So what's the achievement of Ptolemaic astronomy and what are the shortcomings? Let's start with the achievement. Every one of those planets appear to have multiple degrees of freedom in their motion. If it takes 71 years to pick up the pattern, that looks like there's a lot of variability.

In fact, he reduces it to exactly seven. In the case of the Sun, two less than that. Elements are parameters. The eccentricity, the ratio of epicycle, the deferent radii, the angular location of the line of apsides along the zodiac. The sidereal period or the number of degrees per day moving along the zodiac.

The synodic period, the period between two retrograde loops. Then you need a starting point, a location on an epicycle at sometime, usually the ascension to the throne of some king or something like that. Most astronomy was done under the Julian Calendar and your Julius Caesar is zero. It's still used for most astronomy but we need to locate on the epicycle and we need to locate the epicycle on the deferent and in epochal time.

So, two of those are just to get the model started. The other five are the five basic parameters. They are the same five basic parameters. We need no more than that for any of these objects, including Mercury or the Moon. It's always radius, ratio, eccentricity, line of apsides and the periods.

One period for the Sun and the Moon, two periods for the others. Now that's a reduction of an enormous amount of complexity down to a very small number of parameters, number one. Number two, you could now take the models incorporating those parameters, identify preferred observations with which to measure their values.

Sit then, get success at getting the retrograde loop patterns and timing and have the parameters for those models keep repeating over time with new observations. That's the reason Ptolemaic astronomy is called the majestic one and dominated for fourteen centuries. It not only succeeded, it succeeded brilliantly, reducing things to a very manageable computational procedure that high schoolers can learn to work with, working with circles is very ideal, very easy to do, etc.

What are the shortcomings? There are two sets of shortcomings, I've listed here. One specifically identified by Islamic astronomers and the other that just seemed not to get mentioned before we get to the Renaissance. So let's start with the Islamic astronomers. The Moon approaches way too close to the Earth than the apparent diameters imply and that everyone just said his theory of the Moon cannot be right.

Procession of the equinox is as slower than observed. That's a cumulative error but you can fix it very easily because everything starts from the location of the vernal equinox on each of the calculational models, you just have to reset the location before you do the calculation. It doesn't infest anything else.

Similarly, those two are out and out empirical errors. The next three I call philosophic because the Islamists kept complaining he's violating Aristotle. They would also make two other complaints. It's not mechanically realizable and he's inconsistent with what he says in his planetary hypothesise when he tries to describe them.

So let me run through those three, then take Professor Stan's question. So it's not uniform circular motion along the deferent. Mercury, Mars, Jupiter, Saturn, and the Moon, all in one way or another violate uniform circular motion and that was a serious philosophic objection. Second, the Earth is not at the center of the planetary system and third, the account of latitude seems to not be physically realizable.

Certainly, not realizable by circles. Now the ones below the line, errors in latitude and longitude greater than two moon diameters, non-cumulative, I pointed that out, they just go unnoticed. No solution for the distance of the planets from the Earth. So we have to guess on how far the things are away.

No constraints from one planet orbit on any other. That is, there's not a system here, there are separate orbits, one after another. No interaction among them. Finally, the centers of the deferents, the larger circles, do not coincide with one another. There's a different center for every deferent. So, if there are spheres and they have different centers, what's going on with it?

Now, I wanna end with a thought and a question. I have just the time I need. The last part of the notes, addresses the following question, Ptolemaic astronomy from the 17th century forward has been our primary example of bad science, laughable science. Epicycles, what a crazy idea. What I've tried to show you tonight is its not at all apparent what's bad about Ptolemaic astronomy, even by modern scientific standards.

It looks an awful lot like a great deal of modern science. It's empirically driven, and making relatively weak initial assumptions, and they get verified by the stability of measurements that presuppose them. If you asked me and the last part of the notes go through all the usual proposals, Ptolemy's too complicated, Copernicus has the same number of epicycles as Ptolemy does.

Ptolemy is false, so is Newton. I can do others, it's just not obvious what's wrong. The only thing that I can see that differentiates it somewhat for modern science, is the decision not to continue learning from discrepancies between the models and observations. Ptolemy did in the case of the Moon.

Nobody did it in the case of the planets. It was sitting there to be done, and the obvious question, is that a feature of modern science? Regardless, let me turn to my last slide. The main reason, I think, for studying this material that's gonna be done for two semesters, is this question.

If Ptolemaic astronomy was not such bad science by modern standards, then what, if anything, is it about our current science that assures us that large parts of it are not going to be rejected, as fundamentally wrong and even ridiculed in the future in just the manner that happened with Ptolemy astronomy?

The most prominent and charismatic sociologist of science, Bruno Latour, would not only tell you flat, nothing guarantees our modern science is any better. He will virtually guarantee you that if we're around a thousands years from now, current science will be a joke to the people of the time and it's grounds for saying that is the way we do science is no interesting way different sociologically from the way it was done then.

I view this course as an answer to that question, 28 weeks of it. That is, I'm going to try to find a way in which we can say modern science gives us assurances that Ptolemaic astronomy did not have. So that is why I started doing this kind of research and why I still teach this course because I don't know any other way to answer that question other then look at one episode over a long period of time and see how the evidence changed.

Thank you. We're done.