In a review for the Royal Society of Martin Kahle’s 1735 book
Elementa Logicae Probabilium, Abraham De Moivre wrote:
“For altho’ the ancients had the same Idea of Probability as we have; and they mentioned several degrees of it, as in the words
Probabile and Probability often used by Cicero & other writers, yet the Author observes, that the distinct measure of it was never assigned till the times above mentioned.”
Those times spanned the latter half of the 17
th century to the first quarter of the 18
th century. We explore this insight through three episodes in the history of probability: (1) the archaeological record for dice from ancient Rome, (2) two manuscripts from near the end of the High Middle Ages, and (3) Blaise Pascal’s friendship with Antoine Gombaud, chevalier de Méré. Episode 1 demonstrates that Roman dice could be highly asymmetrical and biased. We carry out an empirical study through a database of these dice, leading to the conclusion that ancient Romans would find it very difficult to develop a concept of long-run frequency from these dice, confirming the insight from the quotation. From Episode 2, the Latin poem,
De Vetula (
About the Old Woman) contains some elementary calculations related to probability with some influences from Arabic mathematics. This manuscript and another,
Libro de los juegos (
Book of Games), commissioned by Alfonso X of Castile, León, and Galica, contain expressions of an appreciation for long-run frequency. Definite progress, but no distinct measure of probability as we would know it. In an undated letter to Pascal, Gombaud made claims about his priority in the development of the probability calculus. In Episode 3, we explore Gombaud’s claim and contributions to formulating the distinct measure.
David Bellhouse is Professor Emeritus in the Department of Statistical and Actuarial Sciences at the University of Western Ontario. He received his Ph.D. at the University of Waterloo in 1975. Professor Bellhouse’s research interests are in the history of probability, statistics and actuarial science. He has published several articles and three books on these topics.
Christian Genest is a professor in the Department of Mathematics and Statistics at McGill University, Montréal, Canada. His research interests include multivariate analysis, nonparametric inference, extreme-value theory, and the history of probability and statistics. He has published extensively and served the community in many ways, notably as President of the Statistical Society of Canada (2007-08) and Editor-in-Chief of the
Journal of Multivariate Analysis (2015-19).
Moderator: Paul Smith, University of Southampton (RSS History of Statistics Section member)
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