All right, so the Principia, let's spend the rest of our time on Descartes save for one letter he wrote, that we'll look at next week. A letter saying everything that's wrong with Galileo's two new sciences, and it's a letter that Newton read, so it's fairly important to understand.

Principia was published in 1644. There is not a second edition of it in his lifetime. There is a French edition in which he did clean things up, add some things, etc. Published as you see this time in Amsterdam. Holland was the place to publish. Now there's an obvious question for those who've actually read any of the Principia.

There's an obvious question, why am I assigning it? Because the vast majority of the science in it is so transparently false that one reaction is I'm simply showing how wrong Descartes can be. So in defense of my assigning Descartes Principia, and by the way when I'm forced Stanford to reduce this into a ten week course, one of the things I telescope is Descartes Principia into a single week.

I always feel bad about that because I think there's a lot going on. So there are good reasons to read it. First of all, it was enormously influential. You can't imagine, given the science versus what we think is the truth, the science in it would've been that influential.

Not just 10 or 20 years, all the way up to at least 1730. It was extraordinarily influential. So that's one reason to read it. You're not going to understand the climate in which Newton's Principia was received unless you appreciate what it is about the Principia that had so many people enamored with it.

Second reason, Newton, the very title tells you this, I mentioned it last week, Newton is responding to Descartes. One way to read his book, let me say it more carefully. One reason the first edition of his book is 510 pages long Is because he wanted to thoroughly refute Descartes, including on points that have nothing whatever to do with the rest of the Principia.

He will go out of his way to, there's a whole section on lenses. In the Principia section 14, book one, and all it's really doing is a diatribe against Descartes. He really disliked Descartes, and he really disliked the Principia, and he pretty much disliked the mathematics once he reached a certain point.

So that's a reason, the way I put it in the notes Is you're not gonna understand all of the Newton's Principia without recognizing what it's responding to. And why it treats certain problems, namely the Descartes. A third reason is almost all the opposition to Newton's Principia and by opposition I mean virtually no one on the continent bought into Newton's theory of gravity before 1730.

Very nearly zero people. And the reason primarily was the influence of Descartes and the Principia against it. When the dam was finally broken by Mopar Twee, he was from a younger generation and his mentor Johannes Bernule was less than pleased. But it was a turning point, and it came after Newton died.

So the time Newton died, I'll give you one last twist on this, you will read next semester an ollogium, written by Fontanelle, the recording secretary of the Royal Academy, it's a beautiful, beautiful illogium. When Jed Buchwald and I had to write one for Tom Kuhne, he tried to use that as a model until we realized we weren't good enough to write one that well.

So then we did our best with what we had to work with. When it was read at the Royal Society, it caused a near riot. Because the whole of the of the illogium is comparing Descartes and Newton. And the view in England was Descartes shouldn't be mentioned in the same breath with Newton.

So that's a further indication of just how strong the influence of Cartesianism was, and Fontenelle himself was a Cartesian. A fourth reason is, it's going to put on display, let's begin to see it tonight, but I'll fill it out completely next week because I want you to see a lot of this before we start filling it out.

A conception of how to do science that's still with us in various places. I can summarize it right now, just in a few words. It's very, very hard to, use my phrase, turn data into evidence. So, what you do to do it are two things. You impose constraints on theories that eliminate most possibilities.

And then you insist the theory cover everything to safeguard against any local, successful result being systematically misleading. So an example of this in modern times is functionalism in cognitive psychology. And it's imposed in the constraint that the brain has to work in a manner of a computer. Pure symbol manipulation.

Impose that constraint and start then taking experiments and interpreting them under that constraint. Now there's no fundamental reason why that constraint has to be true. But it's a way of getting a lot more out of experiments than if you drop the constraint. I can think of other choices, Michael, isn't it true to some extend in Cosmology, that by imposing constraints and insisting you do everything, you think you can get much more out of paltry data than the data can do in and of themselves.

At any rate, I just throw it out, you'll see it showing up again and again and it's worth seeing. It contrasts with doing piecemeal science, taking some local phenomenon or set of phenomenon and investigating them separately. As, of course, most of science has done. But then the most important reason why I'm having you read it is the Principia, would have done it, but Principia actually does it much better.

It totally recasts the way we conceptualize curve of linear motion so radically and so completely that it is a different world after this is published than before. And that's most of what I'll be dealing with tonight and much of next week. The way in which it reconceptualizes curvilinear motion.

That reconceptualization takes place in eight pages. Four in part two and four in part three. And so I'm giving you this week, the four in part two in Latin so you can compare it to the translation if you distrust the translation. First thing to notice here is the format.

What you're seeing and you're reading as an introductory line with a number followed by a paragraph, that's not the format it was written in. The format is postal in the margin with the text going continuously. That is also the format Newton originally wrote his system of the world in before he decided to suppress that version and turn it into a set of mathematical propositions for reasons you'll see the last week of this semester.

He wanted to make the book more difficult to read, frankly. No. I mean openly. But the postal here says, first law of nature. First striking thing about that is the word, lex. Laws were talked about all the time in Renaissance Naturalism, but they dropped out of what the movement is science because of course the laws of Renaissance naturalism were all over the place, and they had very little foundation.

I'll talk later about what Descartes meant by a law, but I assure you, our use of the word law in physics dates from this. It's one step removed, but this lead to Newton, well, this lead to a series of people talking about laws of motion, which lead Newton to adopt laws as well, but that's the tradition of talking about laws and physics dates from this one.

Next thing to notice is postals. What's proposition 38, On Projectile Motion? What's the point he's making? This is part of his reconceptualization. The question Aristotle faced and answered, why when we throw an object does it keep moving? And his answer was, because of the air rushes in behind it keeps it moving, okay and Descartes' answer is, boils down to, why shouldn't it keep moving?

Okay. Sure enough the air will stop it, but absent in the air it's just gonna move, there's not a problem here. And that's the first step towards the reconceptualization that you don't have to do anything to keep something moving. Rather you have to stop it from moving. Second law of nature, which says that motion is in a straight line in the absence of impediment.

That's the law. That's not what the postal says. The most postal talks all about circular movement and the tendency always to recede from the center when moving circularly. That's a radical reconceptualization of circular motion, because it's immediately announcing circular motion cannot occur without some external cause, caused external to the motion.

We have never, nor I don't think anybody had ever proposed that before. Once it got proposed, this principal was just accepted blindly almost immediately by everyone, and then the question became what's holding the planets in orbit? And that changed everything. Finally, this last, the third law. It's striking because it talks about is the transfer of motion from one body to another, in which no total motion is lost.

That's another fairly extraordinary notion. That whenever anything changes motion another body has to be involved and there has to be a transfer between them. Okay. That's less important to me than the curvilinear result but it's still very important. So that's the ultimate reason I think we have to read this