tasteslikenoise

3 ms·

1. 1.▲
   by tasteslikenoise 2y ago

   The whole polynomial functions that give the truncations of the exponential Taylor series are also well-behaved in a way that's really surprising if you haven't thought about it before. For example, if you plot 1, 1 + x + x^2&#x2F
2. 2.▲
   by tasteslikenoise 2y ago

   A different but to my taste more mathematically conventional way to make this argument would be instead to say that a symbol is a function from the square to [0, 1], that is, a grayscale image. A symbol, because of limitations of either its
3. 3.▲
   by tasteslikenoise 2y ago

   That's right, here log(k) - H(p) is really the relative entropy (or KL divergence) between p and the uniform distribution, and all the same stuff is true for a different "reference distribution" of the probabilities of balls
4. 4.▲
   by tasteslikenoise 2y ago

   I've always favored this down-to-earth characterization of the entropy of a discrete probability distribution. (I'm a big fan of John Baez's writing, but I was surprised glancing through the PDF to find that he doesn't s