> I don't really get the thing about "too flexible". According to Wikipedia there is apparently some myths floating around regarding the science history of epicycles, but I assure there is nothing magical about them - at least they are not any more magical than Newtonian mechanics.

I think we may be talking at cross purposes here, but I wanted to give it another shot. I do not think that there is anything magical about epicycles, and my objection to them is scientific; it has nothing to do with their history. My claim is that a scientific tool is valid science only to the extent that it has predictive power. If your model has so many parameters that, by setting them to appropriate values, you can fit any outcome, then (absent some other data telling you which values of the parameters to use) you'll never actually predict anything, only scramble setting them to 'post-dict' existing observations—which is, effectively, useless.

(For example, any finite collection of observations can be 'post-dicted' by a high-degree polynomial, and we can accommodate more observations simply by increasing the degree of the interpolating polynomial. This is not magical, and mathematically totally sound; but its very flexibility means that it is scientifically useless, because there's no reason to believe that our perfect fit to the `n` values we've seen so far says anything about the (`n + 1`)st value we'll see next.)

OK how is it you think epicycles differ in this respect from say the keplerian model of the solar system? I struggle to understand what you think is "special" about epicycles. No model of the solar system will allow you to predict the movement of the planets if you don't enter the correct parameters, which you have to find through observation. Given the correct initial parameters, the ptolmaic system with epicycles will yield predictions about the movements of the planet, predictions you can verify or falsify through observation.

> OK how is it you think epicycles differ in this respect from say the keplerian model of the solar system?

Just to be clear, I'm not in any way insulting the intelligence of those who proposed them. It was a clever mechanism for dealing with what seemed at the time to be a blemish on an otherwise beautiful theory, and the fact that it turned out to be (factually) wrong does not mean that it was wrong to propose and test it.

With that said, here's my stab at what I see as the difference. The Keplerian model predicts elliptical orbits. To be sure, one must do some tuning of parameters to find the semimajor and semiminor axes of these ellipses; there is no way for someone sitting in a windowless room, with access only to Kepler's laws, to predict exactly, say, the length of a Jovian year, or even the existence of Jupiter.

However, what is crucial is that that person sitting in a windowless room can say, definitively, that, if Jupiter has been observed in these five positions at these five times, then it will be in this position at this sixth time. If it's not there, then the Keplerian model is wrong; it has been falsified.

Now suppose instead that another person in another windowless room knows about, not just Kepler's laws, but also epicycles. Given the same five measurements, he or she can make a prediction (which won't require epicycles). This prediction might or might not agree with the sixth measurement, but, if it doesn't, then that's no problem; just add on an epicycle to account for that measurement. If the result of that correction doesn't agree with the seventh measurement, then just add another epicycle.

To me, these two systems are meaningfully different. It is not the reliance on parameters to which I object, but the extreme flexibility; a model that can literally never be falsified, because it can always be adjusted to match new observations, is worthless as a scientific model.

That would be a valid criticism if epicycles were added to the model post-hoc to explain previous observations, and adding those epicycles to the model did not improve future predictions.

Is that really how you think epicycles were used?

> Is that really how you think epicycles were used?

Yes. So, if that's not true, then you've been right all along, and my objection was mostly founded on a misunderstanding of the history. Do you have a reference I could read?

(I should say that, even if it's not actually how they were used, it's still how they could have been used, and I think that the spirit of my objection applies; but the actual practicalities of it would certainly be undermined by my historical misunderstanding.)

In short: Before the Ptolemaic system, it was assumed the planets moved in circular orbits around the earth. The problem is, this did not explain the phenomenon of "retrograde motion", which is when a planet apparently slows down and moves backwards in its path over the sky, as observed from the earth. Ptolemaus added the epicycles which describes the planets as additionally moving in smaller orbits along the path - just as the moon moves in a smaller circle around the earth, which would result in retrograde motion if observed from the sun. In other words, the epicycles explained a phenomenon and allowed the model to better predict the future movements of the planets.

The thing is, this model is not wrong and makes reasonable correct predictions about the motion of the planets as observed from the earth. The Copernican model is just simpler because by describing the planets as orbiting the sun rather than the earth, you don't need as many epicycles in the model. The Tychonian model, by the way, solves the same issue by having the planets orbit the sun, but the sun oribiting the earth, thereby additionally solving the parallax problem which the Copernican model could not explain given the knowledge at the time. All three models needed additional epicycles, which Kepler simplified by describing the orbit as a elliptical.

You will note these models are actually equivalent in modern understanding, where neither the sun or the earth is at the center of the universe.

The current model of the solar system still have epicycles (eg. for moons), so if the presence of epicycles somehow turns a model into pseudoscience, then what?