Eugene Wigner’s treasonous claim: God and mathematics are related

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January 20, 2019

Intelligent Design, Mathematics, Naturalism, Religion

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A photograph of the Greek letter pi, created as a large stone mosaic embedded in the ground. — pi in mosaic, Berlin/Holger Motzkau

Eugene Wigner (1902–1995) won the Nobel Prize in physics in 1963 but he was more famous for something else, an essay published in 1960 called The Unreasonable Effectiveness of Mathematics in the Natural Sciences where he said things like:

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…
“The miracle of the appropriateness of the language of mathematics to the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

Whoa! What happened to the pre-human of evolutionary psychology, who spread his selfish genes by knowing arithmetic the way a hog knows truffles?

Wigner’s essay was viewed as a sort of “treason” against science, meaning that his thinking did not lead in a naturalist (nature is all there is) direction. Naturalism is often called “materialism.”

We are reminded of the story in a review of astrophysicist Mario Livio’s 2009 book, Is God a Mathematician?, which attempted to counter Eugene Wigner’s insight:

In his 1960 article, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” Wigner stated the truth which every atheist scientist and philosopher knew and was afraid to tackle: Mathematics and physics, originating from two completely different quarters, the former from the pure speculations of the mind, the latter from the empirical data the physical reality feeds our experience with, have no reason to be connected in any comprehensible or predictable way. And yet, mathematics has been wonderfully effective in describing physical laws and predicting outcomes of experiments in the real world. Why, asked Wigner, and couldn’t find an answer. No one can. Scientists keep using math and relying on math, as if they know for sure that math must be relevant to our physical experience. But they can’t explain why. The arrogant claim that science will explain the world more and more came to an end; science can’t even explain itself anymore.

Wigner added insult to injury when he ended his article using almost religious language of humbleness, gratitude and faith …

In short, Wigner committed a treason against science. He didn’t, in an Einsteinian fashion, just declare a personal faith in a God that had only marginal relevance to his scientific studies. He went farther than that: he implied that science was impossible and inexplicable without accepting a higher reality, transcending the mind of man and its capabilities for reasoning and experimentation. The short and ostensibly innocent article faced some really violent reactions; some objected to the conclusions in it, others to the premises, and still others refused to even deal with it, pretending it had never been written. But Wigner remained right about one thing: Despite the many attempts, no one could give a rational explanation for what Wigner described as the “uncanny ability of mathematics to describe and predict accurately the physical world.” Bojidar Marinov, “Mario Livio, or the Poverty of Atheist Philosophy: A Review of “Is God a Mathematician?”” at American Vision
(2011)

Of course, people who know that there is no such thing as truth in our multiverse are somehow wiser now than Wigner…

See also: Neil deGrasse Tyson’s Cosmos and “the artistic license to lie” One thing readers may not know is that, in a series that leaned heavily on the supposed conflict between religion and science, obvious and widely noted misrepresentations were excused in the service of a “greater truth”

