At Mind Matters News: Why would a purely physical universe need imaginary numbers?

_{Denyse O'Leary

February 17, 2022

Intelligent Design, Mathematics}

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Our computers and the entire modern world depend on them, says science writer Michael Brooks in an excerpt from his new book:

In an excerpt from his new book, The Art of More: How Mathematics Created Civilization, science writer Michael Brooks offers the intriguing idea that the modern world arose from imaginary numbers:

But what does his claim that the numbers are “not some deep mystery about the universe” leave us? Recent studies have shown that imaginary numbers — which we can’t really represent by objects, the way we can represent natural numbers by objects — are needed to
describe reality. Quantum mechanics pioneers did not like them and worked out ways around them:

In fact, even the founders of quantum mechanics themselves thought that the implications of having complex numbers in their equations was disquieting. In a letter to his friend Hendrik Lorentz, physicist Erwin Schrödinger — the first person to introduce complex numbers into quantum theory, with his quantum wave function (ψ) — wrote, “What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Ψ is surely fundamentally a real function.”
Ben Turner, “Imaginary numbers could be needed to describe reality, new studies find” at LiveScience (December 10, 2021)

But recent studies in science journals Nature and Physical Review Letters have shown, via a simple experiment, that the mathematics of our universe requires imaginary numbers.
News, “Why would a purely physical universe need imaginary numbers?” at Mind Matters News (February 16, 2022)

Takehome: The most reasonable explanation is that the universe, while physical, is also an idea, one that cannot be reduced to its physical features alone.

You may also wish to read:

Why the unknowable number exists but is uncomputable. Sensing that a computer program is “elegant” requires discernment. Proving mathematically that it is elegant is, Chaitin shows, impossible. Gregory Chaitin walks readers through his proof of unknowability, which is based on the Law of Non-contradiction.

Most real numbers are not real, or not in the way you think. Most real numbers contain an encoding of all of the books in the US Library of Congress. The infinite only exists as an idea in our minds. Therefore, curiously, most real numbers are not real. (Robert J. Marks)

and

Can we add new numbers to mathematics? We can work with hyperreal numbers using conventional methods. Surprisingly, yes. It began when the guy who discovered irrational numbers was—we are told—tossed into the sea. (Jonathan Bartlett)

