A math major's take on math and physics

[sapmarten]

Quoting myself from another forum, I think this best describes what the average math major believes (assuming that I am the average math major, which is presumptive of me, but I think a fair assumption). I'd also like to strike up a debate on either of the two topics.

Spoiler

Show

I'm no physicist, so help me understand this. On subjects as exotic as the nature of the universe, whether things exist "outside" (bad terminology, but you know what I mean) the universe, extra dimensions, and string theory, most physicists admit that there's little they could do to actually test these theories. But the attitude towards these things is surprisingly accepting (especially concerning the extra dimensions). Now, if you can't get empirical evidence to prove these hypotheses, then why even assume for a moment that it's true?

I don't know the math behind it, but let's say that the physicists can extrapolate the existence of eleven dimensions through mathematical reasoning. But as Bertrand Russell himself said, in Principles of Mathematics, math does not prove or disprove axioms, but merely formalizes a relationship between said axioms. So math cannot prove that the statement a is true, nor can it prove that the subsequent implication b is true, but it can demonstrate the implication to be correct, only insofar as the original statements were true.

I can understand the argument that if the original proposition a was a tested and verified hypothesis, then the untested consequent implication b (that there are eleven dimensions) demonstrated by mathematical reasoning should still be as true as the original proposition. Nevertheless, given the nature of physics I somehow doubt that any moderately complex original proposition (that could possibly imply the existence of eleven dimensions) could be a fully tested hypothesis (and therefore a law)--and, as such, I am still wary of the accepting tone some physicists have towards the theory of eleven dimensions.

Well, ignore me, I'm just an undergraduate math major trying to understand physics. But I'd like to hear what actual physicists and/or better mathematicians than I have to say about this subject.

Spoiler

Show

I think most here are familiar with Bertrand Russell's take on the issue. He contends that pure mathematics is the formalization of implications; for instance, math cannot prove the proposition x, nor can it prove the consequent implication y, but it can prove that x implies y assuming x to be true. Otherwise, math is an information communication device. It holds no claim towards demonstrating the truthfulness of the information within, but it allows extrapolation of the information and communication thereof. I think due to this that math is largely a language, albeit a very concise one. Science, however, is the collection and analysis of empirical data--by its very core, science is for demonstrating the truthfulness of information, not for communication or unsupported extrapolation.

I had always assumed that other mathematicians would agree on this issue, but I'd like to see how many actually do.

[LostOne]

I found Feynman's take on it to be persuasive; see if you agree. Essentially, it argues that physics is more than than the mathematics it depends on and extrapolation beyond what is mathematically proven appears to have predictive power. Why this is true is a fascinating question.

[A Rainy Knight]

I'm just a student in high school physics, but based on a video we've watched in class, your take on it is pretty similar to what some physicists think. According to these folks (and in my opinion after watching the video), the mathematical reasoning that checks out in string theory doesn't create a truly solid theory, but it does provide an interesting idea that's worth looking into. As one of the physicists they interviewed roughly put it, anything with that much mathematical appeal probably isn't entirely garbage. Our problem now is just figuring out how we're going to get the evidence.

[AsteriskAmp]

Short answer: We've reached the point were we can't really do much other than wait for some research to conclude, the main one and the most publicised one, the LHC, which will either make SUSY or make a lot of physicists say they screwed up and that our Universe shouldn't work since they would have to redo a great deal of the model. So the best thing they can do with their degree and for getting paid is pretty much just thinking, and writing some of that stuff down until the LHC gets going. There are other areas advancing with physics but none of them really are as vital as the one in getting to confirm that our universe holds up.

[averagejoe]

Short answer: We've reached the point were we can't really do much other than wait for some research to conclude, the main one and the most publicised one, the LHC, which will either make SUSY or make a lot of physicists say they screwed up and that our Universe shouldn't work since they would have to redo a great deal of the model. So the best thing they can do with their degree and for getting paid is pretty much just thinking, and writing some of that stuff down until the LHC gets going. There are other areas advancing with physics but none of them really are as vital as the one in getting to confirm that our universe holds up.

Actually, the LHC experiments regarding string theory won't prove/disprove it. We might find some particles predicted by string theory (and I believe these are the titular large hadrons, but my mind is like a freakin' sieve when it comes to the names of particles), and if we find those particles it kind of points to string theory being accurate, and if we don't it doesn't really mean anything. This is one of the reasons that there are a lot of physicists that criticize the research that's gone into string theory; it's not really a theory that can be disproved right now. Compare that to, say, the experiments they did related to Eisenstein relativity using atomic clocks and planes. If the clocks weren't off, no time dilation, and Einstein was (at least partially) wrong.

I still like string theory though. It's the only theory I know that has the word super in it.

