Galileo's Dream

Chapter one The Stranger

All of a sudden Galileo felt that this moment had happened before—that he had been standing in the artisans’ Friday market outside Venice’s Arsenale and had felt someone’s gaze on him, and looked up to see a man staring at him, a tall stranger with a beaky narrow face. As before (but what before?) the stranger acknowledged Galileo’s gaze with a lift of the chin, then walked toward him through the market, threading through the crowded blankets and tables and stalls spread all over the Campiello del Malvasia. The sense of repetition was strong enough to make Galileo a little dizzy, although a part of his mind was also detached enough to wonder how it might be that you could sense someone’s gaze resting on you.

The stranger came up to Galileo, stopped and bowed stiffly, then held out his right hand. Galileo bowed in return, took the offered hand, and squeezed; it was narrow and long, like the man’s face.

In guttural Latin, very strangely accented, the stranger croaked, “Are you Domino Signor Galileo Galilei, professor of mathematics at the University of Padua?”

“I am. Who are you?”

The man let go of his hand. “I am a colleague of Johannes Kepler. He and I recently examined one of your very useful military compasses.”

“I am glad to hear it,” Galileo said, surprised. “I have corresponded with Signor Kepler, as he probably told you, but he did not write to me about this. When and where did you meet him?”

“Last year, in Prague.”

Galileo nodded. Kepler’s places of residence had shifted through the years in ways Galileo had not tried to keep track of. In fact he had not answered Kepler’s last letter, having failed to get through the book that had accompanied it. “And where are you from?”

“Northern Europe.”

Alta Europa. The man’s Latin was really quite strange, unlike other transalpine versions Galileo had heard. He examined the man more closely, noted his extreme height and thinness, his stoop, his intent close-set eyes. He would have had a heavy beard, but he was very finely shaved. His expensive dark jacket and cloak were so clean they looked new. The hoarse voice, beaky nose, narrow face, and black hair made him seem like a crow turned into a man. Again Galileo felt the uncanny sensation that this meeting had happened before. A crow talking to a bear—

“What city, what country?” Galileo persisted.

“Echion Linea. Near Morvran.”

“I don’t know those towns.”

“I travel extensively.” The man’s gaze was fixed on Galileo as if on his first meal in a week. “Most recently I was in the Netherlands, and there I saw an instrument that made me think of you, because of your compass, which, as I said, Kepler showed me. This Dutch device was a kind of looking glass.”

“A mirror?”

“No. A glass to look through. Or rather, a tube you look at things through, with a glass lens at each end. It makes things look bigger.”

“Like a jeweler’s lens?”

“Yes.”

“Those only work for things that are close.”

“This one worked for things that were far away.”

“How could that be?”

The man shrugged.

This was interesting. “Perhaps it was because there were two lenses,” Galileo said. “Were they convex or concave?”

The man almost spoke, hesitated, then shrugged again. His stare went almost cross-eyed. His eyes were brown, flecked with green and yellow splashes, like Venice’s canals near sunset. Finally he said, “I don’t know.”

Galileo found this unimpressive. “Do you have one of these tubes?”

“Not with me.”

“But you have one?”

“Not of that type. But yes.”

“And so you thought to tell me about it.”

“Yes. Because of your compass. We saw that among its other applications, you could use it to calculate certain distances.”

“Of course.” One of the compass’s main functions was to range cannon shots. Despite which very few artillery services or officers had ever purchased one. Three hundred and seven, to be precise, had sold over a period of twelve years.

The stranger said, “Such calculations would be easier if you could see things farther away.”

“Many things would be easier.”

“Yes. And now it can be done.”

“Interesting,” Galileo said. “What is your name again, signor?”

The man looked away uneasily. “I see the artisans are packing to depart. I am keeping you from them, and I must meet a man from Ragusa. We will see each other again.”

With a quick bow he turned and walked along the tall brick side wall of the campiello, hurrying in the direction of the Arsenale, so that Galileo saw him under the emblem of the winged lion of St. Mark that stretched in bas relief over the lintel of the great fortress’s entryway. For a second it looked as if one bird-beast were flying over another. Then the man turned the corner and disappeared.

Galileo turned his attention back to the artisans’ market. Some of them were indeed leaving, folding up their blankets in the afternoon shadows and putting their wares into boxes and baskets. During the fifteen or twenty years he had been advising various groups in the Arsenale, he had often dropped by the Friday market to see what might be on display in the way of new tools or devices, machine parts, and so on. Now he wandered around through the familiar faces, moving by habit. But he was distracted. It would be a good thing to be able to see distant objects as if they were close by. Several obvious uses sprang to mind. Military advantages, in fact.

He made his way to one of the lens-makers’ tables, humming a little tune of his father’s that came to him whenever he was on the hunt. There would be better lenses in Murano or Florence; here he found nothing but the usual magnifying glasses that one used for close work. He picked up two, held them in the air before his right eye. St. Mark’s lion couchant became a flying ivory blur. It was a poorly done bas relief, he saw again with his other eye, very primitive compared to the worn Roman statues under it on either side of the gate.