Comments

My beginning assumption is that the root of reality is unknowable. We are limited to the experiences and tools that we have in this universe, which is where I start. I have speculations about metaphysics that I like best because they make the most sense to me in comparison to other speculations offered by others, but I understand that all such speculations can't be shown to be true: their value comes from the ways they help structure our understanding about life here and now in a way that furthers our chosen values, beliefs, needs, etc.Viola Lee_{February 17, 2022
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Seeing that the ‘divine will’ of God, (sustaining the universe in its continual existence), played such an integral part in the scientific revolution that Newton was integral in starting, (and although modern science has certainly come a long way since Newton first started the Scientific Revolution), let’s just simply say that Newton would be very pleased to see the recent closing of the “freedom of choice” loophole within quantum mechanics,
Closing the ‘free will’ loophole: Using distant quasars to test Bell’s theorem – February 20, 2014 Excerpt: Though two major loopholes have since been closed, a third remains; physicists refer to it as “setting independence,” or more provocatively, “free will.” This loophole proposes that a particle detector’s settings may “conspire” with events in the shared causal past of the detectors themselves to determine which properties of the particle to measure — a scenario that, however far-fetched, implies that a physicist running the experiment does not have complete free will in choosing each detector’s setting. Such a scenario would result in biased measurements, suggesting that two particles are correlated more than they actually are, and giving more weight to quantum mechanics than classical physics. “It sounds creepy, but people realized that’s a logical possibility that hasn’t been closed yet,” says MIT’s David Kaiser, the Germeshausen Professor of the History of Science and senior lecturer in the Department of Physics. “Before we make the leap to say the equations of quantum theory tell us the world is inescapably crazy and bizarre, have we closed every conceivable logical loophole, even if they may not seem plausible in the world we know today?” https://www.sciencedaily.com/releases/2014/02/140220112515.htm Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars – Anton Zeilinger – 14 June 2018 Abstract: This experiment pushes back to at least approx. 7.8 Gyr ago the most recent time by which any local-realist influences could have exploited the “freedom-of-choice” loophole to engineer the observed Bell violation, excluding any such mechanism from 96% of the space-time volume of the past light cone of our experiment, extending from the big bang to today. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.080403
Moreover, when we rightly allow the Agent causality of God ‘back’ into physics, (as the Christian founders of modern science originally envisioned, Isaac Newton, Michael Faraday, James Clerk Maxwell, and Max Planck, to name a few of the Christian founders,,,, and as quantum mechanics itself now empirically demands with the closing of the “freedom-of-choice” loophole by Anton Zeilinger and company), then rightly allowing the Agent causality of God ‘back’ into physics provides us with a very plausible resolution for the much sought after ‘theory of everything’ in that Christ’s resurrection from the dead bridges the infinite mathematical divide that exists between General Relativity and Quantum Mechanics and provides us with an empirically backed reconciliation, via the Shroud of Turin, between Quantum Mechanics and General Relativity into the much sought after ‘Theory of Everything”
Jesus Christ as the correct “Theory of Everything” – video https://www.youtube.com/watch?v=Vpn2Vu8–eE December 2021 – When scrutinizing some of the many fascinating details of the Shroud of Turin, we find that both General Relativity, i.e. gravity, and Quantum Mechanics were both dealt with in Christ’s resurrection from the dead. https://uncommondescent.com/intelligent-design/in-time-for-american-thanksgiving-stephen-meyer-on-the-frailty-of-scientific-atheism/#comment-741600
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_{February 17, 2022
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A few notes and quotes; (per the late Steven Weinberg), "we will not be able to derive them, (the mathematical laws of the universe), on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don’t describe the world as we know it. And we will always be left with a question ‘why are the laws of nature what they are rather than some other laws?’. And I don’t see any way out of that."
“I don’t think one should underestimate the fix we are in. That in the end we will not be able to explain the world. That we will have some set of laws of nature (that) we will not be able to derive them on the grounds simply of mathematical consistency. Because we can already think of mathematically consistent laws that don’t describe the world as we know it. And we will always be left with a question ‘why are the laws of nature what they are rather than some other laws?’. And I don’t see any way out of that. The fact that the constants of nature are suitable for life, which is clearly true, we observe,,,” (Weinberg then comments on the multiverse conjecture of atheists) “No one has constructed a theory in which that is true. I mean,, the (multiverse) theory would be speculative, but we don’t even have a theory in which that speculation is mathematically realized. But it is a possibility.” Steven Weinberg – as stated to Richard Dawkins at the 8:15 minute mark of the following video - Leonard Susskind - Richard Dawkins and Steven Weinberg - 1 in 10^120 - Cosmological Constant points to intelligent design - video https://youtu.be/z4E_bT4ecgk?t=495
