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On Mathematical Beauty in Physics

blogs.unimelb.edu.au

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Re: On Mathematical Beauty in Physics

#21

Post by ta1234567890 »

mrfox321 wrote: post #20
ta1234567890 wrote: post #18

Earlier quoted context omitted.

Who performs the measurements? What instruments are used to perform those measurements? If there's someone or something performing the measurements, then they depend on that someone or something to interpret them. You are right that measurements and models facilitate a better human understanding of nature/ourselves. However, it is important to keep in mind that these things are maps, not the terrain.

A measurement can be the interaction between two sufficiently decoupled subsystems. But I don't really understand why there needs to be some "interpreter." Nature could be some computer/system that is minimizing Action over all possible trajectories. Humans attempt to communicate an approximation to this truth by writing down nonlinear differential equations.

> But I don't really understand why there needs to be some "interpreter."

More than there needing to be, it's just all we have.

It's impossible for us to know what the universe without us is like. All of our knowledge has been gathered and interpreted by us.

Maybe there is a reality that doesn't depend on us, but how could we ever know that?

We cannot remove ourselves from our experiences, so how could we ever know what those experiences/reality would be like without us?

How could you ever know what truth is, if there is no you to know it (or approximate it)?

Re: On Mathematical Beauty in Physics

#22

Post by 613style »

ses1984 wrote: post #19
MaximumYComb wrote: post #17

Earlier quoted context omitted.

Math is a description of our reality. If we discovered something that math couldn't explain we'd expand math to explain it.

How does that square with something like godel's incompleteness therom?

Don't confuse the terrain with the map. The formal systems which underly mathematics describing the universe are incomplete (containing true but unprovable statements), but that is not a statement about the universe.

Re: On Mathematical Beauty in Physics

#23

Post by air7 »

__MatrixMan__ wrote: post #6

> as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen There is a fair bit of mysticism that gets bandied about along these lines--and I can certainly see why a mathematical platonist might marvel at the spooky correspondence between beautiful mathematics and to-be-discovered physical theories. But if you can let go of t…

The spooky thing is that the physicist that "finds things that correspond nicely to the mathematician's list" is so freaking good at predicting nature and yielding it to his will.

People always looked at nature through the lens of their minds and came up with creative explanations for reality (like the gods/4 elements/mysticism etc) the difference is that they were much worse at any actual real-world predictions/control compared to modern day physicists.

So we much be on to something here.

Re: On Mathematical Beauty in Physics

#24

Post by auntienomen »

__MatrixMan__ wrote: post #6

> as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen There is a fair bit of mysticism that gets bandied about along these lines--and I can certainly see why a mathematical platonist might marvel at the spooky correspondence between beautiful mathematics and to-be-discovered physical theories. But if you can let go of t…

Except that sometimes the resonances are extremely peculiar. It's not terribly surprising that differential geometry was the right language for describing physics on spacetime. It's a bit more surprising (to me anyways) that the same probability distribution describes both the energy levels of complicated nuclei and the distribution of zeros on the critical line of the Riemann zeta function.

Re: On Mathematical Beauty in Physics

#25

Post by pnx »

univalent wrote: post #3

Reminds me of this paper in Nature from some time back. Especially, the Euler's identity graph from the paper is pretty amazing. https://www.nature.com/news/equations-are-art-inside-a-mathe...

I find it odd that people think that equation is beautiful. Rewriting it in polish notation/lisp you end up with:

    (= (+ (exp (* i pi)) 1) 0)
Which is neither beautiful nor very enlightening.

Re: On Mathematical Beauty in Physics

#26

Post by chr1 »

Does anyone know example of math that is not beautiful? As far as i can tell everything that explains something more complex in terms of simpler rules is called beautiful, but that is all the math! So it's not very surprising that math in physics is beautiful too.

Re: On Mathematical Beauty in Physics

#27

Post by ses1984 »

613style wrote: post #22
ses1984 wrote: post #19

Earlier quoted context omitted.

How does that square with something like godel's incompleteness therom?

Don't confuse the terrain with the map. The formal systems which underly mathematics describing the universe are incomplete (containing true but unprovable statements), but that is not a statement about the universe.

I'm not sure I see the point. Or rather, I see The tautology. We discover something math can't explain. By definition, you can't expand math to explain it. You can try, and if you succeed you were wrong all along, in that your discovery could have been explained by math you just couldn't prove it at the time.

Re: On Mathematical Beauty in Physics

#28

Post by disconcision »

MaximumYComb wrote: post #17
empath75 wrote: post #8

I think it’s mostly a case of the drunk looking for his keys under the lamp post because that’s where the light is. We have no idea how much there is to know about reality. We do know how to describe some parts with mathematics, but who knows how much there is out there which is not possible to describe with mathematics. We may just be discovering infinitesimally small part ls of reality which math happens to describ…

Math is a description of our reality. If we discovered something that math couldn't explain we'd expand math to explain it.

We know about lots of things that math doesn't explain. AFAICT there are reasonable information-theoretic grounds for suspecting that many if not most things we might want to ask about won't yield the the kind of explanations we find satisfying. Irreducible complexity is a thing, at least apparently, and among documented phenomena there is a spectrum of amenability to formal modelling. Statements expositing an 'unreasonable effectiveness of mathematics' or TFA's aesthetic rendition don't seem to amount to more than 'some phenomena admit simple explanations'. Much more often the best effective mathematical explanation is a lukewarm admixture of awkward cludges, or is simply non-existent.

Re: On Mathematical Beauty in Physics

#29

Post by matt_j »

pnx wrote: post #25
univalent wrote: post #3

Reminds me of this paper in Nature from some time back. Especially, the Euler's identity graph from the paper is pretty amazing. https://www.nature.com/news/equations-are-art-inside-a-mathe...

I find it odd that people think that equation is beautiful. Rewriting it in polish notation/lisp you end up with: (= (+ (exp (* i pi)) 1) 0) Which is neither beautiful nor very enlightening.

There is more to a beautiful equation than the shape of the symbols used to describe it. The beauty of Euler's identity is the relationship between 5 fundamental constants (0, 1, e, i, pi). It's simple, elegant and far reaching.

The relationship is the same regardless of the notation.

Re: On Mathematical Beauty in Physics

#30

Post by emmelaich »

gowld wrote: post #15

I expected this to be an a new article or report of Sabine Hossenfelder's work, but apparently the author S is someone else? Hossenfelder's counterpoint, disussed on HN in the past: https://www.amazon.com/Lost-Math-Beauty-Physics-Astray/dp/04... "A contrarian argues that modern physicists' obsession with beauty has given us wonderful math but bad science Whether pondering black holes or predicting discoveries at CERN…

Yep, this is Stella (someone); click on the author's tiny blue S and be rewarded with similar articles.

https://blogs.unimelb.edu.au/sciencecommunication/author/sst...

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