That look cut Galileo’s mind. It never left him, he could always see it, and it always brought the same hot flush of shame and defilement. He tried to banish the memory of it, but sometimes he even dreamed it; it jumped out of other faces and stabbed him. One of the Bad Looks of his life, for sure; one of the ever-growing collection of terrible looks that haunted him in the sleepless hours.
No one else remembered the horoscope at all, as far as he could tell. That was the way it was with astrological pronouncements; they were meant for the moment, and no one expected anything more of them. Even if they proved right, no one remembered them. People were so scared.
It did not follow, of course, that because one horoscope was wrong, all astrology was wrong; nor that if astrology were wrong, all Ptolemy was wrong; nor that if all Ptolemy were wrong, all Aristotle was wrong; nor even that if Aristotle was wrong, Copernicus was therefore right. Those were bad syllogisms; and even good syllogisms were not for Galileo conclusive.
But that look!
After that he had tried to restrict himself to making only those assertions he could demonstrate the truth of. He tried not to speak of causes. Probably the Copernican explanation was correct, but he would not speak of it. He could not see the proof for it. Kepler obviously believed it, but Kepler was crazy. Although even Kepler had said it: “Astrology is the prostitution of mathematics.”
The look always remained in him, stuck in his mind like poor Fra Sarpi’s face. In the pursuit of patronage, he had prostituted his mathematics.
“So you knew you were a hypocrite,” Hera said to him. Under the ghastly yellow light of Jupiter, her broad face before him was as big and cruel as one of the Fates. Mnemosyne had metamorphosed, as she so often did, into dire Atropos, chopping into his brain with her scissors—a pair of scissors injected from the inside of the helmet on his head, scissors made of mirrors that reflected broken images of his staring face, his misspent life. He shut his eyes, but Mnemosyne lived there too, on the inside of his eyelids.
“You refused to marry the woman who was the mother of your three children,” she said, “precisely because she was like you, in that she had sold access to herself to better her position. It was the same thing you did with the horoscope, and so you knew you were wrong about her. But by then it was too late.”
“I wasn’t wrong!” Galileo said. “And it wasn’t just that. We didn’t get along. Even so, I kept her in a house and took care of her and the kids. I found her a husband.”
“But you wouldn’t marry her yourself. That’s why the two of you didn’t get along.”
“Not so! I didn’t want it to be the way it was. She was a bitch. She laughed at my work and tried to wreck it. If she had been different I would have married her; she wasn’t any different from the servant girls that professors marry, that old widowers marry.”
“But you had pretensions to higher things. You wanted a patron, and you thought a wife from a low background would hurt the effort.”
“That’s true. But that’s just the way it was. I needed to do my work.”
“So then maybe you shouldn’t have had any conjugal associations at all.”
“I’m not a saint. I just need to do my work.”
“Work. How many banquets a week? How much time at Salviati’s? You feasted while your people starved.”
He heaved a big sigh, tried to take the helmet off his head. “You’re just torturing me,” he said. “Everyone makes mistakes, everyone commits crimes! Why do you shove my face in it?”
Very slowly, emphasizing each word, she said, “You need to know your life.” She stared at his face for a while. “Do you know what you did that really mattered to you?”
“No.”
“And do you know what you did that really matters to us?”
“No!”
“Look.” And she touched him.
Mazzoleni had planed the edge of a long board of fine-grained hardwood, then cut a smooth groove in it, so that they had as perfect a Euclidean plane and line as they could make in this world. He pegged this board into a big L-shaped framework of boards with holes drilled into them at different heights, so the plane’s inclination could be adjusted at will. The balls to be rolled down the plane were iron musket balls, ground and polished and dropped time after time through circular holes just big enough to fit them, until Galileo was convinced they were as close to geometrical spheres as humans could achieve. When they were done, they had a really interesting apparatus.
After that they spent hours and hours, day after day, in the workshop running tests of different kinds. Balls that were dropped through the air fell faster than Galileo and Mazzoleni could time them, so now they tilted their plane sufficiently to slow balls in their descent. By altering the angle of inclination in a regular way, and comparing times of descent for the same balls over and over again, Galileo came to see that the tilt of the plane made a proportional ratio with the speed of the descents—a relationship so clear that he could conclude that balls in free fall would accelerate in the same proportion, as an end case; so the inclined plane was teaching them things about free fall as well.
Even given this gift of stretched time, their clocks were not good enough. Galileo muttered about a pendulum clock, remembering the observation of periodicity that had come to him when he was a boy; but he had not figured out how to keep the pendulum swinging without disturbing it, and meanwhile the balls were ready to roll.
Finally it came to him, right out there in the workshop staring at the inclined plane apparatus. “Mat-zo-len-iiiiiii!”
“Maestro?”
“We will weigh time.”
Mazzoleni laughed. “Maestro, you’re funny.”
“No, it’s perfect. We can weigh time easier than we can mark its passing, in fact we can weigh differences very closely! Ha!”
He did his little jig and kick, a sign that he was feeling the rung-bell feeling, which he described as being like sexual afterglow, only better.
“It’s just what Archimedes would have done. It’s like his weighing density, more or less. Here’s how we’ll do it. We’ll make a kind of clepsydra. When the balls drop, have a mechanism also open the stopper on a jug of water.”
Mazzoleni frowned. “How about just put your thumb on the stopper and do it yourself when you see the ball start,” he suggested. “Your eye would be more accurate than any gate I can make. Water is slippery stuff.”
“All right, that’s fine. That being the case, I’ll also stop the water by eye and by thumb. The water that has been released will have run into a flask. We can then weigh the water to within a featherweight! A featherweight of time, in this case, because the weights will always be proportional to the times we were letting the water flow. We’ll be accurate to the speed of our eyes and thumbs, which means a tenth of a pulse, or even better!”
“Good idea.”
Mazzoleni’s gap-toothed grin: this was the sigil of the rung-bell feeling. When his bell was rung, he was always seeing Mazzoleni’s battered face. The face of God in an old man’s face. It made Galileo laugh.
So they weighed time, and continued the work of investigating falling bodies. He tried all kinds of things. He dropped balls down one inclined plane and watched them roll up another, and found that no matter how the two planes were inclined inward to each other, the balls always rolled back up to the same height they had been dropped from. Preservation of momentum: this fit well with Galileo’s earlier studies of balance and leverage. It also shattered the Aristotelian notion that things wanted to be one place or another, but by now he was far beyond mere refutation of Aristotle; there were new things to discover. A ball returned to the height it was dropped from, no matter the shape of the V: so what happened if they set the second plane horizontally? The ball would roll forever, it seemed, neither accelerating nor decelerating, except that the resistance of wood and the air itself finally stopped it. If not for friction, in other words, it would roll forever. So it seemed, though that was rather amazing. Of course any supposedly perfect plane set on Earth was actually covering a part of a large sphere, so that one might say the tendency of things to move in circles, as the stars did, was an appearance saved even here. But in principle, on a true plane, motion would continue. Once something started to move, it would continue moving until something changed it.