Probability, Planets, and Newton’s Methodology

Abstract

The early development of some aspects of probability was closely guided by experience, rewarding or otherwise, of games of chance. This association was fortunate so far as the origin of the ‘doctrine of chances’ in the seventeenth century was concerned; then, as now, simple games involving coins, dice or playing cards provided suitable models for understanding the relevant combinatorial arguments. But there were topics other than gambling which shared its characteristic vocabulary — ‘chance’, ‘luck’, ‘fate’, ‘coincidence’, ‘random’, etc. — and by the beginning of the eighteenth century a number of people skilled in calculating chances were finding opportunities to apply their expertise to some of these topics. John Arbuthnot’s startling memoir for the Royal Society of London on the slight, and perhaps coincidental, preponderance of births of male rather than female children is one well known example of such thinking.¹ Another is the anonymous memoir, also published in the Philosophical Transactions, concerned with the credibility of testimony, where the chance of reports being false if corroborated by independent witnesses is examined. But perhaps the best example is Jakob Bernouilli’s clear and thorough account of the conditions necessary for extending the scope of the mathematical theory of chances.