If memory serves, users of epicycles were generally not interested in being ‘predictive’ in a grand sense; but in building a model that fits past astronomical observations and can be expected to predict future ones.
For that purpose, it gets a bit messy; but does work. “Because epicycles” is deeply unsatisfactory as a grand theory, since it doesn’t tell you how many epicycles, where to put them, etc. but if you accept that epicycles and circular orbits are the tools to use, and your model has to be reconciled with historical observations, you can get to a model that will do a pretty good job of predicting future observations.
Kepler and Newton blow it out of the water in terms of elegance and economy; but the criteria for model building haven’t really changed. The moving parts that you postulate for the purposes of building your model are always underdetermined until you’ve tuned things to match observations. We generally only complain if things are predictively useless even after the model has been tuned. If you can use the model to make predictions, people will grumble at your various hacky magic constants, but they’ll put up with them.
g, e, π and why the speed of light squared appears as a proportional constant between energy and mass. Yes, we put up with them, but in a properly designed universe all the constants would be powers of √2 (not 2, because then √2 would be irrational).
You are right, I should have said “explanatory” rather than “predictive”. In truth, epicycles are quite predictive for periodic phenomena. For example, as process of finding the epicycles is fundamentally the same as the Fourier transform, people have created quite predictive machines to compute the tides based largely on observations: https://en.wikipedia.org/wiki/Tide-predicting_machine
On the issue of tuning to observations, it really matters whether you are looking at it from the standpoint of an engineer or theory builder. If you want to know where the planets are because you are trying to navigate a ship in the open ocean, then you don’t care how much tuning was used, you just don’t want to get lost at sea.
However, if you are trying to figure out why the planets move the way they do, you want a model which minimizes tuning. (By minimize, I mean both the number and the magnitude of the parameters.)
But when you adopt the heliocentric model, the number of equations you have to do in order to make sense of things drops by an enormous amount, to the point where it’s hard to imagine why anyone wouldn’t want to default to this model.
Oh, I know why. The lack of a point of reference in our universe is the perfect opening for pedantic trollies who like to argue with people on the internet. Since neither geocentrism or heliocentrism is objectively right (or wrong), it’s the perfect wind-them-up tool for cranks everywhere.
I can’t help thinking that the difficulties of quantum mechanics, the weird things we can’t wrap our heads around, are very similar to the strange explanations they came up with to explain the motions of the planets. I don’t think the universe is stranger than we CAN know; we’re just not looking at it right.
For common sense purposes of everything you said there, I agree. In fact, our current view of the universe necessarily scores 100/100 by our current ability to grade such things, and Newton and Ptolemy and all the rest much less. Even though we know it’s not the whole picture, we necessarily think our current world-view is the best one, if we’re inclined to make those assessments. Otherwise we’d believe something else!
That said, remember that what Ptolemy would have regarded as “wrong” (or “useful,” or whatever other metric we might want to use) is different from ours. He wasn’t doing our particular brand of astronomy any more than Socrates’ Athens was doing 21st-century American democracy. It had different aims, a different epistemological and ontological basis, and it was competing in a very different marketplace of ideas. So while I completely agree that Ptolemy is much more wrong than any given episode of Carl Sagan’s Cosmos, and Sagan more wrong than Tyson’s Cosmos, and so forth to the future, I’m sort of less interested in cross-cultural comparative wrongness than I am in how people situated in their own times and places explored the world around them. And for those purposes, how “wrong” some other time and place would have regarded them is sort of beside the point.
In fact, Ptolemy’s own writings make it clear that he didn’t consider his model an actual physical model of the heavens, but just a sort of ‘planetary positions calculator’ that worked reasonably well.
(And did a better job of it than the Copernican circular/heliocentric model, too.)
The supposed contrast in ‘elegance’ here is a bit biased, though - try plotting the heliocentric orbits of the planets relative to the same fixed Terran POV, and they look every bit as loopy and weird as the geocentric epicycle orbits.
The choice of the sun as the fixed POV is what skews the ‘elegance’.
And even that’s an oversimplification - the planets don’t revolve around the sun; the planets AND the sun revolve around each other, orbiting their respective mutual centers of mass (the “barycenter”.).
Because the Earth is so much smaller than the Sun, it’s easy to assume that the earth revolves around the sun, since the Earth/Sun barycenter is often inside the sun itself.
Regardless of complexity (our pattern matching brains just prefer ‘elegant’ things and nature doesn’t always deliver) you could make the calculations for a geocentric model and they are very good at explaining and predicting the observations. However, on quick observation of the orbits you would notice that they cross constantly and it likely wouldn’t take long before something collides. You can even run the calculation backwards and find that Jupiter and the Sun collided not long ago and that doesn’t seem to have happened (unless Jupiter is just a point of light and can just pass through the sun)
If the scale of that diagram is anything close to being accurate, there’s an order of magnitude between the distance of the barycentre from the centre of the sun at its closest and at its furthest.
Since the relative masses of the Earth and the Sun aren’t changing measurably, and the Earth doesn’t get ten times closer to the Sun at its closest compared to at its furthest, how is that possible?
But when you adopt the heliocentric model, the number of equations you have to do in order to make sense of things drops by an enormous amount, to the point where it’s hard to imagine why anyone wouldn’t want to default to this model.
