3 ms·

I think you've changed what you're meaning by entropy, it isn't really a meaningful measure of "randomness". Afterall, how can U(0,1) be considered to be "less

• jefftk 3y ago
  If you look at this from a computers ("everything is discrete eventually") perspective, U(0,1) is less random than U(0,1000) because U(0,1000) != 1000U(0,1). For example, if you're using a fixed-point encoding that allocates values uniformly, it will have 1000x as many possible values for [0,1000] as [0,1], and so getting any specific value from U(0,1) is 1000x more likely than any specific value from U(0,1000). If you draw from U(0,1) and then multiply by 1000 you'll never produce most values that U(0,1000) could produce. If you look at it from a math ("continuous is actually possible") perspective I have a much weaker handle on it, but I think the problem is that the entropy of 1000U(0,1) is not the same as the entropy of U(0,1)?