Mathematics

[Perpetual Student]

Is the part I highlighted begging the question?

No, I was referring to the difference between atomic and diatomic hydrogen, which cannot exist without number.

 

[marplots]

No, I was referring to the difference between atomic and diatomic hydrogen, which cannot exist without number.

Again, it seems like you are defining the difference with a number - essentially making "number" part of the package. I thought the idea was to see if "number" was an immutable, mandatory item. Couldn't I describe the difference between the types of hydrogen by their properties instead?

I'm not disagreeing that mono and di are real or useful, but the question is whether we impose this on the world or whether it is a real property of the world and not merely our preferred way of describing things.

I might ask, for example, how an innumerate animal "understands" the world. When I do, I see that number might not be as ingrained as it first appears. But it might, I'm not sure.

Would mathematics emerge if I experienced and described the world based only on a sense of color?

 

[Perpetual Student]

The point is that if two hydrogen atoms did not bind to form diatomic hydrogen, diatomic hydrogen would not exist. In this context, our word "two" is used to describe this condition of reality, a reality that exists in the absence of humanity. Two-ness (duality, if you prefer) is an aspect of reality as much as are electric charge and time -- which also exist without us.

 

[marplots]

The point is that if two hydrogen atoms did not bind to form diatomic hydrogen, diatomic hydrogen would not exist. In this context, our word "two" is used to describe this condition of reality, a reality that exists in the absence of humanity. Two-ness (duality, if you prefer) is an aspect of reality as much as are electric charge and time -- which also exist without us.

Couldn't we describe diatomic hydrogen as a system of quarks though? Even calling it "di" atomic reveals we've already snuck math labels in.

 

[Perpetual Student]

Couldn't we describe diatomic hydrogen as a system of quarks though? Even calling it "di" atomic reveals we've already snuck math labels in.

Why is it relevant that we have "snuck math labels in" to describe its nature -- some other number of atoms would alter its characteristics.
A meson is a physical entity with specific characteristics and is made of two quarks, for example, not one or three. There is no "di" in meson.
Why is ozone different than most atmospheric oxygen? There is no "tri" in ozone.
Sexual reproduction involves two sexes.
There are two types of electric charge and two magnetic poles.
Quarks come in three colors.
Space has three dimensions.
Nature is what it is -- and the number of things that constitute differing and/or composite things is part of nature. Our numbers are simply linguistic labels to describe the reality of our universe.

 

[annnnoid]

Can you define space and time? Give it a try. Are these concepts unscientific if you cannot do so?

Your own incredulity notwithstanding, even something as simple as a single diatomic hydrogen atom cannot exist without number.
Number is as much an aspect of the universe as are all the other fundamental concepts involving space, time, matter and energy. Centuries of discovery have revealed that at every every aspect and at all scales the universe is demonstrably mathematical. Sorry, claiming otherwise demonstrates ignorance.

Where...is...the...number????

It’s got absolutely nothing to do with me (and whether I can or cannot effectively define anything). The whole point of science is its ability to generate coherent knowledge. If space and time can be defined in some variety of coherent form within the epistemology of science…then they have scientific credibility (so far the concepts of space and time have varieties of coherent scientific meaning…not least of all because they can be interpreted mathematically). If they can’t be coherently defined within the epistemology of science…then they do not have scientific credibility. It’s as simple as that. So far, your ‘number’ concept cannot even begin to be coherently defined within the epistemology of science (google confirms this quite convincingly).

You have utterly failed to present any kind of coherent scientific justification for this new concept you’ve created. You've created a metaphysical justification by pointing here and there and insisting that 'number' is everywhere. That's called hand waving. What you have to demonstrate to achieve scientific credibility…is the direct connection between, for example, this single diatomic hydrogen atom you are referring to…and the number 1 (since you are insisting that the number 1 is somehow relevant to this phenomenon). In order to do that...you will have to explicitly define what the number 1 even is. What it exists as. How, specifically and explicitly, whatever-the-number-1-is orients this diatomic atom. Good luck with that. You will be first in line for a Nobel prize if you can accomplish such a thing.

There are only two conceivable ways to scientifically establish that the universe is fundamentally mathematical (however convincing the circumstantial evidence). Either whatever-the-universe-is-made-of can be examined somehow in such a way as to explicitly reveal its mathematical qualities (and science becomes guilty of proving that the universe is intelligent [how ironic])…or consciousness can be unraveled to the degree that we discover how the physical electro-bio-chemical activity of the brain generates the specific conscious activity of mathematics (thus we will have a direct relationship between physics and mathematics...which sounds kind of eerie somehow).