Hat tip: Philip Cunningham

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Comments

@News, another scholar that made the same discovery is Soviet mathematician Leonid Levin. He was unable to publish his findings while in the USSR, but was able to make his proofs known once here in the USA. His work anticipates much of what Dembski published in information theory, such as complex specified information and the conservation of information. Levin is a foundational figure in computer science. He is famous for being a co-discoverer of the NP-Complete complexity class, which is a class of problems for which we have no known fast algorithm to solve. Incidentally, many of our everyday tasks that we'd like to have computers do for us unfortunately fall into this problem class, which is why AI has so much trouble scaling to work on anything other than toy problems.EricMH_{January 22, 2019
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I have some more thoughts about the essay, and especially the part I quoted in 4 above, but they really belong on the Logic and First Principles 7 thread.hazel_{January 21, 2019
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Bornagain77 @13: Plainly mathematics is, like consciousness, an illusion. Nothing to see here: move along now, citizen.ScuzzaMan_{January 21, 2019
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Thanks, Hazel.EugeneS_{January 21, 2019
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Thanks, EugeneS. As I said at 6, I think the headline is misleading, and I'm not sure seeing it as a "treason" against science was the general reaction. If you are interested, I encourage you to read the whole article, as I don't see it as being against science. Also, the Wikipedia article on the essay is interesting. The essay has been a popular stimulant for discussion since it was published.hazel_{January 21, 2019
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Hazel No, I did not mean Wigner. I rather meant some commenters who suggested that he, as it were, betrayed science by making the known statements about mathematics. That was actually the main point of this OP.EugeneS_{January 21, 2019
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No, it is whining. Pure and simple.ET_{January 21, 2019
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Wasn't a whine, ET. It was, dare I say, a chuckle. :-)hazel_{January 21, 2019
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hazel needs some cheese to go with that whine...ET_{January 21, 2019
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"A few notes on Eugene Wigner...", followed by three posts and 4000 words. :-)hazel_{January 21, 2019
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As well it is just plain bizarre to me that anyone could possibly imagine that their own mind, all by its lonesome, has the causal sufficiency within itself to collapse the wave function. (Which would be required if solipsism were actually true). The quantum wave, prior to measure, is mathematically defined as being in a 'infinite dimensional-infinite information' state,
The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner – 1960 Excerpt: We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity.,,, The two theories operate with different mathematical concepts: the four dimensional Riemann space and the infinite dimensional Hilbert space, http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html Wave function Excerpt "wave functions form an abstract vector space",,, This vector space is infinite-dimensional, because there is no finite set of functions which can be added together in various combinations to create every possible function. http://en.wikipedia.org/wiki/Wave_function#Wave_functions_as_an_abstract_vector_space Explaining Information Transfer in Quantum Teleportation: Armond Duwell †‡ University of Pittsburgh Excerpt: In contrast to a classical bit, the description of a (quantum) qubit requires an infinite amount of information. The amount of information is infinite because two real numbers are required in the expansion of the state vector of a two state quantum system (Jozsa 1997, 1) http://www.cas.umt.edu/phil/faculty/duwell/DuwellPSA2K.pdf Quantum Computing – Stanford Encyclopedia Excerpt: Theoretically, a single qubit can store an infinite amount of information, yet when measured (and thus collapsing the superposition of the Quantum Wave state) it yields only the classical result (0 or 1),,, http://plato.stanford.edu/entries/qt-quantcomp/#2.1 WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT? Infinity – Max Tegmark Excerpt: real numbers with their infinitely many decimals have infested almost every nook and cranny of physics, from the strengths of electromagnetic fields to the wave functions of quantum mechanics: we describe even a single bit of quantum information (a qubit) using two real numbers involving infinitely many decimals. https://www.edge.org/response-detail/25344
Simply put, in order to adequately explain quantum wave collapse we must postulate something with the causal sufficiency within itself in order to explain the 'effect' of the 'infinite dimensional-infinite information' quantum wave state collapsing to a single bit of information. In other words, we must postulate the omnipresent and omniscient Mind of God in order to explain why the 'infinite dimensional-infinite information' quantum wave state collapses to a single bit of information. Thus in conclusion, the three reasons that Wigner gave for giving up his own 'consciousness causes collapse' interpretation of quantum mechanics, (i.e. solipsism, quantum mechanics only applies to the microscopic scale, and his 'suggested amendment' to the Schrödinger equation), are all found to be wanting and/or overturned. Thus, much to the consternation of Atheistic Materialists, multiple lines of evidence from quantum mechanics have provided a constant and unceasing barrage that has blown their materialistic view of reality completely to smithereens, as well as having continually supported the Christian's contention that the infinite Mind of God must precede all of physical reality:
Albert Einstein vs. Quantum Mechanics and His Own Mind – video https://www.youtube.com/watch?v=vxFFtZ301j4 Should Quantum Anomalies Make Us Rethink Reality? Inexplicable lab results may be telling us we’re on the cusp of a new scientific paradigm By Bernardo Kastrup on April 19, 2018 Excerpt: ,, according to the current paradigm, the properties of an object should exist and have definite values even when the object is not being observed: the moon should exist and have whatever weight, shape, size and color it has even when nobody is looking at it. Moreover, a mere act of observation should not change the values of these properties. Operationally, all this is captured in the notion of “non-contextuality”: ,,, since Alain Aspect’s seminal experiments in 1981–82, these predictions (of Quantum Mechanics) have been repeatedly confirmed, with potential experimental loopholes closed one by one. 1998 was a particularly fruitful year, with two remarkable experiments performed in Switzerland and Austria. In 2011 and 2015, new experiments again challenged non-contextuality. Commenting on this, physicist Anton Zeilinger has been quoted as saying that “there is no sense in assuming that what we do not measure [that is, observe] about a system has [an independent] reality.” Finally, Dutch researchers successfully performed a test closing all remaining potential loopholes, which was considered by Nature the “toughest test yet.”,,, It turns out, however, that some predictions of QM are incompatible with non-contextuality even for a large and important class of non-local theories. Experimental results reported in 2007 and 2010 have confirmed these predictions. To reconcile these results with the current paradigm would require a profoundly counterintuitive redefinition of what we call “objectivity.” And since contemporary culture has come to associate objectivity with reality itself, the science press felt compelled to report on this by pronouncing, “Quantum physics says goodbye to reality.” The tension between the anomalies and the current paradigm can only be tolerated by ignoring the anomalies. This has been possible so far because the anomalies are only observed in laboratories. Yet we know that they are there, for their existence has been confirmed beyond reasonable doubt. Therefore, when we believe that we see objects and events outside and independent of mind, we are wrong in at least some essential sense. A new paradigm is needed to accommodate and make sense of the anomalies; one wherein mind itself is understood to be the essence—cognitively but also physically—of what we perceive when we look at the world around ourselves. https://blogs.scientificamerican.com/observations/should-quantum-anomalies-make-us-rethink-reality/
