“The Grand Duke has his own doctors, but thank you. How soon can he expect your horoscope?”
“Oh, let us say a week, or perhaps ten days—” As it was not the kind of thing that should be performed too quickly. “But in any case, as fast as I can.”
When Vinta was gone, without discussing remuneration at all, Galileo sat down heavily on a bench in his workshop.
It was a system that could be defended, if you granted its premises, which were probably true. Every event was the effect of some prior cause, everything moved in a woven tangle of cause and effect, which included of course the stars and planets. But unweaving the tangle was very difficult, and in that sense astrology was a doomed project, or at least quite radically premature, no matter its antiquity. But he could not say that to the Medici. And one could at least calculate the positions of the planets at the time of the subject’s birth. Do what everyone else did.
He groaned and called out for a new folio, quills, ink, a dusty old ephemerides. Vinta had left a big packet of papers containing the grand duke’s birth information.
For a long time he stared at all these things. He had paid sixty lire each for birth charts for the girls when they were born. He had only passed on one for Vincenzio because by then he could not afford it. He pulled the relevant tomes from the dusty top shelf on the back wall of the workshop. The basic text was Ptolemy himself: just as his Almagest covered all Greek astronomy, his Tetrabiblios described all their astrology. His description of celestial influences was derived from a mix of philosophers: Zeno, Pythagoras, Plato, Aristotle, Plotinus … Archimedes made no appearance. There was no way to apply to this problem the mechanics of Galileo’s hero.
In the more typical Greek way, Ptolemy and most of his sources saw the idios cosmos in the koinos kosmos, and vice versa; they spiritualized matter, materialized spirit. Fine; no doubt true. But the action at a distance! The unsupported assertions! Galileo cursed aloud as he read. The Tetrabiblios was simply an endless string of assertions. To use that as a basis for genethlialogy, the construction of individual horoscopes …
Well, Kepler had done it, and was still doing it. His Latin was so weird (if the problem did not reside in Kepler’s thinking itself), that Galileo was not sure what his books said; he had only paged around in them trying to find things he could understand. The astrological sections were worst of all in that regard. There Kepler was even more confusing than Ptolemy.
For one thing, Kepler called himself a Copernican, and Galileo tended to agree with him on that; but astrology was Ptolemaic. Perhaps Kepler’s incomprehensibility had to do with his attempt to make his astrology as Copernican as his astronomy, to save the appearances there as well as in the sky. St. Augustine had reconciled astrology with Christianity; perhaps Kepler felt he could reconcile it with Coperni-canism.
But there wasn’t the time to work through Kepler to find out. He had to set all the foundational issues aside and focus on Ferdinando. His chart marked the locations of all the planets at his birth moment, either square, oppositional, sextile, or in conjunction. Jupiter had been in the strong ascendant at his birth, Venus in conjunction. Consult the Tetrabiblios for the main significations for these luminaries. For Jupiter these were expansion, increase, honor, advancement, enjoyment of patronage, financial gain, joy, charitable instincts, travel, legal matters, religion, and philosophy. All these qualities suggested that Galileo himself must be a Jovian, but he knew already that Jupiter was not his Great Benefic, but rather Mercury. The slippery go-between; it didn’t seem right. Possibly he needed to make for himself a prosthaphaeresis, which was that correction necessary to find the “true” place of a planet, as opposed to its apparent or “mean” place.
But Ferdinando seemed to have been born under a good description. Good, good, and more good. Of course, almost everywhere in the sky was good. Clearly, no matter which benefic was in the ascendant, astrology focused on what good could be found in it. Ptolemy himself had noted this in the introduction to the Tetrabiblios—”one looks to the stars for the good that can be seen,” he had written—which was very convenient. Jupiter was definitely good. Enjoyment of patronage? Financial gain? Who wouldn’t want to be born under Jupiter!
He shrugged away his unruly thoughts and worked through the querents, the aspects and ceremonies, the conjunctions retrograde and indulgent, the oppositions and squares, houses and cusps, sextiles and tines. He applied the simpleton mathematics, so basic that he wondered if he could perhaps construct an astrological compass like his military one—or if perhaps his military compass already had the capacity to calculate horoscopes. He would have shared this joke with Marina had she been there. One more thing it could do.
