Descartes says in parts of, sections of part two, that I'm reserving more for next week, that geometrically all motion is relative. That is geometrically all we have to refer motion to somebody or other taken to be at rest and motion concerns it. And that is a variant on the question Maris raised namely how can we be talking about motion here?
And in particular, how can we be distinguishing between rest and motion as an absolute distinction the way he does? Okay, and I think the answer is fairly straightforward. It's not my answer, it's one by I think his name is Phillippe Gero, in a book that came out on Descartes before I started teaching this course.
Geometrically, motion has to be referred to a place. But metaphysically, the presence of forces alters that situation. It can tell you what's really moving and not moving but virtue of looking at the forces and which ones cause which. Now that sounds, I don't know what your reaction is to that, but that's not very far removed from Newton.
In fact that, to say it's not very far removed is right at the heart of Newton, Newton's going to distinguish real motion from apparent motion. Or if you prefer, absolute changes of motion from relative changes of motion by forces. Can't be done geometrically, but by forces. But that seems to be in these rules exactly what Descartes is doing.
The additional introduction of the notion of force is major step. What in the hell does he mean by force? It's not very clear at all. So what I will do, I couldn't get it up tonight because of the copier being down. There's a long paper by Alan Gabbey when he was very young.
He's now, I think retired, but he's been at Barnard College for many years. But at this time he was at Queen's College in northern Ireland working under a man named Haravel, wrote a beautiful article on force and inertia, the two concepts running through the 17th century. It's a quite famous article.
And part two of it goes a good deal of length trying to sort out what Descartes means by force and what Descartes means by resistance to change of motion. And what he means by these laws, and how to make sense of these rules. So I'll put that up.
The rules themselves are not very important to us because there gonna be supplanted by Huygens' fairly early on. And then from there on Descartes rules just become a curiosity. But this notion of force doing, force as causation, allowing us to distinguish things like rest from motion. Notice, he does distinguish rest from motion.
If this body is at rest, you get a different rule from if it's moving. Go back, seven and eight have the motion going in the same direction. Those rules are different from the ones with the body at rest in four, five, and six. Therefore, forces can distinguish whether the body, before impact, was at rest or not at rest.
That's a real difference. So in effect Descartes is not insisting that all motion be relative. He's just saying geometrically, all motion is relative. But once one takes into account the metaphysics of forces and causes, we get something different. So what he does say, right near the end of part two, preparing for part three, and the vortex theory.
Article 61, and remember those numbered things, they belong as postals. I just haven't figured out how to do postals the way he does them on Word and I don't want to spend the time doing it. That when an entire fluid body moves simultaneously in some direction, it must necessarily carry along with it, any solid body which is immersed in it.
He's gonna give an argument for that. I don't know how much you're gonna like the argument. From the preceding, it is clearly perceived that a solid body immersed in a fluid and at rest in it, is held there as if in equilibrium. I trust by now you've noticed how often it is clearly perceived.
You know, it's like the mathematicians say, it is obvious.
But for him, clearly perceived means much more than it's obvious. It means it's clear and distinct, etc. It's clearly perceived. Further, no matter how large it may be, it can always be driven in one direction or another by the least force.
Whether this force comes from elsewhere, or whether it consists in the fact that this entire fluid simultaneously moves in a certain direction as rivers flow to the ocean, or as all the air flows toward the west when the east wind blows. When this occurs, it is absolutely necessary for a solid body situated in such a fluid to be carried along with it, nor is this contradicted by the fourth rule according to which as I stated before, a body which is at rest cannot be set in motion, etc.
So he hasn't told us how it's not contradicted by the fourth rule, he just told us it's not. Now of course the fourth rule applies to bodies in isolation, this is not in isolation. So I think that's what he means. But now the next one. That a solid body which is thus carried along, that should be by a fluid, I'm sorry, by a fluid is not therefore moving.
That's slightly strange. I've got this object in a river, the river is flowing and the conclusion is the body's not moving. Okay. If moreover we turn our attention to the true and absolute nature of movement. Now that's back in article 26, which we'll look at next time. I intentionally skipped it tonight.
