fine tuning], and there are regions of the configuration space our physical universe would be excluded from accessing, even if those states may be equally consistent and permissible under the microscopic laws of physics (starting from a different initial state). Thus according to the standard picture, we require special initial conditions to explain the complexity of the world, but also have a sense that we should not be on a particularly special trajectory to get here (or anywhere else) as it would be a sign of fine–tuning of the initial conditions. [ --> notice, the "loading"] Stated most simply, a potential problem with the way we currently formulate physics is that you can’t necessarily get everywhere from anywhere (see Walker [31] for discussion). ["The “Hard Problem” of Life," June 23, 2016, a discussion by Sara Imari Walker and Paul C.W. Davies at Arxiv.]
In short, we are looking at a class of powerful constraints and the Godel incompleteness, Turing machine challenge is just a start point. For simple example, there is no universal decoder that can detect and reduce to plain text any arbitrary intelligent signal. The halting problem is extremely powerful. (BTW, this means that detection of design is not algorithmically reducible to a simple framework, instead it is a body of knowledge built up through praxis.) Whether we program some super computer to run the deductions or do it with chalk on boards step by step makes but little difference, abstract logic model worlds of significant complexity are inherently limited in their power to reach conclusions constrained by finite frameworks defining start points and rules-compliant stepwise successions. Yes, one may then extend the axiomatic or modelling framework, but then the same problems of potential incoherence and/or undecidability continue to haunt the system. Undecidability and incoherence potential are built-in issues. Godel and Church-Turing rule the roost. It's not just Q-theory or Relativity etc, this is a broad, deep challenge. KFkairosfocus
January 31, 2021
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Re BA's post at 106 Turing machines are an abstract axiomatic system: they have certain definite concepts and certain rules to follow. The fact that they can be actualized in a deterministic physical computer is no different than the fact that math is actualized in a series of logical proposition in writing. This is different than describing a real-world phenomena in which we are modeling the system mathematically to see if we have a good model, but which itself may have (almost certainly does have) properties or indeterminacies not included in our model. So I don't think BA is correct when he says "the halting problem itself is proof that Godel’s incompleteness can be applied to physical systems." A computer is a physical manifestation of a logical axiomatic system, to which Godel's proofs apply, but that is different than saying Godel's proofs apply to our attempts to create a mathematical model of real-world phenomena. Also, the "proof" that "that the microscopic descriptions of quantum mechanics cannot be extended to the macroscopic descriptions of General Relativity" is a video where one scientist drew an analogy between their understanding of a situtation and Godel. One quote does not a proof make. Also, to KF at 107 wrote, "VL, The Godel result is anything but narrow; that is why it blew up the grand programme of mathematical unification 90 years ago. The general force is that complex mathematical systems are incomplete or incoherent and there is no scheme to guarantee coherence." Yes, I've said that several times. For instance, at 105 I wrote, "Godel’s proofs are, I think, commonly assumed to apply to any axiomatic system. That is what JVL, KF, and I have been saying." I don't think we have disagreed about the impact of Godel's proofs on abstract axiomatic systems ast all. As to the paper BA points to, note this paragraph towards the end:
The reason this problem is impossible to solve in general is because models at this level exhibit extremely bizarre behaviour that essentially defeats any attempt to analyse them. But this bizarre behaviour also predicts some new and very weird physics that hasn't been seen before.
