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On Mathematical Beauty in Physics

blogs.unimelb.edu.au

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Re: On Mathematical Beauty in Physics

#51

Post by dr_dshiv »

joes223 wrote: post #48
dr_dshiv wrote: post #12

Earlier quoted context omitted.

Keeping in mind that Tegmark's idea is 2,500 years old and the basis of Western civilization. Pythagoras was the biggest philosophical influence on Plato. And, according to Aristotle (150 years later), Pythagoras believed that "all is number". Thales (the "first" Greek philosopher) believed that the underlying principle of the world was water, a kind of flowing force. Anaximenes, his student, believed the underlying…

Pythagoras had some insider knowledge, while Thales et al just speculated.

I'm curious what you mean, insider knowledge!

Re: On Mathematical Beauty in Physics

#52

Post by mqduck »

yesenadam wrote: post #43
matt_j wrote: post #29

Earlier quoted context omitted.

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.

Mostly serious comment: I'm not sure why the form e^{i\pi}=-1 isn't better. Only it doesn't have 0, but is it worse, less beautiful? (It doesn't seem to have the same "relationship between 5 fundamental constants", although it adds the negative number realm, to the imaginary and transcendental–neat.) Would E-mc^2=0 be similarly be better than E=mc^2, because it has an additional "fundamental constant"?

I don't want to start an argument about tau versus pi, but I like a tau form (or modification) of Eulor's Identy: [e^(ikτ) = 1] for all integer values of [k]. This gets across rather well that this formula expresses a complete turn around a unit circle. You can't get something quite equivalent using pi.

I even more prefer the full form of Euler's Formula: [e^(ix) = cos(x) + isin(x)]. The real beauty of Euler's Formula I think is that it shows an equivalence between an algebraic function and a trigonometric function.

(Note that I'm only a mildly learned laymen when it comes to mathematics. Any experts in math should feel very free to tell me why I'm wrong.)

Re: On Mathematical Beauty in Physics

#53

Post by Chico11Kidlet »

Who wrote this? Because its content is uninspired and its writing poor. It doesn't even address the question: is the universe beautiful? The mathematicians whose brains registered the signs of appreciating beauty when presented with "beautiful equations," could easily have made the association themselves; implying the result means equations are beautiful is the simplest post hoc ergo propter hoc. I myself hope the base principles of the universe are by human standards horrid. Human notions of beauty are too easy and accommodating; something as immense and monstrous as the universe should make us shudder with the strangeness of its true nature. Humans are tiny, deranged beings, and our beauty ought to be filthy rags compared to the universe's standard of beauty.

Re: On Mathematical Beauty in Physics

#54

Post by auntienomen »

raattgift wrote: post #41
Mugwort wrote: post #31

I'll say something regarding string theory which has been accused of leading physicists astray because of its "mathematical beauty". First of all, string theory in its present form is NOT mathematically beautiful. The mathematical theories used in string theory are in fact beautiful but the way they are stitched together is an UGLY Frankenstein mess. It's essentially the same ugly math that particle physics was built…

> the Penrose singularity theorems in General relativity were impossible until Einstein's theory was formulated correctly with rigorous mathematics I wonder if you would please justify that statement, specifically and only with respect to one of the things called the [Hawking-]Penrose singularity theorem? In particular, what was sufficiently unrigorous or alternatively missing from classical General Relativity that b…

I think OP's argument is that string theory is probably in roughly the same state as the Bohr model of the hydrogen atom: It's got some of the essential tensions right, but it's probably wrong in important details and it's missing a framework in which it all just makes sense.

In a similar vein, I wouldn't expect that the singularity theorems necessarily hold for some of Einstein's early attempts at GR.

Re: On Mathematical Beauty in Physics

#55

Post by univalent »

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.

As others have said, it is beautiful because of the relationship between e and pi. This is mind blowing. What do these 2 constants have in common? Not a thing. I feel the same way about the pi / 4 = 3/4 x 5/4 x .... infinite series. Why a relationship between pi and prime numbers?

Re: On Mathematical Beauty in Physics

#56

Post by chr1 »

klyrs wrote: post #32
chr1 wrote: post #26

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.

The classification of finite simple groups. From an outsider's perspective, it's ream upon ream of brutal case analysis. Some will certainly find beauty in the thousands of pages; the historicity nature of the ~150y effort is undeniable and awe-inspiring. Classification theorems, in general, are frequently beautiful in their structure. But they often involve delving deep into rabbit holes, in order to prove the non-e…

Good point, proofs that require brute force enumeration of all possibilities are not nice, but the physicists who use the results to describe some symmetries still think the results are beautiful.
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