Secondly: the Cartesian Quantity of Motion, mass multiplied by velocity (mv), is not conserved by falling bodies. And yet by doing, or even imagining, a very simple experiment, you can demonstrate that mass multiplied by the square of velocity (mv2) is conserved by such bodies.
This quantity mv2 has certain properties of interest. For one, it measures the amount of work that a moving body is capable of doing. Work is something that has an absolute meaning, it is free from the problem of relativity that I mentioned a moment ago, a problem unavoidably shared by all theories that are founded upon the use of rulers. In the expression mv2 the velocity is squared, which means that it has lost its direction, and no longer has a geometrickal meaning. While mv may be plotted on the Cartesian plane and subjected to all the tricks and techniques of Euclid, mv2 may not be, because in being squared the velocity v has lost its directionality and, if I may wax metaphysical, transcended the geometrickal plane and gone into a new realm, the realm of Algebra. This quantity mv2 is scrupulously conserved by Nature, and its conservation may in fact be considered a law of the universe-but it is outside Geometry, and excluded from the dome that Newton has built, it is another contingent, non-geometrickal truth, one of many that have been discovered, or will be, by Natural Philosophers. Shall we then say, like Newton, that all such truths are made arbitrarily by God? Shall we seek such truths in the occult? For if God has laid these rules down arbitrarily, then they are occult by nature.
To me this notion is offensive; it seems to cast God in the role of a capricious despot who desires to hide the truth from us. In some things, such as the Pythagorean Theorem, God may not have had any choice when He created the world. In others, such as the inverse square law of gravity, He may have had choices; but in such cases, I like to believe he would have chosen wisely and according to some coherent plan that our minds-insofar as they are in God’s image-are capable of understanding.
Unlike the Alchemists, who see angels, demons, miracles, and divine essences everywhere, I recognize nothing in the world but bodies and minds. And nothing in bodies but certain observable quantities such as magnitude, figure, situation, and changes in these. Everything else is merely said, not understood; it is sounds without meaning. Nor can anything in the world be understood clearly unless it is reduced to these. Unless physical things can be explained by mechanical laws, God cannot, even if He chooses, reveal and explain nature to us.
I am likely to spend the rest of my life explaining these ideas to those who will listen, and defending them from those who won’t, and anything you hear from me henceforth should probably be viewed in that light, Daniel. If the Royal Society seems inclined to burn me in effigy, please try to explain to them that I am trying to extend the work that Newton has done, not to tear it down.
Leibniz
P.S. I know the woman Eliza (de la Zeur, now) whom you mentioned in your most recent letter. She seems to be attracted to Natural Philosophers. It is a strange trait in a woman, but who are we to complain?
“Dr. Waterhouse.”
“Sergeant Shaftoe.”
“Your visitors have arrived-Mr. Bob Carver and Mr. Dick Gripp.”
Daniel rose from his bed; he had never come awake so fast. “Please, I beg you, Sergeant, do not-” he began, but he stopped there, for it had occurred to him that perhaps Sergeant Shaftoe’s mind was already made up, the deed was all but done, and that Daniel was merely groveling. He got to his feet and shuffled over the wooden floor towards Bob Shaftoe’s face and his candle, which hung in darkness like a poorly resolved binary star: the face a dim reddish blob, the flame a burning white point. The blood dropped from Daniel’s head and he tottered, but did not hesitate. He’d be nothing more than a bleating voice in the darkness until he entered the globe of light balanced on that flame; if Bob Shaftoe had thoughts of letting the murderers into this room, let him look full on Daniel’s face first. The brilliance of the light was governed by an inverse square law, just like gravity.
Shaftoe’s face finally came into focus. He looked a little sea-sick. “I’m not such a black-hearted bastard as’d admit a pair of hired killers to spit a helpless professor. There is only one man alive whom I hate enough to wish such an end on him.”
“Thank you,” Daniel said, drawing close enough now that he could feel the candle’s faint warmth on his face.
Shaftoe noticed something, turned sideways to Daniel, and cleared his throat. This was not your delicate pretentious upper-class ‘hem but an honest and legitimate bid to dislodge an actual phlegm-ball that had sprung into his gorge.
“You’ve noticed me pissing myself, haven’t you?” Daniel said. “You imagine that it’s your fault-that you put such a terror into me, just now, that I could not hold my urine. Well, you did have me going, it is true, but that’s not why piss is running down my leg. I have the stone, Sergeant, and cannot make water at times of my own choosing, but rather I leak and seep like a keg that wants caulking.”
Bob Shaftoe nodded and looked to have been somewhat relieved of his burden of guilt. “How long d’you have then?”
He asked the question so offhandedly that Daniel did not get it for a few moments. “Oh-you mean, to live?” The Sergeant nodded. “Pardon me, Sergeant Shaftoe, I forget that your profession has put you on such intimate terms with death that you speak of it as sea-captains speak of wind. How long have I? Perhaps a year.”
“You could have it cut out.”
“I have seen men cut for the stone, Sergeant, and I’ll take death, thank you very much. I’ll wager it is worse than anything you may have witnessed on a battlefield. No, I shall follow the example of my mentor, John Wilkins.”
“Men have been cut for the stone, and lived, have they not?”
“Mr. Pepys was cut nigh on thirty years ago, and lives still.”
“He walks? Talks? Makes water?”
“Indeed, Sergeant Shaftoe.”
“Then, by your leave, Dr. Waterhouse, being cut for the stone is not worse than anything I have seen on battlefields.”
“Do you know how the operation is performed, Sergeant? The incision is made through the perineum, which is that tender place between your scrotum and your anus-”
“If it comes down to swapping blood-curdling tales, Dr. Waterhouse, we shall be here until this candle has burnt down, and all to no purpose; and if you really intend to die of the stone, you oughtn’t to be wasting that much time.”
“There is nothing to do, here, but waste time.”
“That is where you are wrong, Dr. Waterhouse, for I have a lively sort of proposition to make you. We are going to help each other, you and I.”
“You want money in exchange for keeping Jeffreys’s murderers out of my chamber?”
“That’s what I should want, were I a base, craven toad,” Bob Shaftoe said. “And if you keep mistaking me for that sort, why, perhaps I shall let Bob and Dick in here.”
“Please forgive me, Sergeant. You are right in being angry with me. It is only that I cannot imagine what sort of transaction you and I could…”
“Did you see that fellow being whipped, just before sundown? He would’ve been visible to you out in the dry-moat, through yonder arrow-slit.”
Daniel remembered it well enough. Three soldiers had gone out, carrying their pikes, and lashed them together close to their points, and spread their butts apart to form a tripod. A man had been led out shirtless, his hands tied together in front of him, and the rope had then been thrown over the lashing where the pikes were joined, and drawn tight so that his arms were stretched out above his head. Finally his ankles had been spread apart and lashed fast to the pikes to either side of him, rendering him perfectly immobile, and then a large man had come out with a whip, and used it. All in all it was a common rite around military camps, and went a long way towards explaining why people of means tried to live as far away from barracks as possible.