Exploring the Physical Reality of Math

[spartandfm18]

Hey guys, quick question, I was wondering about this and thought maybe you guys would know.

Do you think math is built into nature, or is it something we made up to describe the world around us? I'm a senior ME major and I've seen math all the way up through PDE's and such, but I still can't figure out whether it's physically real or just falls out from unit analysis.

Thanks,

Kevin

 

[ZapperZ]

Please read this:

http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Your thread is being considered to be moved to the Philosophy forum. Please note that threads in the physics forums must contain topics with actual physics content.

Zz.

 

[spartandfm18]

Oh, sorry, my bad. Thanks for your help.

 

[russ_watters]

One apple plus one apple equals two apples.

 

[spartandfm18]

Clearly. To be honest i was kind of hoping for a yes or no answer from someone who has already thought this through, because the internet is loaded with philosophical discussions on this but they tend to be very long and drawn out and not make any sense to me.

 

[ZapperZ]

Clearly. To be honest i was kind of hoping for a yes or no answer from someone who has already thought this through, because the internet is loaded with philosophical discussions on this but they tend to be very long and drawn out and not make any sense to me.

But I thought Wigner's article has clearly addressed the issue that you've brought up!

Or maybe you don't buy his argument?

Zz.

 

[AlephZero]

Clearly. To be honest i was kind of hoping for a yes or no answer from someone who has already thought this through, because the internet is loaded with philosophical discussions on this but they tend to be very long and drawn out and not make any sense to me.

Well, as Wigner implies, if the discussions were not like that they wouldn't be "philosphy", they would be something else.

I forget which 20th century philosopher said "the whole of western philosophy is just a series of footnotes to the works of Aristotle", but ignore the cynicism in the comment and there is a lot of truth in it. Trying to answer unanswerable questions tends to take an infinite amount of time.

 

[spartandfm18]

No, the Wigner article was pretty much exactly what I was looking for. I was referring to all the stuff I had previously read about it.

 

[Math Is Hard]

Note: Moved to Phil, since Zz was kind enough to reply and provide some discussion topic reference.
-MIH

 

[Jocko Homo]

Clearly. To be honest i was kind of hoping for a yes or no answer from someone who has already thought this through, because the internet is loaded with philosophical discussions on this but they tend to be very long and drawn out and not make any sense to me.

No, math is not "built into nature." It is "something we made up to describe the world around us..."

 

[apeiron]

No, math is not "built into nature." It is "something we made up to describe the world around us..."

We made up the language, but did we make up the patterns and relationships the language describes?

 

[Jocko Homo]

We made up the language, but did we make up the patterns and relationships the language describes?

Well, surely we didn't "make up the patterns and relationships" our mathematical language describes but is that what spartandfm18 was asking?

Do you think math is built into nature, or is it something we made up to describe the world around us? I'm a senior ME major and I've seen math all the way up through PDE's and such, but I still can't figure out whether it's physically real or just falls out from unit analysis.

The emphasis is mine...

It depends on what is meant by "nature."

It might be tempting to say that anything we can describe is "in nature" since you'd like to call the reality we all exist in "nature" and our descriptions exist in it but I don't think this is a useful definition. Fictional stories don't exist in nature... well, the stories do but what's described in the stories don't...

For example, I can describe 17 dimensional Euclidean space mathematically but I don't believe such a thing exists "in nature." If you do then we likely have a mere disagreement in semantics...

 

[apeiron]

For example, I can describe 17 dimensional Euclidean space mathematically but I don't believe such a thing exists "in nature." If you do then we likely have a mere disagreement in semantics...

Good point. This draws a distinction between the possible and the actual. Maths starts off by describing actual patterns and then becomes generalised enough so it can describe patterns that are merely possible, or that may exist, we just don't know.

So yes, the relationship is a tricky one. That is why it is the subject of constant debate. Don't expect a simple answer.

However, for the sake of the OP, it is worth starting out as gently as possible. To say math is just constructed and is "not in nature" is too extreme. Just as it is to go the other way and say reality is mathematical (in the way Pythagoras and Plato were said to claim).

So instead we can point out that reality is patterned. It has self-consistent form. And the variety of these forms is in fact also self-limiting. There might be reasons why 17 dimensions is indeed impossible, yet some other number of dimensions has the right global symmetry.

So string theory, for example, could be both a mathematical statement and a pattern of nature. Whereas a 17 dimensional Euclidean space would just be a mathematical statement, with no convincing reason to exist. I mean you cited it because it did seem so obviously arbitrary I presume.

 

[n.karthick]

In my view nature and math can be viewed as two intersecting circles A and B
where $$A \cap B$$ relates to the part of nature which has mathematical description as we know today. Still many things in nature remain to be mathematically described, which is $$A - B$$. Same way we have math for some things which doesn't exist in nature $$B - A$$ .