Note that the undecidability comes from the predication of some new, weird physics. That is, it comes from ways in which their model is not sufficient to solve the problem. However, rather than assume that this is a product of Godel's proofs in respect to their model it is more reasonable to assume that this is because their model is incomplete, which seems to be what the quoted paragraph is saying.Viola Lee
January 30, 2021
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Q, BA77 actually clipped above, abstract from a paper in Nature pointing to undecidability in Quantum theory. Undecidability is a term for when it is concluded that a frasmework [here, Q-theory] faces results that are at least plausibly true but are unreacheable from axioms. AS2 You have already had link enough above on multiple points of correlation that give reason to conclude the two items came from the same crucified man (from a site in Palestine), complete with confirmation of the blood and water observation. There is no good reason to take your extensive skeptically dismissive clip above seriously. VL, The Godel result is anything but narrow; that is why it blew up the grand programme of mathematical unification 90 years ago. The general force is that complex mathematical systems are incomplete or incoherent and there is no scheme to guarantee coherence. Relative to systems we build -- logic model worlds -- we face the prospect of undecidable propositions. I would suggest that complex theoretical constructs are liable to face such. The claim in a paper linked by BA77 is that such has actually popped up in Quantum theory. where, BA77 also aptly bridges to the matter of computability, and uncomputability. From given start-points on a turing machine, certain valid results will be unreacheable. Of course natural halting of a machine is a classic challenge . . . in the real world we can pull the plug or force a halt in software of course, but such is the opposite of creating a feasible algorithm that naturally progresses to a good solution in finite cycles and on recognising such, reports and halts. Where, clearly defined start points, operations, inference or computing rules etc are amenable to such an analysis. String theory, notoriously is troubled by the infinite. The trick then is that our theories effectively function like that and are prone to incoherence and undecidability or simple contradiction to valid observation. KFkairosfocus
January 30, 2021
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In sum, it seems, in order to try to undermine the argument I made in the video that the atheists on UD are now trying to deny that Godel's proof can be extended to physical systems altogether,, for instance Viola Lee states, "from what I’ve read Godels’ proofs apply to axiomatic mathematical systems, not real world mathematical descriptions." Which is an interesting tactic for them to try to take since Turing's 'halting problem' itself was the extension Godel's proof in computers and was therefore a 'real world' example of the fact that Godel's proof could in fact be extended to physical systems. In fact, the invention of the computer itself is directly linked to Turing's desire to make Godel's incompleteness theorem clearer and simpler, i.e. more 'concrete', to understand,
Narrator: "(Turing) is also the man who made Godel's already devastating incompleteness theorem even worse. Turing was a much more practical man than Godel. And simply wanted to make Godel's incompleteness theorem clearer and simpler. How it came to him, as he said later, was in a vision. That vision was the computer. The invention that has shaped the modern world was first imagined simply as the means to make Godel's incompleteness theorem more concrete. Because for many Godel's proof had simply been too abstract." Gregory Chaitin: It is an absolutely devastating result from a philosophical point of view that we still haven't absorbed. But the proof was too superficial. It didn't get to the real heart of what was going on. It was more tantalizing than anything else. It was not a good reason for something so devastatingly fundamental. It was too clever by half. It was too superficial. It said 'I'm unprovable',, "so what?',, It doesn't give you any insight into how serious the problem is. But Turing, five years later, his approach to incompleteness, that I felt was getting more in the right direction." Narrator: Turing recast incompleteness in terms of computers, and showed that since they are logic machines, incompleteness meant there would always be some problems they would never solve. A machine fed one of these problems would never stop. And worse, Turing proved that there was no way of telling beforehand which problems these were.",,, Georgory Chaitin: "But Turing makes it very down to earth because he talks about machines. He talks about whether a machine will halt or not.,, You know computers are physical devices . You start it running and there are two possibilities if you start a program.,, One possibility is that it will come up with an answer and stop. The other possibility is that it is going to run forever and never finish the calculation. (And you can never