Summary: A statistical analysis of polysemy in sixteen English and French dictionaries has revealed that, in each dictionary, the number of senses per word has a near-exponential distribution. A probabilistic model of historical semantics is presented which explains this distribution. This mathematical model also provides a means of estimating the average number of distinct concepts per word, which was found to be considerably less than the average number of senses listed per word. The grouping of word senses into concepts is based on whether they could inspire the same new senses (by metaphor, metonymy, etc.), that is, their potential future rather than their history.