Galton Machine and Unpredictability We are all familiar with the Galton Machine and the images of the balls cascading through the device and ending up in bins which ultimately show a likeness to the binomial distribution. Most everyone will agree that the balls exhibit random and unpredictable behavior. My question is twofold: **(1)** Can the emergence of the balls into the binomial curve be considered a mathematical proof that the behavior of any single ball is unpredictable? **(2)** Can the emergence of the binomial curve for any mathematical function be considered a mathematical proof that the elements which create the distribution are in fact unpredictable?

The answer on both accounts is No.

There are (deterministic!) algorithmns, called pseudo random number generators (PRNG) which create, well pseudo random numbers. These numbers _in princple_ follow a deterministic pattern, but in pratice behave like truely random numbers. In particular, you can use a PRNG to simulate statistical experiments like throwing a dice, and for the right kind of experiment, the results will be binomially distributed.