Why are we even wondering?:

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” atLive Science(December 21, 2021)

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.

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.”

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.”

Moreover, even though Schrödinger himself found the use of complex (imaginary) numbers in quantum theory to be “disquieting”,,,

,,, 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,,,

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,”

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.

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.”

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.”

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).

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.”

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..),

,,, 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”

Verse:

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.

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 thingmysterious about any of this.For anyone interested, get to know what

phase relationshipsmeans.Bad OP, Denise. Sorry (but not sorry.)

–Ram

Viola Lee:

How do you know?

Ram:

Right. They work because materialism is false, and the universe was intelligently designed using mathematics.

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.

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

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.”,,,

,,, 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.”

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,,,”

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.,,”

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’.

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.”

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:

Also of note:

Quote and Verse:

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

correspondenceends 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.

Ram:

How do you know?

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.

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?

A general idea here, which BA expressed, is that

allmathematics 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.

JVL:

There isn’t any. That’s the point.

They work because materialism is false, and the universe was intelligently designed using mathematics.JVL:

Not what I said. Try again.

They did not come up with the idea. They discovered the existing concept.

Viola Lee:

So you keep saying but still cannot form a coherent argument for that.

^^^ Ditto ^^^

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

Does this article boils down to:

?

Imaginary numbers aren’t imaginary.

The fact the universe was intelligently designed using mathematics, means materialism was dead, already.

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.

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.

Querius states,

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.

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?”

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.,,,”

Verse:

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’?

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.

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!

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.

Bornagain77 @24,

Not exactly.

What I

intendedto 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

‘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.

Bornagain77: Hmm go figure, so basically you are just honestly admitting that materialism can’t possibly explain higher dimensional ‘imaginary’ numbersWhat? 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.

Figure that …”turned out” 🙂

Theology is much more complex than math and every atheist is “expert”.

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.

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

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. >>

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.

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.

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.”

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.,,,”

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.,,,”

Of related note:

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.

Whereas Christianity, on the other hand, ‘predicted’ the universe to be ‘insanely flat’ long before the ‘insane flatness’ of the universe was even discovered.

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:

Verse and quote:

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: “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. 🙂

Viola Lee:

Right, because materialism is a non-starter.

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.”,,,

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.”

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,”

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.”,,,

,,, 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.

JVL:

That is false. Imaginary numbers always existed. Mathematicians discovered them.

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: 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.

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:

No, they only started to write about them when they wanted to work on a particular kind of problem.

We have not invented anything. Ever.

Cuz you say so? Really?

It has to be able to account for everything that exists.

Nice projection.

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.

Exactly right! Mathematics is profoundly immaterial and cannot possibly be reduced to materialistic explanation.

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)

As the late Steven Weinberg, an atheist, explained,

JVL then states:

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?

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.”

in response to that quote, JVL, (without citation), responds thusly,

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, 🙂

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.

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.

“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.”

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: thus stressing the quantum-mechanical assertion that reality does not exist when we’re not observing itThat’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:

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:

Can YOU? You NEVER support what you spew. Hypocrite.

Materialism cannot account for mathematics

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: 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:

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.

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.

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,”,,,

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.,,,”

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.

Verse:

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

Kairosfocusdisagrees with you. And I’m certainDr Dembskidoes 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.

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.

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.

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.

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’

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’.

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?

I also wonder if JVL also thinks he is smarter In math than Leonhard Euler was?

And here is what Leonhard Euler had to say about atheists in his day:

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:

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.

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.

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

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?

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.

Is there such a world?

Is it just in one’s imagination? If that is what you mean?

And very, very useful.

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.

So there is a limit in reasoning ability ? Bad news for atheists.

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?

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.

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 .

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

Bornagain77: Whatever JVL, via your stubborn refusal to even be semi-reasonable towards the evidence, or the mathI’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.

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 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.

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.

Late entry into ironic comment of year!!!!

Could be a winner.

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?

Someone with a poor memory who likes to use ad hominems.

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.

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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?