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

VL I pointed out the contradiction in your claim. I think you've acknowledged it.
I’m not offering this Taoist perspective as true,
Ok, so you think it is not true. It is therefore false.
However, I personally find this perspective the most satisfying.
You're satisfied with something that you think is not true. That's just believing in an illusion. This undercuts what you're saying. As I explained before, a person who says "the topic I'm discussing is unknowable" will quickly run out of anything to say. It's better to just be quiet and speak about what you know, instead of insisting that what you're saying is non-knowledge or even what you know to be false (as you say of the Tao). I don't think I can go any farther on this. I've done what I could - it's just at a standstill unless you want to rethink/adjust your views. I'm not demanding that. It certainly takes time for a person to think through these issues. It's ok to say "I don't know" - nothing wrong with that. But to insist that "nobody can know" when people actually do present knowledge (or you yourself present knowledge in contradiction to the 'unknowable' claim), then this just creates problems in understanding and communication. I say this with respect for you and your viewpoints. Again, I just think we reached a dead-end here.Silver Asiatic_{February 21, 2022
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SA said:
The origin and source of those features possesses free will, mind and rationality. It confers those things on us because it possesses them. One cannot give what one does not have – thus, the origin of all that, possesses all that.
The logic from this continues into: the only way the black box source can confer on us the sense of being time-linear finite beings with doubts, fears, confusion, hate, schizophrenia, lust, anger, etc., is if that black box experiences itself as a time-linear finite being with doubts, fears, confusion, hate, schizophrenia, lust, anger, etc. You don't get to arbitrarily draw the line of what it is like to be "the black box" at the border of convenient qualia. A flashlight is not light. It has the potential to emanate light, but it is not itself light.William J Murray_{February 21, 2022
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^^^^ Apparently superficially rationalizing away deep contradictions in logic are Viola Lee's bread and butter. Frankly, I think I'll go do something much more entertaining, like watching paint dry. :)
10 Hours of Paint Drying https://www.youtube.com/watch?v=PLOPygVcaVE
bornagain77_{February 21, 2022
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SA, re 251. I have a physical body. Do I therefore assume the Black Box has a physical body? I have a wide range of emotions. Do I assume the Black Box has a wide range of emotions. Etc.... You write, “It confers those things on us because it possesses them.” SA, there is just a gulf between our understandings. It doesn’t “confer” anything. It underlies all, from innumerable immense galaxies to all the moments of our lives, but I don’t think it “wants” anything. It just is. The Feser article called this “apophatic”: The Tao can only be described by saying what it is not, because any attempt to say what it is runs into the false duality problem of language that I have been describing. And to SA, re 254: You write, “You just made a positive, defining assertion about something you’ve claimed to be “unknowable”” Let me reiterate something: I’m not offering this Taoist perspective as true, because my belief is that all metaphysics, including religious metaphysics, are human inventions to account for the unaccountable. However, I personally find this perspective the most satisfying. I have also been interested in explaining it in order to make it clear that theism and materialism aren’t the only two possible ways to see the world.Viola Lee_{February 21, 2022
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VL
The Black Box is beyond the material/immaterial duality, as it is beyond all dualities.
You just made a positive, defining assertion about something you've claimed to be "unknowable". You just provided boundaries and a definition. So, you know quite a lot already and are trying to correct people in their understanding of something you're claiming we can know nothing about. That's a problem as I see it.Silver Asiatic_{February 21, 2022
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VL to Jerry:, "but “choices” is an excessively anthropomorphized word to use here." Funny that that "excessively anthropomorphized" conception, i.e. the free will of God, was a necessary presupposition that was essential for the rise of modern science itself
February 2022 – The free will of God and the founding of modern science (pertinent references are half way down the following post) https://uncommondescent.com/intelligent-design/at-mind-matters-news-why-would-a-purely-physical-universe-need-imaginary-numbers/#comment-747234
All of which is proof yet again that VL is not arguing in a rationally coherent, good faith, manner. She was corrected on her claim that we have inappropriately 'anthropomorphized' God in post 166. And yet here she sits, continuing to falsely claim that we have inappropriately 'anthropomorphized' God. So again, (and via post 166),
anthropomorphize attribute human characteristics or behavior to (a god, animal, or object).
In short, VL, and her cheerleaders, are sneering at the Judeo-Christian presupposition that we were, and are, made in the image of God.
Genesis 1:26 Then God said, “Let us make mankind in our image, in our likeness, so that they may rule over the fish in the sea and the birds in the sky, over the livestock and all the wild animals, and over all the creatures that move along the ground.”