know beforehand which is which). And this is Turing's version of incompleteness. Turing gets incompleteness, Godel's profound discovery, he gets as a corollary of something more basic which is uncomputability.,, Things which no computer can calculate. In certain domains, most things cannot be calculated." ,,”,,,, ,,, "Turing's personality is one thing. His mathematics doesn't have to be consistent with his personality. There is his work on artificial intelligence where I think he believes that machines could become intelligent just like people. or better, or different, but intelligent. But if you look at his first paper, when he points out that machines have limits because there are numbers, in fact most numbers, cannot be calculated by any machine, he is showing the power of the human mind to imagine thing that escape what any machine could ever do. So that may go against his own philosophy. He may think of himself as a machine but his very first paper is smashing machines. Its creating machines and then its pointing out their devastating limitations." - Gregory Chaitin - Alan Turing & Kurt Gödel - Incompleteness Theorem and Human Intuition - video http://www.metacafe.com/watch/8516356/
Thus, contrary to what the atheists on UD are trying to say, i.e "from what I’ve read Godels’ proofs apply to axiomatic mathematical systems, not real world mathematical descriptions", the halting problem itself is proof that Godel's incompleteness can be applied to physical systems. Hence, the proof I cited in my video, via Godel and Turing, that the microscopic descriptions of quantum mechanics cannot be extended to the macroscopic descriptions of General Relativity, contrary to what the atheists on UD are trying to insinuate, remains very much a valid proof. Godel's proof can, and indeed has, via Turing himself, been extended to physical systems!bornagain77
January 30, 2021
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Q, you write, "Viola Lee, ... but it seems odd to me that you confine Gödel’s theorems to a very narrow application. The extensibility of his theorems does seem plausible. For example, why can’t his use of natural numbers be extended to negative whole numbers?" I am a bit confused about why I am not being clear. Above, I wrote,
As KF points out, Godel's proofs are about the natural numbers, but it seems reasonable to assume that the undecidability features extends to other axiomatic extensions of the natural numbers. However, I don't know (and don't think I would know, as that is pretty esoteric) what mathematical work might have been done on broader extensions beyond the natural numbers.
It seems like I said exactly what you're saying I didn't say??? Also, you wrote,
"Gödel’s two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories." Where exactly do you disagree with the introduction posted on the Stanford Encyclopedia of Philosophy? It seems that they also feel extensibility of Gödel’s theorems is plausible.
I don't disagree with that statement at all. Godel's proofs are, I think, commonly assumed to apply to any axiomatic system. That is what JVL, KF, and I have been saying. I don't know (because I am not expert enough) whether anyone has actually worked the proofs out for extensions to the natural numbers, but the general conclusions are, I think, assumed to axiomatic systems in general. And last, you write, "So, I would assume that the operations in, for example, existential logic would also quality, wouldn’t you?" Formal logic is an axiomatic system, so yes I would assume that Godel's proofs would apply, In summary, I don't think I'm saying anything that disagrees with what you are saying.Viola Lee
January 30, 2021
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Querius: I appreciate your response, but it seems odd to me that you confine Gödel’s theorems to a very narrow application. The extensibility of his theorems does seem plausible. For example, why can’t his use of natural numbers be extended to negative whole numbers? The negative whole numbers are part of the basic axiomatic system of mathematics so, yes, it applies. So, I would assume that the operations in, for example, existential logic would also quality, wouldn’t you? I would want it to be shown that existential logic was a formal axiomatic system. Is it? And yes, it appears the commenting system has been corrected. I hope.JVL
January 30, 2021
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Kairosfocus, Thank you for the explanation, which I'm going to have to study a bit to disabuse myself of some misconceptions or oversimplifications. Viola Lee, I appreciate your response, but it seems odd to me that you confine Gödel’s theorems to a very narrow application. The extensibility of his theorems does seem plausible. For example, why can't his use of natural numbers be extended to negative whole numbers?
Gödel’s two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories.
Where exactly do you disagree with the introduction posted on the Stanford Encyclopedia of Philosophy? It seems that they also feel extensibility of Gödel’s theorems is plausible. The article goes on to state
Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.
