If imaginary numbers are needed to describe reality, then isn’t materialism dead already?

_{Denyse O'Leary

December 22, 2021

Intelligent Design, Mathematics}

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The researchers stressed, however, that their experiment only rules out theories that forgo imaginary numbers if the reigning conventions of quantum mechanics are correct. Most scientists are very confident that this is the case, but this is an important caveat nonetheless.
The result suggests that the possible ways we can describe the universe with math are actually much more constrained than we might have thought, Renou said.
Ben Turner, “Imaginary numbers could be needed to describe reality, new studies find” at Live Science (December 21, 2021)

Comments

Jerry: But mathematics is applied to a lot of contrived situations such as geometric figures which don’t exist in the real world. What about electronic circuits? Or population growth? Or quantum effects? JVL

it doesn’t make any difference
No it doesn’t. I said mathematics was a form of logic. Is logic invented? But mathematics is applied to a lot of contrived situations such as geometric figures which don’t exist in the real world. So people confuse the process with what the process is applied to. (The geometric figures approximate real entities but the actual figures are only in our imagination). Then there is really contrived situations that don’t exist such as frictionless surfaces and weightless elephants. And greater than 3 dimensional spaces. So it is a mixture of logic with processes on invented Imaginary situations that are very close to real situations. Infinite situations don’t exist, geometric figures don’t exist except in our minds. Thus, integrals and differentials don’t really exist but are extremely useful processes on imaginary objects. So yes, the distinction doesn’t make any difference. Aside: The Great Courses has all their courses on sale this week. Some very interesting courses on math are available for very low prices. My favorite
Great Thinkers, Great Theorems
https://www.thegreatcourses.com/courses/great-thinkers-great-theorems The link I have is https://www.thegreatcourses.com/ There is a link to all their sale courses jerry

So says a sideline smirker who thinks they know stuff they don’t.
Someone with a poor memory who likes to use ad hominems. jerry

Jerry: Late entry into ironic comment of year!!!! Could be a winner. So says a sideline smirker who thinks they know stuff they don't. If you did study mathematics at university level then you should be able to tell us which university and who was your advisor. I seem to remember you bailed on this before. Not very convincing is it? JVL

since you don’t actually understand the real work.
Late entry into ironic comment of year!!!! Could be a winner. jerry

Bornagain77: Says the man who very foolishly, (and self-refutingly), believes his ‘beyond belief’ brain, and all his beliefs, are the result of an endless series of unguided Darwinian accidents. Typical that you should start off by misrepresenting the actual scientific notions. I guess you have to OR you simply can't remember what the responses to your statements like this have been. OR, even worse, you just continually stick your fingers in your ears and do your best to not consider anything that speaks against your beliefs. Which is it I wonder . .. Meanwhile, you have conveniently abandoned the mathematics. Probably a good move since you don't actually understand the real work. JVL

JVL to me: "If you don’t understand the math then you don’t know what is actual evidence and what isn’t." JVL to Jerry: "Afraid of looking foolish?" Says the man who very foolishly, (and self-refutingly), believes his 'beyond belief' brain, and all his beliefs, are the result of an endless series of unguided Darwinian accidents.
It’s Really Not Rocket Science - Granville Sewell - November 16, 2015 Excerpt: In a 2005 American Spectator article, Jay Homnick wrote: "It is not enough to say that design is a more likely scenario to explain a world full of well-designed things. It strikes me as urgent to insist that you not allow your mind to surrender the absolute clarity that all complex and magnificent things were made that way. Once you allow the intellect to consider that an elaborate organism with trillions of microscopic interactive components can be an accident… you have essentially “lost your mind.” It has never required a PhD in science to understand the key issue in the debate between Darwinism and intelligent design. It is blindingly obvious to non-scientists like Jay Homnick that unintelligent forces alone cannot design hearts, eyes, ears, and brains. Darwinists dismiss the layman’s intuition that there is something terribly “unnatural” about evolution, and claim that while it may seem implausible to the uneducated, there is no scientific principle that prevents the basic, unintelligent, forces of physics alone from reorganizing the basic particles of physics into computers and science texts and jet airplanes. But there is such a principle, and the layman understands it perfectly well: unintelligent forces cannot do intelligent things.,,, - Granville Sewell is professor of mathematics at the University of Texas El Paso. He has written four books on numerical analysis,,, https://evolutionnews.org/2015/11/it_really_isnt/ “It seems to me immensely unlikely that mind is a mere by-product of matter. For if my mental processes are determined wholly by the motions of atoms in my brain I have no reason to suppose that my beliefs are true. They may be sound chemically, but that does not make them sound logically. And hence I have no reason for supposing my brain to be composed of atoms. In order to escape from this necessity of sawing away the branch on which I am sitting, so to speak, I am compelled to believe that mind is not wholly conditioned by matter.” - J.B.S. Haldane [“When I am dead,” in Possible Worlds: And Other Essays [1927], Chatto and Windus: London, 1932, reprint, p.209. (per wikipedia, With innovative use of statistics in biology, he (Haldane) was one of the founders of neo-Darwinism.)
bornagain77

Jerry: They don’t exist in the real world. Angles don’t exist. Neither do straight lines or any geometric figure such as circles, squares, or triangles. They are extremely useful for making approximations to solve real world problems. Thanks for showing your ignorance by avoiding answering the questions! Afraid of looking foolish? JVL

Bornagain77: Whatever JVL, via your stubborn refusal to even be semi-reasonable towards the evidence, or the math I'm not the one pontificating on a topic I don't actually understand!! Too funny. If you don't understand the math then you don't know what is actual evidence and what isn't. If I tried telling you that you're wrong about theology you'd tell me off quickly because you know a lot more about that than I do. But when it comes to something you actually don't grasp you're happy to tell everyone else they're wrong. JVL

I see, Jerry. You don't have a view about the question I asked because it doesn't make any difference. Viola Lee

Many people here have some type of Platonic view of math as existing immaterially in some way
Math and people are both created by a Mind(I would guess that math was created first because probably was used to create the human body ) . People discover math like a CD player "discovers" a CD that is inserted except humans would have the choice to run it part/ full / or eject it .Both are created to fit together . Lieutenant Commander Data

What is your view?
What difference does it make? The answer to that is none. Math is a form of logic. But then again logic is a discipline of math. Math is extremely useful. No one is arguing that is not true. But concepts such as shapes, and non integers don't exist in the real world. The real world is finite. You were part of the discussion earlier this year on math. jerry

Jerry writes, "Is there such a world? [An abstract world of immaterial pure mathematics] Is it just in one’s imagination? If that is what you mean?" Many people here have some type of Platonic view of math as existing immaterially in some way, independent of the physical world and of our mental understanding of it. Therefore, they believe math is discovered, not invented. When you ask "is it just in one's imagination" that seems to imply that math just exists in the minds of people, as something we have invented. What is your view? Viola Lee

It’s not irrelevant. It points out that your reasoning ability is limited.
So there is a limit in reasoning ability ? Bad news for atheists. Lieutenant Commander Data

Jerry, does infinity exist in the abstract world of immaterial pure mathematics?
Is there such a world? Is it just in one's imagination? If that is what you mean? And very, very useful.
What is the tangent of 89 degrees? Of 89.5 degrees? Of 89.7 degrees? Of 89.9 degrees? Of 89.99 degrees? Of 89.999 degrees? Of 89.9999 degrees? Of 89.99999 degrees? Of 89.999999 degrees? Of 89.9999999 degrees? Of 89. 99999999 degrees? What does that tell you about the value of the tangent of 90 degrees?
They don't exist in the real world. Angles don't exist. Neither do straight lines or any geometric figure such as circles, squares, or triangles. They are extremely useful for making approximations to solve real world problems. jerry

Whatever JVL, via your stubborn refusal to even be semi-reasonable towards the evidence, or the math, I am quite satisfied to let my comment stand as stated. bornagain77

Jerry: Are we back to arguing what mathematics is and what actually exists. For one thing, infinity does not exist in the real world. No one can point to an example of it. What is the tangent of 89 degrees? Of 89.5 degrees? Of 89.7 degrees? Of 89.9 degrees? Of 89.99 degrees? Of 89.999 degrees? Of 89.9999 degrees? Of 89.99999 degrees? Of 89.999999 degrees? Of 89.9999999 degrees? Of 89. 99999999 degrees? What does that tell you about the value of the tangent of 90 degrees? What about the tangent of 91 degrees? Of 90.5 degrees? Of 90.2 degrees? Of 90.1 degrees? Of 90.01 degrees? Of 90.001 degrees? Of 90.0001 degrees? Of 90.00001 degrees? Of 90.000001 degrees? Of 90.0000001 degrees? What does all that tell you about the tangent of 90 degrees? This is all old stuff that mathematicians had to learn how to deal with centuries ago. Can you deal with it? JVL

Jerry, does infinity exist in the abstract world of immaterial pure mathematics? Viola Lee

Bornagain77: Yet, the empirical evidence itself disagrees with JVL’s ‘non-belief’ that human brain is ‘beyond belief’ No, some people's interpretation of the empirical evidence disagrees with me. What do the laws of mathematics and physics actually say? I am very much aware of Euler and his beliefs, he was one of the greatest mathematicians of all time, no question. Please indicate which laws of mathematics or physics Euler used in support of his theology. His famous equation linking some basic constants does not imply theology. That is an interpretation not a direct implication of the mathematics. Here's some homework for you: what area of mathematics did Euler discover/create with the Konigsberg Bridge problem? If you have to look it up you are not a mathematician. You will have to look it up so . . . guess what? Here's a follow up: what famous problem in that area of mathematics is named after an Irish mathematician? You will have to do some searching to figure that out as well which, guess what, tells me your background in mathematics. I'll give you a hint: this is the guy who worked with quaternions. JVL

Are we back to arguing what mathematics is and what actually exists. For one thing, infinity does not exist in the real world. No one can point to an example of it. It’s a very useful concept but it exists only in one’s imagination. Without it much of modern technology would not exist but in reality there is no example of it. We had this discussion before. jerry