And, "an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms."
The Limits Of Reason – Gregory Chaitin – 2006 Excerpt: Unlike Gödel’s approach, mine is based on measuring information and showing that some mathematical facts cannot be compressed into a theory because they are too complicated. This new approach suggests that what Gödel discovered was just the tip of the iceberg: an infinite number of true mathematical theorems exist that cannot be proved from any finite system of axioms. http://www.umcs.maine.edu/~chaitin/sciamer3.pdf
And, "The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,,? Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.”
Bruce Gordon: Hawking’s irrational arguments – October 2010 Excerpt: ,,,The physical universe is causally incomplete and therefore neither self-originating nor self-sustaining. The world of space, time, matter and energy is dependent on a reality that transcends space, time, matter and energy. This transcendent reality cannot merely be a Platonic realm of mathematical descriptions, for such things are causally inert abstract entities that do not affect the material world,,,?Rather, the transcendent reality on which our universe depends must be something that can exhibit agency – a mind that can choose among the infinite variety of mathematical descriptions and bring into existence a reality that corresponds to a consistent subset of them. This is what “breathes fire into the equations and makes a universe for them to describe.” Anything else invokes random miracles as an explanatory principle and spells the end of scientific rationality. http://www.washingtontimes.com/news/2010/oct/1/hawking-irrational-arguments/
And, "Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information."
Algorithmic Information Theory, Free Will and the Turing Test - Douglas S. Robertson Excerpt: Chaitin’s Algorithmic Information Theory shows that information is conserved under formal mathematical operations and, equivalently, under computer operations. This conservation law puts a new perspective on many familiar problems related to artificial intelligence. For example, the famous “Turing test” for artificial intelligence could be defeated by simply asking for a new axiom in mathematics. Human mathematicians are able to create axioms, but a computer program cannot do this without violating information conservation. Creating new axioms and free will are shown to be different aspects of the same phenomena: the creation of new information. http://cires.colorado.edu/~doug/philosophy/info8.pdf
And, (during the founding of modern science in Medieval Christian Europe), "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."
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/
And, "(contingency) was a huge concept,,, it is an order that is contingent upon the will of the Creator. It could have been otherwise."
“That (contingency) was a huge concept (that was important for the founding of modern science). The historians of science call that ‘contingency’. The idea that nature has an order that is built into it. But it is an order that is contingent upon the will of the Creator. It could have been otherwise. Just as there are many ways to make a timepiece, or a clock,,, there are many different ways God could have ordered the universe. And it is up to us not to deduce that order from first principles, or from some intuitions that we have about how nature ought to be, but rather it is important to go out and see how nature actually is.” – Stephen Meyer – 5:00 minute mark – Andrew Klavan and Stephen Meyer Talk God and Science https://idthefuture.com/1530/
And, “The belief that it was by divine will and not by some shadow of necessity that matter existed and possessed its properties, had a direct impact on Newton’s science. It was necessary to discover laws and properties by experimental means, and not by rational deduction. As Newton wrote in another unpublished manuscript, “The world might have been otherwise,,”
Newton — Rationalizing Christianity, or Not? – Rosalind W. Picard – 1998 Excerpt: The belief that it was by divine will and not by some shadow of necessity that matter existed and possessed its properties, had a direct impact on Newton’s science. It was necessary to discover laws and properties by experimental means, and not by rational deduction. As Newton wrote in another unpublished manuscript, “The world might have been otherwise,,” (see Davis, 1991) https://web.media.mit.edu/~picard/personal/Newton.php
And, "Newton rejected both the clockwork metaphor itself and the cold mechanical universe upon which it is based. His conception of the world reflects rather a deep commitment to the constant activity of the divine will, unencumbered by the “rational” restrictions that Descartes and Leibniz placed on God,,,"