Yet the belief that we are made in the image of God, (i.e. the 'anthropomorphized' version of God that she sneers at), was, (again), a necessary, and essential, presupposition that lay at the founding of modern science itself. And that presupposition continues to be a presupposition that is essential to the successful practice of modern science, For instance, “Modern science was inspired by the conviction that the universe is the product of a rational mind who designed it to be understood and who (also) designed the human mind to understand it.” (i.e. human exceptionalism),
“Science in its modern form arose in the Western civilization alone, among all the cultures of the world”, because only the Christian West possessed the necessary “intellectual presuppositions”. – Ian Barbour Presupposition 1: The contingency of nature “In 1277, the Etienne Tempier, the bishop of Paris, writing with support of Pope John XXI, condemned “necessarian theology” and 219 separate theses influenced by Greek philosophy about what God could and couldn’t do.”,, “The order in nature could have been otherwise (therefore) the job of the natural philosopher, (i.e. scientist), was not to ask what God must have done but (to ask) what God actually did.” Presupposition 2: The intelligibility of nature “Modern science was inspired by the conviction that the universe is the product of a rational mind who designed it to be understood and who (also) designed the human mind to understand it.” (i.e. human exceptionalism), “God created us in his own image so that we could share in his own thoughts” – Johannes Kepler Presupposition 3: Human Fallibility “Humans are vulnerable to self-deception, flights of fancy, and jumping to conclusions.”, (i.e. original sin), Scientists must therefore employ “systematic experimental methods.” (Francis Bocon’s inductive methodology) – Stephen Meyer on Intelligent Design and The Return of the God Hypothesis – Hoover Institution https://www.youtube.com/watch?v=z_8PPO-cAlA
i.e. Why even bother practicing science in the first place if you truly believe, like atheists and VL apparently do, that you do not have, at least, the capacity within yourself to understand and/or ‘know’ the deep mysteries behind the universe? Apparently VL, in total disregard to simple logic, is willing to simultaneously believe that the root of reality is 'unknowable', (i.e. an insoluble mystery), and yet at the same time hold that we are 'somehow' able to discover deep truths about the nature of reality. Sorry, it simply doesn't work that way. As the old saying goes, you can't have your cake and eat it to. Contradictions in logic are fatal to arguments. Apparently VL does not care that her argument is inherently contradictory. So again, I hold that VL is not arguing in good faith. Moreover, in a rather stunning confirmation of the fact that Francis Bacon, and the other Christian founders of modern science, did not falsely 'anthropomorphize' God, when they brought forth modern science, we can appeal to recent findings in modern science to directly support the Christian’s belief that we are indeed made in the image of God. In 2014, an impressive who’s who list of leading ‘Darwinian’ experts in the area of language research, authored a paper in which they honestly admitted that,,, “(we have) essentially no explanation of how and why our linguistic computations and representations evolved.,,,”
Leading Evolutionary Scientists Admit We Have No Evolutionary Explanation of Human Language – December 19, 2014 Excerpt: Understanding the evolution of language requires evidence regarding origins and processes that led to change. In the last 40 years, there has been an explosion of research on this problem as well as a sense that considerable progress has been made. We argue instead that the richness of ideas is accompanied by a poverty of evidence, with essentially no explanation of how and why our linguistic computations and representations evolved.,,, (Marc Hauser, Charles Yang, Robert Berwick, Ian Tattersall, Michael J. Ryan, Jeffrey Watumull, Noam Chomsky and Richard C. Lewontin, “The mystery of language evolution,” Frontiers in Psychology, Vol 5:401 (May 7, 2014).) Casey Luskin added: “It’s difficult to imagine much stronger words from a more prestigious collection of experts.” http://www.evolutionnews.org/2014/12/leading_evoluti092141.html
The late best selling author Tom Wolfe was so taken aback by this honest confession from leading Darwinists that he wrote a book on the subject. Here is a general outline of his main argument;
“Speech is 95 percent plus of what lifts man above animal! Physically, man is a sad case. His teeth, including his incisors, which he calls eyeteeth, are baby-size and can barely penetrate the skin of a too-green apple. His claws can’t do anything but scratch him where he itches. His stringy-ligament body makes him a weakling compared to all the animals his size. Animals his size? In hand-to-paw, hand-to-claw, or hand-to-incisor combat, any animal his size would have him for lunch. Yet man owns or controls them all, every animal that exists, thanks to his superpower: speech.” —Tom Wolfe, in the introduction to his book, The Kingdom of Speech
In other words, that humans should master the planet due to his unique ability to understand, communicate, and create, information is completely contrary to the ‘survival of the fittest’ thinking that undergirds Darwinian thought. i.e. Although humans are fairly defenseless creatures in the wild compared to other creatures, such as lions, bears, sharks, etc.., nonetheless, humans have, completely contrary to Darwinian ‘survival of the fittest’ thinking, managed to become masters of the planet, not by brute force, but simply by our unique ability to understand, create, and communicate information and also to, more specifically, infuse immaterial information into material substrates in order to create, i.e. ‘intelligently design’, objects that are extremely useful for our defense, basic survival in procuring food, furtherance of our knowledge, and also merely for our pleasure. What is more interesting still about the fact that humans have a unique ability to understand and create information, and have come to ‘master the planet’ through the ‘top-down’ infusion of immaterial information into material substrates, is the fact that, due to advances in science, both the universe and life itself, are now found to be ‘information theoretic’ in their foundational basis.
