So let's start looking at the so-called Laws of Motion. We start with this principle of conservation of total motion. And it's worth reading the whole thing. I've had to italicize the part that I want emphasis, of course.

"As far as the general" - and anything in brackets is, of course, added in the French - "As far as the general and first cause is concerned, it seems obvious to me that this is none other than God Himself, who, being all powerful in the beginning created matter with both movement and rest; and now maintains in the sum total of matter, by His normal participation, the same quantity of motion and rest as He placed in it at that time."

"For although motion is only a mode of the matter which is moved, nevertheless" - and now the italics - "there is a fixed and determined quantity of it; which, as we can easily understand, can be always the same in the universe as a whole even though there may at times be more or less motion in certain of its individual parts. That is why we must think that when one part of matter moves twice as fast as another twice as large, there is as much motion in the smaller as in the larger; and that whenever the movement of one part decreases, that of another increases exactly in proportion."

Okay? The idea here - what he's calling motion - the word he uses is moles (bulk), and it came to be a widely used word for this. It's a word that Newton started using at one point and then introduced the word mass instead. But it's moles (bulk) times speed with no vectorial element in it. So in a paper you're going to read in two weeks that Leibniz published - it's '86, is it not, that he... - An Error In Descartes. By then Huygens had shown that what we call total motion is not preserved, but that what we call momentum - which is a directional quantity - is, and so Leibniz was offering a proposal for... as a substitute for this, and it led - most physics textbooks will tell you - a controversy ensued as to which was conserved, momentum or energy, and of course they were both right and both wrong.

The trouble is this is not our momentum at all; it's not directional. And so the natural reaction is to ask what's going on and the key to understanding it is - and it's so simple once you think of this - think of yourself as a fish deep down in an ocean, two or three miles below the surface, in which you don't see any surfaces; everything is just liquid. What's going to happen in a liquid like that to any motion? Okay, it doesn't matter what direction it is; it's always got to be a circuit. And it's a principle of fluid mechanics. It's called the principle of continuity, and it's fundamental to all fluid mechanics.

The problem is we're looking at this with vacuums; we're looking at it in a world where there are objects free to move, not impeded, whereas Descartes is looking at us as if we're totally surrounded at all times by fluid matter. There are no boundaries, there's just fluid matter everywhere, some of it coheres more closely than another.

Now the interesting thing about this is this was absolutely clear to young Spinoza. One of Spinoza's very first writings is the Principles of the Philosophy of Descartes, and he sets it up exactly right. Notice what it says. Proposition nine: "If a circular pipe ABC is full of water and is four times as broad at point A as at point B, when the water (or any other fluid body) at point A begins to move toward B, the water at B will be moved four times more quickly than the water at A."

And he then goes on to say, "A fluid body moved through pipe ABC admits indefinite degrees of speed." You know this principle every time you look at a nozzle. It's the principle of continuity. The way to say it crudely is the speed times the cross-sectional area is always a constant. Reduce the cross-sectional area, the speed increases. It's just an absolutely fundamental principle of fluid mechanics. One could legitimately say it's the first principle of fluid mechanics. And it's called the principle of continuity.

The way it's put vectorially is del dot rho V equals - in steady state - equals zero. That is, any change of rho V in any direction... the sum of that has to be zero.

Okay? So it's not as crazy as it looks. The problem is reading this as having anything to do with our principle of momentum. Our principle of momentum is not something... our principle of momentum still holds in fluid mechanics, folks, that's a separate thing... but the simple fact is if you can just make the intellectual adjustment of thinking about the universe the way Descartes did - that we're immersed in fluid at all times - this is not a terribly crazy position whatsoever. And the vectorial element isn't relevant.

What Descartes ends up concluding is that all motion has to be in a closed circuit. Which is very much true in a fluid where the boundaries don't enter in in any way. Actually, it's true even when the boundaries enter in. The fluid has nowhere to go; it's still got to be a circuit.