I’m not holding my breath for either development.

 

[marplots]

It's hard for me to frame the subject without appearing silly or argumentative.

Nature is what it is -- and the number of things that constitute differing and/or composite things is part of nature. Our numbers are simply linguistic labels to describe the reality of our universe.

My question is then whether mathematics is just a description or a property of the thing being described. For example, there are things which are not quite so easy to describe with simple numbers - like colors. We wouldn't say you have two reds or blue is the combination of some discrete parts.

I'm not sure if we could capture what we want without numbers, but I'm unwilling to say it's impossible. I think the hardest to get rid of would be more and less.

 

[The Man]

It's hard for me to frame the subject without appearing silly or argumentative.



My question is then whether mathematics is just a description or a property of the thing being described. For example, there are things which are not quite so easy to describe with simple numbers - like colors. We wouldn't say you have two reds or blue is the combination of some discrete parts.

I'm not sure if we could capture what we want without numbers, but I'm unwilling to say it's impossible. I think the hardest to get rid of would be more and less.

Well, numbers are generally taught in relation to geometry (at least they were in my day, some number of decades ago). Hence, the number line. Geometry is a property of things, some perhaps abstract but certainly some real. Likewise numbers are properties of things as well. Though to free ourselves of the arbitrary nature of our selective ascription (as much as possible) one has to go with ratios, resulting in dimensionless numbers. As a block that has a ratio of 6 for length over thickness and 2 for width over thickness still has a ratio of 3 for length over width. So the properties that are numbers are those relations. Consider different relations of such an object and you get different numbers but all those relations are still just properties of the object. So in the example given it is both a description of the property of the object (its proportional shape) and that very property. More and less are also comparative descriptions/properties but ratios just give you more exacting and practical detail.

 

[Perpetual Student]

Where...is...the...number????

It’s got absolutely nothing to do with me (and whether I can or cannot effectively define anything). The whole point of science is its ability to generate coherent knowledge. If space and time can be defined in some variety of coherent form within the epistemology of science…then they have scientific credibility (so far the concepts of space and time have varieties of coherent scientific meaning…not least of all because they can be interpreted mathematically). If they can’t be coherently defined within the epistemology of science…then they do not have scientific credibility. It’s as simple as that. So far, your ‘number’ concept cannot even begin to be coherently defined within the epistemology of science (google confirms this quite convincingly).

I don't do science by google popularity. I said this before, but you are clearly not interested. We have a few undefined concepts in physics like space and time. It is what it is.

You have utterly failed to present any kind of coherent scientific justification for this new concept you’ve created. You've created a metaphysical justification by pointing here and there and insisting that 'number' is everywhere. That's called hand waving. What you have to demonstrate to achieve scientific credibility…is the direct connection between, for example, this single diatomic hydrogen atom you are referring to…and the number 1 (since you are insisting that the number 1 is somehow relevant to this phenomenon). In order to do that...you will have to explicitly define what the number 1 even is. What it exists as. How, specifically and explicitly, whatever-the-number-1-is orients this diatomic atom. Good luck with that. You will be first in line for a Nobel prize if you can accomplish such a thing.

You missed the point -- again.
In nature, we find hydrogen in atomic form, diatomic form and triatomic form.
The thing that distinguishes these forms of hydrogen is the number of bound atoms. We have invented labels for those: one, two, three -- but those exist without our labels.

There are only two conceivable ways to scientifically establish that the universe is fundamentally mathematical (however convincing the circumstantial evidence). Either whatever-the-universe-is-made-of can be examined somehow in such a way as to explicitly reveal its mathematical qualities (and science becomes guilty of proving that the universe is intelligent [how ironic])…or consciousness can be unraveled to the degree that we discover how the physical electro-bio-chemical activity of the brain generates the specific conscious activity of mathematics (thus we will have a direct relationship between physics and mathematics...which sounds kind of eerie somehow).

I’m not holding my breath for either development.

Mathematical discoveries have been made where decades and even centuries later we find those discoveries describe some reality. Complex numbers, non-Euclidean geometry, group theory are some obvious ones that come to mind. Newton's laws, Maxwell's equations, GR, QM all reveal the mathematical behavior of the universe. No deities are required.
As soon as a distinction is made by nature, number exists. No one has to be there to fire his neurons in approval and no deity is needed to consecrate the event.