Quotes and Verses:
Why the Quantum? It from Bit? A Participatory Universe? Excerpt: “In conclusion, it may very well be said that information is the irreducible kernel from which everything else flows. Thence the question why nature appears quantized is simply a consequence of the fact that information itself is quantized by necessity. It might even be fair to observe that the concept that information is fundamental is very old knowledge of humanity, witness for example the beginning of gospel according to John: "In the beginning was the Word." Anton Zeilinger - a leading expert in quantum mechanics http://www.metanexus.net/archive/ultimate_reality/zeilinger.pdf 48:24 mark: “It is operationally impossible to separate Reality and Information” 49:45 mark: “In the Beginning was the Word” John 1:1 Prof Anton Zeilinger speaks on quantum physics. at UCT - video http://www.youtube.com/watch?v=s3ZPWW5NOrw Colossians 1:17 He is before all things, and in him all things hold together. John 1:1-4 In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. In him was life, and that life was the light of all mankind.
bornagain77_{January 21, 2019
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In regards to Wigner's suggestion for an amendment. I know of no ‘amendment' that has ever been adopted since Wigner suggested "an amendment of the Schrödinger equation" that has ever solved the measurement problem in quantum mechanics. Perhaps it was tried and rejected since it did not work. I have no idea why the ‘amendment’ suggested by Wigner is never discussed in the literature since the measurement problem is still very much alive and well and shows no signs of ever 'going quietly away into the good night' for materialists.:
The Measurement Problem in quantum mechanics – (Inspiring Philosophy) – 2014 video https://www.youtube.com/watch?v=qB7d5V71vUE
As Weinberg himself, an atheist, stated in 2017 "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,"
The Trouble with Quantum Mechanics - Steven Weinberg - January 19, 2017 Excerpt: The instrumentalist approach,, (the) wave function,, is merely an instrument that provides predictions of the probabilities of various outcomes when measurements are made.,, In the instrumentalist approach,,, humans are brought into the laws of nature at the most fundamental level. According to Eugene Wigner, a pioneer of quantum mechanics, “it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness.”11 Thus the instrumentalist approach turns its back on a vision that became possible after Darwin, of a world governed by impersonal physical laws that control human behavior along with everything else. It is not that we object to thinking about humans. Rather, we want to understand the relation of humans to nature, not just assuming the character of this relation by incorporating it in what we suppose are nature’s fundamental laws, but rather by deduction from laws that make no explicit reference to humans. We may in the end have to give up this goal,,, Some physicists who adopt an instrumentalist approach argue that the probabilities we infer from the wave function are objective probabilities, independent of whether humans are making a measurement. I don’t find this tenable. In quantum mechanics these probabilities do not exist until people choose what to measure, such as the spin in one or another direction. Unlike the case of classical physics, a choice must be made,,, http://www.nybooks.com/articles/2017/01/19/trouble-with-quantum-mechanics/
Thus the 'measurement problem' is certainly still very much alive and well as has certainly not been solved by any 'suggested amendment' by Wigner to the Schrödinger equation. Moreover, the claim from Wigner, in his rejection of his own 'consciousness causes collapse' interpretation of quantum mechanics, that "quantum mechanics is not valid for macroscopic systems" is now known to be just plain wrong. Quantum Entanglement has now been demonstrated for hundreds of miles.
Physicists Just Smashed a Record to Achieve Quantum Entanglement in Space - June 2017 Excerpt: In a new study, scientists have successfully transmitted entangled photons between a satellite and Earth at a distance of over 1,200 kilometres (750 miles). This smashes the previous record for entanglement distribution, which only reached up to 100 kilometres. https://www.sciencealert.com/physicists-just-quantum-entangled-photons-between-earth-and-space
As Vlatko Vedral states, "the fact that quantum mechanics applies on all scales forces us to confront the theory’s deepest mysteries. We cannot simply write them off as mere details that matter only on the very smallest scales."
LIVING IN A QUANTUM WORLD - Vlatko Vedral - 2011 Excerpt: Thus, the fact that quantum mechanics applies on all scales forces us to confront the theory’s deepest mysteries. We cannot simply write them off as mere details that matter only on the very smallest scales. For instance, space and time are two of the most fundamental classical concepts, but according to quantum mechanics they are secondary. The entanglements are primary. They interconnect quantum systems without reference to space and time. If there were a dividing line between the quantum and the classical worlds, we could use the space and time of the classical world to provide a framework for describing quantum processes. But without such a dividing line—and, indeed, without a truly classical world—we lose this framework. We must explain space and time (4D space-time) as somehow emerging from fundamentally spaceless and timeless physics. http://phy.ntnu.edu.tw/~chchang/Notes10b/0611038.pdf
Thus Wigner's belief that quantum mechanics only applies at the microscopic scale, which he cited as one of the primary reasons for him rejecting his own 'consciousness causes collapse' interpretation, is now shown to be just plain wrong. As to Wigner's rejection of his own interpretation because of "solipsism", it is bizarre that Wigner would reject his own interpretation of quantum mechanics because he was 'embarrassed' by solipsism, (i.e. the view or theory that the self is all that can be known to exist), since Wigner was the one who came up with the ‘Wigner’s Friend ‘ thought experiment in the first place. At the 8:30 minute mark of the following video, Schrodinger’s cat and Wigner’s Friend are highlighted:
Divinely Planted Quantum States – video https://youtu.be/qCTBygadaM4?t=512
In fact, the Wigner’s friend thought experiment made its first appearance in 1961 in the very paper in which Wigner stated that, “It will remain remarkable, in whatever way our future concepts may develop, that the very study of the external world led to the scientific conclusion that the content of the consciousness is the ultimate universal reality”
