Random Numbers
Random numbers are incredibly useful. They are of course central to the study of statistical mechanics (where they are needed to produce ``random thermal motions'') and disordered systems (where the ``dirt'' is assumed randomly arranged in space). They provide some of the best means to do multi-dimensional integrals (evaluate the integrand at a bunch of random positions, and average to find the integral!) and are used extensively in search methods for optimization and good solutions to difficult problems (simulated annealing).What does it mean to be ``random''? What matters to most of these problems is that there is a sequence of numbers with no observable patterns. One could generate such a sequence by looking at radioactive decay or something, but on a computer one usually generates a new random number from the old one (no randomness at all!) One starts these random number generators with a seed: if you don't change the seed, you get exactly the same random numbers every time!