“Newton’s Rejection of the “Newtonian World View”: The Role of Divine Will in Newton’s Natural Philosophy – (Davis, 1991) Abstract: The significance of Isaac Newton for the history of Christianity and science is undeniable: his professional work culminated the Scientific Revolution that saw the birth of modern science,,, Newton’s voluntarist conception of God had three major consequences for his natural philosophy. First, it led him to reject Descartes’ version of the mechanical philosophy, in which matter was logically equated with extension, in favor of the belief that the properties of matter were freely determined by an omnipresent God, who remained free to move the particles of matter according to God’s will. Second, Newton’s voluntarism moved him to affirm an intimate relationship between the creator and the creation; his God was acted on the world at all times and in ways that Leibniz and other mechanical philosophers could not conceive of, such as causing parts of matter to attract one another at a distance. Finally, Newton held that, since the world is a product of divine freedom rather than necessity, the laws of nature must be inferred from the phenomena of nature, not deduced from metaphysical axioms — as both Descartes and Leibniz were wont to do. http://home.messiah.edu/~tdavis/newton.htm
bornagain77_{February 17, 2022
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VL
I don’t look at it from the “God created it” point of view, but you do, so we have different views that flow from some beginning assumptions.
Yes, well stated. I propose God as the origin - so God creating the rational, mathematically consistent structure of the universe is my beginning assumption. What do you propose as your beginning assumption?Silver Asiatic_{February 17, 2022
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Yes, there are different ways of looking at it. I don't look at it from the "God created it" point of view, but you do, so we have different views that flow from some beginning assumptions.Viola Lee_{February 17, 2022
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VL
That’s considerably different from math as an abstraction directly causing the world to be a certain way.
It depends on how you look at it. When we construct something, there's a blueprint or architecture. God created math, then created the universe to map into the mathematical constructs. So, math caused the world to be a certain way. God could have created a non-mathematically based world. But at the structure of our world is math - which is another way of saying "order, reason, harmony and logic are at the foundation of the world -- and those things cause our world to be a certain way and not another way".Silver Asiatic_{February 17, 2022
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I'll agree that "the math causes understanding, and therefore is the cause of human activity." That's considerably different from math as an abstraction directly causing the world to be a certain way.Viola Lee_{February 17, 2022
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I'll argue that math is a cause. Something like the effect of compound interest on savings come from mathematical projections. The projections do not exist as present-day objects, but only as math. It's a model of something that does not yet exist. But clearly, the math causes understanding, and therefore is the cause of human activity. So, math has causal power in the universe. Is it the actual cause of the universe? I know that Dr. Feser would not say that - given he has at least one book describing the first cause of the universe and the philosophical arguments for it. The first cause is not math - math was created by God (which is what he says in the quote). So, math is not merely something we use, but it is an immaterial force that can cause us to do things via decision making. We don't consciously use math to add the weights of things and decide that we can't carry them. The math is built into our reason - given to us by God, and we use it unconsciously. In fact, even infants are moved by mathematics without knowing what it is. They see three blocks and only have 2 hands, so they do the math and realize they can't grab all three.Silver Asiatic_{February 17, 2022
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I did read 32, and agree with some of it, KF.Viola Lee_{February 17, 2022
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I see. Math is certainly not arbitrary. My point is to make this distinction: that math does not cause the world to be what it is, but math is used to describe certain aspects of the world that stem from our experience of the world in a way that suits our nature, both practically and aesthetically (at times.) I agree with KF above when he says "Such abstracta do not exert causal forces," although he and I see other things about the nature of abstractions quite differently.Viola Lee_{February 17, 2022
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VL, kindly see 32 above. KFkairosfocus_{February 17, 2022
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VL
when you write “Agreed” you mean that you agree that there is also a different perspective, not that you agree with that different perspective?
I agreed that math could be seen as an effect not a cause - although an effect bound to the cause in a way that we could say it contributes to it. In other words, not arbitrarily.Silver Asiatic_{February 17, 2022
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KF, pardon, but as a math teacher who taught for over 30 years that math in the real world is always an approximation to the idealized math in our models, I know that!!! And it doesn't really relate to the topic being discussed.Viola Lee_{February 17, 2022