Galileo put the lenses back on their table and walked down to the Riva San Biagio, where one of the Padua ferries docked. The splendor of the Serenissima gleamed in the last part of the day. On the riva he sat on his usual post, thinking it over. Most of the people there knew to leave him alone when he was in thought. People still reminded him of the time he had shoved a bargeman into the canal for interrupting his solitude.

A magnifying glass was convex on both sides. It made things look larger, but only when they were a few fingers from the glass, as Galileo knew very well. His eyes, often painful to him, had in recent years been losing their sharpness for nearby things. He was getting old: a hairy round old man, with failing eyesight. A lens was a help, especially if ground well.

It was easy to imagine a lens grinder in the course of his work holding up two lenses, one in front of the other, to see what would happen. He was surprised he hadn’t done it himself. Although, as he had just discovered, it didn’t do much. He could not immediately say why. But he could investigate the phenomenon in his usual manner. At the very least he could look through different kinds of lenses in various combinations, and simply see what he saw.

There was no wind this Friday afternoon, and the ferry’s crew rowed slowly along the Canale della Giudecca and onto the open lagoon, headed for the fondamente at Porta Maghere. The captain’s ritual cursing of the oarsmen cut through the cries of the trailing seagulls, sounding like lines from Ruzante. You girls, you rag dolls, my mother rows better than you do—

“Mine definitely does,” Galileo pitched in absently, as he always did. The old bitch still had arms like a stevedore. She had been beating the shit out of Marina until he had intervened, that time the two had fought; and Galileo knew full well that Marina was no slouch when it came to landing a punch. Holding them apart, everyone screaming …

From his spot in the ferry’s bow he faced the setting sun. There had been many years when he would have spent the night in town, usually at Sagredo’s pink palazzo—“The Ark”—with its menagerie of wild creatures and its riotous parties. But now Sagredo was in Aleppo on a diplomatic assignment, and Paolo Sarpi lived in a stone monk’s cell, despite his exalted office, and all the rest of Galileo’s partners in mischief had also moved away or changed their night habits. No, those years were gone. They had been good years, even though he had been broke—as he still was. Work all day in Padua, party all night in Venice. Thus his rides home had usually been on a dawn barge, standing in the bow buzzing with the afterglow of wine and sex, laughter and sleeplessness. On those mornings the sun would pop over the Lido behind them and pour over his shoulders, illuminating the sky and the mirror surface of the lagoon, a space as simple and clear as a good proof: everything washed clean, etched on the eye, glowing with the promise of a day that could bring anything.

Whereas coming home on the day’s last barge, as now, was always a return to the home fire of his life’s endlessly tangled problems. The more the western sky blazed in his face, the more likely his mood was to plummet. His temperament was volatile, shifting rapidly among the humors, and every histrionic sunset threatened to make it crash like a pelican diving into the lagoon.

On this evening, however, the air was clear, and Venus hung high in a lapis lazuli dusk, gleaming like some kind of emblem. And he was still thinking about the stranger and his strange news. Could it be true? And if so, why had no one noticed before?

On the long dock up the estuary he debarked, and walked over to the line of carts starting out on their night journeys. He hopped on the back of one of the regulars that went to Padua, greeting the driver and lying on his back to watch the stars bounce overhead. By the time the cart rolled past Via Vignali, near the center of Padua, it was the fourth hour of the night, and the stars were obscured by cloud.

With a sigh he opened the gate that led into his garden, a large space inside the L formed by the big old house. Vegetables, vine trellises, fruit trees: he took a deep breath to absorb the smells of the part of the house he liked best, then steeled himself and slipped into the pandemonium that always existed inside. La Piera had not yet entered his life, and no one before her could ever keep order.

“Maestro!” one of the littlest artisans shrieked as Galileo entered the big kitchen, “Mazzoleni beat me!”

Galileo smacked him on the head as if driving a tomato stake into the ground. “You deserved it, I’m sure.”

“Not at all, maestro!” The undeterred boy got back to his feet and launched into his complaint, but did not get far before a gaggle of Galileo’s students surrounded him, begging for help with a problem they were to be tested on next day in the fortifications course at the university.

“We don’t understand,” they wailed contrapuntally, though it appeared to be a simple problem.

“Unequal weights weigh equally when suspended from unequal distances having inversely the same ratio as the weights,” Galileo intoned—something he had tried to teach them just the previous week. But before he could sit down and decipher their teacher Mazzoni’s odd notation, Virginia threw herself into his arms to recount in officious detail how her younger sister Livia had misbehaved that day. “Give me half an hour,” he told the students, picking up Virginia and carrying her to the long table. “I’m starving for supper, and Virginia is starving for me.”