 

[annnnoid]

I don't do science by google popularity. I said this before, but you are clearly not interested. We have a few undefined concepts in physics like space and time. It is what it is.

You missed the point -- again.
In nature, we find hydrogen in atomic form, diatomic form and triatomic form.
The thing that distinguishes these forms of hydrogen is the number of bound atoms. We have invented labels for those: one, two, three -- but those exist without our labels.

Mathematical discoveries have been made where decades and even centuries later we find those discoveries describe some reality. Complex numbers, non-Euclidean geometry, group theory are some obvious ones that come to mind. Newton's laws, Maxwell's equations, GR, QM all reveal the mathematical behavior of the universe. No deities are required.
As soon as a distinction is made by nature, number exists. No one has to be there to fire his neurons in approval and no deity is needed to consecrate the event.

Actually you’re not doing science at all. Again...those other terms you mentioned (spin, charge, mass, chirality) all have coherent, explicit, and commonly accepted scientific definitions and applications. Is it possible that popularity has nothing to do with it? Generally speaking…in the world of science (and in the world of most reasonable people) if an idea has plausibility it will achieve credibility irrespective of the social appeal of whoever presented it. The question of the relationship between mathematics and the universe it describes and occurs in has been debated ever since mathematics has been in use. Nobody, anywhere, has come anywhere close to any kind of definitive conclusion. That is not because there isn’t sufficient evidence that implicates…something. It is simply because the questions are incomprehensible. They can’t be answered. At least…not with the knowledge currently at our disposal.

But you are claiming to have answered these questions. This is beyond an extraordinary claim. The problem is…you have not provided a shred of substantive evidence to support these assertions. You have resorted to nothing more than vague metaphysics. Hardly scientific. How can you be surprised or offended when your audience insists on something more substantial…especially when you are presenting your conclusion as some variety of scientific fact!

…and this is the first time you’ve made any effort to define this concept you refer to as ‘number’. Here you suggest that it occurs as a consequence of something you describe as a ‘distinction’ in nature? Would there be any point in asking what that even means? Science is fundamentally dependent upon explicitly defined syntax and semantics (this is this and not that). Your terms, so far, are beyond vague so it can hardly be called science.

…and yes, as soon as you verify that the entire universe is functionally mathematical, you have immediately introduced and implicated intelligence (on however vast a scale). Call it a deity…call it peanut butter…doesn’t matter what you call it, mathematics implicates intelligence according to what is generally regarded as conventional reasoning.

 

[W.D.Clinger]

Mathematical discoveries have been made where decades and even centuries later we find those discoveries describe some reality. Complex numbers, non-Euclidean geometry, group theory are some obvious ones that come to mind. Newton's laws, Maxwell's equations, GR, QM all reveal the mathematical behavior of the universe. No deities are required.

That shouldn't even be controversial, but annnnoid says it goes against "conventional reasoning":

…and yes, as soon as you verify that the entire universe is functionally mathematical, you have immediately introduced and implicated intelligence (on however vast a scale). Call it a deity…call it peanut butter…doesn’t matter what you call it, mathematics implicates intelligence according to what is generally regarded as conventional reasoning.

No. The facts stated by Perpetual Student do not introduce or implicate intelligence, deities, or peanut butter.

Intelligence might be needed to discover that reality is described by certain laws that can be stated mathematically, but the universe presumably behaved as described by that mathematics long before the mathematics was noticed/discovered/invented by intelligent beings/deities/peanuts. Hence the mathematical behavior of the universe does not imply intelligence.

That is, of course, the conventional reasoning. annnnoid is free to use unconventional reasoning even as he/she/it falsely claims support from conventional reasoning.

 

[marplots]

It seems to me that when mathematics fails to describe something we have discovered adequately, we set about inventing new mathematics, in much the same way we might create new words. But then some would say that we created nothing, but only discovered mathematics which already - in some sense - existed.

I shall ask it another way then. I propose there are branches of mathematics which do not map onto the universe as we have found it so far. If this is the case (and I assume some math literate can say it is or isn't), then can we say with confidence that eventually we shall find some bit of the universe to match the arcane maths? In other words, shouldn't it work both ways round - new observations generating mathematical discoveries and mathematical discoveries unveiling reality? And I don't mean in a soft way, but in an "anything the math produces must exist" way.