“The most fundamental definition of reality is not matter or energy, but information–and it is the processing of information that lies at the root of all physical, biological, economic, and social phenomena.” Vlatko Vedral – Professor of Physics at the University of Oxford, and CQT (Centre for Quantum Technologies) at the National University of Singapore, and a Fellow of Wolfson College –
It is hard to imagine a more convincing scientific proof that we are ‘made in the image of God’, than finding that both the universe and life itself are ‘information theoretic’ in their foundational basis, and that we, of all the creatures on earth, uniquely possess an ability to understand and create information, and have come to ‘master the planet’, not via brute force as is presupposed in Darwinian thought, but precisely because of our ability to infuse immaterial information into material substrate
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.
Thus, despite VL's repeated false assertion that we Christians have inappropriately "anthropomorphized" God, the fact of the matter is that modern science itself has now provided Christians with fairly powerful scientific evidence that we are indeed made in the image of God. Whereas VL's false assertion that we have inappropriately "anthropomorphized" God is severely wanting for any empirical support. Scientifically speaking, her false assertion is 'naked as a Jay-bird' as the old saying goes. One final note, a more convincing proof that we are made in the image of God could be if God Himself became a man, walked on water, healed the sick, raised the dead, and then defeated death itself on a cross. And that just so happens to be precisely the evidence that is claimed within Christianity. One rather powerful piece of scientific evidence supporting the validity of Christianity is the Shroud of Turin
Shroud of Turin: From discovery of Photographic Negative, to 3D Information, to Quantum Hologram – video https://www.youtube.com/watch?v=F-TL4QOCiis The evidence for the Shroud’s authenticity keeps growing stronger. (Timeline of facts) – November 08, 2019 What Is the Shroud of Turin? Facts & History Everyone Should Know – Myra Adams and Russ Breault https://www.christianity.com/wiki/jesus-christ/what-is-the-shroud-of-turin.html John 20:3-8 So Peter and the other disciple started for the tomb. Both were running, but the other disciple outran Peter and reached the tomb first. He bent over and looked in at the strips of linen lying there but did not go in. Then Simon Peter, who was behind him, arrived and went into the tomb. He saw the strips of linen lying there, as well as the burial cloth that had been around Jesus’ head. The cloth was folded up by itself, separate from the linen. Finally the other disciple, who had reached the tomb first, also went inside. He saw and believed.
bornagain77_{February 21, 2022
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KF, you list a lot of things in many previous posts that you think that you know about the root of reality that I don't think are true, so there's quite a bit that we would/do disagree about what we know. One problem is that to even try to talk about what we don't know we have to use words which make it sound like we do know something. An example, saying that since the material world can't have been caused by something material we know the immaterial exists. This is the kind of dilemma about language that we have discussed above. As you frequently point out, duality is an immediate consequence of claiming identity, as what is is separated from what it isn't. In Taoist terms, all things exist as parts of complementary dualities, but the Tao is beyond those dualities. The Black Box is beyond the material/immaterial duality, as it is beyond all dualities. So I think that you think that logic tells you much more about the root of reality than is justified.Viola Lee_{February 21, 2022
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VL Here's the way I see it. You propose that:
we have genuine, libertarian free will mind is a feature of the universe we have rational cognitive skills that allow us to understand, though abstract modeling
All of those features come from a source you're calling a black-box, unknowable. What is the objection to the idea that logically follows: The origin and source of those features possesses free will, mind and rationality. It confers those things on us because it possesses them. One cannot give what one does not have - thus, the origin of all that, possesses all that.Silver Asiatic_{February 21, 2022
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SA, for one thing, I'm not discussing deism. You write, "Decision-making is not limited to humans." Are you referring to animals? What are you referring to.Viola Lee_{February 21, 2022
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VL
I think it would be more appropriate (with all the usual disclaimers about indescribability) to say the Black Box has effects by its manifested immanent presence that pervades the world we experience.
