Before I get any criticisms, if any, I'd like to explain a little bit about why I wrote this past at that time.
Quora, among other places, is rife with people who spout the same-old same-old about various topics.
"What's the most beautiful equation?" And you get this at the very top. "What's the most amazing piece of code?" And you get that unreadable inverse square root hack.
The goal of the post was to have the reader question what they think is beautiful and why. I, too, thought that equation was beautiful, but it was beautiful until I wrote it in Lisp:
It was not at all because Lisp is ugly. (I find it—Lisp—quite elegant myself!) Rather, it was because equivalent non-contrived syntactic transformations of the equation made it lose its appeal, and made me realize its only appeal is purely visually aesthetic.
I also knew, but it had not really sunk in, that, in pseudo-Lisp notation,
e^(i*t) = #C(cos t, sin t)
is just a rotation, identical to the rectangular point representation
I liked your breakdown. I think without linear algebra, it's not very intuitive that it's simply a rotation, and the power series itself is quite interesting. So to most people, without a high level of mathematics to discern each component, it's the combination using all of the constants together in one equation.
Just curious, what is your favorite/most beautiful equation? Fractal geometry? (just guessing...)
pi*sqrt(163)
e = 640320^3 + 744 - 0.00000000000075...
to be much more beautiful, only because it invokes very deep, rich mathematics in number theory. Note that the above is very close to an integer, and it's no accident that 163 or 640320 show up.
I'm sorry, but can you elaborate? It kind of went over my head, and I would love to learn something new. What do you mean by the number theory/no accident comment?
You found it ugly that the approximations used by computers to model real numbers are approximate? What's that got to do with the equation being ugly or not?
It had nothing to do with the floating point approximation of things. I don't think I said that anywhere. It had more to do with the syntactic transformation while remaining precisely the same.
Quora, among other places, is rife with people who spout the same-old same-old about various topics.
"What's the most beautiful equation?" And you get this at the very top. "What's the most amazing piece of code?" And you get that unreadable inverse square root hack.
The goal of the post was to have the reader question what they think is beautiful and why. I, too, thought that equation was beautiful, but it was beautiful until I wrote it in Lisp:
It was not at all because Lisp is ugly. (I find it—Lisp—quite elegant myself!) Rather, it was because equivalent non-contrived syntactic transformations of the equation made it lose its appeal, and made me realize its only appeal is purely visually aesthetic.I also knew, but it had not really sunk in, that, in pseudo-Lisp notation,
is just a rotation, identical to the rectangular point representation as I explain in the post.