Hmm, JVL clarifies that he does not believe the human brain to be 'beyond belief'. Yet, the empirical evidence itself disagrees with JVL's 'non-belief' that human brain is 'beyond belief'
The Human Brain Is 'Beyond Belief' by Jeffrey P. Tomkins, Ph.D. * - 2017 Excerpt: The human brain,, is an engineering marvel that evokes comments from researchers like “beyond anything they’d imagined, almost to the point of being beyond belief”1 and “a world we had never imagined.”2,,, Perfect Optimization The scientists found that at multiple hierarchical levels in the whole brain, nerve cell clusters (ganglion), and even at the individual cell level, the positioning of neural units achieved a goal that human engineers strive for but find difficult to achieve—the perfect minimizing of connection costs among all the system’s components.,,, Vast Computational Power Researchers discovered that a single synapse is like a computer’s microprocessor containing both memory-storage and information-processing features.,,, Just one synapse alone can contain about 1,000 molecular-scale microprocessor units acting in a quantum computing environment. An average healthy human brain contains some 200 billion nerve cells connected to one another through hundreds of trillions of synapses. To put this in perspective, one of the researchers revealed that the study’s results showed a single human brain has more information processing units than all the computers, routers, and Internet connections on Earth.1,,, Phenomenal Processing Speed the processing speed of the brain had been greatly underrated. In a new research study, scientists found the brain is 10 times more active than previously believed.6,7,,, The large number of dendritic spikes also means the brain has more than 100 times the computational capabilities than was previously believed.,,, Petabyte-Level Memory Capacity Our new measurements of the brain’s memory capacity increase conservative estimates by a factor of 10 to at least a petabyte, in the same ballpark as the World Wide Web.9,,, Optimal Energy Efficiency Stanford scientist who is helping develop computer brains for robots calculated that a computer processor functioning with the computational capacity of the human brain would require at least 10 megawatts to operate properly. This is comparable to the output of a small hydroelectric power plant. As amazing as it may seem, the human brain requires only about 10 watts to function.11 ,,, Multidimensional Processing It is as if the brain reacts to a stimulus by building then razing a tower of multi-dimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D), and then more complex geometries with 4D, 5D, etc. The progression of activity through the brain resembles a multi-dimensional sandcastle that materializes out of the sand and then disintegrates.13 He also said: We found a world that we had never imagined. There are tens of millions of these objects even in a small speck of the brain, up through seven dimensions. In some networks, we even found structures with up to eleven dimensions.13,,, Biophoton Brain Communication Neurons contain many light-sensitive molecules such as porphyrin rings, flavinic, pyridinic rings, lipid chromophores, and aromatic amino acids. Even the mitochondria machines that produce energy inside cells contain several different light-responsive molecules called chromophores. This research suggests that light channeled by filamentous cellular structures called microtubules plays an important role in helping to coordinate activities in different regions of the brain.,,, https://www.icr.org/article/10186
JVL also clarified that he did not think he was smarter than all ID advocates in math and science, just smarter than me. Well OK then, I never claimed to be particularly gifted in science or math. I just claim to be a Christian, i.e. a 'child' of the one who created, besides the universe, all of math and therefore all of 'science'.
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
Moreover, I don't really blame JVL for ignoring anything I might personally say, but why does he ignore all the 'smarter in math' ID advocates that I cite. Like, for instance, Robert Marks and company?
Top Ten Questions and Objections to ‘Introduction to Evolutionary Informatics’ – Robert J. Marks II – June 12, 2017 Excerpt: “There exists no model successfully describing undirected Darwinian evolution. Hard sciences are built on foundations of mathematics or definitive simulations. Examples include electromagnetics, Newtonian mechanics, geophysics, relativity, thermodynamics, quantum mechanics, optics, and many areas in biology. Those hoping to establish Darwinian evolution as a hard science with a model have either failed or inadvertently cheated. These models contain guidance mechanisms to land the airplane squarely on the target runway despite stochastic wind gusts. Not only can the guiding assistance be specifically identified in each proposed evolution model, its contribution to the success can be measured, in bits, as active information.,,,”,,, “there exists no model successfully describing undirected Darwinian evolution. According to our current understanding, there never will be.,,,” https://evolutionnews.org/2017/06/top-ten-questions-and-objections-to-introduction-to-evolutionary-informatics/
I also wonder if JVL also thinks he is smarter In math than Leonhard Euler was?
(Leonhard) Euler is held to be one of the greatest mathematicians in history and the greatest of the 18th century. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all."[4][5] Carl Friedrich Gauss remarked: "The study of Euler's works will remain the best school for the different fields of mathematics, and nothing else can replace it."[6] https://en.wikipedia.org/wiki/Leonhard_Euler
And here is what Leonhard Euler had to say about atheists in his day:
A Defense of the (Divine) revelation against the objections of freethinkers (atheists), by Mr. (Leonhard) Euler Excerpt: "The freethinkers (atheists) have yet to produce any objections that have not long been refuted most thoroughly. But since they are not motivated by the love of truth, and since they have an entirely different point of view, we should not be surprised that the best refutations count for nothing and that the weakest and most ridiculous reasoning, which has so often been shown to be baseless, is continuously repeated. If these people maintained the slightest rigor, the slightest taste for the truth, it would be quite easy to steer them away from their errors; but their tendency towards stubbornness makes this completely impossible." http://www.math.dartmouth.edu/~euler/docs/translations/E092trans.pdf
As JVL own actions on this thread make clear, "their (atheists) tendency towards stubbornness makes this (i.e. steering them away from their errors) completely impossible" is just as true today as it was when Euler first wrote those words more than two centuries ago. Of supplemental note:
God by the Numbers - Connecting the constants Excerpt: The final number comes from theoretical mathematics. It is Euler's (pronounced "Oiler's") number: e^pi*i. This number is equal to -1, so when the formula is written e^pi*i+1 = 0, it connects the five most important constants in mathematics (e, pi, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation). These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by pi; and analysis, by e, the base of the natural log. e^pi*i+1 = 0 has been called "the most famous of all formulas," because, as one textbook says, "It appeals equally to the mystic, the scientist, the philosopher, and the mathematician.",,, The discovery of this number gave mathematicians the same sense of delight and wonder that would come from the discovery that three broken pieces of pottery, each made in different countries, could be fitted together to make a perfect sphere. It seemed to argue that there was a plan where no plan should be.,,, Today, numbers from astronomy, biology, and theoretical mathematics point to a rational mind behind the universe.,,, The apostle John prepared the way for this conclusion when he used the word for logic, reason, and rationality—logos—to describe Christ at the beginning of his Gospel: "In the beginning was the logos, and the logos was with God, and the logos was God." When we think logically, which is the goal of mathematics, we are led to think of God. http://www.christianitytoday.com/ct/2006/march/26.44.html?start=3
bornagain77

As I recall ET thinks that there are fewer even integers than there are integers as a whole. I believe that disqualifies him from making judgments about who does and doesn't understand math. And JVL is right: math is math no matter what one's metaphysical beliefs are about where it comes from, how we as creatures came to be able to understand it, and why it fits the world so well in many circumstances. Those are additional points that go beyond the math itself: the devout theist and the confirmed materialistic atheist use exactly the same math. Viola Lee

Bornagain77: In this thread JVL has repeatedly claimed to be much wiser in science and math than Intelligent Design advocates are, yet he holds, (against what mathematics and empirical evidence indicate I might add), that his ‘beyond belief’ brain is the result of the unguided materialistic processes of Darwinian evolution. I don't think it is beyond belief. You do. That's your view projected onto me and my views. And I didn't say I was wiser than all ID advocates. But I think I do understand mathematics better than you do. And I think that is obvious. The way you attempt to argue about mathematics and physics indicates to me that you don't practice either of those two disciplines; you observe them and pick out bits and pieces you think support your views. It doesn't work that way. Mathematics and physics are true not based on any philosophy, they can be proved (in the case of mathematics) or strongly demonstrated (in the case of physics) independent of any particular belief system. Instead of starting with a preconceived notion of reality you should start with what is clearly true: the mathematics and the established physics. If you begin there where do you get? You can quote mine all you like but you cannot disprove the mathematics or overthrow the core principles of physics. And if you start with those core principles what do you get? I think you don't get theology. You would disagree. But let's start our discussion accepting that which is known to be true. The core principles of physics do not imply a designer; that's your interpretation of the situation. But you cannot show how any of the basic physics law force design. Stick with the known stuff. JVL

ET: Nice projection. You don’t even understand infinity. And you can’t even formulate a coherent argument. Too funny. You think that you understand infinity better than decades, generations of mathematicians that have spent years thinking about it, arguing with their peers about it, working out the details. You got it right and all those people got it wrong. Even Kairosfocus disagrees with you. And I'm certain Dr Dembski does as well. And it is irrelevant that some people understand mathematics better than I do. It's not irrelevant. It points out that your reasoning ability is limited. You can't get your head around advanced mathematics. Millions of people can but you can't. What does that say about you? The point is that materialism cannot account for mathematics. And it has to because mathematics exists. If materialism cannot account for what exists then it is useless- or less than useless. But you are too stupid to even grasp that simple point. Materialism is a view separate from mathematics. That is clear. I don't give a toss if materialism or theology can explain mathematics. It doesn't matter to mathematics. The math is what it is. AND it's constant for those of faith and those without. It's true beyond and regardless of any kind of philosophy. Start with the mathematics and see what that tells you about reality. That's the place to start. With something unarguably true. JVL