But they were more afraid of Mazzoni than they were of him, and he ended up reviewing the relevant equations for them, and insisting they work out the solution for themselves, while eating the leftovers from their dinner, all the while bouncing Virginia on his knee. She was light as a bird. He had banned Marina from the house five years before, a relief in many ways, but now it was up to him and the servants to raise the girls and find them a way in the world. Inquiries at the nearby convents, asking for prenovitiate admissions, had not been well received. So there were some years yet to go. Two more mouths, lost among all the rest. Among thirty-two mouths, to be exact. It was like a hostel in Boccaccio, three stories of rooms all overoccupied, and every person there dependent on Galileo and his salary of 520 florins a year. Of course the nineteen students boarding in-house paid a tuition plus room and board, but they were so ravenous he almost always fed them at a loss. Worse, they cost time. He had priced his military compasses at five scudi each, with twenty more charged for a two-month instructional session, but considering the time it took from him, it had become clear that he made each sale at a loss. Really, the compasses had not turned out as he had hoped.

One of the houseboys brought him a small stack of letters a courier had brought, which he read as he ate and tutored and played with Virginia. First up was another letter from his sponge of a brother, begging for money to help support him and his large family in Munich, where he was trying to make it as a musician. Their father’s failure in that same endeavor, and the old dragon’s constant excoriation of him for it, had somehow failed to teach his brother Michelangelo the obvious lesson that it couldn’t be done, even if you did have a musical genius, which his brother did not. He dropped the letter on the floor without finishing it.

The next one was worse: from his sister’s unspeakable husband Galetti, demanding again the remainder of her dowry, which in fact was Michelangelo’s share, but Galetti had seen that the only chance for payment was from Galileo. If Galileo did not pay it, Galetti promised to sue Galileo yet again. He hoped Galileo would remember the last time, when Galileo had been forced to stay away from Florence for a year to avoid arrest.

That letter too Galileo dropped on the floor. He focused on a half-eaten chicken, then looked in the pot of soup hanging over the fire, fishing around for the hunk of smoked pork that ballasted it. His poor father had been driven to an early grave by letters just like these, and by his Xantippe ferreting them out and reading them aloud fortissimo. Five children, and nothing left even to his eldest son, except a lute. A very good lute, it was true, one that Galileo treasured and often played, but it was no help when it came to supporting all his younger siblings. And mathematics was like music in this, alas: it would never make enough money. Five hundred twenty florins a year was all he was paid for teaching the most practical science at the university, while Cremonini was paid a thousand for elaborating Aristotle’s every throat-clearing.

But he could not think of that, or his digestion would be ruined. The students were still badgering him. Hostel Galileo rang with voices, crazy as a convent and running at a loss. If he did not invent something a little more lucrative than the military compass, he would never get out from under his debts.

This caused him to remember the stranger. He put Virginia down and rose to his feet. The students’ faces turned up to him like baby birds jammed in a nest.

“Go,” he said with an imperious wave of the hand. “Leave me.”

Sometimes, when he got really angry, not just exploding like gunpowder but shaking like an earthquake, he would roar in such a way that everyone in the house knew to run. At those times he would stride cursing through the emptied rooms, knocking over furniture and calling for people to stay and be beaten as they deserved. All the servants and most of the students knew him well enough to hear the leading edge of that kind of anger, contained in a particular flat disgusted tone, at which point they would slip away before it came on in full. Now they hesitated, hearing not that tone, but rather the sound of the maestro on the hunt. In that mood there would be nothing to fear.

He took a bottle of wine from the table, polished it off, then kicked one of the boys. “Mazzoleni!” he bellowed. “MAT! ZO! LEN! EEEEEEEEEE!”

No earthquake tonight; this was one of the good sounds of the house, like the cock crowing at dawn. The old artisan, asleep on the bench by the oven, pushed his whiskery face off the wood. “Maestro?”

Galileo stood over him. “We have a new problem.”

“Ah.” Mazzoleni shook his head like a dog coming out of a pond and looked around for a wine bottle. “We do?”

“We do. We need lenses. As many as you can find.”

“Lenses?”

“Someone told me today that if you look through a tube that holds two of them, you can see things at a distance as if they were nearby.”

“How would that work?”

“That’s what we have to find out.”

Mazzoleni nodded. With arthritic care, he levered himself off the bench. “There’s a box of them in the workshop.”

Galileo stood jiggling the box back and forth, watching the lamps’ light bounce on the shifting glasses. “A lens surface is either convex, concave, or flat.”

“If it isn’t defective.”

“Yes yes. Two lenses means four surfaces. So there are how many possible combinations?”

“Sounds like twelve, maestro.”

“Yes. But some are obviously not going to work.”

“You’re sure?”

“Flat surfaces on all four sides are not going to work.”

“Granted.”

“And convex surfaces on all four sides would be like stacking two magnifying lenses. We already know that doesn’t work.”

Mazzoleni drew himself up. “I concede nothing. Everything should be tried in the usual way.”

This was Mazzoleni’s stock phrase for such situations. Galileo nodded absently, putting the box down on the workshop’s biggest table. He reached up to dust off the folios lying aslant on the shelf over it; they looked like guards who had died on watch. While Mazzoleni gathered lenses scattered in pigeonholes around the workshop, Galileo lifted down the current working folio, a big volume nearly filled with notes and sketches. He opened it to the first empty pages, ignoring the rest of the volumes above—the hundreds of pages, the twenty years of his life moldering away, never to be written up and given to the world, the great work as lost as if it were the scribblings of some poor mad alchemist. When he thought of the glorious hours they had spent working with the inclined planes they had built, a pain stuck him like a needle to the heart.