Which consists in the transfer of a moving body from the vicinity of other bodies contiguous to it. So that's the nature, true and absolute nature of movement. A body is moving only if it changes position with respect to those things touching it. Okay? Of course it's not going to do that in the fluid.
Body from the vicinity of other bodies contiguous to it, and which is equal in both the body which is said to move and the contiguous body away from which it is said that it had moved. That's an insert by the Millers. Although it is not customary to speak of the two in the same way, and to say that both move.
We will clearly know that a solid body which is thus carried along by the fluid to which it is contained, does not strictly speaking move as much as it would if it were not carried along by the fluid etc. So in effect he's saying here motion is always relative.
But, relative to what, to the matter that's immediately contiguous to the moving body. In Le Monde, he doesn't say anything remotely like that. Not remotely like that. What he says first is to berate, partly to berate the Eratosthenes, so which terms are so obscure that I am constrained to leave them here in their language because I can not interpret them?
Now it's going to give you the words, in my case, in English and his case, in French. And in fact the words, motion is the act of being in potency in so far as it is in potency. Okay, that's nice scholastic account of what motion is. And he's laughing at that.
So what he says is, no clearer being in French than if he gave them to you in Latin. The nature of motion of which I speak here, is so easy to know, that mathematicians themselves who among all men studied most who conceived very distinctly the things they were considering, judged it simpler and more intelligible than their surfaces and their lines.
So it appears from the fact that they explained the line by the motion of a point. And the surface by that of a line. Okay, motion to mathematicians is even clearer than straight line or planes, okay? Continuing. This is before the geometry folks, this is Le Monde. The philosophers also suppose several motions that they think could be accomplished without any bodies changing place.
Such as those they call the motion of form, the motion of heat, the motion of quantity. Motion with respect to form, motion with respect of heat, motion with respect to quantity, and myriad others. That's Aristotle, of course. The word kinesis really means change. It's motion is any form of change.
Not just change of place. That's what he's berating. As for me, I conceive of none except that which is easier to conceive of than the lines of mathematicians. The motions by which bodies pass from one place to another and successively occupy all the spaces in between. That's a very nice description of motion, it's the one Newton adopts at one juncture.
Rather strikingly, I don't think he had seen Le Monde to see that Descartes did as well as we'll see later. So there's a natural question, why in the hell did he change it to where real motion is only displacement to parts touching one another? I'll give you the answer now.
We'll look at it next week. Therefore, the Earth being carried by a vortex around the Sun is not in motion. Because it's not changing location with respect to the fluid and the vortex continues to, therefore, the Bible's okay. His vortex theory is not violating any biblical scripture. That's what he thinks.
That's his way of getting out of having a clearly Copernican system not involve the motion of the Earth, okay. Newton thought this a total subterfuge. Whether Descartes took it seriously or not, I don't know. Let me give you the last thought for the day. This is the last word in all of part two.
I openly acknowledge that I know of no kind of material substance other than that which can be divided, shaped, and moved in every possible way, in which geometers call quantity, and take as the object of their demonstrations. And that there is absolutely nothing to investigate about this substance except those division, shapes, and movements.
And that nothing concerning these can be accepted as true unless it is deduced from common notions whose truth we cannot doubt, with such certainty that it must be considered as a mathematical demonstration. And because all natural phenomenon can thus be explained, the Latin is not explanara, it's explicare.
As will appear in what follows. I think no other principles of physics should be accepted, or even desired. And what this leads into is part three on the universe, where he's gonna explain everything. And part four on what's around the Earth, where he's gonna explain everything, just using these principles.
So part three and part four are gonna, as it were, support the claim that he's got everything he needs. We're not gonna do anything more in part four othan read the closing passages where he tells you why you should believe all this. But we'll look at part three with a fair amount of care because it became the alternative to Newton's account of planetary motion, right though to the 1730s was the alternative subversion of