If the universe only consists of some subset of mathematical possibilities, then how could I say that math exists "out there?"

 

[annnnoid]

That shouldn't even be controversial, but annnnoid says it goes against "conventional reasoning":

Huh?????....where did I say that? What I said was…establishing a direct causal link between the physical activity of the brain and the conceptual activity of mathematics would be beyond even a Nobel worthy achievement. As would discovering that this universe is somehow ontologically mathematical. Anybody who has any understanding of these issues would hardly disagree. You either misunderstood my point or simply don’t understand THE point. If you wish to clarify feel free to do so.

No. The facts stated by Perpetual Student do not introduce or implicate intelligence, deities, or peanut butter.

Intelligence might be needed to discover that reality is described by certain laws that can be stated mathematically, but the universe presumably behaved as described by that mathematics long before the mathematics was noticed/discovered/invented by intelligent beings/deities/peanuts. Hence the mathematical behavior of the universe does not imply intelligence.

That is, of course, the conventional reasoning. annnnoid is free to use unconventional reasoning even as he/she/it falsely claims support from conventional reasoning.

I guess you didn’t notice but PS is not suggesting that reality is ‘described by laws that can be stated mathematically.’ There is not the slightest controversy in that position. PS is going much further. He is suggesting that the universe IS mathematics. That is the whole point of this thread. Perhaps you would benefit from reading some previous posts. If I am mistaken in this interpretation I’m sure PS will correct me.

Based on conventional paradigms…the occurrence of math is a sign of intelligence. So far, intelligence (human consciousness) is the ONLY phenomenon (that we know of) that has the capacity to conceptualize mathematically. Without intelligence, there is no mathematics. Simple logic implies that …wherever we discover mathematics…there must be some variety of intelligence behind-within-above-whatever it (whatever that could possibly mean). Your obvious distaste for such a conclusion cannot change the collective syntax and semantics that generate it. I guess you’ll just have to find a way to deal with it.

 

[The Man]

It seems to me that when mathematics fails to describe something we have discovered adequately, we set about inventing new mathematics, in much the same way we might create new words. But then some would say that we created nothing, but only discovered mathematics which already - in some sense - existed.

I shall ask it another way then. I propose there are branches of mathematics which do not map onto the universe as we have found it so far. If this is the case (and I assume some math literate can say it is or isn't), then can we say with confidence that eventually we shall find some bit of the universe to match the arcane maths? In other words, shouldn't it work both ways round - new observations generating mathematical discoveries and mathematical discoveries unveiling reality? And I don't mean in a soft way, but in an "anything the math produces must exist" way.

If the universe only consists of some subset of mathematical possibilities, then how could I say that math exists "out there?"

Actually, as noted by Perpetual Student, what has happened at times is the new mathematics is invented before its applicability to physical relations is eventually found. One of the benefits of mathematics is its ability to be abstract as well as physically descriptive. That's what allows the new math to be explored before its physical applicability can be found. Even new physical entities (particles) to be found because the math predict their existence. However, that also means that some math may never have any physical applicability. So "anything the math produces must exist" wouldn't be a physically valid assertion nor would it be expected to be one. If only some subset of dragons exist then surely you can say 'there be dragons out there' while still understanding not every dragon you can think of has to exist.

 

[marplots]

Actually, as noted by Perpetual Student, what has happened at times is the new mathematics is invented before its applicability to physical relations is eventually found. One of the benefits of mathematics is its ability to be abstract as well as physically descriptive. That's what allows the new math to be explored before its physical applicability can be found. Even new physical entities (particles) to be found because the math predict their existence. However, that also means that some math may never have any physical applicability. So "anything the math produces must exist" wouldn't be a physically valid assertion nor would it be expected to be one. If only some subset of dragons exist then surely you can say 'there be dragons out there' while still understanding not every dragon you can think of has to exist.

Indeed, that was my point. In some sense, I could make the case for words being a part of the universe in the same way mathematics is. Certainly nouns and verbs are wonderfully descriptive. But if I create a new word from a couple of old ones, I have no assurance that my new word will ever be meaningfully attached to reality.

For mathematics, I think we can construct equations that are perfectly valid extensions of things we all accept (I mean valid under the rules of mathematics) but which generate nonsense.

