This chapter examines randomness and how it applies (or does not) in both abstract mathematics and in physical systems. There are many different ways in which a sequence of events could be said to be ‘random’. The mathematical theory of random processes, sometimes called stochastic processes, depends on being able to construct joint probabilities of large sequences of random variables, which can be very tricky to say the least. There are, however, some kinds of random processes where the theory is relatively straightforward. One class is when the sequence has no memory at all; this type of sequence is sometimes called white noise. Random processes can be either stationary or ergodic. The chapter also discusses predictability in principle and practice, and explains why pulling numbers out of an address book leads to a distribution of first digits that is not at all uniform. Aside from sequences of variables, other manifestations of randomness include points, patterns, and Poisson distribution.
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