He opened an ink bottle and dipped a quill into it, and began to sketch his thoughts about this device the stranger had described, figuring out as he did how to proceed. This was how he always worked when thinking over problems of motion or balance or the force of percussion, but light was peculiar. He did not sketch any pattern that looked immediately promising. Well, they would simply try every combination, as Mazzoleni had said, and see what they found.

Quickly the ancient artisan knocked together some little wooden frames they could clamp different lenses into. These could then be attached to the ends of a lead tube Mazzoleni found in a box of odds and ends. While he did that, Galileo laid out their collection of lenses by type, fingering each, holding up two at a time and peering through them. Some he gave to Mazzoleni to attach to the ends of the tube.

They only had the lamplit workshop to look at, and the area of the garden and arbor illuminated by the house windows, but it was enough to check for possibilities. Galileo looked at the lenses in the box, held them in the air. Inward, outward. The images blurred, went absent, grew diffuse, even made things smaller than what one saw with the eye alone. Although an effect the reverse of what one wanted was always suggestive.

He wrote down their results on the open page of the workbook. Two particular convex lenses gave the image upside down. That cried out for a geometrical explanation, and he noted it with a question mark. The inverted image was enlarged, and sharp. He had to admit to himself that he did not understand light, or what it was doing between the lenses in the tube. He had only ventured to give classes on optics twice in seventeen years, and had been unhappy both times.

Then he held up two lenses, and the potted citron at the edge of the garden appeared distinctly larger in the glass closest to his eye. Green leaf lit from the side by lantern light, big and sharp—

“Hey!” Galileo said. “Try this pair. Concave near the eye, convex at the far end of the tube.”

Mazzoleni slotted the lenses into the frames and gave the tube to Galileo, who took it and pointed it at the first tree branch in the arbor, illuminated by the lit windows of the house. Only a small part of the branch appeared in the tube, but it was definitely enlarged: the leaves big and distinct, the bark minutely corrugated. The image was slightly blurred at the bottom, and he shifted the outside frame to tilt the glass, then rotated it, then moved it farther out on the tube. The image became sharper still.

“By God it works! This is strange!”

He waved at the old man. “Go to the house and stand in the doorway, in the lamplight.” He himself walked through the garden out into the arbor. He trained the tube on Mazzoleni in the doorway. “Mother of God.” There in the middle of the glass swam the old man’s wrinkled face, half-bright and half-shadowed, as close as if Galileo could touch him, and they were fifty feet apart or more. The image burned into Galileo’s mind—the artisan’s familiar gap-toothed grin shimmery and flat, but big and clear—the very emblem of their many happy days in the workshop, trying new things.

“My God!” he shouted, deeply surprised. “It works!”

Mazzoleni hurried out to give it a try. He rotated the frames, looked through it backwards, tipped the frames, moved them back and forth on the tube. “There are blurry patches,” he noted.

“We need better lenses.”

“You could order a batch from Murano.”

“From Florence. The best optical glass is Florentine. Murano glass is for colored trinkets.”

“If you say so. I have friends who would contest that.”

“Friends from Murano?”

“Yes.”

Galileo’s real laugh was a low huh huh huh. “We’ll grind our own lenses if we have to. We can buy blanks from Florence. I wonder what would happen if we had a longer tube.”

“This one is about as long as we’ve got. I guess we could make some longer sheets of lead and roll them up, but we would have to make the molds.”

“Any kind of tube will do.” Here Galileo was as good as Mazzoleni or any artisan—good at seeing what mattered, quick to imagine different ways of getting it. “It doesn’t have to be lead. We could try a tube of cloth or leather, reinforced to keep it straight. Glue a long tube of leather to slats. Or just use cardboard.”

Mazzoleni frowned, hefting a lens in his hand. It was about the same size as a Venetian florin, say three fingers wide. “Would it stay straight enough?”

“I think so.”

“Would the inside surface be smooth?”

“Does it need to be?”

“I don’t know, does it?”

They stared at each other. Mazzoleni grinned again, his weathered face an entire topography of wrinkles, delta on delta, the white burn mark on his left temple raising that eyebrow in an impish expression. Galileo tousled the man’s hair as he would a child’s. This work they did together was unlike any other human bond he knew—unlike that with mistress or child, colleague or student, friend or confessor—unlike anyone—because they made new things together, they learned new things. Now once again they were on the hunt.

Galileo said, “It looks like we’ll want to be able to move one lens back and forth.”

“You could fix one glass to the tube, and set the other one in a slightly smaller tube that fitted inside the main one, so you could move that one back and forth but keep it aligned vertically. You could rotate it too, if you wanted.”

“That’s good.” Galileo would have come to some such arrangement eventually, but Mazzoleni was especially quick concerning things he could see and touch. “Can you bang something like that together? By tomorrow morning?”

Mazzoleni cackled. By now it was the middle of the night, the town was quiet. “Simple stuff, compared to your damned compass.”

“Watch what you say. That thing has paid your salary for years.”

