Some people think medieval astronomers kept adding 'epicycles' to the orbits of planets, culminating with the Alfonsine Tables created in 1252. The 1968 Encyclopædia Britannica says:
"By this time each planet had been provided with from 40 to 60 epicycles to represent after a fashion its complex movement among the stars."
But this is complete bullshit!
Medieval astronomers did *not* use so many epicycles. The Alfonsine Tables, which the Brittanica is complaining about above, actually computed planetary orbits using Ptolemy's method, developed way back in 150 AD. This method uses just 6 circles and 6 epicycles - nothing like Britannica's ridiculous claim of between 240 and 360 epicycles.
That's right: Ptolemy got a good fit to planetary orbits using one circle and one epicycle each for the Sun, Mercury, Venus, Mars, Jupiter and Saturn. It's not much worse than what we do now: use one ellipse each for Mercury, Venus, Earth, Mars, Jupiter and Saturn.
I must admit that in Ptolemy's model, the circles weren't centered on the Earth. They were offset, like in the gif below, where the big green dot is the Earth. The big blue circle, offset from the Earth, is called a 'deferent'. This approximates an ellipse. The smaller black circle is called an epicycle. This makes up for how the Earth is not actually stationary, but moving around the Sun.
This gif was created by Richard W. Pogge, Distinguished Professor of Astronomy at Ohio State. You can see more of his animated planetary models here:
https://www.astronomy.ohio-state.edu/pogge.1/TeachRes/Artwork/Anims/index.html
So, just because something is in an encyclopedia, or even an encyclopædia, doesn't mean it's true. Don't believe me? Check out the references in part 2!
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My Encyclopædia Britannica quote comes from their 1968 edition, volume 2, in the article on the Spanish king Alfonso X, which on page 645 discusses the Alfonsine Table commissioned by this king:
"By this time each planet had been provided with from 40 to 60 epicycles to represent after a fashion its complex movement among the stars. Amazed at the difficulty of the project, Alfonso is credited with the remark that had he been present at the Creation he might have given excellent advice."
In "The Book Nobody Read", Owen Gingerich writes that he challenged Encyclopædia Britannica about the number of epicycles. Their response was that the original author of the entry had died and its source couldn't be verified. Gingerich has also expressed doubts about the quotation attributed to King Alfonso X.
Today, Encyclopedia Brittanica says what I just said: just one deferent and one epicycle for each planet:
https://www.britannica.com/science/celestial-mechanics-physics#ref611346
They still manage to take a dig at the medievals, saying Ptolemy's theory "was adopted as absolute dogma and survived more than 1,000 years until the time of Copernicus."
For the controversy over whether medieval astronomers used lots of epicycles, start here:
https://en.wikipedia.org/wiki/Deferent_and_epicycle#The_number_of_epicycles
and then dig into the sources! For example this article says the popular claim that the Ptolemaic system uses about 80 circles seems to have appeared in 1898. It may have been inspired by the non-Ptolemaic system of Girolamo Fracastoro, who used either 77 or 79 orbs. So *some* theories used lots of epicycles, but not the most important theories, and nothing like the 240-360 claimed by the 1968 Brittanica.
The following quote of Gingerich's book is from @pglpm.
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@johncarlosbaez
Epicycles were the Feynman diagrams of antiquity
@BartoszMilewski - Except the ancients didn't keep adding more and more!
Maybe Feynman diagrams are the epicycles of the Enlightement's imaginary version of the Middle Ages.
@johncarlosbaez
This is because the ancients were lazy. If they were serious about epicycles, maybe they would have discovered Uranus and Neptune. After all we were able to detect the Higgs by calculating all the Feynman diagrams for know particles and subtracting them from our observations.
It's that, or they didn't have computers...
@BartoszMilewski @johncarlosbaez Is it the case that with epicycles, as with Feynman diagrams, that adding more and more eventually gets you into trouble?
@internic @johncarlosbaez
I presume epicycles actually work, sort of like the Fourier expansion. With Feynman diagrams, we know that there are problems with the convergence of the perturbative expansion. Not to mention that there's a horrible exponential explosion of terms to be calculated. Thesa are the problems that people like Nima Arkani-Hamed try to bypass with the amplituhedron.
@BartoszMilewski @johncarlosbaez Yes, I guess any orbit could be thought of as a continuous function R -> C, and then the epicycles would just be a Fourier transform, so they could under suitable conditions be convergent under some norm rather than asymptotic like a perturbative expansion.
I'm not familiar with the amplituhedron, but wouldn't the problems to be resolved be generic to perturbation theory (not specific to quantum field theory)?
@johncarlosbaez I guess in a rough sense that's similar to the motivation behind p-adic numbers. @BartoszMilewski
@internic - so far the amplitudohedron and its cousins work only for certain specific quantum field theories, and they don't completely crush the problem either: that is, they amount to summing over a big bunch of Feynman diagrams but not all of them. So, they aren't a silver bullet. But they suggest that whenever you have a mathematically beautiful power series, you should keep thinking about it - and try figure out things that are more intelligent than just summing it term by term!
(Another example would be an imaginary civilization that kept summing over more and more terms of a Fourier series that better and better approximate an elliptical orbit. At some point some genius might have invented the ellipse.)
@BartoszMilewski