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Randomness at the root of things 2: Poisson sequences

This article is the second of a pair of articles about randomness in physics. In the preceding article we have shown how simple random walk arguments can give the mean and standard deviation of a number of random counts. In this article we go a little deeper, and offer a simple and novel teaching approach to the idea of random events. Taking the Poisson sequence as fundamental, very simple arguments show that the time intervals between random events are distributed exponentially. The mathematics needed is merely the familiar mathematics of exponential change, making a good opportunity for revision. Further arguments give the form of the Poisson distribution, on the basis of very elementary assumptions. Several interesting experiments are suggested.