Pitfalls and Paradoxes in the History of Probability Theory

ABSTRACT: This lecture traces the history of probability theory from the throwing of bones, sticks, and dice to modern times. Early 18th century books, Jacob Bernouill’s “The Art of Conjecturing” and Abraham DeMoivre’s “The Doctrine of Chances” were rich with new mathematics, insight and gambling odds. Progress was often made by confronting paradoxes. The first of these confused probabilities with expectations and was explained in the Pascal-Fermat letters of 1654. The St. Petersburg Paradox involved a distribution with an infinite first moment, and Levy discovered a whole class of probabilities with infinite moments that have found a surprising utility in physics connected to fractals. Through conditional probabilities, Bayes introduced what later has become hypothesis testing. Arriving at two different answers, the Bertrand paradox involved measure theory for continuous probabilities, Poisson discovered that adding random variables need not always produce the Gaussian, and Daniel Bernoulli and D’Alembert argued over the probabilities for the safety of smallpox vaccinations. Using these and other anecdotes, this lecture discusses vignettes that have brought us to today’s widespread use of probability and statistics.

BIO: Dr. Michael Shlesinger manages the nonlinear physics program at the Office of Naval Research. He has published over 200 scientific papers on topics in stochastic processes, glassy materials, proteins, neurons, and nonlinear dynamics. He is a Fellow of the American Physical Society and was a Divisional Associate Editor of the Physical Review Letters. In 2006 he received ONR’s Saalfeld Award for Outstanding Lifetime Achievement in Science, and earlier the federal government’s Presidential Rank Award for Meritorious Senior Professionals, and the Navy Superior Civilian Service Award. He held the Kinnear Chair in Physics at the USNA, was the Michelson Lecturer at the USNA, the Regents’ Lecturer at UCSD and received the U. Maryland’s Distinguished Postdoc Alum award. His Ph. D., in Physics, is from the U. of Rochester in 1975, and his 1970 B.S. in Mathematics and Physics is from SUNY Stony Brook.

Hosted by: Paul Bogdan