In this thread JVL has repeatedly claimed to be much wiser in science and math than Intelligent Design advocates are, yet he holds, (against what mathematics and empirical evidence indicate I might add), that his 'beyond belief' brain is the result of the unguided materialistic processes of Darwinian evolution.
The Half-Truths of Materialist Evolution - DONALD DeMARCO - 02/06/2015 Excerpt: but I would like to direct attention to the unsupportable notion that the human brain, to focus on a single phenomenon, could possibly have evolved by sheer chance. One of the great stumbling blocks for Darwin and other chance evolutionists is explaining how a multitude of factors simultaneously coalesce to form a unified, functioning system. The human brain could not have evolved as a result of the addition of one factor at a time. Its unity and phantasmagorical complexity defies any explanation that relies on pure chance. It would be an underestimation of the first magnitude to say that today’s neurophysiologists know more about the structure and workings of the brain than did Darwin and his associates. Scientists in the field of brain research now inform us that a single human brain contains more molecular-scale switches than all the computers, routers and Internet connections on the entire planet! According to Stephen Smith, a professor of molecular and cellular physiology at the Stanford University School of Medicine, the brain’s complexity is staggering, beyond anything his team of researchers had ever imagined, almost to the point of being beyond belief. In the cerebral cortex alone, each neuron has between 1,000 to 10,000 synapses that result, roughly, in a total of 125 trillion synapses, which is about how many stars fill 1,500 Milky Way galaxies! A single synapse may contain 1,000 molecular-scale switches. A synapse, simply stated, is the place where a nerve impulse passes from one nerve cell to another. Phantasmagorical as this level of unified complexity is, it places us merely at the doorway of the brain’s even deeper mind-boggling organization. Glial cells in the brain assist in neuron speed. These cells outnumber neurons 10 times over, with 860 billion cells. All of this activity is monitored by microglia cells that not only clean up damaged cells but also prune dendrites, forming part of the learning process. The cortex alone contains 100,000 miles of myelin-covered, insulated nerve fibers. The process of mapping the brain would indeed be time-consuming. It would entail identifying every synaptic neuron. If it took a mere second to identify each neuron, it would require four billion years to complete the project. http://www.ncregister.com/daily-news/the-half-truths-of-materialist-evolution/
To illustrate just how grossly inadequate Darwinian processes are in explaining the brain, (or anything else in biology for that matter), I refer to 'quantum criticality' in biological molecules.,,, “finding even one (biomolecule) that is in the quantum critical state by accident is mind-bogglingly small and, to all intents and purposes, impossible.,, of the order of 10^-50 of possible small biomolecules and even less for proteins,”,,,
Quantum criticality in a wide range of important biomolecules – Mar. 6, 2015 Excerpt: “Most of the molecules taking part actively in biochemical processes are tuned exactly to the transition point and are critical conductors,” they say. That’s a discovery that is as important as it is unexpected. “These findings suggest an entirely new and universal mechanism of conductance in biology very different from the one used in electrical circuits.” The permutations of possible energy levels of biomolecules is huge so the possibility of finding even one (biomolecule) that is in the quantum critical state by accident is mind-bogglingly small and, to all intents and purposes, impossible.,, of the order of 10^-50 of possible small biomolecules and even less for proteins,”,,, “what exactly is the advantage that criticality confers?” https://medium.com/the-physics-arxiv-blog/the-origin-of-life-and-the-hidden-role-of-quantum-criticality-ca4707924552
To drive this point home, this follow up 2018 article stated that “There is no obvious evolutionary reason why a protein should evolve toward a quantum-critical state, and there is no chance at all that the state could occur randomly.,,,”
Quantum Critical Proteins – Stuart Lindsay – Professor of Physics and Chemistry at Arizona State University – 2018 Excerpt: The difficulty with this proposal lies in its improbability. Only an infinitesimal density of random states exists near the critical point.,, Gábor Vattay et al. recently examined a number of proteins and conducting and insulating polymers.14 The distribution for the insulators and conductors were as expected, but the functional proteins all fell on the quantum-critical distribution. Such a result cannot be a consequence of chance.,,, WHAT OF quantum criticality? Vattay et al. carried out electronic structure calculations for the very large protein used in our work. They found that the distribution of energy-level spacings fell on exactly the quantum-critical distribution, implying that this protein is also quantum critical. There is no obvious evolutionary reason why a protein should evolve toward a quantum-critical state, and there is no chance at all that the state could occur randomly.,,, http://inference-review.com/article/quantum-critical-proteins Gábor Vattay et al., “Quantum Criticality at the Origin of Life,” Journal of Physics: Conference Series 626 (2015); Gábor Vattay, Stuart Kauffman, and Samuli Niiranen, “Quantum Biology on the Edge of Quantum Chaos,” PLOS One 9, no. 3 (2014)
Moreover, the irony in JVL claiming, on the one hand, that he so much smarter in science and math than ID advocates are, and yet, on the other hand, claiming that his own 'beyond belief' brain is the result of an endless series of serendipitous Darwinian accidents, is that it pretty much undermines any claim that he is making for his own superior intelligence, in that it undermines any claim that his own reasoning can be reliable, much less that his reasoning can possibly be true.
“For example, if you knew your computer was the result of a mindless unguided process, you wouldn’t use it or trust it for a moment!” - John Lennox “If Dawkins is right that we are the product of mindless unguided natural processes, then he has given us strong reason to doubt the reliability of human cognitive faculties and therefore inevitably to doubt the validity of any belief that they produce—including Dawkins’s own atheism.” - Plantinga https://melwild.wordpress.com/2017/11/02/what-atheism-cannot-explain/ Why Evolutionary Theory Cannot Survive Itself - Nancy Pearcey - March 8, 2015 Excerpt: An example of self-referential absurdity is a theory called evolutionary epistemology, a naturalistic approach that applies evolution to the process of knowing. The theory proposes that the human mind is a product of natural selection. The implication is that the ideas in our minds were selected for their survival value, not for their truth-value. But what if we apply that theory to itself? Then it, too, was selected for survival, not truth — which discredits its own claim to truth. Evolutionary epistemology commits suicide. Astonishingly, many prominent thinkers have embraced the theory without detecting the logical contradiction. Philosopher John Gray writes, “If Darwin’s theory of natural selection is true,… the human mind serves evolutionary success, not truth.” What is the contradiction in that statement? Gray has essentially said, if Darwin’s theory is true, then it “serves evolutionary success, not truth.” In other words, if Darwin’s theory is true, then it is not true. Self-referential absurdity is akin to the well-known liar’s paradox: “This statement is a lie.” If the statement is true, then (as it says) it is not true, but a lie. Another example comes from Francis Crick. In The Astonishing Hypothesis, he writes, “Our highly developed brains, after all, were not evolved under the pressure of discovering scientific truths but only to enable us to be clever enough to survive.” But that means Crick’s own theory is not a “scientific truth.” Applied to itself, the theory commits suicide. Of course, the sheer pressure to survive is likely to produce some correct ideas. A zebra that thinks lions are friendly will not live long. But false ideas may be useful for survival. Evolutionists admit as much: Eric Baum says, “Sometimes you are more likely to survive and propagate if you believe a falsehood than if you believe the truth.” Steven Pinker writes, “Our brains were shaped for fitness, not for truth. Sometimes the truth is adaptive, but sometimes it is not.” The upshot is that survival is no guarantee of truth. If survival is the only standard, we can never know which ideas are true and which are adaptive but false. To make the dilemma even more puzzling, evolutionists tell us that natural selection has produced all sorts of false concepts in the human mind. Many evolutionary materialists maintain that free will is an illusion, consciousness is an illusion, even our sense of self is an illusion — and that all these false ideas were selected for their survival value. So how can we know whether the theory of evolution itself is one of those false ideas? The theory undercuts itself. A few thinkers, to their credit, recognize the problem. Literary critic Leon Wieseltier writes, “If reason is a product of natural selection, then how much confidence can we have in a rational argument for natural selection? … Evolutionary biology cannot invoke the power of reason even as it destroys it.” On a similar note, philosopher Thomas Nagel asks, “Is the [evolutionary] hypothesis really compatible with the continued confidence in reason as a source of knowledge?” His answer is no: “I have to be able to believe … that I follow the rules of logic because they are correct — not merely because I am biologically programmed to do so.” Hence, “insofar as the evolutionary hypothesis itself depends on reason, it would be self-undermining.” https://evolutionnews.org/2015/03/why_evolutionar/
Verse:
Romans 1:22-23 Claiming to be wise, they became fools, and exchanged the glory of the immortal God for images resembling mortal man and birds and animals and creeping things.
bornagain77

JVL:
You betray your mathematical ignorance all the time.
Nice projection. You don't even understand infinity. And you can't even formulate a coherent argument. Your ignorance of science is legendary. And it is irrelevant that some people understand mathematics better than I do. The point is that materialism cannot account for mathematics. And it has to because mathematics exists. If materialism cannot account for what exists then it is useless- or less than useless. But you are too stupid to even grasp that simple point. ET

ET: Can YOU? You NEVER support what you spew. Hypocrite. You betray your mathematical ignorance all the time. Your education and experience are greater than some but no where near what someone with a bachelor's degree has let alone a masters or Doctorate. Instead of being rude and insulting you should just acknowledge your inexperience. A few classes is only the beginning, the first few steps. And there's millions of people ahead of you on the path. To deny that is to blind yourself to the truth. Accept the truth. Or stay lost. It's your call. JVL

JVL:
People who don’t understand or use mathematics should not make up stuff about mathematics. Or, more charitably: can you prove that?
Can YOU? You NEVER support what you spew. Hypocrite.
No, because you cannot demonstrate or prove that it does.
Materialism cannot account for mathematics
No, it does not.
Of course it does. See, you don't know anything about science. Yes, I have worked on all of that during my school years. I never needed any of it in my professional life. But YOU are totally ignorant of science. You can't even think beyond your own arse. ET

Bornagain77: thus stressing the quantum-mechanical assertion that reality does not exist when we’re not observing it That's it? That's your entire rebuttal? Too funny. And typical of people who don't understand quantum mechanics: you think 'observed' implies consciousness. It doesn't. Observation means any kind of measurement or recording. It's obvious since human beings do not have the physical ability to 'observe' quantum effects without the aid of machines. It's the machines that are doing the observing. What the paper means is that when we 'observe' some situation or effect the way we observe it dictates what we can and can not 'see'. And, you choose NOT to quote the last paragraph:
However, Alain Aspect, a physicist who performed the first Bell-type experiment in the 1980s, thinks the team’s philosophical conclusions are subjective. “There are other types of non-local models that are not addressed by either Leggett’s inequalities or the experiment,” he said. “But I rather share the view that such debates, and accompanying experiments such as those by [the Austrian team], allow us to look deeper into the mysteries of quantum mechanics.”
Stop quote mining. You are going to get caught out over and over again. It just makes you look foolish and manipulative. Faulkner wasn’t remotely claiming for “all of physics and mathematics”, he was claiming for quantum mechanics in particular. Gee, I think I said the same thing. Of course this is going nowhere since you don't actually understand the math or physics involved. How can it go anywhere given that truth? JVL

For crying out loud JVL, you aren't too smart are you ole boy? Try reading for context, Faulkner wasn't remotely claiming for "all of physics and mathematics", he was claiming for quantum mechanics in particular. Moreover, the article in the OP makes the same exact point that "I" is reducible to real numbers in some situations in quantum mechanics, and is not reducible in other instances in quantum mechanics. (That was the MAIN point of the experiment for crying out loud) Oh well, due to your obstinacy, I can see this is going absolutely no where. So I am quite satisfied to let what I have stated in this thread thus far stand as it is. I'll let 'big, and wrong, headed' you have the last word, bornagain77

"Math and science are not spectator sports." Yet, according to the 'science and math' of quantum mechanics, and via the falsification of 'realism' (Leggett's Inequality), reality itself is found to be very much a 'spectator' sport, i.e. " Leggett’s inequality is violated – thus stressing the quantum-mechanical assertion that reality does not exist when we’re not observing it."
Quantum physics says goodbye to reality - 20 Apr 2007 Excerpt: They found that, just as in the realizations of Bell’s thought experiment, Leggett’s inequality is violated – thus stressing the quantum-mechanical assertion that reality does not exist when we’re not observing it. “Our study shows that ‘just’ giving up the concept of locality would not be enough to obtain a more complete description of quantum mechanics,” Aspelmeyer told Physics Web. “You would also have to give up certain intuitive features of realism.” https://physicsworld.com/a/quantum-physics-says-goodbye-to-reality/
bornagain77

