# Some Progress on the Infinitude of Monkeys

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.

## Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

## 4 thoughts on “Some Progress on the Infinitude of Monkeys”

1. Chance would be a fine thing, as they say! I suppose the odds on the lines being in English or Latin would be about the same?

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1. Fair question! (And it did catch my eye that ‘infinitesimal’ is legitimate English, French, or Latin and I wonder how much thought went into that.) If we were looking just at keyboards then the language would hardly matter. But for actual type to set? I don’t know how the standard stockpile of the letters varies between English and French and Latin. This probably wouldn’t make a huge difference in the probability of setting the word, but it would make some difference.

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