So, I would assume that the operations in, for example, existential logic would also quality, wouldn't you? -QQuerius
January 30, 2021
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I can post now: it comes and goes. I like JVL's quote form the Loeb thread:
A common misunderstanding is to interpret Gödel’s first theorem as showing that there are truths that cannot be proved. This is, however, incorrect, for the incompleteness theorem does not deal with provability in any absolute sense, but only concerns derivability in some particular formal system or another.
I also like this line from KF: "That (Euler's Identity) lends confidence to working in practical mathematics, that we have no material reason to dismiss coherence, regardless of abstract possibilities." That is, Godel's proof is about esoteric possibilities. It doesn't cast doubt on the vast body of mathematical knowledge that we can prove. And JVL, I think the commenting problem is a bug, not something about you, or me, or anyone in particular.Viola Lee
January 30, 2021
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Kairosfocus “ SA2, your suggestion of fraud fails, by way of undesigned coincidence of artifacts with geographically and administratively separate histories. Start with, how did these two entities happen to have the same unusual blood type [and matching patterns], centuries before such was known? ” Do you have a link to the paper that proves that they both have AB? I have searched Google but haven’t found it. Although there are a couple that demonstrate that the blood on the shroud can’t even conclusively be shown to be human. But now that we are talking about undesigned coincidence, the letter I posted above was written in the Middle Ages and, “coincidentally”, corresponds with the age of the shroud determined by independent C14 tests. Add to that the fact that the linen used is not consistent with that used at the time and location of the crucifixion, that the image does not match up with how bodies were wrapped at the time and location of the crucifixion, and that a forensic examination of the blood pattern on the shroud concluded that it was most likely a fake, and you have sufficient evidence to convince any impartial jury. Far more evidence that you have for widespread coordinated election fraud in the recent election. “Selective hyperskepticism, is ever and irretrievably a fallacy. ” I agree. You would be well advised to correct your frequent use of it to make your arguments.Steve Alten2
January 30, 2021
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Interesting. I just saw JVL posts on the Loeb thread, saying what I just said here, but now I can post here but can't over there. Weird.Viola Lee
January 30, 2021
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Oh, gosh, now it seems I can reply to this thread. I shall do so in the future when I have something to say. In general I agree with Viola Lee in that: Godel's theorems apply to very narrowly defined axiomatic systems so unless you can put physics (or any other system) on that kind of footing then Godel's work does NOT apply. Sorry.JVL
January 30, 2021
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re 90, to Q: When I said, "There is nothing new in the video that we all haven’t scrolled by before.", you replied, "Apparently, you weren’t thinking of Gödel’s theorems, which as I said was quite surprising to me that they were actually being considered by a serious physicist in terms of the incompatibility of ETR and QM." I think BA has mentioned Godel many times, but maybe you hadn't seen previous statements of his. Then you say, "it’s not implausible that Gödel’s theorems could apply to to these as well as the mathematics underlying ETR. Of course, Gödel’s theorems apply to systems of counting numbers, but it’s not really a stretch to apply the same concepts to whole numbers and even rational numbers, perhaps followed by irrational, imaginary, and other types of numbers." I don't think lack of plausibility is in itself a very strong argument for anything. I'm not an expert at all on this topic, but from what I've read Godels' proofs apply to axiomatic mathematical systems, not real world mathematical descriptions. As KF points out, Godel's proofs are about the natural numbers, but it seems reasonable to assume that the undecidability features extends to other axiomatic extensions of the natural numbers. However, I don't know (and don't think I would know, as that is pretty esoteric) what mathematical work might have been done on broader extensions beyond the natural numbers. But I read the article tha BA quoted about spectral gaps. It seems to me that the quote he offers is an example of something I mentioned in 88: " people tend to apply Godel's ideas to things beyond the bounds of what they apply to." It is very speculative and offers no evidence that some argument similar to Godel's is actually related to the real-world problem they are studying. There are large differences between pure and applied mathematics: between pure axiomatic and logical systems vs. mathematical descriptions of the world that have, among other things, elements of probability and chaos theory which contribute to undecidability.Viola Lee