For example, Hooke's law for springs says F=kX where the force applied is proportional to the distance the spring compresses or extends. But it only applies in a narrow range for X, since the spring will be deformed past its material properties. It would also be nonsensical to treat force as a number and, say, manipulate the equation to get a force with an imaginary component.

In a sense, we are quite forgiving when we say mathematics "matches" reality. The correspondence is not really that good, and not usually extensible. In all cases, reality serves as our checking mechanism, instead of the other way around. A units analysis often serves as the bridge here - an ingredient added to the mathematics to constrain abstract choices.

In mathematics, one plus two gets you three. In the real world, the units have to match, so that one potato plus two weeks off don't give you a sensible result.

"If the math don't fit, you must to quit."

 

[The Man]

Indeed, that was my point. In some sense, I could make the case for words being a part of the universe in the same way mathematics is. Certainly nouns and verbs are wonderfully descriptive. But if I create a new word from a couple of old ones, I have no assurance that my new word will ever be meaningfully attached to reality.

For mathematics, I think we can construct equations that are perfectly valid extensions of things we all accept (I mean valid under the rules of mathematics) but which generate nonsense.

For example, Hooke's law for springs says F=kX where the force applied is proportional to the distance the spring compresses or extends. But it only applies in a narrow range for X, since the spring will be deformed past its material properties. It would also be nonsensical to treat force as a number and, say, manipulate the equation to get a force with an imaginary component.

In a sense, we are quite forgiving when we say mathematics "matches" reality. The correspondence is not really that good, and not usually extensible. In all cases, reality serves as our checking mechanism, instead of the other way around. A units analysis often serves as the bridge here - an ingredient added to the mathematics to constrain abstract choices.

In mathematics, one plus two gets you three. In the real world, the units have to match, so that one potato plus two weeks off don't give you a sensible result.

"If the math don't fit, you must to quit."

Well, yes and no, to at least some extents, which was indeed my point. Sure reality is generally more complicated than the models and to get things to work (engineering wise that is) we commonly use tolerances or limits on values. As you note “reality serves as our checking mechanism” but that also means that there really is something (some value) to check against. Dimensional analysis is also a useful checking tool, while it can’t tell you if your relationship is correct of even physically relevant it can tell you that your relation (as structured) can’t be correct and can’t represent anything physically relevant. Just getting the units correct won’t make the relation correct or physically relevant. In fact just as the relation or physical law should not depend on ones selection of a particular coordinate system it also shouldn’t depend on what system of units one uses. So someone’s numerological notions that gets the value of the gravitational constant has to work just as well in units of Newtons, Meters and Seconds as it does in units of Pounds, Furlongs and Fortnights. The Buckingham Pi theorem generally implies that any physical law should be expressible as a relation of dimensionless values. Such dimensionless quantities or pure numbers are exactly what the counting (more generally cardinal) numbers represent (though as integers). So for your example a set of one potato, one week off and a second week off has three elements. For that counting it doesn’t matter what those elements actually represent.

http://en.wikipedia.org/wiki/Dimensional_analysis

http://en.wikipedia.org/wiki/Buckingham_π_theorem

http://en.wikipedia.org/wiki/Natural_number

http://en.wikipedia.org/wiki/Cardinal_number

 

[Perpetual Student]

I guess you didn’t notice but PS is not suggesting that reality is ‘described by laws that can be stated mathematically.’ There is not the slightest controversy in that position. PS is going much further. He is suggesting that the universe IS mathematics. That is the whole point of this thread. Perhaps you would benefit from reading some previous posts. If I am mistaken in this interpretation I’m sure PS will correct me.

OK. I'll correct you. Actually I will accept full responsibility for not making my meaning clear -- but I did try several times.
So, here it is:
It is patently obvious that the universe behaves mathematically. We have discovered mathematical expressions to describe, mirror and predict that behavior at all levels and in all aspects. Consequently, mathematical behavior is as much an aspect of the universe as are space and time or energy -- perhaps (one can conjecture) mathematics is the most fundamental aspect of all, since it has been suggested that there was no time, space or energy before the big bang. That's it.

Now, when it comes to "mathematics IS the universe," while I find that conjecture fascinating, I have no inclination to take that position.
Max Tegmark makes the interesting observation that if we have a mathematical system that fully describes, say, an electron, then there exists an isomorphism between that system and the electron. In other words, the electron behaves like the mathematics and vice versa. Consequently, they are the same since two isomorphic objects cannot be distinguished by using only the properties used to define their morphism. Expanding this to all other fundamental particles in the universe brings us to the conclusion that "the universe IS mathematics." This is not a position I have ever advocated, but feel free to find some statement by me in these threads to dispute that.

