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.

Who Was Jonas Moore?


I imagine I’m not the only person to have not realized the anniversary of Jonas Moore’s death was upon us again. Granted he’s not in anyone’s short list of figures from mathematical history. The easiest thing to say about him is that he appears to have coined common shorthands for the trigonometric functions: cot for cotangent, that sort of thing. Perhaps nothing exciting, but it’s something that had to be done.

Moore’s more interesting than that. The Renaissance Mathematicus has a biographic essay. Particularly of interest is that Moore oversaw the building of the Royal Observatory in Greenwich, and paid for the first instruments put into it. And, with Samuel Pepys, he founded the Royal Mathematical School at Christ’s Hospital, to train men in scientific navigation. As such he’s got a place in the story of longitude, and time-keeping, and our understanding of how to measure things.

That won’t put him onto your short list of important figures in the history of mathematics and science. But it’s interesting anyway.

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