January 30, 2021
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Undecidability is a key word in the context of Godel.kairosfocus
January 30, 2021
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Since the conversation has turned to Godel, and since Godel's proof is a large part of my argument that there will never be a mathematical 'theory of everything' that bridges, i.e. 'renormalizes', the 'infinite infinities' that separate the macroscopic descriptions of general relativity from the microscopic descriptions of quantum mechanics, i.e. "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.,,,"
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 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/
Since Godel's proof is a large part of that, I will clip the Nature abstract from which the physorg article that I cited is based:
Undecidability of the spectral gap - Toby S. Cubitt, David Perez-Garcia & Michael M. Wolf - 09 December 2015 Abstract The spectral gap—the energy difference between the ground state and first excited state of a system—is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, the question of the existence of gapped topological spin liquid phases, and the Yang–Mills gap conjecture, concern spectral gaps. These and other problems are particular cases of the general spectral gap problem: given the Hamiltonian of a quantum many-body system, is it gapped or gapless? Here we prove that this is an undecidable problem. Specifically, we construct families of quantum spin systems on a two-dimensional lattice with translationally invariant, nearest-neighbour interactions, for which the spectral gap problem is undecidable. This result extends to undecidability of other low-energy properties, such as the existence of algebraically decaying ground-state correlations. The proof combines Hamiltonian complexity techniques with aperiodic tilings, to construct a Hamiltonian whose ground state encodes the evolution of a quantum phase-estimation algorithm followed by a universal Turing machine. The spectral gap depends on the outcome of the corresponding ‘halting problem’. Our result implies that there exists no algorithm to determine whether an arbitrary model is gapped or gapless, and that there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics. https://www.nature.com/articles/nature16059
Again, the implications of this proof are clearly laid out in the physorg article by Professor Michael Wolf. Specifically, “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.” https://phys.org/news/2015-12-quantum-physics-problem-unsolvable-godel.html
Again this finding is simply devastating to any mathematical theory, such as sting theory and/or M-theory, that hopes to bridge the 'infinite infinities' that separate the microscopic descriptions of quantum mechanics from the macroscopic descriptions of general relativity, to become the quote unquote final 'theory of everything'. Of related sidenote, It is interesting to note how this plays into the ancient dichotomy between forms, and/or essences, with 'sensible things' i.e. Sensible bodies are in constant flux and imperfect and hence, by Plato's reckoning, less real than the Forms which are eternal,
Essence Ontological status In his dialogues Plato suggests that concrete beings acquire their essence through their relations to "Forms"—abstract universals logically or ontologically separate from the objects of sense perception. These Forms are often put forth as the models or paradigms of which sensible things are "copies". When used in this sense, the word form is often capitalized.[6] Sensible bodies are in constant flux and imperfect and hence, by Plato's reckoning, less real than the Forms which are eternal,unchanging and complete. Typical examples of Forms given by Plato are largeness, smallness, equality, unity, goodness, beauty and justice. Aristotle moves the Forms of Plato to the nucleus of the individual thing, which is called ousia or substance. Essence is the ti of the thing, the to ti en einai. Essence corresponds to the ousia's definition; essence is a real and physical aspect of the ousia (Aristotle, Metaphysics, I).,,, https://en.wikipedia.org/wiki/Essence#Philosophy
