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"?
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.)
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?
Given notation as a tool of thought, it is really about which notation you are most familiar with. No doubt some people would find lisp notation enlightening, and some people would find the following beautiful.
>Consider something as simple as parsing an integer in a text-based format; there may be whitespace to skip, an optional sign character, and then a loop to accumulate digits and convert them (itself a subtraction, multiply, and add), and there's still the questions of all the invalid cases and what they should do.
^[ *][-?][0-9][0-9]*[ *]$
You're welcome. Anything that passes that regex is a valid number. Now using that as a basis of a lexer means that you can store any int in whatever precision you feel like.
It's unfortunate that the majority of programmers these days are so computer illiterate that they can't write a parser for matching parens and call you an elitist for pointing out this is something anyone with a year of programming should be able to do in their sleep.
I don't get your argument. If something doesn't work on the small scale it certainly won't work on a large scale. That's exactly my original point about managing global finance
That's the converse of my argument. I'm saying that things that don't fly at small scale, don't become good ideas at large scale. Constantly calling the credit card company and asking for a credit raise instead of paying the bill, printing more money to pay the bill, and encouraging not saving for a rainy day by keeping interest rates low are all things that are terrible ideas for the individual so why is it good for 100 individuals grouped together? Actually, the answer is obvious: statistics are easier to manipulate with groups.
>I'm saying that things that don't fly at small scale, don't become good ideas at large scale.
They absolutely do.
Fourier transform multiplication methods are a terrible idea if you run them on numbers that aren't hundreds of digits long, but the only way to multiply truly large numbers.
Why not do some research and learn about this stuff? Very smart people spend a lot of time thinking about how to run economies: at least consider their ideas before you dismiss them.