Bornagain77: Well, actually the mathematics of quantum mechanics destroys a purely ‘deterministic’ and/or materialistic view of reality, (funny, you, being the self professed mathematical savant that you are, should have known that) And then you quote: The trouble is that in quantum mechanics the way that wave functions change with time is governed by an equation, the Schrödinger equation, that does not involve probabilities. It is just as deterministic as Newton’s equations of motion and gravitation. That is, given the wave function at any moment, the Schrödinger equation will tell you precisely what the wave function will be at any future time. There is not even the possibility of chaos, the extreme sensitivity to initial conditions that is possible in Newtonian mechanics. Well funny that you tried to sneak your atheistic materialism in with all those other various ‘non-materialistic’ worldviews. So again, and to repeat, “mathematics is profoundly immaterial and cannot possibly be reduced to materialistic explanation.” You completely ignore the fact that no one, of any faith or non-faith disagrees with any one else of faith or non-faith about mathematical results. Mathematics is independent of faith or non-faith. Tell me JVL, is the number “2” closer to Texas or to Nebraska? How much does Godel’s incompleteness theorem weigh? Is the Pythagorean theorem faster or slower than the speed of light? Non-sensical questions do not require serious consideration. LOL, says the atheists troll who refuses to concede the exceedingly simple point that Darwinian materialism cannot possibly account for our ability to ‘do mathematics’ in the first place. You think no one will notice or care that I already separated mathematical truths from the ability to do mathematics. But since you think you have made some great philosophical statement you have to keep repeating it. Since JVL is apparently wanting me to just take his word that Steve Faulkner is ‘so incredibly wrong’, it is obvious that JVL, (an atheistic troll on UD), is far, far, more impressed with his supposed mathematical prowess than I am. Well, I am really sorry that you are ignorant of the multitude of other uses for complex numbers. That's not my fault or problem. That's your wilful ignorance of mathematics and physics. When you don't actually understand the science and you quote mine for support for your views then you're going to get caught out like you've done. Because you're too lazy or disingenuous to look things up: https://en.wikipedia.org/wiki/Complex_number#In_applied_mathematics It's not really clear that Dr Faulkner thinks that the only place in all of physics and mathematics you need imaginary numbers is in the case you cite. I suspect he is discussing things in a limited situation and I bet he made that clear in the work you quote. But, of course, you would leave that out. It's dead easy to find lots and lots of applications of complex numbers in real-world situations. You just haven't bothered to look because doing so would go against your quote-mined support. That's not how science and mathematics is done. You clearly are not a scientist or a mathematician. You should stop pretending that you understand it as well as actual mathematicians and scientists. Stick to what you actually know and have done instead of thinking you can graze through serious research and pull out a phrase here or there which you think supports your view. Not only is that rude and insulting but it shows your own ignorance. JVL

ET: No, they only started to write about them when they wanted to work on a particular kind of problem. Too funny. People who don't understand or use mathematics should not make up stuff about mathematics. Or, more charitably: can you prove that? We have not invented anything. Ever. Oh good. So different sizes of infinity like aleph-nought have always existed. And Cantor figure it out. Great. Cuz you say so? Really? No, because you cannot demonstrate or prove that it does. It has to be able to account for everything that exists. No, it does not. You are nothing but a poseur. You have proven that you don’t understand science. You have proven that you are not capable of following a discussion. And you are big on spewing false accusations. Too funny. Have you done Fourier analysis? Have you stepped through a proof of the prime number theorem? Off the top of your head can you explain what a Hamiltonian circuit is and what branch of mathematics it belongs to? Is that a discrete or continuous topic? How is a donut different from a vest in terms of topology? What is the area of the Sierpinsky gasket? What is the sum of 1 + 1/3 + 1/9 + 1/27 + . . . Explain what NP-complete means. If you take the function 1/x from x = 1 out to infinity and rotate it about the x-axis what are the volume and surface area of the resulting object? That's just a few undergraduate topics. In mathematics. Would you like to also consider some things in physics and chemistry and biology? For instance: what is the volume of a mole of hydrogen? Give an example of an adiabatic process. What physical measurements are part of Boyle's Law? Entropy is 'opposed' to what other 'value'? You don't work with any of those or thousands of other concepts and topics in science and mathematics. You don't write about them. You don't study them. You don't teach them. Math and science are not spectator sports. Until you've done the time actually playing the game you should just shut up. JVL

"Mathematics has nothing to do with materialism"
Exactly right! Mathematics is profoundly immaterial and cannot possibly be reduced to materialistic explanation.
"You can have a deterministic view or a theological view and still have the same mathematics. It’s independent of both of those world views. "
Well, actually the mathematics of quantum mechanics destroys a purely 'deterministic' and/or materialistic view of reality, (funny, you, being the self professed mathematical savant that you are, should have known that)
Maverick branches, a proof that Everett's (Many Worlds) theory is totally wrong - December 02, 2015 Excerpt: To make any predictions, one must pick a basis and use the Born rule to compute the probabilities of each possible outcome. The basis of "possible outcomes" must be actively chosen by an observer. There can't exist any "canonical" or "objective" way to pick the right basis for the Hilbert space. If the people were thinking about actual physical problems and not some idealized propagandist clichés that are designed to make the MWI paradigm look viable, even though it is not, they would know that what they claim to be possible clearly isn't possible. http://motls.blogspot.com/2015/12/maverick-branches-proof-that-everetts.html?m=1
As the late Steven Weinberg, an atheist, explained,
The Trouble with Quantum Mechanics - Steven Weinberg - January 19, 2017 Excerpt: The trouble is that in quantum mechanics the way that wave functions change with time is governed by an equation, the Schrödinger equation, that does not involve probabilities. It is just as deterministic as Newton’s equations of motion and gravitation. That is, given the wave function at any moment, the Schrödinger equation will tell you precisely what the wave function will be at any future time. There is not even the possibility of chaos, the extreme sensitivity to initial conditions that is possible in Newtonian mechanics. So if we regard the whole process of measurement as being governed by the equations of quantum mechanics, and these equations are perfectly deterministic, how do probabilities get into quantum mechanics?... Today there are two widely followed approaches to quantum mechanics, the “realist” and “instrumentalist” approaches,9 which view the origin of probability in measurement in two very different ways. For reasons I will explain, neither approach seems to me quite satisfactory.10,,,, 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,,,, ,,, 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,,, In the realist approach the history of the world is endlessly splitting; it does so every time a macroscopic body becomes tied in with a choice of quantum states. This inconceivably huge variety of histories has provided material for science fiction. 12 http://quantum.phys.unm.edu/466-17/QuantumMechanicsWeinberg.pdf
JVL then states:
"Christians and Buddhists and Janes and Hindus and Muslims and Zoroastrians and atheists all agree on the same mathematics."
Well funny that you tried to sneak your atheistic materialism in with all those other various 'non-materialistic' worldviews. So again, and to repeat, "mathematics is profoundly immaterial and cannot possibly be reduced to materialistic explanation." Tell me JVL, is the number "2" closer to Texas or to Nebraska? How much does Godel's incompleteness theorem weigh? Is the Pythagorean theorem faster or slower than the speed of light?
"Stop trying to bend everything to your view."
LOL, says the atheistic troll who refuses to concede the exceedingly simple point that Darwinian materialism cannot possibly account for our ability to do 'immaterial' mathematics in the first place. In response to this quote from Steve Faulkner, “the only place where i (the square root of negative one) is needed is in the wave packet prior to measurement.”
Why do you need imaginary numbers (the square root of negative one) to describe Quantum Mechanics? “Quantum theory needs existence of an x such that x^2= -1. The reason for this is that orthogonal function spaces, of dimension greater than 2, cannot exist otherwise. In fact the only place where i (the square root of negative one) is needed is in the wave packet prior to measurement. Even the Canonical Commutation Relation doesn’t need it. And nor do the eigenvalue equations. In those, any general scalar will do. But in the wave packet, you need an i.” – Steve Faulkner – Philosophy of Science, Logic, Epistemology https://www.researchgate.net/post/Why_do_you_need_imaginary_numbers_to_describe_Quantum_Mechanics2
in response to that quote, JVL, (without citation), responds thusly,
"That is just so incredibly wrong that it’s really, really clear you are just quote mining for things that support your pre-held view. You really do not understand mathematics. So stop pretending you do."
Since JVL is apparently, without citation, wanting me to just take his supposedly unquestionable word that Steve Faulkner is 'so incredibly wrong', it is obvious that JVL, (who I remind is an atheistic troll on UD), is far, far, more impressed with his own supposed mathematical prowess than I am. Oh well, if it is all the same with you JVL, I think I will, (since Faulkner has written several papers, and a technical book, on the subject of quantum mechanics, and you are, well, you are an dogmatic atheistic troll on a blog), take Steve Faulkner's word over yours, :)
The Underlying Machinery of Quantum Indeterminacy The Answer to a Century of Questions — A book by Steve Faulkner Excerpt: What this book does The book is a rigorous dissection of Quantum Mathematics, from the standpoint of Mathematical Logic,,, https://quantum-indeterminacy.science https://www.researchgate.net/profile/Steve-Faulkner-4
bornagain77

JVL:
But they only bothered to look for them when they wanted to work on a particular kind of problem.
No, they only started to write about them when they wanted to work on a particular kind of problem.
I guess you think surreal numbers have always existed. And hyper-real numbers. And different sizes of infinity.
We have not invented anything. Ever.
Mathematics has nothing to do with materialism.
Cuz you say so? Really?
Materialism doesn’t have to account for mathematics.
It has to be able to account for everything that exists.
You talk a lot about things you yourself cannot manage.
Nice projection.
Math is not a spectator sport so stop pretending you know anything about it.
You are nothing but a poseur. You have proven that you don't understand science. You have proven that you are not capable of following a discussion. And you are big on spewing false accusations. ET

Bornagain77: but the fact of the matter is that mathematics, (particularly our ability to do mathematics and apply our mathematical understanding to the universe in the first place), has a tremendous amount to say about whether the materialistic worldview of Darwinian Atheism is true or whether the worldview of Intelligent Design is true.” Mathematics has nothing to do with materialism. You can have a deterministic view or a theological view and still have the same mathematics. It's independent of both of those world views. Christians and Buddhists and Janes and Hindus and Muslims and Zoroastrians and atheists all agree on the same mathematics. Stop trying to bend everything to your view. Specifically, “the only place where i (the square root of negative one) is needed is in the wave packet prior to measurement.” That is just so incredibly wrong that it's really, really clear you are just quote mining for things that support your pre-held view. You really do not understand mathematics. So stop pretending you do. JVL

ET: That is false. Imaginary numbers always existed. Mathematicians discovered them. Perhaps. But they only bothered to look for them when they wanted to work on a particular kind of problem. I guess you think surreal numbers have always existed. And hyper-real numbers. And different sizes of infinity. Mathematics destroys materialism. Materialism cannot account for the existence of mathematics. Heck, materialism cannot account for any existence. Uh huh. Mathematics has nothing to do with materialism. Materialism doesn't have to account for mathematics. Mathematics doesn't trump or explain materialism. You talk a lot about things you yourself cannot manage. Math is not a spectator sport so stop pretending you know anything about it. JVL

JVL:
Mathematicians came up with ‘imaginary’ numbers in order to solve certain kinds of problems.
That is false. Imaginary numbers always existed. Mathematicians discovered them.
Oh and by the way, some animals have been shown to have rudimentary arithmetic skills.
That is how they were intelligently designed. Mathematics destroys materialism. Materialism cannot account for the existence of mathematics. Heck, materialism cannot account for any existence. ET