 

[W.D.Clinger]

Huh?????....where did I say that? What I said was…establishing a direct causal link between the physical activity of the brain and the conceptual activity of mathematics would be beyond even a Nobel worthy achievement. As would discovering that this universe is somehow ontologically mathematical. Anybody who has any understanding of these issues would hardly disagree. You either misunderstood my point or simply don’t understand THE point. If you wish to clarify feel free to do so.

There's an entire field of research devoted to establishing causal links "between the physical activity of the brain and the conceptual activity of mathematics". When I was a PhD student, I took seminar courses devoted to that area of research. Those seminars were led by a cognitive psychologist who is now a fellow of the National Academy of Sciences and has chaired the psychology department at Harvard.

Perhaps you would benefit from reading some previous posts. If I am mistaken in this interpretation I’m sure PS will correct me.

He has done so:

OK. I'll correct you. Actually I will accept full responsibility for not making my meaning clear -- but I did try several times.
So, here it is:
It is patently obvious that the universe behaves mathematically. We have discovered mathematical expressions to describe, mirror and predict that behavior at all levels and in all aspects. Consequently, mathematical behavior is as much an aspect of the universe as are space and time or energy -- perhaps (one can conjecture) mathematics is the most fundamental aspect of all, since it has been suggested that there was no time, space or energy before the big bang. That's it.

Now, when it comes to "mathematics IS the universe," while I find that conjecture fascinating, I have no inclination to take that position.

So I interpreted his position correctly, and I stand by what I said in my previous post.

Based on conventional paradigms…the occurrence of math is a sign of intelligence. So far, intelligence (human consciousness) is the ONLY phenomenon (that we know of) that has the capacity to conceptualize mathematically. Without intelligence, there is no mathematics. Simple logic implies that …wherever we discover mathematics…there must be some variety of intelligence behind-within-above-whatever it (whatever that could possibly mean). Your obvious distaste for such a conclusion cannot change the collective syntax and semantics that generate it. I guess you’ll just have to find a way to deal with it.

You may not be aware of the fact that almost all mathematics (including all mathematics that matters to the sciences) can be generated from one specific small set of axiom schema. The process of generating that mathematics can be performed by a moderately simple computer program that implements a complete proof procedure for first order logic.

This is not a practical way to generate mathematics, because complete proof procedures are slow. They're slow because they explore every blind alley and prove all sorts of stupid things that human mathematicians, scientists, and engineers would never care about. It seems to me, however, that your claim about the necessary connection between mathematics and intelligence is refuted by the facts I have stated—unless, of course, you are willing to regard that moderately simple computer program as intelligent.

 

[annnnoid]

OK. I'll correct you. Actually I will accept full responsibility for not making my meaning clear -- but I did try several times.
So, here it is:
It is patently obvious that the universe behaves mathematically. We have discovered mathematical expressions to describe, mirror and predict that behavior at all levels and in all aspects. Consequently, mathematical behavior is as much an aspect of the universe as are space and time or energy -- perhaps (one can conjecture) mathematics is the most fundamental aspect of all, since it has been suggested that there was no time, space or energy before the big bang. That's it.

Now, when it comes to "mathematics IS the universe," while I find that conjecture fascinating, I have no inclination to take that position.
Max Tegmark makes the interesting observation that if we have a mathematical system that fully describes, say, an electron, then there exists an isomorphism between that system and the electron. In other words, the electron behaves like the mathematics and vice versa. Consequently, they are the same since two isomorphic objects cannot be distinguished by using only the properties used to define their morphism. Expanding this to all other fundamental particles in the universe brings us to the conclusion that "the universe IS mathematics." This is not a position I have ever advocated, but feel free to find some statement by me in these threads to dispute that.

Obvious to us! Understanding that distinction is important. The question then becomes… what is the actual relationship between what we call mathematics and the universe (whatever-it-is) that generates it (mind-brain)? Until we know that, we don’t know what mathematics is. The universe may appear to behave mathematically…as you point out. As I said before, only an idiot would disagree with that. The question is…why?