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VL, pardon, as a physicist I am highlighting the matter of approximation and by extension just how rapidly complexity enters models. For example, for ballistics, we may ponder a fairly simple model often used by shooters, tracing to Pejsa: https://www.mathscinotes.com/2015/05/pejsas-projectile-drop-versus-distance-formula/ which is considerably simpler than those used by militaries but is effective. BTW, ballistics with air resistance is one gateway into aeronautics and rocket science with side helpings of fluid dynamics. One key consideration is low subsonic vs trans sonic vs supersonic regions of flight dynamics. See this comment with a diagram https://www.mathscinotes.com/2015/05/pejsas-projectile-drop-versus-distance-formula/#comment-2712 KFkairosfocus_{February 17, 2022
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KF, I know that an equation like d = 1/2gt^2 is an idealized model that is subject to all sorts of real-world complexities. Among other things, every moment the ball falls g is slightly different. And a sprayed water jet is much more complex than a falling ball. I'm not sure why you thought your comment at 33 was useful or contributed to the discussion.Viola Lee_{February 17, 2022
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Vl, initial motion. Even a sprayed water jet for a fountain within a few feet noticeably deviates from a strict parabolic arc. KFkairosfocus_{February 17, 2022
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Folks, I suggest that we think of Mathematics as a dual matter: [the study of] the logic of structure and quantity. Our study targets a substance, the core of which -- as I discussed here -- is an aspect of the logic of being for possible worlds; with certain aspects being framework to any possible world so necessary and eternal albeit duly abstract entities. Things like two-ness, which is pivotal. Where, this then lends pervasive power to certain aspects of Math, hence for instance power in the physical sciences. Such abstracta do not exert causal forces but reflect logical constraints on being. Less general aspects then help us construct logic model worlds that may be close enough to ours to be useful without necessarily being strictly true. Sometimes, they may actually be true of course. KFkairosfocus_{February 17, 2022
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Chuckdarwin in you trying to distance Einstein from his use of the word 'miracle', I merely note that Einstein chastised 'professional atheists' 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
That certainly does not square very well with your claim that Einstein did not mean what he said when he said the word 'miracle' Moreover, although you try to bring Einstein over to your atheistic side in your rather single minded focus on attacking Christianity, (whilst neglecting to ever really defend your supposed 'science' of Darwinian evolution), I also merely note that, "according to biographer Walter Isaacson, Einstein was more inclined to denigrate atheists than religious people.[28]"
According to biographer Walter Isaacson, Einstein was more inclined to denigrate atheists than religious people.[28] Einstein said in correspondence, "[T]he fanatical atheists...are like slaves who are still feeling the weight of their chains which they have thrown off after hard struggle. They are creatures who—in their grudge against the traditional 'opium of the people'—cannot hear the music of the spheres."[28][29] Although he did not believe in a personal God, he indicated that he would never seek to combat such belief because "such a belief seems to me preferable to the lack of any transcendental outlook."[30] https://en.wikipedia.org/wiki/Religious_and_philosophical_views_of_Albert_Einstein#Agnosticism_and_atheism
Of note, Antony Flew, who was heavily influenced by Einstein in his late-life conversion from atheism to Theism, had this to say in reply to Richard Dawkins's distortion of Einstein's religious views,,, "(Dawkins),, makes no mention of Einstein’s most relevant report: namely, that the integrated complexity of the world of physics has led him to believe that there must be a Divine Intelligence behind it. "
Reviewing Richard Dawkins' 'The God Delusion' - Anthony Flew - Flew amplifies on this charge, and Dawkins' avoidance of a particular statement by Einstein: The fault of Dawkins as an academic ... was his scandalous and apparently deliberate refusal to present the doctrine which he appears to think he has refuted in its strongest form. Thus we find in his index five references to Einstein. They are to the mask of Einstein and Einstein on morality; on a personal God; on the purpose of life (the human situation and on how man is here for the sake of other men and above all for those on whose well-being our own happiness depends); and finally on Einstein’s religious views. But (I find it hard to write with restraint about this obscurantist refusal on the part of Dawkins) he makes no mention of Einstein’s most relevant report: namely, that the integrated complexity of the world of physics has led him to believe that there must be a Divine Intelligence behind it. (I myself think it obvious that if this argument is applicable to the world of physics then it must be hugely more powerful if it is applied to the immeasurably more complicated world of biology.) He continues: Of course many physicists with the highest of reputations do not agree with Einstein in this matter. But an academic attacking some ideological position which s/he believes to be mistaken must of course attack that position in its strongest form. This Dawkins does not do in the case of Einstein and his failure is the crucial index of his insincerity of academic purpose and therefore warrants me in charging him with having become, what he has probably