So, I want to correct myself for doubting that because, sure enough, that's the moment I started digging in. I found out to the contrary. And the other thing I didn't mention just in passing is worth mentioning. The first star catalog after Ptolemy is by Tycho. 777 stars and then when he moved to Prague in, he got kicked out of Denmark, or left Denmark in a huff in 1596.
It took him a while to settle in Prague, but he then decided to expand it to 1,000 stars so that it matched a Talamean number, but I'm not sure he ever did. Just as a remark that may surprise you, Tycho's data was not published in the 17th century.
Kepler had sole control of it until he died so nobody but Kepler was actually seeing it. And then his son, Kepler's son, returned it to Copenhagen where it sits to this day. But anybody who wanted to consult it, and we'll later in the course see a group going to Copenhagen specifically to look at the data, it just didn't get published.
It was nine volumes, so it was quite a huge amount of total observation, the most on the sun. At any rate that's Prague in 1606 when Kepler was there under Tycho, Tycho died in 1601. Why Prague? Because it was the siege of the Holy Roman Empire namely Rudolph.
And, what happened here is that Tycho to get money. People, in these days, did lots of things to get grants and get financial support. Tycho promised Rudolph to put out new tables to replace the Alfonsine tables of the 13th century. And they were, of course, going to be called Rudolphian tables.
Those tables were finally published in 1625 by Kepler. Kepler kept Tycho's promise. But this is the seat of the Holy Roman Empire in 1600 when Kepler first approached to talk about things. And I thought you'd be intrigued at It's quite an extensive city. The big tower is the seat of the emperor.
All right, where are we? We've got a state of mathematical astronomy as of 1600. My choice of 1600, I'll explain in a couple of minutes. It actually has more significance than just being an even date. So we've got four things, the retrograde loops exhibited by the plans. I'm not gonna read this whole thing out but I'll just summarize it.
Second, inequality are attributed to entirely different sources in the three systems. Yet all three systems can be made to yield the same predictions of longitude. So the obvious question, can any empirical considerations at all establish any one of these three approaches to the second inequality? Or still some further approach over the others?
And it was just not clear that that could be done in 1600, and you'll see tonight, it's still not clear after Kepler. Second fact, the longitudes calculated within the systems have been worked out in detail, and that's all of them differ from observation by more than a degree, two moon diameters, and sometimes, by much more.
So what should be made of these discrepancies? And for that matter, what level of agreement with observation is even appropriate to demand for any such calculation system? That question is arising for the first time in a way tonight with Kepler. Third, the equod employed by Ptolemy in the minor epicycle employed by Copernicus give us two to account for changes in speed.
Give us two different claims about the trajectory with the associated with the speed changes, and again, can any empirical considerations establish what the trajectories are, and how they contribute to the apparent changes in speed. And finally the contrasting approaches taking to calculating the latitudes to planets by the different systems, or by the very complicated and yield discrepancies in excess of one degree, two moon diameters.
So, they too were unsuccessful. And now, a slightly different problem. Given the lack of patterns in the observed latitudes, the absence of anything as well behaved in the first or second inequalities, how can empirical considerations be marshal to improve the calculation. So, that's the state of mathematical astronomy as of 1600.
And I take it the questions about whether any empirical considerations at all can do anything is a question with a fair amount of bite, though we'll see tonight what happens. The claim about the very large discrepancies, these are calculations done by Jim Voco and Owen Gingrich. In 2003, Jim Voco was a student in this course, and this week and next week Were very awkward for me cause I had somebody sitting in the audience who was the reigning expert on Kevlar and I was giving six hours lecture on Kevlar watching his face all the time.
Seeing when he would get unhappy. He was in the course cause he wanted to know about Newton etcetera, not because he needed to know about Kevlar. But this is a beautiful paper in putting it on. Supplementary material. And what it shows here is in 1593 there's an almost, Kepler himself in the introduction to Astronomia Nova says an almost five degree discrepancy.
And then says, 15 years later in 1608, there's one greater than 4. And it is a 15 year pattern repeating. Those are very large discrepancies, eight to nine moon diameters, that's not a close question. You have a question? Oh, I thought your hand was up, no problem. So, we'll be watching that disappear tonight.