[AsteriskAmp]

Actually, the LHC experiments regarding string theory won't prove/disprove it. We might find some particles predicted by string theory (and I believe these are the titular large hadrons, but my mind is like a freakin' sieve when it comes to the names of particles), and if we find those particles it kind of points to string theory being accurate, and if we don't it doesn't really mean anything. This is one of the reasons that there are a lot of physicists that criticize the research that's gone into string theory; it's not really a theory that can be disproved right now. Compare that to, say, the experiments they did related to Eisenstein relativity using atomic clocks and planes. If the clocks weren't off, no time dilation, and Einstein was (at least partially) wrong.

I still like string theory though. It's the only theory I know that has the word super in it.

It's not the only theory though. String Theory is the one most referred to since it kinda answers the what's inside everything recurrence with the easiest to grasp concept, one-dimensional strings. Also, similar to string theory ,we have the Multi-verse one, both of which have kinda become a God-of-the-Gaps concepts since they can be used to fit most questions with "it's elsewhere".

Also, the LHC is VERY relevant to String Theory, this article better explains it than I ever could:

http://www.strangehorizons.com/2010/.../white-a.shtml

[averagejoe]

Also, the LHC is VERY relevant to String Theory, this article better explains it than I ever could:

Oh, I don't doubt that it's relevant, I'm just saying that there are physicists out there who are of the opinion that the current treatment of string theory is bad science, and I'm not sure that I disagree with them.

I know it's not the only theory. It's just the only, "Super," theory.

[sapmarten]

I think "theory of everything" is a much super-er name. Maybe it should be renamed the "super theory of everything".

[averagejoe]

I think "theory of everything" is a much super-er name. Maybe it should be renamed the "super theory of everything".

String theory's full name is, "Supersymmetric String Theory." Can't get much more super than that, man.

[AsteriskAmp]

Oh, I don't doubt that it's relevant, I'm just saying that there are physicists out there who are of the opinion that the current treatment of string theory is bad science, and I'm not sure that I disagree with them.

I know it's not the only theory. It's just the only, "Super," theory.

Super-Determinism?
Also, superstring theory is different from string theory
Also, I concur with the treatment opinion hold, there is not enough evidence though if I have to explain Quantum Mechanics presenting String Theory first is normally a good idea to prevent a "what's smaller than a" line of questions, and then telling them the issues with it and the alternatives, it helps calm the doubts and then motivate people to explore sciences, at least on a knowledge level more than the understanding level of it.

[averagejoe]

Also, superstring theory is different from string theory

Correction: it's often what people are referring to.

[AsteriskAmp]

Correction: it's often what people are referring to.

Sadly Science does not obey linguistic laws of "common usage becomes official terminology", they are different even though what you say is true, but it does cause confusion, so if I'm talking on a scientific-y enviroment (or thread) I'd much rather know which one is being referred to.

[factotum]

I think "theory of everything" is a much super-er name. Maybe it should be renamed the "super theory of everything".

Actually, what you're talking about is usually referred to as the Grand Unified Theory--the hoped-for theory that will allow everything in the universe to be understood at both macro and micro scales. At the moment we have Relativity at the macro scale and Quantum Mechanics at the micro, which both work well in their particular areas but which contradict each other in some ways!

[Tirian]

Oh, I don't doubt that it's relevant, I'm just saying that there are physicists out there who are of the opinion that the current treatment of string theory is bad science, and I'm not sure that I disagree with them.

I think of it as the Emperor's New Unification Theory. It doesn't predict much that we can measure, but we're to believe that if we could measure it we'd find that the model can explain everything. And if we don't buy that, it's because we're not smart enough to understand string theory. My feeling is that, hey, maybe those are beautiful clothes that I'm too stupid to see, but until you've got some better proof I'm just going to be over here assuming that you're naked.

One thing that I think is important to realize about the interface between mathematics and physical sciences is that an elegant mathematical model is not in itself evidence of real-world phenomena. For instance, calculus was originally invented largely to describe how Newtonian mechanics would predict large-body physics problems. They found that things worked pretty well in the world the way that they thought it would in paper. To the degree that it didn't though, that is partially because of various sorts of experimental error and partially because Newtonian mechanics is not really an accurate model when the bodies get too small or the speeds get too large. But then we took that new data and thought about it harder and the theoretical physicists of a later generation came up with theories of relativistic mechanics which explained the errors in classical mechanics and predicted further phenomena that have since been verified. But even though every theory of relativity works perfectly well on paper, none of them line up perfectly with whatever the rules of our universe are. So now we're up to playing this game with quantum mechanics which is exactly the same brand of better but still not perfect, and perhaps it's fair to ask whether what the fourth generation of mechanics will look like or even if it's too soon to put a lot of effort into what form it will take.