believed to be an impossibility, a secularist bigot. http://shrineinthesea.blogspot.com/2017/12/reviewing-richard-dawkins-god-delusion.html Here is a related quote from Flew, "I now believe that the universe was brought into existence by an infinite intelligence. I believe that the universe's intricate laws manifest what scientists have called the Mind of God. I believe that life and reproduction originate in a divine Source. Why do I believe this, given that I expounded and defended atheism for more than a half century? The short answer is this: this is the world picture, as I see it, that has emerged from modern science." - Antony Flew – considered world's leading atheist philosopher for most of his adult life until a few years shortly before his death - The Case for a Creator - Lee Strobel – interview (26:00 minute mark) http://www.saddleback.com/mc/m/ee32d/
Moreover, although Einstein is certainly to be afforded a great deal of respect for General Relativity and Special Relativity, let's not forget that Einstein's self admitted 'greatest blunder' in science, (in order to avoid a beginning for the universe), as well as his ad hoc appeal to the now falsified 'hidden variables' in quantum mechanics, (in order to avoid 'spooky action at a distance'), were both motivated by his a-priori commitment to methodological naturalism, and/or Atheistic Materialism. Who knows how far Einstein may have gotten in science with quantum mechanics had he not been blinded by by his a-priori commitment to methodological naturalism and/or Atheistic materialism?
“I must confess that I was not able to find a way to explain the atomistic character of nature. My opinion is that … one has to find a possibility to avoid the continuum (together with space and time) altogether. But I have not the slightest idea what kind of elementary concepts could be used in such a theory.” — Albert Einstein (1954) – Einstein from “B” to “Z” Springer, p. 151 – John Stachel
bornagain77_{February 17, 2022
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I think what I said is a possible explanation of what math is irrespective of one's view about what reality is. The movement of a falling ball, whether you see it from an idealism view or not, can be modeled by the equation d = 1/2gt^2. Math is one way of describing what we experience, irrespective of how one sees the nature of that experience.Viola Lee_{February 17, 2022
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VL @25 said:
However, from another perspective, it could be an effect. Reality is what it is, and math is a description of certain types of aspects of it by creatures (us) who have certain kinds of experiences of it.
What do you mean by "reality" when you say "reality is what it is?" Local reality has been entirely falsified, and recent experiments all but entirely falsify non-local realism. https://www.nature.com/articles/nature05677
Here we show by both theory and experiment that a broad and rather reasonable class of such non-local realistic theories is incompatible with experimentally observable quantum correlations. In the experiment, we measure previously untested correlations between two entangled photons, and show that these correlations violate an inequality proposed by Leggett for non-local realistic theories.
There is apparently no "it" (reality) for us to be describing. How then can "it" be the source of what we are describing, when "it" doesn't even exist absent our observational description?William J Murray_{February 17, 2022
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BA77 @ 8
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.
I don't think you and Einstein mean the same thing by the word "miracle." I don't think Einstein, as you say, viewed the "applicability of mathematics to the universe as a 'miracle,'" rather I think he viewed mathematics simply as a tool to describe the world. The "miracles" to which he referred were more subtle. Given his view of Judaism as an "incarnation of the most childish superstitions" and the Bible as "a collection of honourable, but still primitive legends which are nevertheless pretty childish." (Gutkind letter, 1954), along with the above quote, Einstein seems to be using the term "miracle" to describe an intellectual experience of awe regarding the (1) knowability of the universe and the (2) "high degree of ordering of the objective world." I don't think he is at all referring to things like turning water into wine, casting out demons or even raising people (including Jesus) from the dead, which seem fundamental to Christianity. I think Einstein would consign those claims to the bin labeled "childish superstitions." As an aside, I note that you omit omnibenevolence from your list of omni's relevant to the God of theism. Does that mean that you now concede the notion of God as the author of evil? Or was that simply not in your cut-and-paste reference? In any event, it is a pretty glaring omission....chuckdarwin_{February 17, 2022
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SA, I know that Dr. Feser is describing a theistic-Platonic view. I assume (but I'm not sure) that when you write "Agreed" you mean that you agree that there is also a different perspective, not that you agree with that different perspective???Viola Lee_{February 17, 2022
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VL Agreed. I think Dr Feser is pointing to the connection of cause and effect - that math is a necessary aspect of the cause. But he's not saying it was created by humans to describe things, but rather it exists as built into reality.Silver Asiatic_{February 17, 2022