Darwinists deny the reality of forms and or essences. As Egnor explains,
NOMINALISM: THE STUBBLE LEFT BY OCKHAM’S RAZOR Ockham was a methodological minimalist, not a philosophical minimalist MICHAEL EGNOR Excerpt: The opposite of nominalism is realism. The ancient Greek philosopher Plato (429?–347 B.C.E.) was the archetypal realist. Plato believed that abstract categories such as “mankind” are real. They really exist in the realm of Forms. In fact, Plato believed that the Forms were the ultimate reality, of which particulars merely participate in a shadowy way. One noteworthy kind of Platonic realism was that of Augustine (354-430 C.E., left), who proposed that Platonic Forms are Ideas in the mind of God. Aristotle (384-322 B.C.E.) held to another form of realism, called semi-realism; he held that universals are real but that they exist in nature and in things, not independently in a separate realm. Nominalists deny all of this. They propose that universals are mere categories created in the human mind, without any extra-mental reality of their own. “Mankind” is, in the nominalist view, just a way that we organize ideas in our minds. https://mindmatters.ai/2020/06/nominalism-the-stubble-left-by-ockhams-razor/
With their denial of true forms and/or essences, Darwinists lose the ability to even define what a species actually and truly is
Darwin, Design & Thomas Aquinas The Mythical Conflict Between Thomism & Intelligent Design by Logan Paul Gage Excerpt:,,, In Aristotelian and Thomistic thought, each particular organism belongs to a certain universal class of things. Each individual shares a particular nature—or essence—and acts according to its nature. Squirrels act squirrelly and cats catty. We know with certainty that a squirrel is a squirrel because a crucial feature of human reason is its ability to abstract the universal nature from our sense experience of particular organisms. Denial of True Species Enter Darwinism. Recall that Darwin sought to explain the origin of “species.” Yet as he pondered his theory, he realized that it destroyed species as a reality altogether. For Darwinism suggests that any matter can potentially morph into any other arrangement of matter without the aid of an organizing principle. He thought cells were like simple blobs of Jell-O, easily re-arrangeable. For Darwin, there is no immaterial, immutable form. In The Origin of Species he writes: “I look at the term species as one arbitrarily given, for the sake of convenience, to a set of individuals closely resembling each other, and that it does not essentially differ from the term variety, which is given to less distinct and more fluctuating forms. The term variety, again, in comparison with mere individual differences, is also applied arbitrarily, for convenience’s sake.” Statements like this should make card-carrying Thomists shudder.,,, The first conflict between Darwinism and Thomism, then, is the denial of true species or essences. For the Thomist, this denial is a grave error, because the essence of the individual (the species in the Aristotelian sense) is the true object of our knowledge. As philosopher Benjamin Wiker observes in Moral Darwinism, Darwin reduced species to “mere epiphenomena of matter in motion.” What we call a “dog,” in other words, is really just an arbitrary snapshot of the way things look at present. If we take the Darwinian view, Wiker suggests, there is no species “dog” but only a collection of individuals, connected in a long chain of changing shapes, which happen to resemble each other today but will not tomorrow. What About Man? Now we see Chesterton’s point. Man, the universal, does not really exist. According to the late Stanley Jaki, Chesterton detested Darwinism because “it abolishes forms and all that goes with them, including that deepest kind of ontological form which is the immortal human soul.” And if one does not believe in universals, there can be, by extension, no human nature—only a collection of somewhat similar individuals.,,, https://www.touchstonemag.com/archives/article.php?id=23-06-037-f
I point all this out since it has been known since ancient times that the 'sensible bodies' which are in 'constant flux' can never give rise to the forms and/or essences which are the true objects of our knowledge. Likewise, I hold that it is also obvious that the microscopic descriptions of quantum mechanics, which describe the 'constant flux' of elementary particles, can never give rise to the macrscopic 'form' of General relativity. In short, the impossibility of 'bottom-up explanations for 'form' has been known about since ancient times. Hence, God, and only God, "was free to create this particular form of world among an infinity of other possibilities."