Decision-making is not limited to humans, and thus the term 'choice' is not anthromorphic. But in the attempt to get away from a God that is personal, conscious and free - the term "has effects" is used. This remains a problem because the "effects" have to be caused by something in the source. Free choice can be conscious and willed for a reason. "Effects that are manifested" are determined by something - if deterministic (not free) then what is determining the cause of all things? That's the paradox that deism runs into.Silver Asiatic_{February 21, 2022
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Jerry
“It seems that the notion that we don’t know everything, that any conclusions about what is known should be ignored and any absurd notion anyone has should be given equal credibility.”
This can be applied to the claim that "the root of reality is unknowable". Taken literally, "we can't know anything about the origin of the world". That aligns with what you said above. To make definitions requires knowledge. The Root of Reality, or the ground of being, or the cause of the universe - all of those are definitions.Silver Asiatic_{February 21, 2022
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VL
What we don’t know is about the world we don’t live in: whatever is before/behind/underneath the world that is beyond our experience.
We've been over this, but we know quite a lot about the origin of reality - about the "world we don't live in". Merely pointing to its existence is knowing something. So, even a total skeptic knows something. It's not completely unknowable. Referencing Dr. Fester's article on the Tao - the paradoxes Lao Tzu offers is not to say we know nothing about God, but only "in a certain sense" we know nothing, We know quite a lot. You've concluded that "it's unknowable" based on what you know. For example, if the origin of our being was a material object, that would be knowable. But, simple logic tells us, the origin of material being cannot be a material thing. That logic tells us something about the supposed "unknowable" - it cannot be a material object. So, that which is immaterial exists. Tracing back causality, contingent beings depend on something for their existence - the root of reality is the ground of that being. I could go on and on, but there's a lot we know. Even obscurantist Eastern philosophy tells us quite a lot about the ground of being. That's what it was written to do.Silver Asiatic_{February 21, 2022
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CD & Sev, we see through a glass, darkly, but then . . . KFkairosfocus_{February 21, 2022
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KF, My list at 231 is about what I believe about this world. It is not about the source of those things, which is the unknowable Black Box. Also, the things in my list are things I accept based on my experience, and by making a choice to believe them. I can't prove my mind is a separate entity, and I can't prove that I have libertarian free will, but my internal experience seems to support those beliefs, so I choose to believe them. I accept my rationality because I can test my beliefs against further experience, and thus can confirm or fail to confirm what I believe. Rationality works when applied to the objects of my experience: that's a testable claim. However, as is the subject of this thread, there are limits to what our rationality can address. That the universe is such that interesting, orderly things happens is one of those testable claims.Viola Lee_{February 21, 2022
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CD, Ram and WJM are deists. Viola is a non-Darwinian, immaterialist-atheist - a "we don't know ist" Seversky is a materialist atheist, although modern version of it. Deism and immaterialism are compatible with ID. But there are several different flavors of deism possible. Some of them are just atheism with an unknown non-material force out there. It's an improvement over materialism, but surrenders almost nothing over atheism. I think it just fills the gap for the first cause. The deist god can't be material since it is outside space and time, but if it could be it would. The gap created by materialist atheism is filled by deism, but another big gap opens up between deism and theism. Deism is a step forward in supplying an answer. But to just say "it's unknowable" or an impenetrable "black box" dismisses what we necessarily must know about the deist god. What we do know poses some logical pathways to follow. It's not like we're totally clueless. There are solid inferences one can make. Some ideas are more reasonable than others, some more supported by what we know. Human beings experience timelessness, spacelessness to some degree. Some have experienced more transcendent moments. But they remain human beings, using the same human mind to experience that. The idea that a timeless, spaceless God is completely incomprehensible doesn't follow from what people actually experience. We are not totally linear, finite thinkers. The human mind (and soul) is capable of extending to the farthest ends of the universe, to contemplate infinite entities and to create imaginary worlds.Silver Asiatic_{February 21, 2022
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VL, I see your 231, responding to my 223. I notice the shift to I believe and I accept which is very different from the declarations of un-know-ability. I suggest, a good start, though it would be interesting to see warrant, and I note that we know enough from the self referential incoherence that we do know somewhat. Not all we would like but enough for a start. KFkairosfocus_{February 21, 2022
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Have you been reading all the posts about this, or are you just joining the party?