I understand Tegmarks position (didn't he stop by at JREF a while back?)…but it is a metaphysical point. It is not a scientific point (though…when all is said and done…science is metaphysics). Thus we are back where we began: link between math and the universe…or link between brain and math.

There's an entire field of research devoted to establishing causal links "between the physical activity of the brain and the conceptual activity of mathematics". When I was a PhD student, I took seminar courses devoted to that area of research. Those seminars were led by a cognitive psychologist who is now a fellow of the National Academy of Sciences and has chaired the psychology department at Harvard.

“We have no idea how consciousness emerges from the physical activity of the brain.”

This quote is from a group of neuroscientists at University College London and represents the status quo. Basically…no one has any idea why / how a certain NCC generates 0dfj34;af0d9a4 and not 895na,.ad9ad or 9vmnaidfkef94k4’/4. In addition, the capacity to explicitly adjudicate neural events is extremely limited. The link you provided is generally associated with psychology…not physiology.

He has done so:

So I interpreted his position correctly, and I stand by what I said in my previous post.

You didn’t interpret his position at all. All you did was misinterpret my response…which I corrected earlier. The central issue is…is the universe fundamentally mathematical. PS has clarified his position above….to some degree. He is not insisting (as a scientific fact)…only suggesting… that mathematics has some manner of fundamental relationship with the universe (though earlier he did seem to insist that there is some ontological feature that he refers to as ‘number’ that must orient reality). My point…which I made abundantly clear…is that the first person who can explicitly establish what that relationship is…will be in line for a Nobel prize.

As I said…quite clearly…so far no one has come anywhere close to identifying an ontological mathematical feature in reality …. or explicitly describing the causal link between any cognitive mathematical event and the physical activity of the brain that produces it. No one knows what mathematics ‘is’ (or what consciousness ‘is’ for that matter).

IOW…in no way, shape, or form is it even remotely possible to suggest a particular NCC (described with-in-through whatever limited electro-bio-chemical neurological terminology we currently have the capacity to understand) AND generate the particular cognitive mathematical construct that would be associated with it (nor is the reverse possible...not even remotely).

No neuroscientist on the planet would even begin to dispute this claim (I asked a few and most were incredulous that I would even ask such an inane question).

What this means…in nuts and bolts…is that (as the initial quote clearly establishes)…no one has any idea how consciousness emerges from the physical activity of the brain.

You may not be aware of the fact that almost all mathematics (including all mathematics that matters to the sciences) can be generated from one specific small set of axiom schema. The process of generating that mathematics can be performed by a moderately simple computer program that implements a complete proof procedure for first order logic.

This is not a practical way to generate mathematics, because complete proof procedures are slow. They're slow because they explore every blind alley and prove all sorts of stupid things that human mathematicians, scientists, and engineers would never care about. It seems to me, however, that your claim about the necessary connection between mathematics and intelligence is refuted by the facts I have stated—unless, of course, you are willing to regard that moderately simple computer program as intelligent.

Who…programs…the…computer (not to mention…who built it?)?

 

[Perpetual Student]

<...>
…and this is the first time you’ve made any effort to define this concept you refer to as ‘number’. Here you suggest that it occurs as a consequence of something you describe as a ‘distinction’ in nature? Would there be any point in asking what that even means? Science is fundamentally dependent upon explicitly defined syntax and semantics (this is this and not that). Your terms, so far, are beyond vague so it can hardly be called science.
<...>

I would like to follow up on this thought.
It has been pointed out to you many times that there are a small number of undefined concepts that seem to be inevitable in dealing with the universe:
SPACE, NUMBER, ETC.

(Nevertheless, we do have the Peano axioms, which I an certain you would argue cannot be linked to the universe since they are introspective and not about the universe.)

OK, then I suggest you consider this: Number is an inevitable consequence of distinction. When we contemplate the universe around us, making a distinction is the first primitive perception we make.
That is an idea I came across decades ago in a book called Laws of Form by G. Spencer Brown. Distinction is simply

"differentiating a "this" from "everything else but this."

This then leads to duality and the concept of number easily follows.
See: LAWS OF FORM
If you still find this an unsatisfactory response, then, as an exercise, try to define SPACE. If you cannot do so, does that negate all of physics as unscientific? Yes, there are certain aspects of reality that we accept as fundamental and undefined in order to go forward and do physics. It is my position that number is one of those fundamental aspects of reality.
I suggest you try to understand my words rather than responding with pre-programed knee-jerk reactions about the human brain and deities.