A Moment Which Turns Out to Be Universal

I was reading a bit farther in Charles Coulson Gillispie’s Pierre-Simon Laplace, 1749 – 1827, A Life In Exact Science and reached this paragraph, too good not to share:

Wishing to study [ Méchanique céleste ] in advance, [ Jean-Baptiste ] Biot offered to read proof. When he returned the sheets, he would often ask Laplace to explain some of the many steps that had been skipped over with the famous phrase, “it is easy to see”. Sometimes, Biot said, Laplace himself would not remember how he had worked something out and would have difficulty reconstructing it.

So, it’s not just you and your instructors.

(Gillispie wrote the book along with Robert Fox and Ivor Grattan-Guinness.)

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.

A printer reports to William Shakespeare: 'There's no way I can deliver 37 plays and 150 sonnets. I've got no monkeys, and typewriters haven't been invented yet.'
Piraro and Wayno’s Bizarro for the 18th of January, 2022. I’m not promising a return to regular Reading the Comics posts. But essays that feature Bizarro, past and future, are at this link.

In Our Time podcast has episode on Pierre-Simon Laplace

I have another mathematics-themed podcast to share. It’s again from the BBC’s In Our Time, a 50-minute program in which three experts discuss a topic. Here they came back around to mathematics and physics. And along the way chemistry and mensuration. The topic here was Pierre-Simon Laplace, who’s one of those people whose name you learn well as a mathematics or physics major. He doesn’t quite reach the levels of Euler — who does? — but he’s up there.

Laplace might be best known for his work in celestial mechanics. He (independently of Immanuel Kant) developed the nebular hypothesis, that the solar system formed from the contraction of a great cloud of dust. We today accept a modified version of this. And for studying the question of whether the solar system is stable. That is, whether the perturbations every planet has on one another average out to nothing, or to something catastrophic. And studying probability, which has more to do with these questions than one might imagine. And then there’s general mechanics, and differential equations, and if that weren’t enough, his role in establishing the Metric system. This and more gets discussion.

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