[averagejoe]

I think of it as the Emperor's New Unification Theory. It doesn't predict much that we can measure, but we're to believe that if we could measure it we'd find that the model can explain everything. And if we don't buy that, it's because we're not smart enough to understand string theory. My feeling is that, hey, maybe those are beautiful clothes that I'm too stupid to see, but until you've got some better proof I'm just going to be over here assuming that you're naked.

One thing that I think is important to realize about the interface between mathematics and physical sciences is that an elegant mathematical model is not in itself evidence of real-world phenomena. For instance, calculus was originally invented largely to describe how Newtonian mechanics would predict large-body physics problems. They found that things worked pretty well in the world the way that they thought it would in paper. To the degree that it didn't though, that is partially because of various sorts of experimental error and partially because Newtonian mechanics is not really an accurate model when the bodies get too small or the speeds get too large. But then we took that new data and thought about it harder and the theoretical physicists of a later generation came up with theories of relativistic mechanics which explained the errors in classical mechanics and predicted further phenomena that have since been verified. But even though every theory of relativity works perfectly well on paper, none of them line up perfectly with whatever the rules of our universe are. So now we're up to playing this game with quantum mechanics which is exactly the same brand of better but still not perfect, and perhaps it's fair to ask whether what the fourth generation of mechanics will look like or even if it's too soon to put a lot of effort into what form it will take.

Of course the degree to which math is used in modern physics, and the (relatively) exotic types of maths that accurately model quantum mechanics... it's all completely amazing when you really stop to think about it. To this day it's still kind of hard to believe that math works as well as it does.

I suppose on a philosophical level that's a problem I have with string theory. (And, though philosophy tends not to be pertinent to most science, in this case it's fair game because the string theorists started it. ) Admittedly I've examined the theory hardly at all, so this is a fairly uneducated perspective, but from what I've seen there's nothing about it that's really weird. It's just kind of a neat little thing that that's trying to be an endpoint, when the most compelling theories have, historically, opened up whole new avenues of thought that we couldn't even imagine before. I'll grant that it's not a good reason to reject the theory, but there are already plenty of good reasons.

[GrassyGnoll]

I think most here are familiar with Bertrand Russell's take on the issue. He contends that pure mathematics is the formalization of implications; for instance, math cannot prove the proposition x, nor can it prove the consequent implication y, but it can prove that x implies y assuming x to be true. Otherwise, math is an information communication device. It holds no claim towards demonstrating the truthfulness of the information within, but it allows extrapolation of the information and communication thereof. I think due to this that math is largely a language, albeit a very concise one. Science, however, is the collection and analysis of empirical data--by its very core, science is for demonstrating the truthfulness of information, not for communication or unsupported extrapolation.

I had always assumed that other mathematicians would agree on this issue, but I'd like to see how many actually do.

QFT. This is my impression after two years of uni.

I don't play the physics game, attempting to construct sets of rules that are more true/super than others. I am a student of mathematics and cognitive science. I usually explain my interest in math as one of 'truth-preserving linguistics'. The human brain is very well equipped to sort through recursive grammar and semantic distinctions (You know that I know that you know what I mean when I say this, right?). However, pure mathematics insists that we can shuffle our axioms to whatever we fancy, and biological determinism rains all over that parade. Truth preserving operations are limitless, our brains are not! Certain percepts are just not possible (describe a reddish-green hue, if you will).

I haven't married my two disciplines yet, but I'm revving up for a Cognition of Mathematics course and series on vector calculus next year @UCSD. On one hand, I want to study how concepts such as numerosity and spatial orientation are represented in cortical activity; and at the same time, study the pattern of activation of the motor cortex in the scheme of population vectors.

http://en.wikipedia.org/wiki/Numerical_cognition
(Sadly, I am older than the field I wish to study.)

[Devils_Advocate]

Now, if you can't get empirical evidence to prove these hypotheses, then why even assume for a moment that it's true?

At the moment we have Relativity at the macro scale and Quantum Mechanics at the micro, which both work well in their particular areas but which contradict each other in some ways!

My understanding is that the second above quote is part of the answer to the first. A new theory is needed because at least one current theory must be incorrect somehow. So you get theoretical physicists paying attention to ideas which seem like they might lead to such a new theory.

Also, having a single theory that explains all of the fundamental forces of nature is just cooler. You want to be one of the cool physicists, don't you?

[ZombyWoof]

Math : Physics :: Masturbation : Sex

"So I've discovered that the integral of Xdx is X^2/2"
"... ok. Sure."

"So I've discovered a way to blow up the entire planet three times over."
"SWEET DUDE! Let's go test this right away!"

"E^i(pi) = 1"
"Hmmm... that's interesting."

