Quite some time ago I started writing up notes, for my own amusement, on the history of astronomy. I’ve worked on it on-an-off over the years, but there always seems to be a bit more I should add. Eventually the pdf version will be ready for prime time. Meanwhile I’ve decided to convert what I have into a series of posts. Enjoy!
Ptolemy gets a bum rap, his system the go-to example of a Rube Goldberg theory. Supposedly, any right-thinking person should have seen its flaws long before the Renaissance. This remark, floating around the internet, typifies the popular impression:
“Epicycles'” are cycles on top of cycles. When traditional astronomy began to collapse in the years before Copernicus, True Believers reacted by adding lots of little cycles on top of the great cycles of the planetary orbits, to protect their faith. Trouble is, they had to add so many cycles on top of cycles that eventually, the whole system became a laughingstock.
As we shall see, this is pure myth.
Or consider the apocryphal quote from Alfonso the Wise (1221–1284), King of Castile. He assembled a team of scholars to create the Alfonsine astronomical tables. When shown the details of the Ptolemaic system, legend has it he exclaimed, “Had I been present at the creation, I would have given some hints for the better ordering of the universe!'”
Copernicus and Kepler, so the story continues, swept Ptolemy’s tangled heap of epicycles into the trash-bin, replacing it with a system boasting elegance and accuracy.
Not quite. You may already know that Copernicus kept lots of epicycles around, and his system was no more accurate than its Ptolemaic competitors. The elegance and accuracy first appears with Keplerian astronomy. But if we look closely, we can discern the seeds of Kepler’s system in Ptolemy’s.
Ptolemaic astronomy approximates Keplerian astronomy fairly well. This shouldn’t surprise us: astronomy is the one quantitative observational science from antiquity. Ptolemy’s system had to make decent predictions to survive. Yet more is at stake. The Babylonians achieved much success with pure computational rules—no geometric model in sight. We can compare the models numerically but nothing more. The connections between the Ptolemaic and Keplerian systems run deeper 1.
In Part 1 of this series, I’ll explore these connections, working backwards from Kepler to Ptolemy. In Part 2, I’ll explore the Ptolemaic system more fully on its own terms. In Part 3, I’ll explore Kepler’s work.
The typical textbook “history box'” on Kepler says that he took Tycho Brahe’s huge mass of observations and distilled them down to two laws, much as the Curies boiled a ton of pitchblende down to a tenth of a gram of radium. Well, sort of: Kepler did take possession of Tycho’s data, and he did spend years analyzing it. He published his first two laws in the Astronomia nova. But this history box omits many fascinating facets. To quote from Kepler’s Physical Astronomy by Bruce Stephenson:
[The Astronomia nova] has been portrayed as a straightforward account of converging approximations, and it has been portrayed as an account of gropings in the dark. Because of the book’s almost confessional style, recounting failures and false trails along with successes, it has in most cases been accepted as a straightforward record of Kepler’s work. It is none of these things. The book was written and (I shall argue) rewritten carefully, to persuade a very select audience of trained astronomers that all the planetary theory they knew was wrong, and that Kepler’s new theory was right. The whole of the Astronomia nova is one sustained argument… [Stephenson]
You know, I’m sure, how Newton’s physics later justified Kepler’s laws. But Kepler had his own physics—unfortunately wrong nearly point-for-point. This incorrect theory never gained traction with any of Kepler’s contemporaries, and history soon consigned it to oblivion. Yet again and again Kepler’s ad-hoc physics steered him around serious pitfalls; Tycho’s observations alone would never have guided Kepler to his remarkable results.
The whole story illustrates the adage that history is never simple. In what follows, I will get hip-deep into the weeds. Feel free to skip according to your interests.
[1] One sometimes hears the claim that Ptolemy was just practicing an early form of Fourier analysis. Good math, bad history. This idea seems to originate as an over-simplification of Hanson’s paper [Hanson].
Diagonal Argument 
The connection between epicycles and Fourier analysis was probably noted much before Hanson. Actually Hanson never mentions Fourier analysis in his article – which always made me wonder if he was unaware of the connection. Gallavotti traces it to Schiaparelli (1874), but arguably Gauss was the first to use Fourier analysis (1805, unpublished as usual) to fit orbits to observations. But Gauss obviously did not recognize his work as either Fourier or epicyclical in nature. We can only draw this connection in hindsight.
Thanks for the references!
You’re right, I had forgotten that Hanson never explicitly uses the words “Fourier analysis”. On the other hand, the formula on the middle of p.157 pretty clearly alludes to it:
Also, he never explicitly says that Ptolemic astronomers would have added epicycles willy-nilly like this. There’s enough historical discussion in the article to suggest the formulation, “Ptolemy was doing an early form of Fourier analysis.” But he doesn’t actually claim this.