It seems that the objectors here on this thread are basically arguing that there is nothing that is particularly 'weird' with the fact that 'imaginary' complex numbers are now experimentally demonstrated to be irreducible to real numbers in quantum mechanics. Yet, I hold the objectors to be wrong in arguing that there is “Nothing to see here. Please disperse.”,,,
“Nothing to see here. Please disperse” https://tenor.com/view/leslie-nielsen-nothing-to-see-here-disperse-crowd-disperse-disaster-gif-12767181
There is something profoundly 'weird' in our use of 'imaginary' complex numbers is quantum mechanics. Specifically, "the only place where i (the square root of negative one) is needed is in the wave packet prior to measurement."
Why do you need imaginary numbers (the square root of negative one) to describe Quantum Mechanics? “Quantum theory needs existence of an x such that x^2= -1. The reason for this is that orthogonal function spaces, of dimension greater than 2, cannot exist otherwise. In fact the only place where i (the square root of negative one) is needed is in the wave packet prior to measurement. Even the Canonical Commutation Relation doesn't need it. And nor do the eigenvalue equations. In those, any general scalar will do. But in the wave packet, you need an i.” - Steve Faulkner - Philosophy of Science, Logic, Epistemology https://www.researchgate.net/post/Why_do_you_need_imaginary_numbers_to_describe_Quantum_Mechanics2
And 'measurement' happens to be precisely where everything that is truly 'weird' about quantum mechanics happens. For instance, as the following article states, “It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,”
New Mind-blowing Experiment Confirms That Reality Doesn’t Exist If You Are Not Looking at It - June 3, 2015 Excerpt: Some particles, such as photons or electrons, can behave both as particles and as waves. Here comes a question of what exactly makes a photon or an electron act either as a particle or a wave. This is what Wheeler’s experiment asks: at what point does an object ‘decide’? The results of the Australian scientists’ experiment, which were published in the journal Nature Physics, show that this choice is determined by the way the object is measured, which is in accordance with what quantum theory predicts. “It proves that measurement is everything. At the quantum level, reality does not exist if you are not looking at it,” said lead researcher Dr. Andrew Truscott in a press release.,,, “The atoms did not travel from A to B. It was only when they were measured at the end of the journey that their wave-like or particle-like behavior was brought into existence,” he said. Thus, this experiment adds to the validity of the quantum theory and provides new evidence to the idea that reality doesn’t exist without an observer. http://themindunleashed.org/2015/06/new-mind-blowing-experiment-confirms-that-reality-doesnt-exist-if-you-are-not-looking-at-it.html
Thus, although the objectors on this thread may complacently try to claim that there is nothing particularly 'weird' about our use of 'imaginary' complex numbers in quantum mechanics, i.e. “Nothing to see here. Please disperse.”,,,
“Nothing to see here. Please disperse” https://tenor.com/view/leslie-nielsen-nothing-to-see-here-disperse-crowd-disperse-disaster-gif-12767181
,,, contrary to that misplaced complacency on the part of objectors on this thread, I find the fact that "the only place where i (the square root of negative one) is needed is in the wave packet prior to measurement", and that, "measurement is everything. At the quantum level, reality does not exist if you are not looking at it” to be an extraordinarily 'weird' thing to behold. bornagain77

Viola Lee:
And, following from that, therefore learning new things about the role of complex numbers doesn’t change anything.
Right, because materialism is a non-starter. ET

JVL: "I implied the MATHEMATICS has nothing to do with any worldview." Yes indeed, you directly implied that, “it (mathematics) has nothing to do with any kind of worldview except mathematics.” And as I clearly demonstrated, that is a patently false implication and/or claim on your part. i.e. "Thus in conclusion, JVL may falsely claim that “”it (mathematics) has nothing to do with any kind of worldview except mathematics”, but the fact of the matter is that mathematics, (particularly our ability to do mathematics and apply our mathematical understanding to the universe in the first place), has a tremendous amount to say about whether the materialistic worldview of Darwinian Atheism is true or whether the worldview of Intelligent Design is true." JVL, for someone who prides himself on his own supposedly superior mathematical prowess, you, ironically, seem to be having an extremely difficult time following a simple logical argument. :) bornagain77

Bornagain77: So our ability to even be able to ‘do mathematics’ in the first place has nothing whatsoever to say about the materialistic worldview of Darwinian Evolution??? nor about the worldview of Intelligent Design??? I implied the MATHEMATICS has nothing to do with any worldview. I don't happen to believe that the ability to reason and 'do' mathematics has anything to do with any worldview either but that is a separate issue. Clearly. Oh and by the way, some animals have been shown to have rudimentary arithmetic skills. I know you'll continue to talk about mathematics even though you yourself can't 'do' mathematics but you really shouldn't. Math is not a spectator sport. JVL

JVL falsely claims that, "it (mathematics) has nothing to do with any kind of worldview except mathematics." Really??? So our ability to even be able to 'do mathematics' in the first place has nothing whatsoever to say about the materialistic worldview of Darwinian Evolution??? nor about the worldview of Intelligent Design??? (which holds, as a primary presupposition, that only intelligent (immaterial) minds have the capacity within themselves to create (immaterial) functional information?) Sorry JVL, but for someone who assumes himself to 'understand math' far better than I do, you are not really thinking too deeply about the 'ontology' of mathematics, nor are you thinking too deeply about our unique ability to even do mathematics in the first place.
"Why should a limited and finite organ such as the human brain have the power to see into the heart of matter or mathematics? These are subjects that have nothing to do with the Darwinian business of scrabbling up the greasy pole of life. It is as if the liver, in addition to producing bile, were to demonstrate a unexpected ability to play the violin. This is a question that Darwinian biology has not yet answered." - David Berlinski - The Devil's Delusion - page 16 “Either mathematics is too big for the human mind or the human mind is more than a machine.” - Kurt Godel The mathematical world - James Franklin - 7 April 2014 Excerpt: the intellect (is) immaterial and immortal. If today’s naturalists do not wish to agree with that, there is a challenge for them. ‘Don’t tell me, show me’: build an artificial intelligence system that imitates genuine mathematical insight. There seem to be no promising plans on the drawing board.,,, - James Franklin is professor of mathematics at the University of New South Wales in Sydney. - per aeon The danger of artificial stupidity – Saturday, 28 February 2015 “Computers lack mathematical insight: in his book The Emperor’s New Mind, the Oxford mathematical physicist Sir Roger Penrose deployed Gödel’s first incompleteness theorem to argue that, in general, the way mathematicians provide their “unassailable demonstrations” of the truth of certain mathematical assertions is fundamentally non-algorithmic and non-computational” http://machineslikeus.com/news/danger-artificial-stupidity 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? “Algorithm and data-driven products will always reflect the design choices of the humans who built them,” Benenson explained in a recent Q&A with Technically Brooklyn, “and it’s irresponsible to assume otherwise.” https://www.technologyreview.com/s/601775/why-we-should-expect-algorithms-to-be-biased/?set=601766
Alfred Russel Wallace himself, (co-discoverer of natural selection), held that "Mathematics is alone sufficient to prove" that the human soul must have been a "separate creation", and to therefore disprove Darwinian evolution.
“Nothing in evolution can account for the soul of man. The difference between man and the other animals is unbridgeable. Mathematics is alone sufficient to prove in man the possession of a faculty unexistent in other creatures. Then you have music and the artistic faculty. No, the soul was a separate creation.” Alfred Russel Wallace – 1910
And as Dr. Michael Egnor pointed out, because of our unique ability to think about mathematics, literature, art, language, justice, mercy, and an endless library of abstract concepts, “We are more different from apes than apes are from viruses. Our difference is a metaphysical chasm.”,,, "Human rationality is not merely a highly evolved kind of animal perception. Human rationality is qualitatively different — ontologically different — from animal perception. Human rationality is different because it is immaterial."
The Fundamental Difference Between Humans and Nonhuman Animals Michael Egnor – November 5, 2015 Excerpt: Human beings have mental powers that include the material mental powers of animals but in addition entail a profoundly different kind of thinking. Human beings think abstractly, and nonhuman animals do not. Human beings have the power to contemplate universals, which are concepts that have no material instantiation. Human beings think about mathematics, literature, art, language, justice, mercy, and an endless library of abstract concepts. Human beings are rational animals. Human rationality is not merely a highly evolved kind of animal perception. Human rationality is qualitatively different — ontologically different — from animal perception. Human rationality is different because it is immaterial. Contemplation of universals cannot have material instantiation, because universals themselves are not material and cannot be instantiated in matter.,,, We are more different from apes than apes are from viruses. Our difference is a metaphysical chasm. https://evolutionnews.org/2015/11/the_fundamental_2/
And you don't have to take Alfred Russel Wallace or Michael Egnor's word for the fact that Darwinian materialism cannot possibly account for our unique ability to think about an 'endless library' of abstract 'immaterial' concepts such as mathematics. In 2014, an impressive who’s who list of leading ‘Darwinian’ experts in this area of language research, authored a paper in which they, (after 4 decades of research) honestly admitted that they 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.” - per evolution news
Moreover, it is not only that the materialistic explanations of Darwinian atheists are 'already dead' in so far as ever giving us a coherent account for our ability to do 'immaterial' mathematics in the first place, but the 'bottom up' materialistic explanations of Atheists are also "already dead' as to ever being able to give an account for why the immaterial realm of mathematics should. 'miraculously' (Wigner, Einstein), be applicable to the universe in the first place. Specifically, the universe is found to be 'insanely' flat. And since the universe is 'insanely' flat, then we are able to make 'mathematical sense' of the universe, i.e. "parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,,"
How do we know the universe is flat? Discovering the topology of the universe – by Fraser Cain – June 7, 2017 Excerpt: With the most sensitive space-based telescopes they have available, astronomers are able to detect tiny variations in the temperature of this background radiation. And here’s the part that blows my mind every time I think about it. These tiny temperature variations correspond to the largest scale structures of the observable universe. A region that was a fraction of a degree warmer become a vast galaxy cluster, hundreds of millions of light-years across. The cosmic microwave background radiation just gives and gives, and when it comes to figuring out the topology of the universe, it has the answer we need. If the universe was curved in any way, these temperature variations would appear distorted compared to the actual size that we see these structures today. But they’re not. To best of its ability, ESA’s Planck space telescope, can’t detect any distortion at all. The universe is flat.,,, We say that the universe is flat, and this means that parallel lines will always remain parallel. 90-degree turns behave as true 90-degree turns, and everything makes sense.,,, Since the universe is flat now, it must have been flat in the past, when the universe was an incredibly dense singularity. And for it to maintain this level of flatness over 13.8 billion years of expansion, in kind of amazing. In fact, astronomers estimate that the universe must have been flat to 1 part within 1×10^57 parts. Which seems like an insane coincidence. - per physorg
Of related note:
“When a geometry is described by a set of axioms, the notion of a line is usually left undefined (a so-called primitive object).” per wikipedia 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
Atheistic Materialists simply have no clue why the universe should be 'insanely' flat so as to allow the universe to even make 'mathematical sense' to humans in the first place.
"The Universe today is actually very close to the most unlikely state of all, absolute flatness. And that means it must have been born in an even flatter state, as Dicke and Peebles, two of the Princeton astronomers involved in the discovery of the 3 K background radiation, pointed out in 1979. Finding the Universe in a state of even approximate flatness today is even less likely than finding a perfectly sharpened pencil balancing on its point for millions of years, for, as Dicke and Peebles pointed out, any deviation of the Universe from flatness in the Big Bang would have grown, and grown markedly, as the Universe expanded and aged. Like the pencil balanced on its point and given the tiniest nudges, the Universe soon shifts away from perfect flatness." ~ John Gribbin, In Search of the Big Bang
Whereas Christianity, on the other hand, 'predicted' the universe to be 'insanely flat' long before the 'insane flatness' of the universe was even discovered.
Job 38:4-5? “Where were you when I laid the earth’s foundation? Tell me, if you understand. Who marked off its dimensions? Surely you know! Who stretched a measuring line across it?
Thus in conclusion, JVL may falsely claim that ""it (mathematics) has nothing to do with any kind of worldview except mathematics", but the fact of the matter is that mathematics, (particularly our ability to do mathematics and apply our mathematical understanding to the universe in the first place), has a tremendous amount to say about whether the materialistic worldview of Darwinian Atheism is true or whether the worldview of Intelligent Design is true. Of supplemental note:
A BIBLICAL VIEW OF MATHEMATICS Vern Poythress - Doctorate in theology, PhD in Mathematics (Harvard) 15. Implications of Gödel’s proof B. Metaphysical problems of anti-theistic mathematics: unity and plurality Excerpt: Because of the above difficulties, anti-theistic philosophy of mathematics is condemned to oscillate, much as we have done in our argument, between the poles of a priori knowledge and a posteriori knowledge. Why? It will not acknowledge the true God, wise Creator of both the human mind with its mathematical intuition and the external world with its mathematical properties. In sections 22-23 we shall see how the Biblical view furnishes us with a real solution to the problem of “knowing” that 2 + 2 = 4 and knowing that S is true. http://www.frame-poythress.org/a-biblical-view-of-mathematics/
Verse and quote:
John 1:1 “In the beginning was the Word, and the Word was with God, and the Word was God” What is the Logos? Logos is a Greek word literally translated as “word, speech, or utterance.” However, in Greek philosophy, Logos refers to divine reason or the power that puts sense into the world making order instead of chaos.,,, In the Gospel of John, John writes “In the beginning was the Word (Logos), and the Word was with God, and the Word was God” (John 1:1). John appealed to his readers by saying in essence, “You’ve been thinking, talking, and writing about the Word (divine reason) for centuries and now I will tell you who He is.” https://www.compellingtruth.org/what-is-the-Logos.html
bornagain77