Remarks on the mind-body question – E.P. Wigner (1961), Excerpt: “It will remain remarkable, in whatever way our future concepts may develop, that the very study of the external world led to the scientific conclusion that the content of the consciousness is the ultimate universal reality” – http://www.projects.science.uu.nl/igg/jos/foundQM/wigner.pdf
As well, Wigner’s solipsism objection was touched upon by Richard Conn Henry when the 2007 Leggett’s results came out when Henry stated "a theistic view of our existence becomes the only rational alternative to solipsism",,,
Alain Aspect and Anton Zeilinger by Richard Conn Henry – Physics Professor – John Hopkins University Excerpt: Why do people cling with such ferocity to belief in a mind-independent reality? It is surely because if there is no such reality, then ultimately (as far as we can know) mind alone exists. And if mind is not a product of real matter, but rather is the creator of the “illusion” of material reality (which has, in fact, despite the materialists, been known to be the case, since the discovery of quantum mechanics in 1925), then a theistic view of our existence becomes the only rational alternative to solipsism (solipsism is the philosophical idea that only one’s own mind is sure to exist). (Dr. Henry’s referenced experiment and paper – “An experimental test of non-local realism” by S. Gröblacher et. al., Nature 446, 871, April 2007 – “To be or not to be local” by Alain Aspect, Nature 446, 866, April 2007 (Leggett’s Inequality: Violated, as of 2011, to 120 standard deviations) http://henry.pha.jhu.edu/aspect.html
bornagain77_{January 21, 2019
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A few notes on Eugene Wigner. As Hazel noted Wigner won a Nobel prize. In 1963, the Nobel prize was awarded to Wigner for his work laying the foundation for "Quantum Symmetries".
Symmetry in quantum mechanics Excerpt: Symmetries in quantum mechanics describe features of spacetime and particles which are unchanged under some transformation, in the context of quantum mechanics, relativistic quantum mechanics and quantum field theory, https://en.wikipedia.org/wiki/Symmetry_in_quantum_mechanics
Here is a short video of Wigner receiving his Nobel prize in 1963 for his work laying the foundation for "Quantum Symmetries".
Eugene Wigner receives his Nobel Prize for Quantum Symmetries - video 1963 http://www.nobelprize.org/mediaplayer/index.php?id=1111
Wigner's Quantum Symmetries is one line of empirical evidence, out of five converging lines of empirical evidence, that I have used to provide empirical proof for the "Argument for God from Consciousness." ,,, To summarize, putting all the lines of evidence together from the Double Slit experiment, Wigner’s Quantum Symmetries, Wheeler’s Delayed Choice, Leggett’s Inequalities, and the Quantum Zeno effect, the argument for God from consciousness can now be formulated like this:
1. Consciousness either preceded all of material reality or is a ‘epi-phenomena’ of material reality. 2. If consciousness is a ‘epi-phenomena’ of material reality then consciousness will be found to have no special position within material reality. Whereas conversely, if consciousness precedes material reality then consciousness will be found to have a special position within material reality. 3. Consciousness is found to have a special, even a central position within material reality. 4. Therefore, consciousness is found to precede material reality. - Quantum Mechanics and Consciousness: 5 Experiments – video https://www.youtube.com/watch?v=t5qphmi8gYE
And here is Wigner commenting on the key experiment that led Wigner to his Nobel Prize winning work on quantum symmetries,,,
Eugene Wigner - Excerpt: This, (1925-26), is when Wigner's interest started in symmetry. Let us listen to his recollection: -- When I returned to Berlin, the excellent crystallographer Weissenberg asked me to study: why is it that in a crystal the atoms like to sit in a symmetry plane or symmetry axis. After a short time of thinking I understood: being on the symmetry axis ensures that the derivatives of the potential energy vanish in two directions perpendicular to the symmetry axis. (In case of a symmetry plane the derivative of the potential energy vanishes in one direction.) This is how I became interested in the role of symmetries in quantum mechanics. I spent the holidays -- Christmastime and summertime -- in Hungary, in Budapest and in Alsógöd, on the shore of the Danube. There I wrote the book on "Group Theory and its Application to the Quantum Mechanics of Atomic Spectra." [To the author 1983.] -- The intrusion of group theory into quantum mechanics was not received with applause. Wolfgang Pauli called the idea Gruppenpest. Albert Einstein and Erwin Schrödinger also expressed their uneasiness. Max Born and Max von Laue were more encouraging. John von Neumann and Leo Szilard enthusiastically encouraged Wigner's efforts. It was worth to do so: these efforts later resulted in a Nobel Prize. If an experiment is repeated elsewhere in another laboratory under similar conditions, it will give identical result. The experiment today yields the very same result as it yielded yesterday. If we turn the whole equipment by 300, it will not influence the result. The outcome depends neither on the location and timing of the experiment, nor on the spacial orientation of the equipment. Even speed (e.g. that of the Earth) does not influence the way the laws of Nature work. To express this basic experience in a more direct way: the world does not have a privileged center, there is no absolute rest, preferred direction, unique origin of calendar time, even left and right seem to be rather symmetric. The interference of electrons, photons, neutrons has indicated that the state of a particle can be described by a vector. possessing a certain number of components. As the observer is replaced by another observer (working elsewhere, looking at a different direction, using an other clock, perhaps being lefthanded), the state of the very same particle is described by another vector, obtained from the previous vector by multiplying it with a matrix. This matrix transfers from one observer to another.,,, In 1930 Wigner showed the utmost power of these experienced symmetry properties of space and time in quantum mechanics. His book has become one of the most important classics of the new science, having been published in German, English, Japanese, and Hungarian. The author is convinced that the long-lasting essence of quantum mechanics has been understood by Eugene Wigner: the basic experiences of superposition and symmetry will serve as a lasting foundation; it will influence how this intellectual achievement of the 20th century with utmost importance will be taught in the schools of the 21st century. (When this was told to Wigner, he sharply disagreed. According to him only one person understood quantum mechanics: John von Neumann. ) Wigner received the Nobel Prize in 1963 for his contribution to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles. http://oldweb.reak.bme.hu/Wigner_Course/WignerBio/wb1.htm
And indeed, according to leading experimentalist Anton Zeilinger, Wigner's work in Quantum Symmetries is indeed fostering a 'second quantum revolution' in the 21st century,,