“Yours too!”

Galileo swatted him. The compass had become a pain, there was no denying it. “You have the materials you need?”

“No. I think we’ll need more lead tubes, and thinner staves than what we’ve got around, and longer, if you want leather tubes. More cardboard too. And you’ll want more lenses.”

“I’ll send an order to Florence. Meanwhile, let’s work with what we’ve got.”

In the days that followed, every moment was given over to the new project. Galileo neglected his collegial obligations, made his in-house students teach each other, and ate his meals in the workshop while he worked. Nothing mattered but the project. At times like these it became obvious that the workshop was the center of the house. The maestro was about as irritable as always, but with his attention elsewhere it got a bit easier for the servants.

While the various efforts of manufacture and assemblage and testing went on, Galileo also took time to write his Venetian friends and allies to set the stage for a presentation of the device. Here was where his career up until this point finally helped him. Known mostly as an eccentric if ingenious professor of mathematics, broke and frustrated at forty-five, he had also spent twenty years working and playing with many of the leading intellectuals of Venice—including, crucially, his great friend and mentor, Fra Paolo Sarpi. Sarpi was not currently running Venice for the doge, as he was still recovering from wounds suffered in an assault two years before, but he continued to advise both the doge and Venice’s senate, especially on technical and philosophical matters. He could not have been better positioned to help Galileo now.

So Galileo wrote to him about what he was working on. What he read in Sarpi’s reply letter startled him, even frightened him. Apparently the stranger from the artisan’s market had gone to others as well. And his news of a successful spyglass, Sarpi wrote, was apparently already widespread in northern Europe. Sarpi himself had heard a rumor of such a thing nine months before, but had not considered it significant enough to tell Galileo about it.

Galileo cursed as he read this. “Not significant? My God!” It was hard to believe. In fact, it suggested that his old friend had been damaged mentally as well as physically by the knives that had been stuck into his head during the assault.

But there was nothing to be done about that now. People in northern Europe, especially the Flemish and Dutch, were already producing little spyglasses. This Dutch stranger, Sarpi wrote, had contacted the Venetian senate, offering to sell them such a glass for a thousand florins. Sarpi had advised the senate against the purchase, certain that Galileo could do as well or better in manufacturing any such object.

“I could have if you would have mentioned it to me,” Galileo complained.

But he hadn’t, and now news of a primitive version of the device was in the air. It was a phenomenon Galileo had noticed before. Improvements at the artisanal level passed from workshop to workshop without scholars or princes knowing anything about them, and so it often happened that suddenly workshops everywhere could all make a smaller gear, or a stronger steel. This time it was a little spyglass. The claim going around was that they enlarged things by about three times.

Quickly Galileo wrote back to Sarpi, asking him to convene a meeting with the doge and his senators in order to examine a new and improved spyglass that Galileo was inventing. He also asked him to ask the doge to refuse to entertain any other such offers during that time. Sarpi replied the next day with a note saying he had done as asked, and the requested meeting was set for August 21. It was now August 5. He had two weeks to make a better glass.

The action in the workshop intensified. Galileo told his frantic students that they were on their own—even Count Alessandro Montal-ban, who had recently moved into the house to study for his doctoral exams, and was not pleased at being neglected. But Galileo had tutored many sons of the nobility by now, and brusquely he told the young man to study with the others, to lead them, that it would be good for him. Galileo then moved out into the workshop, where he examined very closely the devices they had made already, trying to figure out how to better them.

Understanding what was going on with the doubled lenses was no easy feat. For Galileo, everything physical came down to matters of geometry, and clearly this bending of the light was a geometrical action, but he lacked any laws of refraction, and could not discover them merely by substituting lenses one after the next. There were tangible variables involved, however, that they could subject to the workshop techniques they had already honed in previous pursuits.

So the workshop’s artisans met in the hour after sunrise, some of them servants of the house, others local ancients retired from arsenals, or lads from the neighborhood, still rubbing the sleep from their eyes, squeezing the bellows to get the fires in the furnaces going, picking up the work they had laid down the night before. They followed Galileo’s routines: they measured things twice, wrote everything down. They worked while breaking their fast. They watched the rainstorms out the open side of the shed, waiting for the light to get better so they could get back to work. The brick furnace was a bulwark just outside the roof, and they could stand near the back of it and stay warm while the rain came down, although as it was summer the afternoon thunderstorms weren’t so cold. The large central area of the shop was earthen floored and held several long tables, the one under the back wall devoted to all their tools. In the dim rain light they could clean or sharpen tools, put things in order, or pick away at the goose carcass from the night before. When the sun came out they returned to the work.