BA77, materialism is a long since dead horse. Unfortunately, like the warhammer 40k god emperor, reeking, it is propped up as an institutionally backed idol, dressed in a lab coat. KF PS: Wiki: >>The Imperium of Man is an authoritarian human empire that comprises approximately 1 million worlds, and has existed for over 10,000 years. Its culture is highly religious, with their chief deity being the Emperor of Mankind, an extremely powerful psyker whom they mistake for a god. Anyone who does not revere the Emperor properly is liable to be persecuted for heresy. The Emperor founded the Imperium and is still its nominal ruler, but roughly two centuries after founding the Imperium he was mortally wounded in battle and has been on life support in an unresponsive state ever since. Despite his condition, his mind still generates a psychic beacon by which starships navigate the Warp, making him the linchpin of the Imperium's infrastructure. Although the Imperium has highly advanced technology, it has long ceased practicing science and its technologies have not improved for thousands of years. Imperial citizens are taught to obey authority without question, to worship the Emperor, to hate and fear aliens, and to be incurious about anything that does not concern their duties. Most Warhammer 40,000 fiction has humans of the Imperium as the protagonists, with other races being antagonists or supporting characters. Of all the factions, the Imperium has the largest catalogue of models spread across numerous subfactions, which gives Imperium players the flexibility to design their army for any style of play. That said, players tend to build their armies around specific sub-factions which have more focused playstyles. For instance, an army of Space Marines will consist of a small number of powerful infantry, whereas an Imperial Guard army will have weak but plentiful infantry combined with strong artillery. >> kairosfocus

F/N: Here is the vid https://uncommondesc.wpengine.com/physics/the-reality-of-imaginary-numbers-discovery-not-invention/ kairosfocus

Eugen, Actually your definition is tantamount to describing the role of sqrt - 1 in a vector system of numbers, extensible to the ijk vectors and onward to quaternions etc. I often just say take the j* operator as rot 0x 90 degrees anticlockwise. do a double and we see j*j* x --> - x, i.e, the sqrt has a natural, rotation linked sense as j^2 = - 1. Where, oscillations and waves including transients [think here Laplace and Fourier transforms] are closely tied to rotations. Where of course waves are pervasive in quantum mechanics, the Schrodinger expression is about waves and of course energy with standing waves under constraints naturally being quantised as we know from school physics. Further to such, I showed that from {} --> 0 thence N,Z,Q,R,C,R* etc, once distinct identity of possible worlds obtains, core math is embedded in any possible world which gives it universal power as Wigner marvelled at. KF PS: I've been meaning to post a vid for weeks, this is my excuse and Christmas gift. kairosfocus

then turned out to be a useful construct for other situations.
Figure that ..."turned out" :)
People who don’t understand
Theology is much more complex than math and every atheist is "expert". Lieutenant Commander Data

Bornagain77: Hmm go figure, so basically you are just honestly admitting that materialism can’t possibly explain higher dimensional ‘imaginary’ numbers What? Too funny. Mathematicians came up with 'imaginary' numbers in order to solve certain kinds of problems. It has nothing to do with any kind of worldview except mathematics. It then turned out to be a useful construct for other situations. People who don't understand mathematics should really not comment about it. JVL

‘Imaginary numbers needed to describe reality’ sounds like a puckish play on words. And, ‘isn’t materialism dead already’ is a rhetorical question naturally following the word-play, given away by the ‘already’ ending. So I read it. Normally this sort of thing is philosophical at best, leading to, ‘can any number describe reality’? and ‘don’t numbers measure rather than describe?’ And ‘can anything describe reality?’ And ‘what is the nature of reality?’ Good for 500 comments into the New Year and Covid is in the rear-view mirror. Viola’s comment that materialism is irrelevant is true enough, but adding that the headline was a ‘snark’ meant that the irrelevancy now became an issue for taking sides. I hope VL doesn’t stay away. Happy Christmas everyone, if it isn’t spreading misinformation to say so. Belfast

Bornagain77 @24,
If I get your argument correctly, you are assuming that since Newton’s mathematical description of gravity failed “such as with the orbit of mercury” then you believe that all of our current ‘higher dimensional’ mathematical models may eventually fail at some extreme? and therefore math is “not a fundamental reality”?
Not exactly. What I intended to say is that math is routinely applied to reality based on how well it conforms to our observations. However, every mathematical system deals with logic based on certain axioms. According to Gödel's incompleteness theorems, we cannot prove all true statements in any one system, nor can we prove any system is consistent. It might be that more than one system is applicable to our reality and it may also be true that some mathematical systems (I'm thinking of non-Euclidean geometries) might not be applicable to our reality. Similarly, at extremes of many phenomena, mathematical formulae often need to be modified to contain additional terms or parameters. I didn't intend to take a position on the reality of mathematics, which does exist conceptually. For example probabilities certainly exist, but they have no temperature, volume, energy, or mass. I also think that the term "imaginary" is misleading, especially when one considers how "real" they are in electrical computations. However, I stand by my rejection of the statement, "If Imaginary Numbers Are Needed To Describe Reality, Then Isn’t Materialism Dead Already?", as a confusion of two very different meanings of the word "imaginary." It analogous to the problems that emerge when "nothing" and "zero" are confused. Hope this clarifies my previous comment. -Q Querius

No, I'm not saying that, BA. As usual, you hear what you want to hear, not what others are saying. Every once in a while I drop back in here and am quickly reminded of why I left. Viola Lee

VL, "I’m just saying that on this thread the people who have had some objections about the OP are not arguing for (or against) materialism." Hmm go figure, so basically you are just honestly admitting that materialism can't possibly explain higher dimensional 'imaginary' numbers (or any other mathematical objects for that matter). i.e. materialism, since you refuse to defend it in this instance, is, practically speaking, 'dead already' as to ever giving us a coherent account of higher dimensional ‘imaginary’ numbers!
"If Imaginary Numbers Are Needed To Describe Reality, Then Isn’t Materialism Dead Already?" The Mathematics Of Higher Dimensionality – Gauss & Riemann – video https://www.youtube.com/watch?v=mxy3JhPRlV0
bornagain77

No, I'm just saying that on this thread the people who have had some objections about the OP are not arguing for (or against) materialism. The article in the OP is not about (for or against) materialism, and thus New's headline is not relevant to the actual paper she cites. Viola Lee

VL "No one here is arguing for materialism." HUH??? Darwinists on UD have finally honestly admitted that their reductive materialistic model is 'not even wrong'? bornagain77