Eugene Wigner – A Gedanken Pioneer of the Second Quantum Revolution - Anton Zeilinger - Sept. 2014 Conclusion It would be fascinating to know Eugene Wigner’s reaction to the fact that the gedanken experiments he discussed (in 1963 and 1970) have not only become reality, but building on his gedanken experiments, new ideas have developed which on the one hand probe the foundations of quantum mechanics even deeper, and which on the other hand also provide the foundations to the new field of quantum information technology. All these experiments pay homage to the great insight Wigner expressed in developing these gedanken experiments and in his analyses of the foundations of quantum mechanics, http://epjwoc.epj.org/articles/epjconf/pdf/2014/15/epjconf_wigner2014_01010.pdf
In regards to his work in Quantum Symmetries, Wigner stated this in 1961
"It will remain remarkable, in whatever way our future concepts may develop, that the very study of the external world led to the scientific conclusion that the content of the consciousness is the ultimate universal reality" - Eugene Wigner - (Remarks on the Mind-Body Question, Eugene Wigner, in Wheeler and Zurek, p.169; 1961)
And again in 1970 Wigner further stated that,,
"It was not possible to formulate the laws (of quantum theory) in a fully consistent way without reference to consciousness." Eugene Wigner (1902 -1995) from his collection of essays "Symmetries and Reflections – Scientific Essays" - 1970;
There is even an "consciousness causes collapse [of the wave function]" interpretation in Quantum Mechanics that is named after Eugene Wigner (and John Von Neumann)
Von Neumann–Wigner - interpretation Excerpt: The von Neumann–Wigner interpretation, also described as "consciousness causes collapse [of the wave function]", is an interpretation of quantum mechanics in which consciousness is postulated to be necessary for the completion of the process of quantum measurement. http://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Wigner_interpretation#The_interpretation
John von Neumann stated this in regards to the 'measurement problem' within quantum mechanics,,,
"We wish to measure a temperature.,,, But in any case, no matter how far we calculate -- to the mercury vessel, to the scale of the thermometer, to the retina, or into the brain, at some time we must say: and this is perceived by the observer. That is, we must always divide the world into two parts, the one being the observed system, the other the observer.” John von Neumann - 1903-1957 - The Mathematical Foundations of Quantum Mechanics, pp.418-21 - 1955
Stephen Barr elaborates a little more fully here:
Does Quantum Physics Make it Easier to Believe in God? Stephen M. Barr - July 10, 2012 Excerpt: Couldn’t an inanimate physical device (say, a Geiger counter) carry out a “measurement” (minus the 'observer' in quantum mechanics)? That would run into the very problem pointed out by von Neumann: If the “observer” were just a purely physical entity, such as a Geiger counter, one could in principle write down a bigger wavefunction that described not only the thing being measured but also the observer. And, when calculated with the Schrödinger equation, that bigger wave function would not jump! Again: as long as only purely physical entities are involved, they are governed by an equation that says that the probabilities don’t jump. That’s why, when Peierls was asked whether a machine could be an “observer,” he said no, explaining that “the quantum mechanical description is in terms of knowledge, and knowledge requires somebody who knows.” Not a purely physical thing, but a mind. https://www.bigquestionsonline.com/content/does-quantum-physics-make-it-easier-believe-god
Later in his life in 1982 Wigner backed off of his "consciousness causes collapse [of the wave function]" interpretation in Quantum Mechanics,,,
"In a lecture of 1982, he then regards the issue of solipsism as a sufficient reason to repudiate his earlier views on measurement in quantum mechanics (pp. 73–74, and also p. 230). In order to avoid solipsism, Wigner considers it to be necessary to admit state reductions independently of an observer’s consciousness. And his conclusion, based on Zeh’s argument, that quantum mechanics is not valid for macroscopic systems opens up the way for him to conceive state reductions when it comes to macroscopic systems. Changing his mind, Wigner makes a concrete suggestion for an amendment of the Schrödinger equation which is intended to describe a physical process of state reduction (pp. 75–77, 242–243) " http://www.unil.ch/files/live//sites/philo/files/shared/DocsPerso/EsfeldMichael/1999/SHPMP99.pdf Von Neumann–Wigner interpretation Wigner actually shifted to those interpretations (and away from "consciousness causes collapse") in his later years. This was partly because he was embarrassed that "consciousness causes collapse" can lead to a kind of solipsism, but also because he decided that he had been wrong to try to apply quantum physics at the scale of everyday life ,,, https://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Wigner_interpretation#Objections_to_the_interpretation
bornagain77_{January 21, 2019
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Hi EugeneS. You may have just been making a general remark, but I don't think it is accurate to say that Wigner is "advocating there is no God". I think he is saying that even though he rejected Christianity as a youth, and doesn't believe one can prove God's existence, he recognizes that there is some kind of miracle in both the existence of our world and our ability to understand it, but that understanding why that is is a mystery beyond our grasp. Wigner was not a materialist, and was in fact one of the main proponents of the idea that consciousness is a necessary component of the collapse of a waveform in quantum mechanics.hazel_{January 21, 2019
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It seems a bit inconsistent that people who are advocating for "there is no God" are bothered about truth at all. BTW, IMHO there is a genuine conflict between science -- as it is understood today -- and theism in that science only deals with natural causes. Consequently, in questions concerning the beginning of nature, which necessarily could not have been natural, science is simply wrong. Of couse, this conflict can easily be removed if science is kept in its proper quarters and is not arm-twisted to provide natural 'explanations' of everything.EugeneS_{January 21, 2019
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Wigner was a famous physicist and won a Nobel prize - did work in quantum physics. I've read about him in some books on particle and quantum physics, and I though the article on the unreasonable effectiveness of math was interesting. And, my unasked-for advice is to just oil up your scroll wheel and zip past long posts that you don't want to even look at. Obviously, they're all done making enhancements to the site.hazel_{January 20, 2019
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I am ashamed to say that I have never heard of Wigner. He sounds like an interesting guy. It sounds like I have some reading ahead of me.Ed George_{January 20, 2019
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I assume that it is too late to ask for a “read more” button.Ed George_{January 20, 2019
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Nor, if platonic perfection were not present for the flatness of the universe would we have eventually been able to deduce the ‘platonic perfection’ that is revealed in the ‘higher dimensional’ mathematics that lay behind Relativity and Quantum Mechanics.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner – 1960 Excerpt: We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity.,,, The two theories operate with different mathematical concepts: the four dimensional Riemann space and the infinite dimensional Hilbert space, http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