Don’t have to since I am responding to summations which are absurd.
Absolutely no one here is making that claim
I stand on my comments. There have been hundreds of threads here where people ignore the obvious after thousands of comments.jerry_{February 21, 2022
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And Jerry, you just added this: "It seems that the notion that we don’t know everything, that any conclusions about what is known should be ignored and any absurd notion anyone has should be given equal credibility." Absolutely no one here is making that claim.Viola Lee_{February 21, 2022
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Jerry, you just added, "We know a lot. Because we don’t know everything, it doesn’t mean we have to be stupid about what we do know." I totally agree. See post 231, #3 above. We know a great deal about the world we live in. What we don't know is about the world we don't live in: whatever is before/behind/underneath the world that is beyond our experience. That's what we are discussing.Viola Lee_{February 21, 2022
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Again, you are thinking of some kind of entity that is analogous to us, using words like "reason for things" and "objectives" and "choices". I think those words are not likely to apply to the Black Box, but saying that is not to say that their negatives apply either. Have you been reading all the posts about this, or are you just joining the party?Viola Lee_{February 21, 2022
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I think it would be more appropriate (with all the usual disclaimers about indescribability) to say the Black Box has effects by its manifested immanent presence that pervades the world we experience.
Gobbledegook. Specifics happened. Why? Are you saying there is no reason for the specifics? That is an extremely incoherent belief.
I don’t think evolution is part of this discussion.
It doesn’t have to be. I’m just pointing out the absurdity of a remark. Maybe to point out the incoherence of the comment and commenter. It would have just as much relevance to the nature of reality too. We know a lot. Because we don’t know everything, it doesn’t mean we have to be stupid about what we do know. It seems that the notion that we don’t know everything, that any conclusions about what is known should be ignored and any absurd notion anyone has should be given equal credibility.jerry_{February 21, 2022
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re 235: Jerry, I don't think evolution is part of this discussion. I think Sev is referring to the ultimate nature of the root of reality (or whatever you want to call it), which has been the topic for quite a while.Viola Lee_{February 21, 2022
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I don't know whether you've been carefully following the discussion Jerry (I'm guessing not, perhaps), but "choices" is an excessively anthropomorphized word to use here, and even more to so to think the Black Box has "objectives". I think it would be more appropriate (with all the usual disclaimers about indescribability) to say the Black Box has effects by its manifested immanent presence that pervades the world we experience.Viola Lee_{February 21, 2022
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I would say the single, best (and honest) comment in this whole lengthy string.
Referenced comment should be headline in any discussion of Evolution. Especially in textbooks on biology. That would be a major breakthrough. ChuckDarwin endorses ID approach to Evolution. jerry_{February 21, 2022
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there is some underlying something (the Black Box) behind the existence and nature of both the physical universe and our minds
This Black Box also makes choices. And if it makes choices, that indicates an objective (unless this something with massive powers is just a capricious entity.) Can we ascertain some of what these objectives might be by the choices made?jerry_{February 21, 2022
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From Seversky @ 220:
What we do know is that there is still an awful lot that we don’t know.
I would say the single, best (and honest) comment in this whole lengthy string.chuckdarwin_{February 21, 2022
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Sev, I had to look up ailurophile, and now I know! So you might like this in today's comics: Speed BumpViola Lee_{February 21, 2022
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KF writes, “As a test, kindly identify a few points where you disagree with the key tenets of said naturalism as described, why, and what difference it makes.” Sure. 1. I believe mind is a feature of the universe, and that my mind is different from my physical brain. The two interact in significant ways in some unknown ways, but the interaction goes both ways. 2. I believe we have genuine, libertarian free will. 3. I believe that our minds have rational cognitive skills that allow us to understand, though abstract modeling, the world we experience. 4. I accept that this universe is such that many features work together to make a universe where interesting things happen (physics, chemistry, biology) and that there is some underlying something (the Black Box) behind the existence and nature of both the physical universe and our minds. How’s that?Viola Lee_{February 21, 2022
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If we don't know- as seversky says- then that is what needs to be taught in schools! Yet that is NOT what is being taught! So where is the outrage? Why is it OK to teach lies to unsuspecting children?ET_{February 21, 2022
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seversky:
I also believe that the theory of evolution is currently the best explanation we have for the diversity of life on Earth but that could change as we learn more.
1- There isn't any scientific theory of evolution 2- We haven't even learned what determines biological form! 3- Given starting populations of prokaryotes there isn't any naturalistic mechanism capable of producing eukaryotes seversky is either lying or just a damn foolET_{February 21, 2022
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