They made so many alterations in every new spyglass, and Galileo was not quite sure what change was having what effect, but it was too interesting to slow down and isolate the variables to make sure of things, except when pursuing a crucial point. The epistemology of the hunt was to follow one thing after another, without much of an overall plan. They found that tubes made of cardboard, sometimes reinforced by slats or covered with leather, worked perfectly well. The interiors did not have to be smooth, although one saw a clearer image if they were painted black. Most important were the lenses. The one next to the eye they called the eyepiece, the one at the far end, the objective. Both concave and convex lens surfaces, if properly ground, constituted sections of spheres, bulging either in or out. Spheres of differing radii gave different curvatures. The radius of the complete sphere that was implied by a lens, Galileo called its focal length, following the lensmakers’ usage. Fairly soon, their repeated trials with different lenses revealed to him that larger magnifications resulted from a long focal length for the convex lens at the far end of the tube, combined with a short focal length for the concave lens of the eyepiece. Grinding the convex lenses was easy enough, although it was important to eliminate small irregularities if possible, as these made for blurred patches. Grinding truly smooth curved depressions into the much smaller concave lenses, however, was harder to do. A small ball set in a rotating steel-milling mechanism that they screwed to one of the worktables served as their grinding tool. To see better, they wore spectacles made of lenses ground earlier in the effort.

While this was going on, Mazzoleni was also making cardboard tubes that would snug into his main tubes of leather and staves, giving them the ability to adjust the distance between the lenses and thus sharpen the image. The eyepieces were smaller, so they put the drawtube at that end, and fitted it with felt shims.

To find out what degrees of magnification they were getting, Galileo affixed a gridwork to a whitewashed part of the garden wall. This enabled him to measure accurately the difference between the enlarged image of the grid and the image he saw through the other eye at the same time.

On the afternoon of the seventeenth of August, Galileo looked over their three best performers. All were about the same length, which was just over a braccio, as measured by their in-house yardstick. Studying the notes, Galileo compared all their dimensions, scribbling more notes as he did so.

All at once he laughed out loud. One of his special moments had come again—a flash of sudden insight at the end of a period of investigation, giving him a jolt and a shiver, as if he were a bell and the clapper had just tapped him. He shouted, “MAT! ZO! LEN! EEEEEEE!”

The old man appeared, more disheveled and whiskery than ever, red-eyed with lack of sleep. “Look!” Galileo commanded. “You take the focal length of the objective—for this one, a hundred minims—and you divide that by the focal length of the eyepiece, in this case eleven minims—and you get a number which identifies the device’s power of magnification, thus here about nine times! It’s a ratio! It’s geometry again—” He seized the old man by the shoulder. “Not only that, but look! Subtract the eyepiece focal length from the objective focal length, and you get the distance apart that the lenses are when the thing is focused properly! In this case, just short of one braccio. It’s a simple piece of subtraction!”

At this realization he grew somewhat glorious, as he often did when he was able to say new things of that sort. He congratulated everyone in the household, called for wine, and threw crazia and other small coins at the servants and students who poured out into the courtyard to join the celebration. He hugged them one by one while he was giving thanks to God and also indulging his most boastful humor, which was something to witness. He praised his genius for coming through for him again, he danced, he laughed, he grabbed Mazzoleni by the ears and shouted in his face: “I’m the smartest man in the world!”

“Probably so, maestro.”

“The smartest man in history!”

“That’s how much trouble we’re in, maestro.”

This kind of poke in these moments of glory would only make him laugh and toss Mazzoleni aside, to continue his jig. “Florins and ducats, crowns and scudi, I’ll buy Rachel and I’ll buy Trudi!”

No one in the household understood quite why he believed the glass was going to make him rich. The servant girls thought he meant to use it to watch them doing the laundry down at the river, which he did already from what he thought was a discreet distance.

Eventually everyone went back to work. Mazzoleni was left holding the glass, shaking his head at it. “Why should there be such proportions?” he asked.

“Don’t ask why.” Galileo snatched up the glass. “Why is what our philosophers ask, and that’s why they’re so full of shit. Because we don’t know why. Only God knows why. If He does.”

“All right, I know,” Mazzoleni said. “Just ask what, just ask how. Still. You can’t help but wonder, can you?” Waving at the new page of Galileo’s folio, filled with diagrams and numbers, he added, “It seems so …”

“So neat? Yes. Quite a coincidence, for sure. Quite the what-have-you. But it’s just more proof of what we already knew. God is a mathematician.”

As a mathematician himself, Galileo found this sentence immensely satisfying; often it was enough to bring tears to his eyes. God is a mathematician. He would emphasize the thought by taking a hammer to their anvil. And indeed the thought rang him like a bell. He would bring his hands together as if in prayer, and take a deep breath and expel it tremulously. To read God like a book, to solve him like an equation—it was the best sort of prayer. Ever since that time when he was a boy, and he had looked up in church and seen a lamp swinging on its chain, and realized by timing it to his pulse that it took the same time to make its sweep back and forth no matter how far it was swinging, he had felt the direct touch of God in all these things. There was a method to His madness, clearly, and that method was mathematics. This was a comfort when the madness seemed all, as when he was sick, or in pain, or struck down by melancholy; or witnessing the effects of the plague; or contemplating the immense realm of human wickedness. Then his only comfort was the world’s inherent geometries.

The day for his Venetian demonstration approached. Their best tube showed things nine times larger than the eye saw it. Galileo wanted better, and thought he knew how to get it, but time had run out. For now, nine times bigger would have to do.