Simply put, no experimental test to date has ever been able to detect any ‘imperfection’ for what the "platonically perfect' theories of Special relativity, General relativity, and Quantum Mechanics predict. As Berlinski noted,
“On the other hand, I disagree that Darwin’s theory is as `solid as any explanation in science.; Disagree? I regard the claim as preposterous. Quantum electrodynamics is accurate to thirteen or so decimal places; so, too, general relativity. A leaf trembling in the wrong way would suffice to shatter either theory. What can Darwinian theory offer in comparison?” (Berlinski, D., “A Scientific Scandal?: David Berlinski & Critics,” Commentary, July 8, 2003)
Moreover, these 'higher dimensional' areas in the universe where 'platonic perfection' are reached are very comforting to Christian presuppositions:
And whereas, atheists have no compelling evidence for all the various extra dimensions, parallel universe and/or multiverse scenarios that they have put forth, (Sept. 2018),,, https://uncommondescent.com/intelligent-design/uchicago-researchers-those-extra-dimensions-aint-out-there/#comment-665287 ,,,, Christians, on the other hand, can appeal directly to the higher dimensional mathematics behind Quantum Mechanics, Special Relativity and General Relativity to support their belief that God upholds this universe in its continual existence, as well as to support their belief in a heavenly dimension and in a hellish dimension. (December 2018 - (with quarter power scaling)) https://uncommondescent.com/intelligent-design/what-is-the-platonic-realm/#comment-670144
Thus, Wigner's multiple uses of the word 'miracle' in his 1960 paper is entirely appropriate. Verse and video:
2 Corinthians 12: 2-4 I know a man in Christ who fourteen years ago was caught up to the third heaven. Whether it was in the body or out of the body I do not know—God knows. And I know that this man—whether in the body or apart from the body I do not know, but God knows— was caught up to paradise and heard inexpressible things, things that no one is permitted to tell. Quantum Mechanics, Special Relativity, General Relativity and Christianity - video https://www.youtube.com/watch?v=h4QDy1Soolo
bornagain77_{January 20, 2019
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And 'platonic perfection' for a sphere is also approached rather closely in the Cosmic Background Radiation (CBR). ,,, Of the supposed “imperfections” in the sphere of the CBR, the following author comments, “the discovery of small deviations from smoothness (anisotopies) in the cosmic microwave background is welcome, for it provides at least the possibility for the seeds around which structure formed in the later Universe”
The Cosmic Background Radiation Excerpt: These fluctuations are extremely small, representing deviations from the average of only about 1/100,000 of the average temperature of the observed background radiation. The highly isotropic nature of the cosmic background radiation indicates that the early stages of the Universe were almost completely uniform. This raises two problems for (a naturalistic understanding of) the big bang theory. First, when we look at the microwave background coming from widely separated parts of the sky it can be shown that these regions are too separated to have been able to communicate with each other even with signals traveling at light velocity. Thus, how did they know to have almost exactly the same temperature? This general problem is called the horizon problem. Second, the present Universe is homogenous and isotropic, but only on very large scales. For scales the size of superclusters and smaller the luminous matter in the universe is quite lumpy, as illustrated in the following figure. ,,, Thus, the discovery of small deviations from smoothness (anisotopies) in the cosmic microwave background is welcome, for it provides at least the possibility for the seeds around which structure formed in the later Universe. However, as we shall see, we are still far from a quantitative understanding of how this came to be. http://csep10.phys.utk.edu/astr162/lect/cosmology/cbr.html
And indeed, these imperfections in the the sphere of the CMBR, (which 'provides at least the possibility for the seeds around which structure formed in the later Universe'), 'surprising' line up with the earth, and thus overturns the Copernican principle by showing the earth has a 'privileged position' in this universe. This fact is touched upon in further detail in the following post:
Thus, contrary to the presumption of atheists, far from the temperature variations in the CMBR being a product of randomness as they presuppose, the temperature variations in the CMBR correspond to the ‘largest scale structures of the observable universe’ and these ‘largest scale structures of the observable universe’ reveal “a surprising rotational coincidence for Earth”. Moreover, the way in which they were able to detect the anomalies in the CMBR, which ‘strangely’ line up with the earth and solar system, is that they ‘smeared’ and/or ‘averaged out’ the tiny temperature variations in the CMBR.,,, etc.. etc.. https://uncommondescent.com/intelligent-design/our-solar-system-is-a-lot-rarer-than-it-was-a-quarter-century-ago/#comment-669546
The one exception to this rule of ‘no platonic perfection’ for Euclidean objects within this universe is the axiomatic ‘primitive object’ in Euclidean geometry of the line.
“When a geometry is described by a set of axioms, the notion of a line is usually left undefined (a so-called primitive object).” https://en.wikipedia.org/wiki/Line_(geometry)
That is to say, the place where “platonic perfection” is, not only approached, but, (as far as our best scientific measurements will allow us to see), ‘perfectly reached’ in the universe, is for the ‘flatness’ of the universe.
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. https://phys.org/news/2017-06-universe-flat-topology.html
Moreover, this ‘insane coincidence’ of ‘plantonic perfection’ being reached for the axiomatic ‘primitive object’ of the line just so happens to be necessary for us to even be able to practice math and science, (and apply technology in our world), in the first place:
How do we know the universe is flat? Discovering the topology of the universe – by Fraser Cain – June 7, 2017 Excerpt: 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.,,, https://phys.org/news/2017-06-universe-flat-topology.html 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
Simply put, if the universe were not ‘ever-so-boringly’ flat (and if the universal constants were not also ‘ever-so-boringly’ constant), but the universe were instead governed by randomness, as atheists presuppose, or governed by some other of the infinitude of ‘platonic topologies’ that were possible, modern science and technology would have never gotten off the ground here on earth.
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
bornagain77_{January 20, 2019
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Of related interest to this quote by Wigner, "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.
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.,,, http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
,,, it is interesting to note that Darwinian evolution is based on a materialistic view of reality which denies that anything beyond nature exists. On the other hand, Mathematics, which provides the backbone for all of science, engineering and technology in the first place, exists in a transcendent, beyond space and time, realm which is not reducible any possible material explanation. This transcendent mathematical realm has been referred to as a Platonic mathematical world.
