[Retric]

> 31 cycles and circles

That’s a count of the total need to describe the motion of multiple celestial bodies.

I’m referring to the number of cycles needed to describe the motion of a single celestial body. There wasn’t enough data at high enough precision to need 17 cycles to describe the motion of a single celestial body until much later. At the time lesser precision was more common, but that someone really did go to such an extreme to create the best fit.

> Completely arbitrary orbits can be described with finite epicycles.

The number of points isn’t fixed with continuous observations. Your best fit for past data keeps needing new cycles over time unless you’re working backwards from a much better model. Even then you run into issues with earthquakes changing the length of the day etc. The basic assumptions they where working from don’t actually hold up.

Also, I’m reasonably sure you couldn’t actually write out an infinite decimal representation of the irrational number e using a finite number of epicycles. Not something I’ve really considered deeply, but it seems like an obvious counter example.

[jjk166]

Please read the sources I cited. You are arguing about epicycles based on a fictional story you heard about them.

[Retric]

I did read them.

The first is overlooking the issue of overfitting using hand calculation and imperfect observations. The calculated “best fit” for the data available did involved adding a bunch of epicycles and there was no theoretical reason to avoid doing so.

The second is playing fast and loose with a fat line drawn over a squiggly line based on a better model. It’s being mathematically rigorous but intentionally deceptive. You can fairly trivially construct a set of epicycles to fit some desired shape, but working backwards from observation there’s nothing guiding you to the most elegant possible solution for a given situation.