As everybody knows, March 14 is Pi Day, because in month/day format the third month and fourteenth day make 3.14, the first three digits of pi. What not everybody knows is that today, July 22, is Pi Approximation Day, because in day/month format (which is used everywhere but the US) it’s 22/7, and that’s the fraction that is approximately equal to pi. Even Archimedes knew about it.
Pi Approximation Day in 1784 also marked the birth of Friedrich Bessel, who grew up to know a fair bit about pi as well as quite a bit of other math. When he was 14, he was apprenticed to an import-export business in Bremen, Germany. One of their biggest problems was that there wasn’t any good way to know exactly when cargo ships were going to arrive in port.
This was partly because of variations in wind and weather, but Bessel discovered that in many cases, the ships took longer than necessary because of navigational mistakes. It wasn’t always the fault of the captains; there were problems in marine navigation that simply weren’t solved at the time.
“Let me give it a try,” said Apprentice Bessel — or, well, some words to that effect, except in German. Working on navigation problems led him to astronomy, and new ways to figure out your latitude by observing the sky.
He was so good at it that he used old observations of Halley’s Comet to come up with a more precise estimate of its return in 1804 — and he turned out to be right. That got him noticed by Heinrich Olbers, the biggest name in German astronomical circles at the time, and Bessel got a new career in the Lilienthal Observatory. He got particularly busy there and published precise positions for over 3,200 stars.
Bessel, you’ll recall, hadn’t been an academic; instead of school he became an apprentice when he was 14. Nevertheless, when he just 25 the King of Prussia appointed him the director of the brand-new Königsberg Observatory. He was becoming well-known to the astronomers and mathematicians of Europe, and possibly to boost his resume the University of Göttingen awarded him an honorary doctorate the next year, 1811. After that, he was known as Doctor Bessel, and fit in famously with his colleagues.
One of his European colleagues was Gaspard de Prony, a French mathematician and engineer who shared Bessel’s birthday, although de Prony was thirty years older. Astronomers like Bessel needed to do intricate calculations, and in the days before calculators and computers, tables of logarithms were the most efficient tool. It was de Prony who organized a systematic approach to creating those tables. He divided the work into three levels, basing his process on Adam Smith’s book Wealth of Nations, which at the time was fairly recent and being used to create the whole field of economics.
The three levels of work involved expert mathematicians, who figured out the formulas that would produce the right results. There were about five of those mathematicians involved. The second level was about 7 or 8 mathematicians who weren’t as skilled, but could use the formulas to produce starting values and templates to pass along to the third group. That group did the grunt work, and there were about 90 of them. All they needed to know was basic arithmetic, which they used to find the values and fill in the templates they were given.
Oddly enough, most of the 90 “human computers” were out-of-work hairdressers. It was the late 1700s, after all, and the French had just gotten rid of the aristocracy. That meant nobody needed those super-fancy hairstyles any more.
The tables generated by de Prony’s organization were used here and there around Europe (Bessel probably had some of them) but were never published. At first that was because of a lack of funding. Later they weren’t published because the tables, created during the short reign of the French Republic were designed for decimal circles and decimal time. By the time funds were available, everybody had gone back to time measured by 60 minutes and 24 hours, and circles measured by 360 degrees. The other problem with de Prony’s tables was that they were calculated to an incredible degree of precision — far more than anyone could really use at the time.
What did have a widespread effect was de Prony’s idea that you didn’t need to have a PhD in math to just perform calculations; anybody who knew arithmetic could do it as long as you showed them what to do. That model, along with the astonishing-at-the-time idea that women could be really good at it, became the norm for big computational projects for the next couple of centuries. Even the calculations for the atomic bomb were produced using de Prony’s approach.
Charles Babbage, who invented the first mechanical computer (at least the first modern mechanical one, if there is such a category), studied de Prony’s method in great detail and based his designs on the idea that repetitive calculation doesn’t need great expertise — and decided all he really needed was just a set of gears.
Babbage was one of the founders of the Astronomical Society of London in 1820. It was renamed the Royal Astronomical Society, and in 1829 the society awarded a gold medal to…Friedrich Bessel, for figuring out how to measure the distance to a star. They did it again in 1841, that time for his work in “geodesy,” the process of plotting the surface of a ball — say, the Earth, for example — onto a flat surface — like, y’know, a map. It’s thanks to his work in geodesy that the Bessel Fjord in Greenland got its name — although for some reason, there are two Bessel Fjords there. Gaspard de Prony would never have approved of that sort of imprecision.
