So tonight we start what I like to call the third post-Copernican generation when turning to Descartes. The way I think of generations here is probably a little bit unusual. When I divide generations I look at it from the point of view that roughly the time the person is twenty years old.
Between 15 and 20 and what the intellectual climate was at that time. And the mark of all those from Fontana on down is Fontana was 25. He was the oldest of the group. Fermat was too. But the climate had changed in 1610, when Sidereus Nuncius was published. And the telescope revealed that they then knew ever so much less than they thought they knew.
And that's just a radical change in climate. Intellectual climate from there on. The people before that grew up not remotely thinking that they didn't know most of what there is to know about the world like we do nowadays of course and much of the same way. So that's my basis for breaking that group off.
I'll say a little bit about a couple of them, I barely mentioned Vieta. He did the most before the century to introduce algebraic methods into mathematics. He's a very, very important figure. But he did so sort of problem by problem, case by case, not thinking it through on a complete theoretical basis.
So we created as much controversy over whether what he was doing a legitimate as he did solve problems. But he's gonna be a figure that shows up tonight. Other than that I think everyone in the first two groups we've at least mentioned. And the two we focused on were Galileo and Kepler.
Down here, the three most important for our purposes, I'll mention several tonight, are Mercend, Gassendi and Decartes. All of whom died between 1648, Mercend's death and Gassendi in 55, 1655. And they were the three dominant figures in that generation of all the people up there, they had the largest effect.
Tuorcelli probably would have had a comparable effect had he lived longer than 40 years old. Only other comment I have here, I list Hobbs as a philosopher. Hobbs wrote a very important book on motion. That's a philosophic work on motion, and quite controversial. But by listing him as a philosopher is somewhat sloppy on my part.
Any rate, I wanna go to Descartes tonight and next week. Before I do though, I have a couple of parting comments. On Galileo and the two new sciences. There are two slides on this. The first slide's making a point slightly different from what we did the last two weeks.
In the last two weeks I've treated Descartes' theory of local motion as purely mathematical theory of motion with uniform acceleration combined combined actually just orthogonally with uniform motion. And it’s a mathematical theory where the question’s totally open. Okay, here’s a nice mathematical theory of motion, to what does it apply?
That's not the way it came to be viewed. It came to be viewed as what it says up there, motion on and above a flat surface under the effects of uniform gravity acting on parallel lines. That's a key point here. On parallel lines perpendicular to that surface. And the other features then became secondary.
They make all other contributions to motion or compound with the motion produced by gravity. Component of motion governed by gravity always involved equally, increments of equal times. The independence of weight, shape, etc. And what we would now call an energy principle. The speed acquired through gravity depends only on the height through which it falls, etc.
That's gonna be very important. That's the foundation of Leibniz's vis viva principle. Though once removed through Hyugens. Now having said that, thinking of it as a, what I'll start calling it and I'll end up calling it the Galilean Orgenzian theory of Motion under Uniform Parallel Gravity, because that's what it is.
And the natural thing to contrast it with therefore is Newton's Theory of Motion under gravity that's directed toward a center. That's in fact how Newton comes to view this theory. Galileo, it's only a fragment of a theory. He could not do oblique projections, so he couldn't really combine uniform motion, and well he couldn't put an initial velocity and at an angle to gravity and change it into the two components the way we can.
That tour jelly added, so that was the first supplement to the theory. The other thing he can't handle at all is pendulums. As a matter of inductive conclusion he found that the period of a pendulum is proportional to the square root of the length, but beyond that he could not work it out.
That left it open. The entire theory of pendulums was left open for Huygens then, to complete. Along with that, it isn't just pendulum motions, it's curvilinear motions in general. The only curvilinear motion we have in two new sciences Is the problem made up of the two. But there are an awful lot of other curves to consider and they're not considered and this question of motion in the presence of air resistance and what one's supposed to do about it he doesn't even try to do.
But others after him certainly did. Including Newton. In some ways more interesting, I ended last time, or near the end last time, using Galileo's own phrase where he said he thought he could add something beyond mere conjecture, In that case on the nova of 1604. But that seems to me to be the right question to raise.
What's being required here to get beyond mere conjecture and what I wanna do is just compare Kepler and Galileo, the two people from that prior generation and what they were able to achieve. So Kepler's approach to getting beyond mere conjecture was agreement to within more or less observational accuracy for the planets, etc.
And the limitation came from the following. So you know you've managed to get within observational accuracy. What's the status of the result? Is it merely an approximate representation of true motion? Is it a description that would hold exactly under if it weren't for secondary effects of some sort?
Or does it hold exactly? And the point is, he had no basis for attacking that question. I mean, he had a basis. He proposed a basis, physics, but the physics was conjectural. But it's not clear how you are supposed to sort that question out, if all you're gonna do is assess a theory in terms of how well it agrees with the observations that it predicts.
All sorts of theories can predict very, very well and be dead wrong, if you don't ask too much of them. And observational accuracy here was not that great. But that's one approach. And it had a real limitation. Galileo had a totally different approach with a rather different limitation.
In his case, and I chose this carefully. I chose it paparian. The test he proposed of striking predictions coming out of his theory. They were not disconfirmed by various quasi quantitative experiment. Results from experiments. By that I mean things like the one, three, five, seven progression in distances.
Where the really important thing was not perfect agreement with one, three, five, seven. The only important thing was roughly one, three, give, seven, nine, 11, etc. And definitely that was enough not to disconfirm. So that's a form of evidence. You obtain a bunch of striking predictions and you test them and they don't clearly disconfirm.
They to some extent confirm. But then the limitation, again, but in this case it's a different limitation. It was quite unclear as Issac brought out with his question that I answered in a slide near the end showed three different conceptions of science that Galileo seemed to be shifting among.
It's not real clear what you're supposed to make of the theory when you have it. What's its relation to the empirical world? So, fine, you test it for certain very striking conclusions that probably almost never happen in the real world. They are only in contrived circumstances. It passes those tests.
That leaves very much open. What its relationship is to phenomena in the real world. And Galileo's case I was at least intimating partly in response to Isaac. But also with a slide at the end. It isn't that I think Galileo had three distinct conceptions of the relation of his theory to the world.
I think he sort of moved among them because they blurred into one. Here's a mathematical theory that's useful for something. But we're gonna have to figure out what it's actually useful for. But how do you figure that out? By more striking tests? It's not probably gonna do much.
Fair enough? So they take very different approaches to getting beyond mere conjecture on series of motion. But in both cases the limitations stand out. And I'm emphasizing the limitations, obviously, because the Principia is going to claim to get past these limitations, both sets. Okay, the very limitations I put up there, the Principia's gonna claim to have resolved for both kinds of motion.