 

[homology]

There should probably be more "I think" and "I feel" statements in here. Its not like we can prove any of these assertions. I think we 'discover' mathematical truths just as we discover physical ones. Its all there and we're groping through the dark to find it. But that's just the way I view things. But we should also be careful of the applicability of math question. I think its largely an illusion. There are plenty of failed attempts to do one thing or another with math, but those end up in wastebaskets or erased from chalkboards. Journals, textbooks and the like are largely filled with those attempts that worked and so our sample is somewhat skewed.

 

[gb7nash]

There are a lot of mathematical concepts that appear in real life. The very famous fibonacci numbers, golden ratio to name a few.

 

[Jocko Homo]

There should probably be more "I think" and "I feel" statements in here. Its not like we can prove any of these assertions. I think we 'discover' mathematical truths just as we discover physical ones. Its all there and we're groping through the dark to find it. But that's just the way I view things. But we should also be careful of the applicability of math question. I think its largely an illusion. There are plenty of failed attempts to do one thing or another with math, but those end up in wastebaskets or erased from chalkboards. Journals, textbooks and the like are largely filled with those attempts that worked and so our sample is somewhat skewed.

Perhaps you missed this part:

Clearly. To be honest i was kind of hoping for a yes or no answer from someone who has already thought this through, because the internet is loaded with philosophical discussions on this but they tend to be very long and drawn out and not make any sense to me.

 

[homology]

Just to play devil's advocate: there are lots of rational numbers that appear in life that seem close to some notable irrationals.

 

[chiro]

One thing that I want to point is that the tools of math are applied many many times without people even noticing that what they are doing is what scientists, engineers, and applied as well as pure mathematicians do (or at least attempt to) do on a daily basis.

Here is an example of what I mean.

Lets say a young person gets a job. They have a mentor to help them learn whatever the business wants them to learn. The mentor (or trainer) has many many years of experience. Now the trainer has had many many years of experience and has had the ability to get a lot of experience, and time for reflection, analysis and as a result gain further insight into what his field is "in a nutshell".

So the trainer conveys what the field is all about to the trainee. He hasn't provided any specifics or worked examples, but he has condensed his knowledge down into things that when expanded and when properly understood, yield the generality of his field.

That is an example of a non-mathematician creating "axiom-like" details, just like the scientific community tries (or does) do as part of their job.

People will always use this reductionist technique in any area, because it is a generalization of the abstraction mechanism that allows to further abstract knowledge and ideas to a point where further abstraction explains a greater variety of conceptual understandings, ideas, working knowledge and so on.

Without this kind of "axiomitization", I don't think people would benefit from other peoples experience and without the ability I dare say people would have to "reinvent the wheel" every time.

 

[homology]

Perhaps you missed this part:

Thanks, though I didn't. Just because he wants a yes/no answer doesn't mean there is one.

 

[qsa]

Hey guys, quick question, I was wondering about this and thought maybe you guys would know.

Do you think math is built into nature, or is it something we made up to describe the world around us? I'm a senior ME major and I've seen math all the way up through PDE's and such, but I still can't figure out whether it's physically real or just falls out from unit analysis.

Thanks,

Kevin

https://www.physicsforums.com/showthread.php?t=330679&page=19

 

[uhjim]

If we make the assumption that, to quote Tristan Needham, "that our mathematical theories are attempting to capture aspects of a robust Platonic world that is not of our making", what then? if mankind did cook these things we call integers, where everything happens all at once, then who is teaching the other animals how to count?
Maybe Leoplod Kronecker got it backwards, maybe man invented God, and all the rest is the work of integers. Maybe not. We don't know. Maybe the universe is an emergent property of the the integers and maybe the integers are an emergent property of the real numbers. who knows? Not me, not anyone.

 

[Darken-Sol]

that depends on what your definion of "is" is.

 

[SW VandeCarr]

Even when describing common physical entities, math may use abstract concepts to conveniently express ideas for some descriptive purpose. For example a six dimensional vector space is used for the momentum space (phase space) of a particle. The velocity component has two dimensions (speed and direction) for each of the three basis vectors of ordinary three dimensional physical space.

 

[pergradus]

I don't believe so.

I think the universe behaves in a consistent, predictable way which is government by simple interactions at the smallest level.

The ultimate law of physics, in my opinion, should not even need to be a mathematical one, but one which simply explains how the machinery of nature moves.

I think any system which is consistent, predictable and based on simple interactions can be described mathematically - because math follows the same structure.

 

[AstrophysicsX]

Math is just a code we use to describe nature.

 

[tamousfleck]

Just because he wants a yes/no answer doesn't mean there is one.

Especially since he didn't technically ask a yes or no question, eh?

"Do you think math is built into nature"

I'm not too sure what this part of your thought would actually mean. In many ways it seems that math is a language... and the Greeks didn't call nipples, nipples but we all know nipples are part of nature. So, semantically no form of communication is as organic as to say it was "built into nature" because it is all learned. Direct eye contact even means severely different things to different communicators...