The War against the War Between Science and Faith Revisited - July 2010 Excerpt: If science suffered only stillbirths in ancient cultures, how did it come to its unique viable birth? The beginning of science as a fully fledged enterprise took place in relation to two important definitions of the Magisterium of the Church. The first was the definition at the Fourth Lateran Council in the year 1215, that the universe was created out of nothing at the beginning of time. The second magisterial statement was at the local level, enunciated by Bishop Stephen Tempier of Paris who, on March 7, 1277, condemned 219 Aristotelian propositions, so outlawing the deterministic and necessitarian views of creation. These statements of the teaching authority of the Church expressed an atmosphere in which faith in God had penetrated the medieval culture and given rise to philosophical consequences. The cosmos was seen as contingent in its existence and thus dependent on a divine choice which called it into being; the universe is also contingent in its nature and so God was free to create this particular form of world among an infinity of other possibilities. Thus the cosmos cannot be a necessary form of existence; and so it has to be approached by a posteriori investigation. The universe is also rational and so a coherent discourse can be made about it. Indeed the contingency and rationality of the cosmos are like two pillars supporting the Christian vision of the cosmos.?http://www.scifiwright.com/2010/08/the-war-against-the-war-between-science-and-faith-revisited/
bornagain77
January 30, 2021
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F/N, trivially, principle of explosion applies, where [A AND ~A] => any claim, C. From falsity or incoherence, anything. The implication is, axiomatisations that capture all true claims do so by this means, incoherence. KFkairosfocus
January 30, 2021
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F/N: SEP, on Godel: https://plato.stanford.edu/entries/goedel-incompleteness/ >>Gödel’s Incompleteness Theorems First published Mon Nov 11, 2013; substantive revision Thu Apr 2, 2020 Gödel’s two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues. They concern the limits of provability in formal axiomatic theories. The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F. According to the second incompleteness theorem, such a formal system cannot prove that the system itself is consistent (assuming it is indeed consistent). These results have had a great impact on the philosophy of mathematics and logic. There have been attempts to apply the results also in other areas of philosophy such as the philosophy of mind, but these attempted applications are more controversial . . . . In order to understand Gödel’s theorems, one must first explain the key concepts essential to it, such as “formal system”, “consistency”, and “completeness”. Roughly, a formal system is a system of axioms equipped with rules of inference, which allow one to generate new theorems. The set of axioms is required to be finite or at least decidable, i.e., there must be an algorithm (an effective method) which enables one to mechanically decide whether a given statement is an axiom or not. If this condition is satisfied, the theory is called “recursively axiomatizable”, or, simply, “axiomatizable”. The rules of inference (of a formal system) are also effective operations, such that it can always be mechanically decided whether one has a legitimate application of a rule of inference at hand. Consequently, it is also possible to decide for any given finite sequence of formulas, whether it constitutes a genuine derivation, or a proof, in the system—given the axioms and the rules of inference of the system. A formal system is complete if for every statement of the language of the system, either the statement or its negation can be derived (i.e., proved) in the system. A formal system is consistent if there is no statement such that the statement itself and its negation are both derivable in the system. Only consistent systems are of any interest in this context, for it is an elementary fact of logic that in an inconsistent formal system every statement is derivable, and consequently, such a system is trivially complete. Gödel established two different though related incompleteness theorems, usually called the first incompleteness theorem and the second incompleteness theorem. “Gödel’s theorem” is sometimes used to refer to the conjunction of these two, but may refer to either—usually the first—separately. Accommodating an improvement due to J. Barkley Rosser in 1936, the first theorem can be stated, roughly, as follows: First incompleteness theorem Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F . Gödel’s theorem does not merely claim that such statements exist: the method of Gödel’s proof explicitly produces a particular sentence that is neither provable nor refutable in F ; the “undecidable” statement can be found mechanically from a specification of F . The sentence in question is a relatively simple statement of number theory, a purely universal arithmetical sentence. A common misunderstanding is to interpret Gödel’s first theorem as showing that there are truths that cannot be proved. This