So the question came, I'll reword it for him and make it more of an affront to me than he was prepared to do. How can you be calling this the early stages of theory construction when there's a 2,000 year tradition leading up to it? Emily? 2,000 year tradition leading up to it.

And of course, that point is profoundly right, because there's no way Kepler could have done what he did in Astronomia Nova without all the techniques in calculation and inference for an observation that it had been developed, starting with Tolemy and refined over time. Remember, he sits there through half the book doing detailed calculations in all three systems, to show that he can reach the same conclusion each way.

He's very much in that tradition. So what I said in response was, yes, that's true, but the moment you dropped the two key background assumptions that dominated that entire tradition, and the word key is needed in there because there are other background assumptions that he was dropping. Namely, trajectories are always compounds of circles, and second, all motion is always equiangular about some point.

Those are the two. And think for a moment what they do. What I said right away is they constrain all reasoning. Now, what I meant by that, and didn't make clear, is that suppose you're at some juncture and you see a whole host of possibilities in drawing an inference from an observation.

And then you say, but we know, of course, it has to be a circular trajectory and it has to be equiangular, so all the ones that are not like that can be thrown out. That's an enormous simplification that you are making all the time by simply being able to say, I can exclude everything but this.

In that sense, it's very much entering in, constitutionally into evidential reasoning. You drop those, and now the statement I essentially made to you, and you're in a quagmire. You can go any direction you want. Okay, and that's the situation Kepler was in and it so happens that the replacement for equiangular motion he had already been wanting to do beforehand.

But the ellipse, even when it was staring him in the face, it was like 18 months before he finally decided it was correct, when he got the diameter distance rule. Okay? And I'll come back to that tonight. Now, the reason I'm belaboring all of this is to tell you, this is not the first time in the history of modern science where we have a long-standing tradition, decide that the constraints it was imposing on all theorizing were no longer acceptable, and we're lost about what to do.

The event I have in mind was 1911, the first Solvay conference in Belgium, that I'll now summarize the opening address. This was invitation only. The youngest person there, actually, the second youngest person there was Einstein. And at that time, he was not quite so famous as he became a few years later, but he was still a very, very important person there.

But the person who was chosen to be secretary of the first Solvay Conference was Lorentz. And Lorentz opened it, and now I'm being slightly cute, and of course he's in French. But this is very close to what he says. We have this beautiful theory of radiation worked out over the years by a number of people, including Rayleigh.

It does everything we want, except be true.

And now this Planck has come along and shown us that if we quantize the possible frequencies of light, then we get a theory that works. Similarly, we have this beautifully theory of the specific heats of solids that work over an enormous range of temperatures.

But when you lower the temperature they fail entirely. They couldn't be predicting more incorrectly. So along comes Einstein in 1907, and says, you quantize energies, that is, energy is no longer a continuous variable, and look what happens. You get the actual measured ratio of specific heats. So Lorentz points these two things out and then says, that's why we're here.

We have to introduce quanta, and we don't know how to do it. That's the topic. Okay? And it's called radiation and quanta, I think is part of the conference title. They didn't resolve it. It wasn't resolved for 15 years. When Heisenberg and Schroedinger came along 15 years later, they finally got a solution to the problem that was posed in 1911.

And there was a lot of false starts and a lot of struggle over those 15 years. And that's what I should have invoked right away to you. Because I've seen the same thing happen all over again, when we can't presuppose that key variables, frequency and energy are continuous variables.

You know, that's a tradition that goes back forever, of continuous variables. They're not continuous. They jump. What in the world are we supposed to do with that? Okay. So I think the point's well taken, that simultaneously something can be in the very early in the stages of theory construction.

And if you look at the works during the teens and quantum mechanics, the so-called old quantum mechanics, you will see they're very much in the early stages of theory construction. They can't get it to come out. They keep trying things and they don't work, and making proposals that they think are principled and don't work.

So the situation is comparable, except Kepler was all by himself. Not talking to a bunch of others, and the tradition in 1911, the state of physics was an awful lot more advanced than many respects than the state of Astronomy was in the time of Teco. Anyway I'll stop with this now.

I'll accept any questions on that, then I want to jump into tonight. Because I think it's an interesting point, I hope I made my key point. Those working hypotheses, when they're of the form I'm talking about equiangular motion, they profoundly constrain theorizing. And if your theorizing is not constrained, you can go anywhere with it.

And that seems to be the feeling Kepler had with the very idea of departing from a circle. Anything is possible. Why should any one thing stand out? And the classic way of representing him as adopting the next simplest curve after the circle, I hope I made clear last week, is not what happened.