Querius states,
"that mathematical models typically fail at some extreme and need to be replaced by more complex mathematics is also telling. For example, the inverse square law applied to gravity produces reasonably good results at our typical scales means it’s pragmatic. That it fails at larger scales such as with the orbit of mercury in proximity of the sun means that it’s not a fundamental reality."
If I get your argument correctly, you are assuming that since Newton's mathematical description of gravity failed "such as with the orbit of mercury" then you believe that all of our current 'higher dimensional' mathematical models may eventually fail at some extreme? and therefore math is "not a fundamental reality"? There is a 'small' problem with your argument and/or assumption. We can find ZERO deviation between the predictions of our current 'higher dimensional' mathematical models and experimental observation, (in so far as far as current technology will allow us to test those mathematical predictions). For instance, researchers, (via some very clever experimental techniques), have been testing General Relativity to greater and greater extremes trying to find some, any, deviation from its predictions with our experimental observation, so as to be able to find some, any, mathematical loop-hole in which they could possibly unite General Relativity with Quantum Mechanics into a single mathematical framework. In all these 'extreme' tests, they can find no deviations and the predictions of General Relativity have, time and time again, passed with flying colors.
Troubled Times for Alternatives to Einstein’s Theory of Gravity - April 30, 2018 New observations of extreme astrophysical systems have “brutally and pitilessly murdered” attempts to replace Einstein’s general theory of relativity. Excerpt: The neutron-star collision was just the beginning. New data in the months since that discovery have made life increasingly difficult for the proponents of many of the modified-gravity theories that remain. Astronomers have analyzed extreme astronomical systems that contain spinning neutron stars, or pulsars, to look for discrepancies between their motion and the predictions of general relativity — discrepancies that some theories of alternative gravity anticipate. These pulsar systems let astronomers probe gravity on a new scale and with new precision. And with each new observation, these alternative theories of gravity are having an increasingly hard time solving the problems they were invented for. Researchers “have to sweat some more trying to get new physics,” said Anne Archibald, an astrophysicist at the University of Amsterdam.,,, https://www.quantamagazine.org/troubled-times-for-alternatives-to-einsteins-theory-of-gravity-20180430/ Tests of general relativity In February 2016, the Advanced LIGO team announced that they had directly detected gravitational waves from a black hole merger.[1] This discovery, along with additional detections announced in June 2016 and June 2017,[2] tested general relativity in the very strong field limit, observing to date no deviations from theory. https://en.wikipedia.org/wiki/Tests_of_general_relativity
As well, the lack of deviation from mathematical prediction is found for special relativity, quantum mechanics, and quantum electrodynamics. If you know of any experimental deviation from our current theories in physics, write a paper and get yourself a Nobel prize. As far as we can presently tell with our current technology, (which is pretty impressive as it is), our current theories in physics are turning out to be 'perfect' mathematical descriptions. As Nima Arkani-Hamed, who discovered the 'higher dimensional' amplituhedron, (which greatly the simplified the calculations of quantum electrodynamics), stated, “It seems inconceivable that this intricate web of perfect mathematical descriptions is random or happenstance. This mystery must have an explanation. But what might such an explanation look like?”
“It seems inconceivable that this intricate web of perfect mathematical descriptions is random or happenstance. This mystery must have an explanation. But what might such an explanation look like?” - Nima Arkani-Hamed - discovered the amplituhedron
In regards to the 'hypergeometric' amplituhedron itself, it also, like 'higher dimensional' complex numbers, challenge fundamental assumptions about materialism. As Rob Sheldon explains, "What are these suspect principles? None other than two of the founding principles of materialism–that there do not exist “spooky-action-at-a-distance” forces, and that material causes are the only ones in the universe.,,,"
Bohemian Gravity – Rob Sheldon – September 19, 2013 Excerpt: Quanta magazine carried an article about a hypergeometric object that is as much better than Feynman diagrams as Feynman was better than Heisenberg’s S-matrices. But the discoverers are candid about it, “The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity. “Both are hard-wired in the usual way we think about things,” said Nima Arkani-Hamed, a professor of physics at the Institute for Advanced Study in Princeton, N.J., and the lead author of the new work, which he is presenting in talks and in a forthcoming paper. “Both are suspect.”” What are these suspect principles? None other than two of the founding principles of materialism–that there do not exist “spooky-action-at-a-distance” forces, and that material causes are the only ones in the universe.,,, http://rbsp.info/PROCRUSTES/bohemian-gravity/
Verse:
1 Thessalonians 5:21 but test all things. Hold fast to what is good.
bornagain77

No one here is arguing for materialism. ET writes, "The fact the universe was intelligently designed using mathematics, means materialism was dead, already." And, following from that, therefore learning new things about the role of complex numbers doesn't change anything. That's my point, ET. Viola Lee

doesn’t add any special new element to to the argument that math disproves materialism.
There is no need of math to disprove materialism. The simplest thought a child is having is a disproval of materialism. The very definition of materialism (that involves formulating a concept/thought)destroys materialism. Lieutenant Commander Data

Imaginary numbers aren't imaginary. The fact the universe was intelligently designed using mathematics, means materialism was dead, already. ET

Does this article boils down to:
Because René Descares called a mathematical construct imaginary God exists
? DiEb

If Imaginary Numbers Are Needed To Describe Reality, Then Isn’t Materialism Dead Already?
Not from my perspective--I agree with JVL's reductio ad absurdum. That several systems of mathematics can be employed to model what we observe from reality is convenient, but not predictive. Plus, that mathematical models typically fail at some extreme and need to be replaced by more complex mathematics is also telling. For example, the inverse square law applied to gravity produces reasonably good results at our typical scales means it's pragmatic. That it fails at larger scales such as with the orbit of mercury in proximity of the sun means that it's not a fundamental reality. -Q Querius

^^^ Ditto ^^^ bornagain77

Viola Lee:
there is nothing special about complex numbers: their usefulness and even necessity in describing the world (which was the actual point of the article in the OP) doesn’t add any special new element to to the argument that math disproves materialism.
So you keep saying but still cannot form a coherent argument for that. ET

JVL:
If you can point to a connection between ‘materialism’ and complex numbers and the number line then, by all means, show us.
There isn't any. That's the point. They work because materialism is false, and the universe was intelligently designed using mathematics. JVL:
Imaginary numbers work because the universe was designed?
Not what I said. Try again.
I just want to be clear here . . . the fact that some mathematicians came up with the idea of there being a square root of a negative number is an indication that the universe was designed?
They did not come up with the idea. They discovered the existing concept. ET

A general idea here, which BA expressed, is that all mathematics disproves materialism because math has an abstract reality. Leaving that point aside, there is nothing special about complex numbers: their usefulness and even necessity in describing the world (which was the actual point of the article in the OP) doesn't add any special new element to to the argument that math disproves materialism. That's in part why I (and Ram, I think) objected to News's headline. And complex numbers are really neat: one of my favorite topics to teach. Viola Lee

ET: They work because materialism is false, and the universe was intelligently designed using mathematics. Imaginary numbers work because the universe was designed? I just want to be clear here . . . the fact that some mathematicians came up with the idea of there being a square root of a negative number is an indication that the universe was designed? Is that what you think? JVL

ET: How do you know? If you can point to a connection between 'materialism' and complex numbers and the number line then, by all means, show us. JVL

Ram:
I do agree materialism is false, but the question of materialism has nothing to do with complex numbers any more than materialism has anything to do with the number line.
How do you know? ET

VL, I think the TL;DR version of what BA77 is arguing is that relationship of mathematics to what we call the physical world can no longer be characterized as descriptive; it can only be described as causal. If it were not causal, there is no reason to expect that everything we experience as the physical world should be constrained to that which is describable by mathematics - especially not if higher-dimensional mathematics are required in that description. BA77 can correct me if I've misunderstood him. There comes a point where the happy coincidence of apparent correspondence ends and causality becomes the only rational explanation. Mathematics appears to be governing, or causing, how physical reality works, not vice-versa. This goes back to the old saw about so-called "physical laws" and "forces," and materialists mistaking their descriptions for causes. Materialists make this conceptual error repeatedly. Gravity, for instance, is not a cause even though it is invoked as such; it is a description of behavior. No materialist can explain how the behavior is instantiated or why, under their view, it should exist at all. Natural laws and forces appear to be mathematically caused, the behavior of physical reality somehow constrained into following abstract, mathematical principles at every level. There is no material explanation for how the behavior of matter is governed/caused by abstract rules and principles. The only rational explanation I can see is that what we call physical reality is the product of a higher, real, abstract dimension that causes it. William J Murray

Viola Lee states, "Also, whether complex numbers are necessary to describe some phenomena has no bearing on whether materialism is true or not." Well actually, although VL is trying to pooh pooh this finding and say that there is "Nothing to see here. Please disperse.",,,
"Nothing to see here. Please disperse" https://tenor.com/view/leslie-nielsen-nothing-to-see-here-disperse-crowd-disperse-disaster-gif-12767181
,,, although VL is trying pooh pooh this finding, the fact of the matter is that it is not just complex numbers that question whether materialism can be true or not. The entire field of mathematics, ('real' numbers, complex 'imaginary' numbers, and classes, sets, functions, and etc.. etc..), all question whether materialism can be true or not. The irresolvable dilemma for materialists is that mathematics, ALL of mathematics, is profoundly immaterial in its foundational essence. As M. Anthony Mills explains, "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."
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 as Michael Egnor explains, "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,,,"
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”?,,, 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/
To clearly illustrate just how problematic mathematics is for atheistic materialists, both Eugene Wigner and Albert Einstein are on record as to regarding it as a 'miracle' that mathematics should even be applicable to the universe in the first place. Eugene Wigner, (after rightly calling into question the ability of natural selection to produce our 'reasoning power'), stated that, "It is difficult to avoid the impression that a miracle confronts us here,,, and "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.,,"
The Unreasonable Effectiveness of Mathematics in the Natural Sciences - Eugene Wigner - 1960 ? Excerpt: ,, The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: 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
Likewise, Albert Einstein is also on record as to regarding the applicability of mathematics to the universe as a 'miracle'. Einstein even went so far as to chastise '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
Thus. although Viola Lee may try to pooh pooh this present finding on 'imaginary' complex numbers as no big deal and having "no bearing on whether materialism is true or not", the fact of the matter is that atheistic materialism and the entire field of 'immaterial' mathematics are completely at odds with each other, even diametrically opposed to each other. The fact that 'higher dimensional', and 'imaginary', complex numbers are presently found to be irreducible in our quantum mechanical description of the universe just makes what was already a bad situation for atheistic materialists exponentially worse. You see, although all of the original theories of modern science, such as Newtonian Mechanics, were all based on 3-Dimensional Euclidean geometry, all of our present, and most accurate, theories in science, (relativity, quantum mechanics, quantum electrodynamics, etc..) are all based on 'higher dimensional mathematics, As Eugene Wigner explained, "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, respectively."
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, respectively. So far, the two theories could not be united, that is, no mathematical formulation exists to which both of these theories are approximations. All physicists believe that a union of the two theories is inherently possible and that we shall find it. Nevertheless, it is possible also to imagine that no union of the two theories can be found.,,, https://www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf?
Thus in conclusion, while atheistic materialists have no clue why the universe should even be 'miraculously' described by mathematics in the first place, the fact that 'higher dimensional' mathematics, instead of 3-Dimensional Euclidean mathematics, are used in all of our best theories in science makes what was already a bad situation for atheistic materialists exponentially worse. Simply put, the Christian Theist, since he holds that God created this universe from a higher heavenly dimension, is very comfortable with the fact, (and even 'expects'), that the universe would be described by higher dimensional mathematics. Whereas on the other hand, and once again, atheistic materialists simply have no clue why the universe should even be 'miraculously' described by mathematics in the first place. Of supplemental note: besides this present experiment confirming the 'reality' of complex 'imaginary' numbers, Near Death Experiencers also testify to the physical reality of a 'higher heavenly dimension' above this 3-Dimensional temporal realm:
December 2021 - Thus in conclusion Einstein himself may not have personally believed in life after death, (nor in a personal God), but Special Relativity itself contradicts Einstein and offers stunning confirmation that Near Death Testimonies are accurate ‘physical’ descriptions of what happens after death, i.e. going to a ‘higher timeless/eternal dimension’, i.e. heavenly dimension, that exists above this temporal realm. https://uncommondesc.wpengine.com/intelligent-design/at-mind-matters-news-einstein-believed-in-spinozas-god-who-is-that-god/#comment-741908
Also of note:
December 2021 - And while most people, (who are at least semi-literate in science), are aware of the fact that all of our best theories in science are all based on ‘higher dimensional’ mathematics, (and are not based on 3-D Euclidean mathematics as Newton’s theory was), most people are unaware of the fact that life itself is based on ‘higher dimensional’ mathematics, and/or principles, and that life is not based on 3-D Euclidean mathematics, and/or principles, as is presupposed within Darwinian materialism. https://uncommondesc.wpengine.com/intelligent-design/at-mind-matters-news-can-higher-dimensions-help-us-understand-biblical-miracles/#comment-742961
Quote and Verse:
“There are more things in heaven and earth, Horatio, Than are dreamt of in your (materialistic 3-D) philosophy.” – Hamlet (1.5.167-8), Hamlet to Horatio (paraphrased) Mark 8:37 Is anything worth more than your soul?
bornagain77