He had Mazzoleni’s crew cover the exterior of the best tube with red leather, embossed with decorative patterns in gold filigree. Mazzoleni also adapted a tripod stand that they sold as an accessory to the military compass, so that they would have something to hold the spyglass steady. A joint on top of the tripod was made of a metal ball held captive in a hemispherical cup, with one screw through the cup to tension the ball, which was screwed on top into a brass sleeve wrapping the spyglass. Using the tripod, one did not have to hold the glass steady while looking through it—something no one could do for more than a second or two. It vastly improved the view through the glass.

The resulting arrangement was a handsome thing, standing there gleaming in the sunlight, strange but purposeful, immediately intriguing, pleasing to both eye and mind. A month earlier there had been no such thing in the world.

On August 21, 1609, Galileo ferried in to Venice on the morning barge, the looking glass and its stand in a long leather case slung from a strap over his shoulder. Its shape was suggestive of a pair of swords, and he saw the glances of people looking at it and thought, Yes, I’m going in to cut the Gordian knot. I’m going in to cut the world in two.

Venice stood on the lagoon, its usual grubby midday self. Magnificence at low tide. Galileo got off the ferry at the molo at San Marco, and was greeted there by Fra Paolo. The great friar looked gaunt in his best robes, his face still a wreck, as it always would be. But his crooked smile remained kindly, his look still penetrating.

Galileo kissed his hand. Sarpi patted the case gently: “So this is your new occhialino?”

“Yes. In Latin I call it a perspicillum.”

“Very good. Your audience is assembled in the Anticollegio. It’s everyone who matters, you’ll be happy to know.”

An honor guard assembled in response to Sarpi’s nod, and escorted them into the Signoria, up the Golden Staircase into the Anticollegio, which was the anteroom to the Signoria’s bigger halls. It was a tall chamber, sumptuously decorated overhead in the usual Venetian style, its octagonal ceiling covered with gilt-framed paintings allegorizing the origin myth of Venice, while the floor underfoot was painted like the pebbled bed of a mountain stream. Galileo had always found it a strange space, in which he had trouble focusing his eyes.

Now it was stuffed with dignitaries. Better yet, as Galileo soon learned, the doge himself, Leonardo Dona, was waiting in the Sala del Collegio, the larger assembly hall next door that was the most sumptuous room in the Signoria. As he entered the room, he saw Dona and the Savi—his six closest advisors—along with the grand chancellor and other state officials, all gathered under the long painting of the battle of Lepanto. Sarpi had outdone himself.

Now the great Servite led Galileo to the doge, and after a cordial greeting Dona led the entire group into the Sala del Quattro Porte, then to the Sala del Senato, where many more senators stood in their purple, around tables loaded with food. Under the intricacy of crowded paintings and gilt trim that covered every wall and ceiling, Galileo pulled the two parts of his device from their case and screwed the spyglass on top of the tripod. His hands moved without a quiver; twenty years of lecturing to audiences large and small had burned all possibility of stage fright out of him. And it was also true that it was never that difficult to speak to a crowd to which you felt innately superior. So even though all his hundreds of lectures were now only the prelude to this culmination, he was calm and at ease as he described the work done to make the device, indicating its various features as he pointed it at Tintoretto’s Triumph of Venice on the ceiling at the far end of the room, fixing the image in the glass so that it revealed the tiny face of an angel, enlarged to the point that it stood out as vividly as Mazzoleni’s had on that first night of work.

With a sweep of his hand, he invited the doge to have a look. The doge looked; pulled away to gaze at Galileo, his eyebrows shot high onto his forehead; looked again. The two big clocks on the long side wall marked ten minutes’ passage as he bumped the glass from one view to another. Ten more minutes passed as one purple-robed man after another took a look through the glass. Galileo answered every question they had about how it was made, although failing to bring up the ratios he had discovered, which they did not even know to ask about. He volunteered often that the process being now clear to him, future improvements were certain to follow, and also (trying to hide a growing impatience) that it was not the kind of device that could best be demonstrated in a room, even a room as big and magnificent as the Sala del Senato. Finally the doge himself echoed this point, and Sarpi was quick to suggest that they take the device to the top of the campanile of San Marco to give it a thorough airing. Dona agreed to this, and suddenly the whole assembly was following him out of the building and across the Piazzetta between the Signoria and the campanile, then inside the great bell tower, winding up the tight iron staircase to the open observation floor under the bells. Here Galileo reassembled the device.

The floor of the viewing chamber stood a hundred braccia above the Piazza. It was a place all of them had been up to many times. From here one could overlook the whole of Venice and the lagoon, and spot the passageway through the Lido at San Niccolo, the only navigable channel into the Adriatic. Also visible to the west was a long stretch of the mainland’s marshy shore, and on clear days one could even see the Alps to the north. A better place to display the powers of the new spyglass could not have been found, and to aim it Galileo looked through the device with as much interest as anyone else, or even more; he had not yet had an opportunity like this, and what could be seen through the glass was as much news to him as anyone. He told them as much as he worked, and they liked that. They were part of the experiment. He stabilized and sighted the glass very carefully, feeling that a little delay at this moment was not a bad thing, in theatrical terms. As always, the image in the eyepiece shimmered a little, as if it were something conjured in a crystal ball by a magician—not an effect he wanted, but there was nothing he had been able to do about it. Feeling a sharp curiosity, he tried to spot Padua itself. On earlier visits to the campanile, he had marked the vague tower of smoke coming from the town, and knew precisely where it lay.