That's gonna be Kepler's achievement is to replace this, which is a 20th century calculation. Replace it with something that I think will impress you when we get there. As I said last time, I spoke of Tycho, but he was not the only one. There are a group of people at this time, Kepler's really one of them too, who really think the questions about the empirical world ought to be settled by the empirical world, not by theology, religion, or even philosophy, where philosophy is invoking considerations that reach beyond the empirical.
The way I like to phrase it I'm thinking to some extent of Charles Sander's Pierces great article the fixation of belief. When I'm saying is, what they wanted is let the empirical world be the ultimate arbiter on all issues about the empirical world. But that turns out to be enormously more difficult to do.
To get the empirical world to give us answers than my simple way of saying it suggests. And, notice the question here. How are questions to be resolved in a principled way on the basis of empirical information? Given the omnipresent problems of separating appearance from reality, especially once Copernicus had emphasized how big of a problem that is.
And then, the aspects of this challenge in the case of orbital astronomy, the observations can be made only from the earth. Yet the primary questions really concern what the motions look like from the fixed stars. Second in so far is the observed stages in motion can be represented geometrically in multiple ways.
We need some other way to identify the real motions from their representations. And third, we are unable to conduct experiments or to intervene, that's in Hackney's work, intervene in any way at that time in the celestial realm. In fact we were unable to intervene in the celestial realm until October 1957.
Yeah, that's right. The first Sputnik that went up. Big day in my life but that's why I can do it so easily, I know exactly where I was, etc. So there's a real challenge here and it's the challenge Kepler himself faced. I said a little bit about this.
Let me say it more dramatically. The point of this course is ultimately to read Newton's Principia, very, very critically evaluating, first laying out with real care his evidential arguments and then assessing what they did and did not show, with intent of what did Newton achieve in the way of knowledge.
And, then we'll look at the period after Newton, and ask what it achieved. So, this semester, I'm putting you in a position to read the Principia that way, to really take apart every evidential argument, to expose every assumption, and to assess what the evidence is for that assumption.
The way somebody would writing a review article. I use this phrase turning data into evidence. In the notes I make the remark that philosophers generally react to that phrase as, what do you mean turn data into evidence? And of course the reason is their picture Is the way you evidence is deduce a conclusion from the theory, and then compare it to observation, and so what's turning the observation into evidence is that deduction.
In fact, those deductions are relatively rare form of evidence. When I say to scientists that science is an endeavor to turn data into evidence. I never get a question about what I mean. I once had to keynote a weekend of federal and state judges on questions of cause Causation in the law.
And they absolutely love that expression because they sit and listen to attorneys try to turn dated evidence hour after hour, usually painfully badly, as they sit there. But the point of this is, of course I said it the other day, data is not a relation, evidence is a relation between data and claims that reach beyond them.
Therefore, something more than raw data is always needed to produce evidence. And that's the thing one wants to critically focus on and ask, is that ether element problematic? Is it undercutting the claim to knowledge, what is it actually doing? Okay, so that's the general thing. I could do a whole night on astronomia nova alone, because it's an extraordinary exercise in turning data into evidence.
One of the most extraordinary exercises ever. Even Charles Sanders Peirce, when he invented the word abduction to describe the opposite of deductive, hypothetical deductive evidence, he singled out Kepler as the most spectacular example of it. What's spectacular about it is not just his proceeding from data, namely Tycho's observations.
He is extraordinarily sensitive to all the problems that gives rise to. And so I'll throw out a snide remark. And then, I love this remark. Pat Soopi has become a very close friend, a 92-year-old at Stanford. He is of course a philosopher. He was also president of the American Psychological Association, and has done a huge amount of empirical research in psychology, and he made the remark one day, off-hand, as we were talking about the state of the philosophy of science.
Talk to any philosopher about science for 15 minutes and you will be able to tell if they've ever worked with real data. And his comment is, almost no philosopher has, and anybody who has, realizes how difficult it is to work with real data. It's just another world. Kepler appreciated that extraordinarily and I'm going to try tonight to show you how much he appreciated it.
Even though Curtis Wilson's simplified the book enormously. I have to simplify it a fair amount too because I just can't get through everything. But I hope I drive home. Just when all the problems are and I am shortly gonna start listing some of those but I'll come to that in a moment.