Platonic mathematical world - image https://image.slidesharecdn.com/quantuminformation2-120301000431-phpapp01/95/quantum-information-14-728.jpg?cb=1330561190
Simply put, Mathematics itself, contrary to the materialistic presuppositions of Darwinists, does not need the physical world in order to exist. And yet Darwinists, although they deny that anything beyond nature exists, need this transcendent world of mathematics in order for their theory to even be considered scientific in the first place. The predicament that Darwinists find themselves in regards to denying the reality of this transcendent, immaterial, world of mathematics, and yet needing validation from this transcendent, immaterial, world of mathematics in order to be considered scientific, should be the very definition of a scientifically self-refuting theory.
What Does It Mean to Say That Science & Religion Conflict? - M. Anthony Mills - April 16, 2018 Excerpt: In fact, more problematic for the materialist than the non-existence of persons is the existence of mathematics. Why? Although a committed materialist might be perfectly willing to accept that you do not really exist, he will have a harder time accepting that numbers do not exist. The trouble is that numbers — along with other mathematical entities such as classes, sets, and functions — are indispensable for modern science. And yet — here’s the rub — these “abstract objects” are not material. Thus, one cannot take science as the only sure guide to reality and at the same time discount disbelief in all immaterial realities. https://www.realclearreligion.org/articles/2018/04/16/what_does_it_mean_to_say_that_science_and_religion_conflict.html
And to try to establish that the "miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics" is in fact a "miracle", and not just a fantastic coincidence, we need to look at the places where this correspondence between the immaterial Platonic realm of mathematics and physics takes place in the universe. In other word, we need to look for 'Platonic perfection" in the universe. To hash this line of thought out it is first necessary to note where 'platonic perfection' is not reached in our three-dimensional world. As Michael Egnor states, "After all, no actual triangle is perfect, and thus no actual triangle in nature has sides such that the Pythagorean theorem holds."
Naturalism and Self-Refutation – Michael Egnor – January 31, 2018 Excerpt: Mathematics is certainly something we do. Is mathematics “included in the space-time continuum [with] basic elements … described by physics”? It seems a stretch. What is the physics behind the Pythagorean theorem? After all, no actual triangle is perfect, and thus no actual triangle in nature has sides such that the Pythagorean theorem holds. There is no real triangle in which the sum of the squares of the sides exactly equals the square of the hypotenuse. That holds true for all of geometry. Geometry is about concepts, not about anything in the natural world or about anything that can be described by physics. What is the “physics” of the fact that the area of a circle is pi multiplied by the square of the radius? And of course what is natural and physical about imaginary numbers, infinite series, irrational numbers, and the mathematics of more than three spatial dimensions? Mathematics is entirely about concepts, which have no precise instantiation in nature,, https://evolutionnews.org/2018/01/naturalism-and-self-refutation/
Michael Egnor could have also mentioned that there are no perfect squares, rectangles, spheres etc,,. in this world. And although 'platonic perfection' is not reached on this earth, it is interesting to note that this immaterial mathematical, (and logical), information still underlies virtually all of our technology today.
Describing Nature With Math By Peter Tyson – Nov. 2011 Excerpt: Mathematics underlies virtually all of our technology today. James Maxwell’s four equations summarizing electromagnetism led directly to radio and all other forms of telecommunication. E = mc2 led directly to nuclear power and nuclear weapons. The equations of quantum mechanics made possible everything from transistors and semiconductors to electron microscopy and magnetic resonance imaging. Indeed, many of the technologies you and I enjoy every day simply would not work without mathematics. When you do a Google search, you’re relying on 19th-century algebra, on which the search engine’s algorithms are based. When you watch a movie, you may well be seeing mountains and other natural features that, while appearing as real as rock, arise entirely from mathematical models. When you play your iPod, you’re hearing a mathematical recreation of music that is stored digitally; your cell phone does the same in real time. “When you listen to a mobile phone, you’re not actually hearing the voice of the person speaking,” Devlin told me. “You’re hearing a mathematical recreation of that voice. That voice is reduced to mathematics.” http://www.pbs.org/wgbh/nova/physics/describing-nature-math.html Recognising Top-Down Causation – George Ellis Excerpt: page 5: A: Causal Efficacy of Non Physical entities: Both the program and the data are non-physical entities, indeed so is all software. A program is not a physical thing you can point to, but by Definition 2 it certainly exists. You can point to a CD or flashdrive where it is stored, but that is not the thing in itself: it is a medium in which it is stored. The program itself is an abstract entity, shaped by abstract logic. Is the software “nothing but” its realisation through a specific set of stored electronic states in the computer memory banks? No it is not because it is the precise pattern in those states that matters: a higher level relation that is not apparent at the scale of the electrons themselves. It’s a relational thing (and if you get the relations between the symbols wrong, so you have a syntax error, it will all come to a grinding halt). This abstract nature of software is realised in the concept of virtual machines, which occur at every level in the computer hierarchy except the bottom one [17]. But this tower of virtual machines causes physical effects in the real world, for example when a computer controls a robot in an assembly line to create physical artefacts. Excerpt page 7: The assumption that causation is bottom up only is wrong in biology, in computers, and even in many cases in physics, ,,, The mind is not a physical entity, but it certainly is causally effective: proof is the existence of the computer on which you are reading this text. It could not exist if it had not been designed and manufactured according to someone’s plans, thereby proving the causal efficacy of thoughts, which like computer programs and data are not physical entities. http://fqxi.org/data/essay-contest-files/Ellis_FQXI_Essay_Ellis_2012.pdf
Given that Wigner wrote his article in 1960, and given the tremendous advance in applying mathematical, and logical information, to technology since 1960, indeed given the fact that we now know that information is ubiquitous within biological life, Wigner, if he were around today, could very well write an article today entitled, "The Unreasonable Effectiveness of Mathematics and Logical Information in the Natural Sciences, Technology, and Biology" And indeed, beside immaterial mathematical and logical information underlying virtually all of our technology today, (as well as being ubiquitous within biology), immaterial information has now also been shown, (directly contrary to the materialistic presuppositions of Darwinian thought), to be a physically real entity that, although it is capable interacting with matter and energy, is completely separate from matter and energy.
