“Answer this then: do you have friends named Bob Carver and Dick Gripp?”
“Never heard of them.”
“That’s funny, for we have come upon a page of written instructions, left with the warder, saying that you’re to be allowed no visitors at all, except for Bob Carver and Dick Gripp, who may show up at the oddest hours.”
“I do not know them,” Daniel insisted, “and I beg you not to let them into this chamber under any circumstances.”
“That’s begging a lot, Professor, for the instructions are written out in my lord Jeffreys’s own hand, and signed by the same.”
“Then you must know as well as I do that Bob Carver and Dick Gripp are just murderers.”
“What I know is that my lord Jeffreys is Lord Chancellor, and to disobey his command is an act of rebellion.”
“Then I ask you to rebel.”
“You first,” said the sergeant.
Hanover, August 1688
Dear Daniel,
I haven’t the faintest idea where you are, so I will send this to good old GRUBENDOL and pray that it finds you in good health.
Soon I depart on a long journey to Italy, where I expect to gather evidence that will sweep away any remaining cobwebs of doubt that may cling to Sophie’s family tree. You must think me a fool to devote so much effort to genealogy, but be patient and you’ll see there are good reasons for it. I’ll pass through Vienna along the way, and, God willing, obtain an audience with the Emperor and tell him of my plans for the Universal Library (the silver-mining project in the Harz has failed-not because there was anything wrong with my inventions, but because the miners feared that they would be thrown out of work, and resisted me in every imaginable way-and so if the Library is to be funded, it will not be from silver mines, but from the coffers of some great Prince).
There is danger in any journey and so I wanted to write down some things and send them to you before leaving Hanover. These are fresh ideas-green apples that would give a stomach-ache to any erudite person who consumed them. On my journey I shall have many hours to recast them in phrasings more pious (to placate the Jesuits), pompous (to impress the scholastics), or simple (to flatter the salons), but I trust you will forgive me for writing in a way that is informal and plain-spoken. If I should meet with some misfortune along the way, perhaps you or some future Fellow of the Royal Society may pick up the thread where I’ve dropped it.
Looking about us we can easily perceive diverse Truths, viz. that the sky is blue, the moon round, that humans walk on two legs and dogs on four, and so on. Some of those truths are brute and geometrickal in nature, there is no imaginable way to avoid them, for example that the shortest distance between any two points is a straight line. Until Descartes, everyone supposed that such truths were few in number, and that Euclid and the other ancients had found almost all of them. But when Descartes began his project, we all got into the habit of mapping things into a space that could be described by numbers. We now cross two of Descartes’ number-lines at right angles to define a coordinate plane, to which we have given the name Cartesian coordinates, and this conceit appears to be catching on, for one can hardly step into a lecture-room anywhere without seeing some professor drawing a great + on the slate. At any rate, when we all got into the habit of describing the size and position and speed of everything in the world using numbers, lines, curves, and other constructions that are familiar, to erudite men, from Euclid, I say, then it became a sort of vogue to try to explain all of the truths in the universe by geometry. I myself can remember the very moment that I was seduced by this way of thinking: I was fourteen years old, and was wandering around in the Rosenthal outside of Leipzig, ostensibly to smell the blooms but really to prosecute a sort of internal debate in my own mind, between the old ways of the Scholastics and the Mechanical Philosophy of Descartes. As you know I decided in favor of the latter! And I have not ceased to study mathematics since.
Descartes himself studied the way balls move and collide, how they gather speed as they go down ramps, et cetera, and tried to explain all of his data in terms of a theory that was purely geometrical in nature. The result of his lucubrations was classically French in that it did not square with reality but it was very beautiful, and logically coherent. Since then our friends Huygens and Wren have expended more toil towards the same end. But I need hardly tell you that it is Newton, far beyond all others, who has vastly expanded the realm of truths that are geometrickal in nature. I truly believe that if Euclid and Eratosthenes could be brought back to life they would prostrate themselves at his feet and (pagans that they were) worship him as a god. For their geometry treated mostly simple abstract shapes, lines in the sand, while Newton’s lays down the laws that govern the very planets.
I have read the copy of Principia Mathematica that you so kindly sent me, and I know better than to imagine I will find any faults in the author’s proofs, or extend his work into any realm he has not already conquered. It has the feel of something finished and complete. It is like a dome-if it were not whole, it would not stand, and because it is whole, and does stand, there’s no point trying to add things on to it.
And yet its very completeness signals that there is more work to be done. I believe that the great edifice of the Principia Mathematica encloses nearly all of the geometrickal truths that can possibly be written down about the world. But every dome, be it never so large, has an inside and an outside, and while Newton’s dome encloses all of the geometrickal truths, it excludes the other kind: truths that have their sources in fitness and in final causes. When Newton encounters such a truth-such as the inverse square law of gravity-he does not even consider trying to understand it, but instead says that the world simply is this way, because that is how God made it. To his way of thinking, any truths of this nature lie outside the realm of Natural Philosophy and belong instead to a realm he thinks is best approached through the study of alchemy.
Let me tell you why Newton is wrong.
I have been trying to salvage something of value from Descartes’ geometrickal theory of collisions and have found it utterly devoid of worth.
Descartes holds that when two bodies collide, they should have the same quantity of motion after the collision as they had before. Why does he believe this? Because of empirical observations? No, for apparently he did not make any. Or if he did, he saw only what he wanted to see. He believes it because he has made up his mind in advance that his theory must be geometrickal, and geometry is an austere discipline-there are only certain quantities a geometer is allowed to measure and to write down in his equations. Chief among these is extension, a pompous term for “anything that can be measured with a ruler.” Descartes and most others allow time, too, because you can measure time with a pendulum, and you can measure the pendulum with a ruler. The distance a body travels (which can be measured with a ruler) divided by the time it took covering it (which can be measured with a pendulum, which can be measured with a ruler) gives speed. Speed figures into Descartes’ calculation of Quantity of Motion-the more speed, the more motion.
Well enough so far, but then he got it all wrong by treating Quantity of Motion as if it were a scalar, a simple directionless number, when in fact is is a vector. But that is a minor lapse. There is plenty of room for vectors in a system with two orthogonal axes, we simply plot them as arrows on what I call the Cartesian plane, and lo, we have geometrickal constructs that obey geometrickal rules. We can add their components geometrickally, reckon their magnitudes with the Pythagorean Theorem, amp;c.
But there are two problems with this approach. One is relativity. Rulers move. There is no fixed frame of reference for measuring extension. A geometer on a moving canal-boat who tries to measure the speed of a flying bird will get a different number from a geometer on the shore; and a geometer riding on the bird’s back would measure no speed at all!