The Emergence of Probability
The Greeks discussed randomness in a qualitative way: Democritus (460BC), Epicurus (341BC) … Yet, mathematical theory of probability came very late:-Gerolamo Cardano (b. 1501, Pavia); Ars Magna 1545-published solutions of cubic and quartic equations (derived by Tartaglia & Ferrari)-1526 Liber de ludo alaea-a gambler's handbook In physics, probability entered very late:-Gauss' theory of errors (~ 1800)-statistical mechanics (Boltzmann, 1871)-this probabilistic theory was not accepted until the 20th C-Einstein (1905) linked macroscopic Brownian motion with atomic properties-quantum mechanics brought genuine randomness into physics in the 1920's Statistics and probability were driven by biological questions:-Francis Galton pioneered biometrics-Karl Pearson developed the mathematics of the normal distribution in order to understand inheritance of continuous traits-Fisher (1918)-showed how continuous variation could be partitioned into components: ANOVA-developed modern statistical inference The course focusses on stochastic models rather than statistical inference-but these are closely connected