Why is Selecting the Simplest Hypothesis (Consistent with Data) a Good Idea? A Simple Explanation

\Everything should be made as simple as possible, but not simpler." A. Einstein, Autobiographical Notes 3] When there are several diierent hypotheses that can explain an observed phenomenon, which of these hypotheses should we choose? Occam, a well known 13th century philosopher, was the rst to formulate a natural idea: choose the simplest of these hypotheses. This principle has been successfully used in many areas of science. Occam's principle works very well: why? In many cases, this Occam's principle is in good accordance with common sense. For example , when we observe that the amount N t of the radioactive material decays exponentially with time t { i.e., that for some constant , we have N t = exp(? t) for t = 1; 2; : : : ; T { then it is natural to select the hypothesis that N t = exp(? t) for all t, although from the purely mathematical viewpoint, a hypothesis that, say, N t = exp(? t) for t T and N t = cos(ln(t)) for t > T would be also equally good in explaining all the data.