is, however, incorrect, for the incompleteness theorem does not deal with provability in any absolute sense, but only concerns derivability in some particular formal system or another. For any statement A unprovable in a particular formal system F, there are, trivially, other formal systems in which A is provable (take A as an axiom). On the other hand, there is the extremely powerful standard axiom system of Zermelo-Fraenkel set theory (denoted as ZF, or, with the axiom of choice, ZFC; see the section on the axioms of ZFC in the entry on set theory), which is more than sufficient for the derivation of all ordinary mathematics. Now there are, by Gödel’s first theorem, arithmetical truths that are not provable even in ZFC. Proving them would thus require a formal system that incorporates methods going beyond ZFC. There is thus a sense in which such truths are not provable using today’s “ordinary” mathematical methods and axioms, nor can they be proved in a way that mathematicians would today regard as unproblematic and conclusive. Gödel’s second incompleteness theorem concerns the limits of consistency proofs. A rough statement is: Second incompleteness theorem For any consistent system F within which a certain amount of elementary arithmetic can be carried out, the consistency of F cannot be proved in F itself. In the case of the second theorem, F must contain a little bit more arithmetic than in the case of the first theorem, which holds under very weak conditions. It is important to note that this result, like the first incompleteness theorem, is a theorem about formal provability, or derivability (which is always relative to some formal system; in this case, to F itself). It does not say anything about whether, for a particular theory T satisfying the conditions of the theorem, the statement “T is consistent” can be proved in the sense of being shown to be true by a conclusive argument, or by a proof generally acceptable for mathematicians. For many theories, this is perfectly possible. >> KFkairosfocus
January 30, 2021
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SA2, your suggestion of fraud fails, by way of undesigned coincidence of artifacts with geographically and administratively separate histories. Start with, how did these two entities happen to have the same unusual blood type [and matching patterns], centuries before such was known? The Shroud is not a main offer of proof of the Christian faith, but it deserves a more responsible discussion than we too often see. Selective hyperskepticism, is ever and irretrievably a fallacy. KFkairosfocus
January 30, 2021
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Q (attn VL), Godel is about irreducible complexity of axiomatisations of mathematical systems, using counting numbers and arithmetic as yardstick. As the chain of sets N,Z,Q,R,C,R* etc is constructable from N, which in turn builds up from {} --> 0 via von Neumann succession of sets, thee result on N logically pervades Mathematics and its extensions. We should note that most mathematical operations are extended from those of arithmetic, perhaps with an injection of structures [e.g. matrices etc], limits involving series and sequences of partial sums etc. Meanwhile, distinct identity and its provision of 0,1,2 in any possible world brings the chain in in any reasonable logic model world, including those intended to provide physical models of our world (and the many forks on many worlds interpretations.) The key point is, we have good reason to accept and acknowledge that
[a] once a mathematical or computational system is tolerably complex beyond demonstration of coherence by direct inspection, [b] we have reason to expect that axiomatisations that entail all true results will be incoherent, likewise, [c] that true results are likely to be beyond reach of our axiomatisations (undecidable), and [d] that there will be no constructive procedure to generate known coherent axiomatisations.
The grand result is that faith as responsible confidence in the face of irreducible Johnson uncertainty is embedded in all significant mathematics and logic pervaded disciplines. In Rumsfeld's terms, we have a known known that there will be known unknowns and likely unknown unknowns. This is a context in which I take significant cognisance of the Euler identity, stated in the full traditional form that explicitly joins together the five key numbers in our systems of Mathematics, to known infinitely fine precision: 0 = 1 + e^(i*pi) The four number form is often presented as just the same, to trivialise; certainly, that has been seen here at UD. That simply reflects failure to distinguish an algebraic transformation from the epistemic significance of a key result. Here, that five key numbers reflecting entire domains of mathematics with extensions to vast provinces of sci-tech, are locked together coherently to infinitely precise convergence. That lends confidence to working in practical mathematics, that we have no material reason to dismiss coherence, regardless of abstract possibilities. KFkairosfocus
January 30, 2021
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ET, by their projections (and cognitive dissonance) shall ye know them. KFkairosfocus
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