"It turns out that occasionally particles will go through barriers that realistically they shouldn't go through in a process called quantum tunneling. It's part of what makes the sun undergo fusion."
"... wait wait wait, back up. Particles sometimes just randomly go through stuff?"

[Ted_Stryker]

^

If I'm reading that right you've gotta flip one side of that first line.

[dangermunk]

The second opinion (in original message) on math seems correct, but science is not just the big theory, but the process that developed the theory that does not take assumptions, questions past results, and sets hypotheses. The scientific theory is the rsult of this process.
This is what differentiates the scientific way of looking at the world from other ways

[Capt Spanner]

I'm no physicist, so help me understand this. On subjects as exotic as the nature of the universe, whether things exist "outside" (bad terminology, but you know what I mean) the universe, extra dimensions, and string theory, most physicists admit that there's little they could do to actually test these theories. But the attitude towards these things is surprisingly accepting (especially concerning the extra dimensions). Now, if you can't get empirical evidence to prove these hypotheses, then why even assume for a moment that it's true?

I think the "surprisingly accepting" attitude you observe is down to two things: first is that pop-science likes these types of things, so the scientists who are interested in it tend to be the ones who get the media attention. What isn't shown in the media is the number of scientists who thing the whole thing is likely to be rubbish. They aren't portrayed because 1. It's boring for the media, 2. they tend to be focussed on their own research and not string theory and 3. it's unscientific to go rubbishing an idea purely based on a hunch or an argument from implausibility. The idea, and science, is much better served by letting a group who are interested pursue a theory for as long as it takes to convince themselves it can't work, or to convince themselves it can work.

These string-theory skeptics are actually much greater in number, and constitute most the scientific community. String theory is acceptable as a pet-project but not as primary project.

As for empirical evidence: this works in many ways. You collect observations and you build a model to explain them. You then use your model to derive other predictions and test them. String theory arises as a model to describe sub-sub-sub-atomic level (sub-atomic = electrons, protons, neutrons, sub-sub-atomic = quarks, bosons, leptons and stuff, sub-sub-sub-atomic = erm...strings, maybe?) and originally proposed that the vast number of sub-sub-atomic particles can be described by vibrations of superdimensional strings. The number of dimensions is derived from horribly complicated mathematics that I can't even begin to understand, but it's too do with stable vibrations, harmonies, etc...

I don't know the math behind it, but let's say that the physicists can extrapolate the existence of eleven dimensions through mathematical reasoning. But as Bertrand Russell himself said, in Principles of Mathematics, math does not prove or disprove axioms, but merely formalizes a relationship between said axioms. So math cannot prove that the statement a is true, nor can it prove that the subsequent implication b is true, but it can demonstrate the implication to be correct, only insofar as the original statements were true.

I can understand the argument that if the original proposition a was a tested and verified hypothesis, then the untested consequent implication b (that there are eleven dimensions) demonstrated by mathematical reasoning should still be as true as the original proposition. Nevertheless, given the nature of physics I somehow doubt that any moderately complex original proposition (that could possibly imply the existence of eleven dimensions) could be a fully tested hypothesis (and therefore a law)--and, as such, I am still wary of the accepting tone some physicists have towards the theory of eleven dimensions.

Well, ignore me, I'm just an undergraduate math major trying to understand physics. But I'd like to hear what actual physicists and/or better mathematicians than I have to say about this subject.

I hope I've been helpful here. May your studies reward your interest.

[Lord Raziere]

an artists take on math and physics:

math is that boring thing on paper.

science is the cool stuff with things happening

/is intentionally playing stupid

[Jallorn]

I think the core of this issue is the fact that it's usually easier to disprove something, rather than prove it, therefore a greater amount of leeway and a lot more, "So far that's possible," is present in modern science. In short, if something hasn't been disproved, then it has a good enough chance of being correct that we shouldn't simply discard it.

[Prime32]

Actually, the LHC experiments regarding string theory won't prove/disprove it. We might find some particles predicted by string theory (and I believe these are the titular large hadrons, but my mind is like a freakin' sieve when it comes to the names of particles)

I was under the impression that it was called the Large Hadron Collider because the collider was large, not the hadrons. IIRC the particle everyone is looking for is the Higgs boson.

[Capt Spanner]

Physicists like terrible puns. The LHC is a large collider looking for large (i.e. high energy) hadrons. If you don't believe me check this experiment out.

Also, while mathematics is basically "the formalisation of implications" that is it's great strength!

Many physical theories involve getting some implications, and working out how the mathematics relates them, and then getting the implications of that and testing them. The two fields complement each other perfectly.

Also, don't forget the important second half to the "maths is to physics as masturbation is to sex" thing: "sure, sex has practical results, but that's not why we do it."