4 ms·

> Which is pretty insane because these two numbers are not supposed to be related Not really, there is Euler's identity: https://en.m.wikipedia.org/wiki/Euler%

• sunshowers 2y ago
  That one's "just" a special case of how complex numbers happen to work. I think the really cool relationship between e and pi is the fact that the Gaussian integral acts as a fixpoint/attractor when sampling and summing data from any distribution (this is the central limit theorem): ∫(−∞ to ∞) e^(-x²) dx = √π I think the attractor property makes it a little more fundamental in some sense, whereas Euler's identity is "just" one special case of e^ix. The Gaussian is kind of the "lowest energy" or "highest entropy" state of randomness, which I think is really cool.
  • octachron 2y ago
    This is only true for distributions with finite variance (and the edge case of distribution with slowly growing infinite variance). And for a given variance, gaussian distributions are exactly the maximal entropy distribution.