Re:On Mathematical Beauty in Physics
by yesenadam on Monday August 19, 2019 @11:06PM
(#20743516)
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"?
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Re:On Mathematical Beauty in Physics
by thanatropism on Monday August 19, 2019 @11:23PM
(#20743580)
People fetishize the formula but the beautiful idea is that multiplication/exponentiation can be expanded in such a way that it describes oscillatory relations. This is how eg. eigenvalues get to play a role in models of harmonic resonance. Or how AC impedance naturally generalizes DC resistance.
Try to imagine complex interest rates. Now try to make them matrix-valued. It works. It all works.
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.)