(December 2018) (the physical reality of immaterial information) https://uncommondescent.com/intelligent-design/a-new-unified-model-of-specified-complexity/#comment-669817
But back to our search for 'platonic perfection' within this universe. Although platonic perfection is not reached on this earth, it is interesting to note where in this universe 'platonic perfection' for spheres is approached rather closely,,,
Sun’s Almost Perfectly Round Shape Baffles Scientists – (Aug. 16, 2012) — Excerpt: The sun is nearly the roundest object ever measured. If scaled to the size of a beach ball, it would be so round that the difference between the widest and narrow diameters would be much less than the width of a human hair.,,, They also found that the solar flattening is remarkably constant over time and too small to agree with that predicted from its surface rotation. http://www.sciencedaily.com/re.....150801.htm Bucky Balls – Andy Gion Excerpt: Buckyballs (C60; Carbon 60) are the roundest and most symmetrical large molecule known to man. Buckministerfullerine continues to astonish with one amazing property after another. C60 is the third major form of pure carbon; graphite and diamond are the other two. Buckyballs were discovered in 1985,,, http://www.3rd1000.com/bucky/bucky.htm
The delicate balance at which carbon is synthesized in stars is truly a work of art.,,, Years after Sir Fred discovered the stunning precision with which carbon is synthesized in stars he stated this:
“I do not believe that any physicist who examined the evidence could fail to draw the inference that the laws of nuclear physics have been deliberately designed with regard to the consequences they produce within stars.” Sir Fred Hoyle – “The Universe: Past and Present Reflections.” Engineering and Science, November, 1981. pp. 8–12
bornagain77_{January 20, 2019
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Got it, ET: I understand the distinction you made in 10.hazel_{January 20, 2019
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as to:
"I can’t find anything about Wigner attributing the unreasonable effectiveness of math to God."
Read the following slowly,,, pause on the word "miracle",,, chew very slowly and thoroughly,,, repeat hundreds of times if necessary
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
definition:
mir·a·cle noun a surprising and welcome event that is not explicable by natural or scientific laws and is therefore considered to be the work of a divine agency.
Of related interest:
Is Religion a Science-Stopper? - REGIS NICOLL - OCTOBER 18, 2017 Excerpt: In his book, Truth Decay, Douglas Groothuis, shares the account of a Russian physicist (in the late 1980's): “I was in Siberia and met God there while working on my equations. I suddenly realized that the beauty of these equations had to have a purpose and design behind them, and I felt deep in my spirit that God was speaking to me through these equations.” In that moment, the young scientist stepped over the chasm from atheism to theism and, ultimately, Christianity. https://www.crisismagazine.com/2017/religion-science-stopper Truth Decay: Defending Christianity Against the Challenges of Postmodernism - By Douglas Groothuis Excerpt page 251: “I was in Siberia and met God there while working on my equations. I suddenly realized that the beauty of these equations had to have a purpose and design behind them, and I felt deep in my spirit that God was speaking to me through these equations. But I don't know much about Him. Could you tell me about Him?” The American professor gladly obliged, and the student was converted and baptized. https://books.google.com/books?id=N8yECwAAQBAJ&pg=PA251#v=onepage&q&f=false
bornagain77_{January 20, 2019
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hazel, Now you are misrepresenting my position. Clearly you have issues. That much is clear to me now. I am happy for his peace. But that does not give him the right to declare:
The full meaning of life, the collective meaning of all human desires, is fundamentally a mystery beyond our grasp.
It is beyond HIS grasp. Quitters try to tell others they have to give up cuz you won't succeed cuz he couldn't and he is better than you. Heh "Argue for your own limitations and you are right, they are yours."- Don ShimodaET_{January 20, 2019
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ET, re 7: it was a direct quote from Wigner's memoirs. Now maybe seeing the quote in full context would change its meaning, or maybe not. I don't have access to the book, so I am tentatively taking it as an accurate statement of Wigner's views. Assuming that is true, your position is that someone who is at peace with the idea that the full meaning of life is a mystery is a quitter. I am clear now.hazel_{January 20, 2019
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Folks, it looks like one of the key themes we need to highlight is the MATH-PHYSICS GAP. Where, again only world-root level can bridge. The key bridge is the logic of being, working through distinct identity and its quantitative-structural implications. Where, a possible world is a sufficiently complete description of a coherent state of affairs that are possible of existence, for such a PW, W to be distinct it must have distinguishing characteristics. Accordingly, we may freely write W = {A|~A} -- A distinct in W, with its complement, which then allows us to identify duality, unity, nullity, thence per von Neumann the succession of naturals per order type. From this Z, Q, R, C follow, giving us an infinite panoply of abstracta manifesting structure and quantity. These are antecedent to our coming along, they are discoveries not inventiions though how we study and represent them will reflect cultural influences and creativity. That is, core mathematical abstract entities, relationships, quantities, structure are inherent in the fabric for a world to exist. The Wigner gap is bridged at world root. KFkairosfocus_{January 20, 2019
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Yes, I am calling him a quitter if what you posted wasn't a quote-mine.ET_{January 20, 2019
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Been reading a little bit online, and I think News' headline is misleading. I can't find anything about Wigner attributing the unreasonable effectiveness of math to God. Perhaps someone can point me to more to read: he seems like an interesting guy.hazel_{January 20, 2019
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to ET:
Andrew Szanton, ed. (1992). The Recollections of Eugene P. Wigner As Told to Andrew Szanton. Basic Books. pp. 60-61. ISBN 9780306443268. "Neither did I want to be a clergyman. I liked a good sermon. But religion tells people how to behave and that I could never do. Clergymen also had to assume and advocate the presence of God, and proofs of God's existence seemed to me quite unsatisfactory. ... I saw that I could not know anything of God directly, that His presence was a matter of belief, I did not have that belief, and preaching without belief is repulsive. So I could not be a clergyman, however many people might gain salvation. And my parents never pressed the point."
hazel_{January 20, 2019
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I like these remarks from Wigner’s article on the Unreasonable Effectiveness of Math, which I think are somewhat compatible with some of the things I have been trying to say.
However, the point which is most significant in the present context is that 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. … [This] 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 [of the motion of bodies] 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.
hazel_{January 20, 2019
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