Contributions to mechanics. There are some really important ones by Descartes. I'm just gonna rattle them off. Global conservation principles as a constraint. I don't know that anybody before him and I, the phrase I don't know has to be in there, Dan Garber, a couple weeks ago, would be you in the 350th year celebration of Galileo's birth.
Actually made the assertion that Descartes is the first to propose a conservation principle. Conservation principles have been with us ever since. They've become more and more important. Newton didn't like them much but you'll see why, but nevertheless, the very idea that there are global conservation principles and they serve as a constraint on all the rest of physics.
By global I mean the sum total of some quantity in the whole universe. Is a constant. That’s what’s conserved. And the one that’s the principle of that today is conservation of energy. Overwhelmingly. That starts with Descartes. Second one, curvilinear motion requires external action and that’s the one I belabored at great length in these two weeks.
Third measuring the magnitude of that action. That's the one I belabored tonight giving you a bunch of Latin pages just to make sure you had all the relevant passages leading to that. Fourth we stressed last time. Force as a determiner, now I'm saying of quantity of motion. But it's also potentially a parent versus true motion.
That is, force a determiner of motion that's true. The phrase determiner is actually is. Is one Descartes liked to use. Of course in French and Latin, not in English. Impact and recoil is a fundamental process. I don't know that there was much work on impact and recoil, of attempt to do anything scientific with it before Descartes.
You're gonna see It popping up very, very dramatically next week where we get the modern solution for perfectly elastic bodies. And you'll see it continue showing up in the Principia. The relevance of fluid motion, especially of course vortex motion. Not that much attention had been paid to fluid motion.
Though Galileo did studies of floods out of rivers. Everybody in Italy was constantly concerned with trying to predict floods. Holland of course was very worried about water, but the idea of looking at getting a kind of science to fluid motion, it's just not there. And with Descartes it becomes an issue, how do real fluids behave?
Why do vortices form? What maintains them? A whole bunch of questions. And finally the demand for universal first principles. The key word there is universal. First principles of mechanics that apply to everything in the universe. Nothing in Galileo remotely suggests that he thinks that's important. OKay? And nothing really in Kepler suggests that, that's crucial.
He picks and chooses his physics for what's needed on the spot. Then there's all these questions highlighted that will remain questions for the rest of the course and next semester. What if any quantity is invariably conserved during every change in motion? Next week you'll see arguments about that initiated by Huygens, but then made very public in a fairly outspoken article by Leibniz.
A fairly young Leibniz, still in his 30's at the time. Second, what's the magnitude of the external action required for curvilinear motion, and with what does it vary? The sole indication of that in Descartes is that one sentence I jumped all over. The tension and the sling displays.
The magnitude of the. But that becomes a key question. And is a question that's most central, becomes most central. It will become most central the 13th week of this course. When not Newton introduces it, but rather it gets introduced by Rennan and Hook. And they turn it into, we know the magnitude of the force, what's the trajectory force of this kind produces, namely an inverse square force.
Third, can mathematically precise rules be given for impact and recoil that agree with everyday observation? Descartes' don't. Descartes say you can't possibly do the real ones because it's a. Huygens didn't think there was a Huygens thought there was a vacuum, others did. So then the question is what are the correct principles for what we actually observed.
Fourth question highlighted, what's the proper measure of quantity of motion and with what does it vary? Descartes has it as speed multiplied by volume, where volume amounts to the same thing as bulk. Since there's no vacuum, volume is just all matter. Fifth, what are the fundamental principles of mechanics?
The principles that have to be met in the solution of every problem in mechanics. Descartes' proposing some of those. Sixth, what's the magnitude of the force, the Latin word is Vis, of bodies to resist changes in motion. And with what does it vary? He makes the claim that we've come to reject that the magnitude of the force to resist is greater the body at rest, than it is in a body in motion.
But we still have the problem of measuring what that magnitude is. That he's raising. Seventh, what's the relationship between the weight of a body, its specific gravity, and the quantity of matter forming it? Descartes expressly says that weight is not proportional to the quantity of matter forming it, but I wanted the portion of that quantity that is solid matter.
Is that right? Or is there some other relation? How does specific gravity enter into that? Which, by the way is the way they measured density. They didn't measure density by determining weight and volume, and dividing the one in the other. They measured density by specific gravity, relative density.
Eighth, how can we determine once and for all whether vacuum space is free of all matter or possible. And ninth, what's the physics of vortex motion and do vortices have gradients in speed and pressure. That Descartes says. Now all of those are questions that are highlighted. Almost all of them are addressed either directly or indirectly in Newton's Principia.
Looking through here he sort of skips over the first one, but not entirely. Now I guess, you'd have to say, I guess all of these to some extent are addressed in Newton's Principia. Though they're gonna change their character, because they're gonna filter through Huygens, and Huygens is gonna be a dominant figure for quite some time.
Now the other thing I wanted to bring out here from Descartes. It started showing up in Galileo. Isaac pressed me about what Galileo's view is of the goals of doing science. Descartes' showing us different goals that I think if you asked people in science today, they would all accede to these three goals without necessarily recognizing the extent to which they can be in conflict with one another.
So the three goals. To provide an account of the world. I chose account to be neutral. Around us, it gives us a better understanding of it, at least to a reasonable degree of detail. Second, to marshal empirical considerations toward establishing secure answers to those questions that at the time lend themselves to such answers.
That's what Kepler for example, was trying to do. To marshal Tycho's observations to give us reasonably secure answers to what the trajectory of Mars is. And third, to provide means for improving our daily practical lives, especially through enabling us to achieve ends we otherwise could not achieve. Now, it's the second one that Descartes is strongly inclined to reject in the Principia, but much less so in the optics.
The optics looks much more like piecemeal science. Working out the consequences of Snell's law all over the place. But it's. At some point, there starts being a serious conflict between doing science in a piecemeal fashion where you have the capacity to use observations to achieve, to turn into, to achieve relatively high quality evidence locally.
You saw Kepler do it. Relatively high quality evidence about what the trajectories are, what the motions are of the planets. High quality versus 1,500 years preceding him. But it was very local. It applied only to those planets. The physics was conjectural, there's nothing about the motion on Earth, etc.
That's something to be very attracted to. It's obviously what Ptolemy was attracted to as well. The very possibility of coming up with a mathematical scheme that could be supported off of empirical considerations. But in doing that, you're walking away from having a total explanatory scheme, and often walking away from understanding why.
So people kept asking, why should the area rule hold? You can easily picture the jokes. You mean there’s somebody in the planet calculating the area being swept down, adjusting the speed for it. That wasn’t, I don’t think that was serious, but it was not at all obvious why something like the area rule had hold.
Okay? And that's the sort of element that Kepler did not succeed in explaining, even when he tried to explain it. So, the point becomes one of, there's conflict between these two, and through the rest of the history of science, we've pursued all three. Depending on what our mood is at the given moment, we pursue what's practically needed.
My favorite example of that is when Reagan declared war on cancer, a remarkable number of people working in molecular biology managed to turn their fundamental research into research on the war on cancer. With the loosest possible connections, cuz all they really wanted to do was continue their research, but the practical elements start showing up and in no time, Congress is demanding practical returns from this.
And the war on cancer ceased being the war on cancer, somewhere along the way. At least it ceased being called that. These three are really not automatically compatible with one another. And which one should be dominant is a very interesting question. I think we've not been consistent through modern history as to which of the three is the primary.