It took two days to complete the work. Happily the horoscope genuinely predicted for Ferdinando long life and good health—both much in the ascendant, in fact, because of the current position of Jupiter in the zodiac. His death was most likely to fall twenty-two years in the future, at a square conjunction of quick Mercury and dour Saturn—not that ordinary horoscopes traditionally sought out such information, but Galileo had run the calculations through to their end, just out of curiosity. Astrology, he understood as he did this, was an articulated structure of hope. One never looked for ends of lives, even though the calculations could be made.
He wrote it all up, not including the end calculations of course, and had the finished drawings done by Arrigheti. He took the handsome foursquare charts and a fair copy of his calculations to the palace, and gave them in person to Vinta, who unceremoniously broke the seal on the leather case, which Mazzoleni had embossed with a gilt version of the Medici arms. Quickly he read the main page, nodding as he did so.
“Jove, Venus and the Sun, all in the ascendant. Good. His Highness and the grand duchess will be very pleased, I am sure.” A sudden piercing glance: “You’re sure about this?”
“The signs are very strong. His subjects can rejoice to know that their most benevolent grand duke is favored by Fortune and the stars.”
Vinta said, “God be thanked. For he complains of a gnawing inside him.”
Galileo nodded; he too was afflicted with such pains. He went home with the gift of a gold cup that could be sold for a decent sum to the goldsmiths.
Twenty-two days later, Ferdinando died.
When Galileo heard the news, his face burned. He cursed the servants scurrying away from his heavy hand. He stormed out of the house and wandered the streets of Padua, glumly imagining the next time he saw Vinta. For a moment he was even afraid; perhaps he would be blamed.
But given this world, in which all prediction eventually proved wrong, in which death touched down anytime, anywhere, such blame was unlikely. There was no reason to be more than embarrassed. He sent a long letter of condolences to the Grand Duchess Christina, and to Cosimo, with also a cover note of bafflement to Vinta—one which even delicately suggested the possibility of poison as an explanation for the discrepancy between Ferdinando’s stars and his actual fate. The celestial influence, he wrote, had somehow been overruled by a mundane cause.
And in the hubbub of the succession, no one actually seemed to remember Galileo’s most inaccurate horoscope. It was the kind of thing people forgot to remember. And it was also true that the new grand duke, Cosimo II, was an ex-student of his. The prospects for patronage were probably enhanced.
Still, the moment he had imagined finally came. Galileo visited the court in Florence to pay his respects, and was welcomed into the room by Vinta. Galileo entered already talking. “So sorry to hear of the grand duke’s unexpected and untimely death,” he began, but Vinta dismissed these sentiments with a flick of the hand—and with it a look of contempt, and even of a kind of unctuous complicity, as if Vinta was now in on a secret truth, which was that all Galileo’s mathematics were as fraudulent as astrology.
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 appe
arance 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.
Again, this was contra Aristotle, but that was no surprise anymore. More important, it was interesting in its own right.
There was so much that was interesting in what they could see with this apparatus. They started dropping balls freely and letting them hit an inclined plane, then a horizontal plane. Other times they sent balls rolling off the end of a horizontal plane, and watched them fall in a quick curve to a bed of sand they had set on the floor, so the balls would leave a mark that could be measured precisely. Very interesting! Different distances, angles, therefore speeds, and all of them timed proportionally, by the weight of water. These various setups divided motion into parts of different kinds, when before motion had been all mixed together in nature, and thus difficult to study. He had been working on these problems for almost twenty years, and never had he been able to articulate differences like he could now. By manipulating the variables one could measure different things, and establish that there were relations—just as one would have expected, but could never before create and measure. Relations of past speed, present speed, future speed.
And so now they were sure, at last, after twenty years of various formulations that had not worked, that the downward acceleration of a ball increased as the square of the time elapsed in its fall. It was as simple as that.
Galileo showed the equations to Mazzoleni: “See? See? Acceleration is a very simple ratio! Why should it be true? Why? God made it that, that’s why! God likes mathematical ratios. He must! He puts them there for all to see.”
“For you to see, maestro. Has anyone else ever seen this?”
“Of course not. Archimedes would have seen it, if he had had such a fine apparatus. But no. I am the first in the world.”
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