In Our Time podcast has an episode on Longitude

The BBC’s In Our Time program, and podcast, did a 50-minute chat about the longitude problem. That’s the question of how to find one’s position, east or west of some reference point. It’s an iconic story of pop science and, I’ll admit, I’d think anyone likely to read my blog already knows the rough outline of the story. But you never know what people don’t know. And even if you do know, it’s often enjoyable to hear the story told a different way.

The mathematics content of the longitude problem is real, although it’s not discussed more than in passing during the chat. The core insight Western mapmakers used is that the difference between local (sun) time and a reference point’s time tells you how far east or west you are of that reference point. So then the question becomes how you know what your reference point’s time is.

This story, as it’s often told in pop science treatments, tends to focus on the brilliant clockmaker John Harrison, and the podcast does a fair bit of this. Harrison spent his life building a series of ever-more-precise clocks. These could keep London time on ships sailing around the world. (Or at least to the Caribbean, where the most profitable, slavery-driven, British interests were.) But he also spent decades fighting with the authorities he expected to reward him for his work. It makes for an almost classic narrative of lone genius versus the establishment.

But, and I’m glad the podcast discussion comes around to this, the reality more ambiguous than this. (Actual history is always more ambiguous than whatever you think.) Part of the goal of the goal of the British (and other powers) was finding a practical way for any ship to find longitude. Granted Harrison could build an advanced, ingenious clock more accurate than anyone else could. Could he build the hundreds, or thousands, of those clocks that British shipping needed? Could anyone?

And the competing methods for finding longitude were based on astronomy and calculation. The moment when, say, the Moon passes in front of Jupiter is the same for everyone on Earth. (At least for the accuracy needed here.) It can, in principle, be forecast years, even decades ahead of time. So why not print up books listing astronomical events for the next five years and the formulas to turn observations into longitudes? Books are easy to print. You already train your navigators in astronomy so that they can find latitude. (This by how far above the horizon the pole star, or the sun, or another identifiable feature is.) And, incidentally, you gain a way of computing longitude that you don’t lose if your clock breaks. I appreciated having some of that perspective shown.

(The problem of longitude on land gets briefly addressed. The same principles that work at sea work on land. And land offers some secondary checks. For an unmentioned example there’s triangulation. It’s a great process, and a compelling use of trigonometry. I may do a piece about that myself sometime.)

Also a thing I somehow did not realize: British English pronounces “longitude” with a hard G sound. Huh.

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.

In Our Time podcast has episode on Émile du Châtelet

I have another in my occasional series of podcasts mentioning something of mathematical interest. This is another one from the BBC’s In Our Time, a 50-minute program of three experts discussing a topic. Here the topic is Émile du Châtelet, an 18th century French noblewoman noted for translating Newton’s Principia Mathematica into French. It’s by accounts an outstanding translation, still regarded as one of the best translations the book has had.

This is not the whole of her work, though my understanding is she’d be worth noticing even if it were. Part of the greatness of the translation was putting Newton’s mathematics — which he had done as geometric demonstrations — into the calculus of the day. The experts on In Our Time’s podcast argue that she did a good bit of work advancing the state of calculus in doing this. She’d also done a good bit of work on the problem of colliding bodies.

A major controversy was, in modern terms, whether momentum and kinetic energy are different things and, if they are different, which one collisions preserve. Châtelet worked on experiments — inspired by ideas of Gottfried Wilhelm Liebniz — to show kinetic energy was its own thing and was the important part of collisions. We today understand both momentum and energy are conserved, but we have the advantage of her work and the people influenced by her work to draw on.

She’s also renowned for a paper about the nature and propagation of fire, submitted anonymously for the Académie des Sciences’s 1737 Grand Prix. It didn’t win — Leonhard Euler’s did — but her paper and her lover Voltaire’s papers were published.

Châtelet was also surprisingly connected to the nascent mathematics and physics scene of the time. She had ongoing mathematical discussions with Pierre-Louis Maupertuis, of the principle of least action; Alexis Clairaut, who calculated the return of Halley’s Comet; Samuel König, author of a theorem relating systems of particles to their center of mass; and Bernard de Fontenelle, perpetual secretary of the Acadeémie des Sciences.

So for those interested in the history of mathematics and physics, and of women who are able to break through social restrictions to do good work, the podcast is worth a listen.

I spent much of the time waiting for a mention of Chatelier’s principle which never came. This because Chatelier’s principle’s — about the tendency of a system in equilibrium to resist changes — is named for Henry Louis Le Chatelier, a late 19th/early 20th century chemist with, so far as I know, no relation to Émile du Châtelet. I hope this spares you the confusion I felt.