Personally, I always liked the criminal forensic analogy. "Blood spatter" is an entirely relevant element of crime solving, and yet for thousands of years it sat entirely arbitrary within the matter of solving crimes. The same thing with finger prints... They've always been there and are simple enough to see just like mathematic interactions, but the actual analysis of them require representations, which almost by definitions cannot physically exist the same way as their host. Math is a language mankind has derived for itself in order to analyze and predict the condition of nature and like any language, the representations are learned but that doesn't make, for example, the Earth's escape velocity, which is represented with a host of equations and symbols but when it comes down to it, you break 25.2k mph and you orbit Earth.

As far as the more complex stuff that seems not to be attached to elements of reality, well just like blood spatter... until people gain the ability to see aspects of nature in a way that communicates to them things seem a lot more arbitrary than they really are.

_________________________________________________
Where's the math that says ∞! is bigger than God's nose hair?

 

[skippy1729]

Which Math??

The axioms of ZFC have widespread but not universal acceptance. There are many mathematicians who do not accept C (the axiom of choice) others would add a variety of large cardinal axioms. There is an small active group of mathematicians investigating and debating the foundations of mathematics. If Math is physical, how do we choose the right one?

Skippy

PS Accepting ZFC leads to some very non-physical paradoxes like the Banach-Tarski paradox and the nonexistence of measure which is invariant under all rigid motions.

 

[atyy]

There's an interesting thought that one might get Penrose's Road to Reality (the picture connecting maths-physics-mind). Can we say maths is physically real because it is in people's brains, and people's brains are physically real?

 

[apeiron]

There's an interesting thought that one might get Penrose's Road to Reality (the picture connecting maths-physics-mind). Can we say maths is physically real because it is in people's brains, and people's brains are physically real?

If you followed the logic of this dualistic position, wouldn't you be forced to say that the maths is still only in the mind-stuff, and not the brain-stuff? If the maths is in anything physically real? Mind and brain may seem co-located, but dualism says they are not "the same place".

But if you like this way of looking at things, you may like the Popper/Eccles three worlds approach to interactive dualism.
http://en.wikipedia.org/wiki/Popperian_cosmology

I prefer the view that brains are modelling the world. What this modelling feels like is consciousness. Brains model both specific and general ideas. Specific ones are those like the perceptual state of the world right now. General ones are like the concepts of maths and science (Popper's world three).

 

[atyy]

If you followed the logic of this dualistic position, wouldn't you be forced to say that the maths is still only in the mind-stuff, and not the brain-stuff? If the maths is in anything physically real? Mind and brain may seem co-located, but dualism says they are not "the same place".

But if you like this way of looking at things, you may like the Popper/Eccles three worlds approach to interactive dualism.
http://en.wikipedia.org/wiki/Popperian_cosmology

I prefer the view that brains are modelling the world. What this modelling feels like is consciousness. Brains model both specific and general ideas. Specific ones are those like the perceptual state of the world right now. General ones are like the concepts of maths and science (Popper's world three).

I wasn't aware what I wrote was dualistic. I would say mind is a state of brain (and body). I'd be in general agreement with your last paragraph. Is what I wrote actually not?

 

[disregardthat]

To ask whether mathematics is physically real is exactly like asking if any other field of study is physically real. Mathematics is, as philosophy, physics, linguistics, psychology etc.. not more physically real than any other activity.

The question as it should have been asked is whether the objects we speak of in mathematics are physically real. The view that they in some sense are amounts to mathematical realism or even mathematical platonism, two views which unfortunately are common among mathematicians.

 

[apeiron]

I wasn't aware what I wrote was dualistic. I would say mind is a state of brain (and body). I'd be in general agreement with your last paragraph. Is what I wrote actually not?

Sorry, when you mentioned Penrose, I assumed you meant his pet theories (he is both a dualist and a Platonist).

So if you step back to just the statement "maths is physically real because it is in people's brains", then I don't see this does add much.

The question still remains how you regard the physical reality of form (in a world which the reductionism would say monistically "is just composed of substance").

Perhaps a better question here is "are the laws of physics physically real?" Do they exist in the actual world (and where) or are they just socially-constructed ideas (and hence exist in books and other "physical" places as well as brains)?

 

[atyy]

Sorry, when you mentioned Penrose, I assumed you meant his pet theories (he is both a dualist and a Platonist).

So if you step back to just the statement "maths is physically real because it is in people's brains", then I don't see this does add much.

The question still remains how you regard the physical reality of form (in a world which the reductionism would say monistically "is just composed of substance").

Perhaps a better question here is "are the laws of physics physically real?" Do they exist in the actual world (and where) or are they just socially-constructed ideas (and hence exist in books and other "physical" places as well as brains)?

Well, I guess physics is dualistic in some sense. We have the laws and reality, and the laws are abstraction by the observer (who is an emergent physical object). In some cases, we know of laws that have more than one physical instantiation. Eg. certain properties of materials near the critical point are universal, dependent only on dimensionality and symmetry. So if those properties are the "character" or "soul", then they don't need a unique body for their existence, and can be "resurrected". (Incidentally, but completely tangentially, I did once come across a mathematical definition of soul http://en.wikipedia.org/wiki/Soul_theorem )

 

[Darken-Sol]

does math = reality?