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"Given the centrality of mathematics to scientific explanation, it seems in some way to be a cause of the natural world and its order." However, from another perspective, it could be an effect. Reality is what it is, and math is a description of certain types of aspects of it by creatures (us) who have certain kinds of experiences of it.Viola Lee_{February 17, 2022
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Reposting from BA77's previous:
Keep It Simple – – by Edward Feser – April 2020 Excerpt: Mathematics appears to describe a realm of entities with quasi-divine attributes. The series of natural numbers is infinite. That one and one equal two and two and two equal four could not have been otherwise. Such mathematical truths never begin being true or cease being true; they hold eternally and immutably. The lines, planes, and figures studied by the geometer have a kind of perfection that the objects of our experience lack. Mathematical objects seem immaterial and known by pure reason rather than through the senses. Given the centrality of mathematics to scientific explanation, it seems in some way to be a cause of the natural world and its order. How can the mathematical realm be so apparently godlike? The traditional answer, originating in Neoplatonic philosophy and Augustinian theology, is that our knowledge of the mathematical realm is precisely knowledge, albeit inchoate, of the divine mind. Mathematical truths exhibit infinity, necessity, eternity, immutability, perfection, and immateriality because they are God’s thoughts, and they have such explanatory power in scientific theorizing because they are part of the blueprint implemented by God in creating the world. For some thinkers in this tradition, mathematics thus provides the starting point for an argument for the existence of God qua supreme intellect. https://www.firstthings.com/article/2020/04/keep-it-simple
"a realm of entities" - real objects that are immaterial.Silver Asiatic_{February 17, 2022
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re 20 and 22. Those are the articles I was thinking about.Viola Lee_{February 17, 2022
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If Imaginary Numbers Are Needed To Describe Reality, Then Isn’t Materialism Dead Already? - Dec. 22, 2021 https://uncommondescent.com/intelligent-design/if-imaginary-numbers-are-needed-to-describe-reality-then-isnt-materialism-is-dead-already/ Imaginary numbers could be needed to describe reality, new studies find - Dec. 21, 2021 Excerpt: In their updated version of the classic Bell test, the physicists devised an experiment in which two independent sources (which they called S and R) would be placed between three detectors (A, B and C) in an elementary quantum network. The source S would then emit two light particles, or photons — one sent to A and the other to B — in an entangled state. The source R also would emit two entangled photons, sending them to nodes B and C. If the universe were described by a standard quantum mechanics based on complex numbers, the photons that arrived at detectors A and C wouldn't need to be entangled, but in a quantum theory based on real numbers, they would. To test this setup, the researchers of the second study performed an experiment in which they shone laser beams onto a crystal. The energy the laser gave to some of the crystals' atoms was later released as entangled photons. By looking at the states of the photons arriving at their three detectors, the researchers saw that the states of the photons arriving at detectors A and C weren't entangled, meaning their data could be described only by a quantum theory that used complex numbers. https://www.livescience.com/imaginary-numbers-needed-to-describe-reality
bornagain77_{February 17, 2022
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WJM
Where did God create “matter?” We can find any here. Where is it?
Immaterial entities are actually created objects. Universals were created by God. The concept of a triangle exists as an immaterial universal - something we can apply to empirical reality (that which we sense). Imaginary numbers exist and are proof that there are immaterial things not explainable by materialism or by evolution.Silver Asiatic_{February 17, 2022
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Polistra: We don’t need imaginary numbers. Everything can be described and calculated without them. They’re just a convenient tool for clearer symbolism and clearer thinking. Generally true, although, it has been recently discovered that certain predictions of quantum networks require complex (real + "imaginary") numbers: https://www.sciencedaily.com/releases/2021/12/211215112812.htm P.S. the term "imaginary" is an unfortunate moniker. When sqrt(-1) and variants are paired with a real number, a better term is "lateral" numbers. There is nothing at all "imaginary" or mysterious about them. --Ramram_{February 17, 2022
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Re Polistra and JVL's statements "We don’t need imaginary numbers. Everything can be described and calculated without them.": I think there was an article here a while back claiming that this wasn't true. The article claimed that there are aspect of QM for which complex numbers are required to describe some phenomena, and can't be replaced by alternate ways of describing ordered pairs. I can't remember the argument, but it was something News posted.Viola Lee_{February 17, 2022
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