I have been reading Pierre-Simon LaPlace, 1749 – 1827, A Life In Exact Science, by Charles Coulson Gillispie with Robert Fox and Ivor Grattan-Guinness. It’s less of a biography than I expected and more a discussion of LaPlace’s considerable body of work. Part of LaPlace’s work was in giving probability a logically coherent, rigorous meaning. Laplace discusses the gambler’s fallacy and the tendency to assign causes to random events. That, for example, if we came across letters from a printer’s font reading out ‘INFINITESIMAL’ we would think that deliberate. We wouldn’t think that for a string of letters in no recognized language. And that brings up this neat quote from Gillispie:
The example may in all probability be adapted from the chapter in the Port-Royal La Logique (1662) on judgement of future events, where Arnauld points out that it would be stupid to bet twenty sous against ten thousand livres that a child playing with printer’s type would arrange the letters to compose the first twenty lines of Virgil’s Aenid.
The reference here is to a book by Antoine Arnauld and Pierre Nicole that I haven’t read or heard of before. But it makes a neat forerunner to the Infinite Monkey Theorem. That’s the study of what probability means when put to infinitely great or long processes. Émile Borel’s use of monkeys at a typewriter echoes this idea of children playing beyond their understanding. I don’t know whether Borel knew of Arnauld and Nicole’s example. But I did not want my readers to miss a neat bit of infinite-monkey trivia. Or to miss today’s Bizarro, offering yet another comic on the subject.