ET: Right. They work because materialism is false, and the universe was intelligently designed using mathematics. I do agree materialism is false, but the question of materialism has nothing to do with complex numbers any more than materialism has anything to do with the number line. Both are the same level of "mystery." --Ram ram

This is a bizarre topic/question. The Schrödinger equation has been shown to be _derivable_. And it is derivable from the most basic assumptions: 1. That observations are real numbers. 2. That there exist both space and time symmetries in the laws of nature. See https://henry.pha.jhu.edu/quantum.html. The derivation ends up needing complex numbers. Btw, there is nothing "imaginary" about complex numbers. Complex numbers are not "a square root of -1". Complex numbers are the ordered pairs of real numbers, with certain rules defined upon those pairs. One of the consequences of those rules is that there exists such a pair of real numbers (0, 1) that (0, 1) * (0, 1) = -1, where "*" is the specific multiplication rule defined for these types of pairs. Eugene

Ram:
All physics, modern electronics design, etc, rely on complex numbers, and we know exactly why they work. No mystery. Period.
Right. They work because materialism is false, and the universe was intelligently designed using mathematics. ET

Viola Lee:
Also, whether complex numbers are necessary to describe some phenomena has no bearing on whether materialism is true or not.
How do you know? ET

All physics, modern electronics design, etc, rely on complex numbers, and we know exactly why they work. No mystery. Period. Substitute the word imaginary/complex with "lateral" and watch a Youtube or two about the subject. There is not one darn thing mysterious about any of this. For anyone interested, get to know what phase relationships means. Bad OP, Denise. Sorry (but not sorry.) --Ram ram

The "Is" in the headline makes no sense. Also, whether complex numbers are necessary to describe some phenomena has no bearing on whether materialism is true or not. Sometimes I'm just baffled about the extraneous implications that News puts in the headlines. Often the stories she highlights are interesting, but then she has to add some extra snark that is just not relevant. Viola Lee

As the "The Mathematics Of Higher Dimensionality" video that I referenced made clear, Gauss’s work on complex numbers, like the square root of negative one, extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part. In this way the complex numbers contain the ordinary real numbers while extending them in order to solve problems that would be impossible with only real numbers. And this ‘higher dimensional number line’, particularly this understanding gained for the ‘higher dimensionality’ of the square root of negative one (i), is essential for understanding the ‘wave packet’ in quantum mechanics prior to measurement. (as the present experiment in the OP has now demonstrated).
Why do you need imaginary numbers (the square root of negative one) to describe Quantum Mechanics? “Quantum theory needs existence of an x such that x^2= -1. The reason for this is that orthogonal function spaces, of dimension greater than 2, cannot exist otherwise. In fact the only place where i (the square root of negative one) is needed is in the wave packet prior to measurement. Even the Canonical Commutation Relation doesn’t need it. And nor do the eigenvalue equations. In those, any general scalar will do. But in the wave packet, you need an i.” – Steve Faulkner – Philosophy of Science, Logic, Epistemology https://www.researchgate.net/post/Why_do_you_need_imaginary_numbers_to_describe_Quantum_Mechanics2
Also of related note to quantum mechanics, and the 'higher dimensional' mathematics used to describe quantum mechanics, is the 'infinite dimensional' Hilbert space. If the 'imaginary' complex number of the square root of negative one ruffled naturalistic presuppositions by being found to 'real' instead of being merely imaginary, then the infinite dimensional Hilbert space that is used within quantum mechanics ought to really give them fits. As the following article states, "The role of Hilbert spaces in quantum mechanics, then, is much more profound than the descriptive role of a single concept. An entire formalism-the Hilbert space formalism-is matched with nature. Information about nature is being “read off” the details of the formalism. (Imagine reading off details about elementary particles from the rules of chess-castling. en passant-a la Lewis Carro;; in Through the Looking Glass.) No physicist today understands why this is possible."
The Applicability of Mathematics as a Philosophical Problem – Mark Steiner – (page 44) Excerpt: Let us now recapitulate: beginning with the concept of a Hilbert space, a certain kind of (usually infinite-dimensional) vector space, and the formal requirement that a unit vector on the space represents all possible information can be gleaned. First, the space cannot be a real vector space; the usual formalism is, therefore, based on a complex Hilbert space. With this formalism the Heisenberg uncertainty principle follows directly. So does the quantization of angular momentum, including the so called “space quantization”. So does the prediction that “electron spin” cannot be due to spatial rotation. And so do the selection rules for the spectrum of hydrogen, based on the “nonphysical” concept of parity. The role of Hilbert spaces in quantum mechanics, then, is much more profound than the descriptive role of a single concept. An entire formalism-the Hilbert space formalism-is matched with nature. Information about nature is being “read off” the details of the formalism. (Imagine reading off details about elementary particles from the rules of chess-castling. en passant-a la Lewis Carro;; in Through the Looking Glass.) No physicist today understands why this is possible.. https://books.google.com/books?id=GKBwKCma1HsC&pg=PA44
Of course much more could be said about the fact that higher dimensional mathematics are essential, (even 'real'), for all of our best theories in science, (i.e. quantum mechanics, Relativity, etc..),
Euler’s Formula Proof & The Beauty of Complex Numbers - Oct. 2021 The use of complex numbers comes from an assumption that seemed useless at the time. Why work with a set of numbers that aren’t real? Since the discovery of complex numbers, they are at least somewhat real. The applications of complex numbers in the real world are endless, control theory, signal analysis, relativity, and fluid dynamics all use complex numbers. Not to mention the advent of the complex plane, https://medium.com/intuition/eulers-formula-proof-the-beauty-of-complex-numbers-a4c8eb9f10d8
,,, although much more could be said, suffice it for now to say that the fact that higher dimensional 'imaginary' numbers are now found to 'really exist', (Hossenfelder), is rather stunning confirmation of the contention, via Neoplatonic philosophy and Augustinian theology, that the (higher dimensional) mathematics that describe this universe really are "God’s thoughts"
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
Verse:
Psalm 115:2-3 Why should the nations say, “Where is their God?” Our God is in heaven; He does as He pleases.
bornagain77

Back in March, when Sabine Hossenfelder first announced this proposed experiment on whether 'imaginary' complex numbers were 'real' or not, I stated, "First off, let me state that I firmly believe that the proposed experiment will be successful. Quantum Mechanics has a very long history of shattering ‘naturalistic’ assumptions about locality and realism."
"First off, let me state that I firmly believe that the proposed experiment will be successful. Quantum Mechanics has a very long history of shattering ‘naturalistic’ assumptions about locality and realism." https://uncommondesc.wpengine.com/intelligent-design/sabine-hossenfelder-asks-do-complex-numbers-exist/#comment-725634
Moreover, when Hossenfelder announced this proposed experiment, she herself stated, if the experiment was successful then, "It would then be fair to say that complex (imaginary) numbers exist."
",,, assuming their result holds up, this means if the experiment which they propose finds the specific entanglement predicted by complex quantum mechanics, then you know you can’t describe observations with real numbers. It would then be fair to say that complex numbers exist. So, this is why it’s cool. They’ve figured out a way to experimentally test if complex numbers exist!" - Sabine Hossenfelder https://uncommondesc.wpengine.com/intelligent-design/sabine-hossenfelder-asks-do-complex-numbers-exist/
Moreover, even though Schrödinger himself found the use of complex (imaginary) numbers in quantum theory to be "disquieting",,,
Imaginary numbers could be needed to describe reality, new studies find - Dec. 21, 2021 Excerpt: 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 (?) — wrote, "What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. ? (the wave function) is surely fundamentally a real function." https://www.livescience.com/imaginary-numbers-needed-to-describe-reality
,,, even though Schrödinger himself found the use of complex (imaginary) numbers in quantum theory to be "disquieting", the argument over whether complex numbers are imaginary or real goes back a long way. Long before quantum theory came along and Schrödinger was upset by that they were "fundamentally a real function." Carl Friedrich Gauss was the mathematician who first clearly explained the higher ‘dimensional extension’ of complex numbers over and above the real number line,,,
The Mathematics Of Higher Dimensionality – Gauss & Riemann – video https://www.youtube.com/watch?v=mxy3JhPRlV0
Yet prior to Gauss's work, (and of all people), “Descartes had rejected complex roots and coined the derogatory term “imaginary” to describe the square root of negative one,”
Descartes coined the term imaginary: “For any equation one can imagine as many roots [as its degree would suggest], but in many cases no quantity exists which corresponds to what one imagines.” https://www.math.uri.edu/~merino/spring06/mth562/ShortHistoryComplexNumbers2006.pdf
Yet both Gauss and Leibniz rejected Descartes's claim that complex numbers were merely ‘imaginary’. Gauss argued that complex (imaginary) numbers were just as real as 'real' numbers are.
Carl Friedrich Gauss (1777-1855) Gauss introduced the term complex number “If this subjet has hitherto been considered from the wrong viewpoint and thus enveloped in mystery and surrounded by darkness, it is largely an unsuitable terminology which should be blamed. Had +1, -1 and ??1, instead of being called positive, negative and imaginary (or worse still, impossible) unity, been given the names say,of direct, inverse and lateral unity, there would hardly have been any scope for such obscurity.” https://www.math.uri.edu/~merino/spring06/mth562/ShortHistoryComplexNumbers2006.pdf
And Leibniz went so far as to state that ”The divine spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and non-being, which we call the imaginary root of negative unity.”
“The Divine Spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and not-being, which we call the imaginary root of negative unity.” — - Gottfried Leibniz https://www2.math.upenn.edu/~deturck/isp/april-22.pdf
And the following article observes that "In the language of Plato’s allegory of the cave, complex numbers represent “forms” from a higher dimension casting “shadows” on the real number line."
Complex Magnitudes Excerpt: Descartes had rejected complex roots and coined the derogatory term “imaginary” to describe the square root of negative one, , but Leibniz thought that “The divine spirit found a sublime outlet in that wonder of analysis, that portent of the ideal world, that amphibian between being and non-being, which we call the imaginary root of negative unity.” Gauss invented the “complex plane” (shown below) to represent these quantities. He suggested that complex magnitudes be called “lateral” instead of “imaginary” magnitudes since they represent a dimensional extension of the continuum. Gauss also proposed that complex magnitudes be awarded “full civil rights.” In the language of Plato’s allegory of the cave, complex numbers represent “forms” from a higher dimension casting “shadows” on the real number line. - per Kepler's discovery
bornagain77

We don't need any numbers to describe reality in a useful way. Carpenters and masons and astronomers were using diagrams and templates long before number symbols came along. Graphs are better than numbers. polistra

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