When he got Padua’s tower of Santa Giustina centered in the glass, as clear as if he were on Padua’s city wall staring at it, he suppressed any shout, any smile, and merely bowed to the doge and moved aside, so Dona and then the others could have a look. A little touch of the mage’s silent majesty was not inappropriate at this point either, he judged.

For the view was, in fact, astonishing. “Ho!” the doge exclaimed when he saw San Giustina. “Look at that!” After a minute or two he gave over the glass to his people, and after that the rush was on. Exclamations, cries, incredulous laughter; it sounded like Carnivale. Galileo stood proudly by the tube, readjusting it when it was bumped. After everyone had had a first look, he spotted terra-firma towns even more distant than Padua, which itself was twenty-five miles away: Chioggia to the south, Treviso to the west, even Conegliano, nestled in the foothills more than fifty miles away.

Moving to the northern arches, he trained the glass on various parts of the lagoon. These views made it clear that many of the senators were even more amazed to see people brought close than they had been buildings; perhaps their minds had leaped as quickly as Galileo’s servants to the uses of such an ability. They gazed at worshippers entering the church of San Giacomo in Murano, or getting into gondolas at the mouth of the Rio de’ Verieri, just west of Murano. Once one of them even recognized a woman he knew.

After that round of viewing, Galileo lifted the device, helped now by as many hands as could touch the tripod, and the whole assembly shifted together to the easternmost arch on the southern side of the campanile, where the glass could be directed over the Lido and the fuzzy blue Adriatic. For a long time Galileo tapped the tube gently from side to side, searching the horizon. Then happily he spotted the sails of a little fleet of galleys, making their final approach to the Serenissima.

“Look to sea,” he instructed them as he straightened and made room for the doge. He had to restrain himself to hide his euphoria. “See how using one’s plain sight, one sees nothing out there. But using the glass …”

“A fleet!” the doge exclaimed. He straightened and looked at the crowd, his face red. “A fleet is approaching, well out from San Niccolo.”

The Sages of the Order crowded to the front of the line to see for themselves. Every Venetian holding in the eastern Mediterranean was subject to attack by Turks and Levantine pirates. Individual ships, fleets, coastal towers, even fortress towns as formidable as Ragusa had suffered surprise assaults. Thus the rulers of Venice, all of them with naval experience of one sort or another, were now nodding to each other meaningfully, and circulating into the crowd surrounding Galileo to shake his hand, slap him on the back, ask for future meetings. Fra Micanzio and General del Monte in particular had worked with him at the Arsenale on various engineering projects, and their congratulations were especially hearty. They had first met him twenty years before, when they had brought him in to consider if there were ways the oars of their galleys could be reconfigured to give them more power, and Galileo had immediately sketched out analyses of the oars’ movement that considered their fulcrum to be not the oarlocks, but the water surface, and this surprising new perspective on the problem had in fact led to improvements in oarlock placement. So they knew what he was capable of. But this time del Monte was shaking his hand endlessly, and Micanzio was grinning, with eyebrows raised as if to say with a laugh, Finally one of your tricks will really matter!

And at this moment, Galileo could afford to laugh with him. Galileo suggested to him that they time the interval between this observation of the fleet through the glass, and the moment when ordinary lookouts saw the ships with their unaided vision. The Doge overheard this and required that it be done.

After that, Galileo had only to stand by the device and accept more congratulations, and point the thing to resight it if someone requested it. He drank their praise and he drank wine from a tall gold cup, feeling expansive and generous. The colorful throng around him, with its impressive percentage of purple, sparked memories of Carnivale—memories that gave every festive evening in Venice an aura of splendor and sex. Combined with the height of the campanile, and the beauty of the watery city below them, it felt like they stood on Olympus.

On the winding way back down the campanile stairs, Galileo was joined on one dark landing by the stranger, who then clomped down the iron stairs beside him. Galileo’s heart leaped in his chest like an animal trying to escape. The man was dressed in black, and must have lurked in waiting for Galileo, like a thief or an assassin.

“Congratulations on this success,” the man said in his hoarse Latin.

“What brings you here?” Galileo asked.

“It seems you listened to what I told you before.”

“Yes, I did.”

“I was sure you would be interested. You of all people. Now I will return to northern Europe.” Again: Alta Europa. “When I come back to your country, I will bring a spyglass of my own, which I will invite you to look through. Indeed I invite you now.” Then, when Galileo did not reply (they were nearing the bottom of the stairs and the door to the Piazzetta), he said, “I invited you.”

“It would be my pleasure,” Galileo said.

The man touched the case Galileo carried from his shoulder. “Have you used it to look at the moon?”

“No—not yet.”

The man shook his head. If his face was a blade, his nose was its sharpened edge, long and curved, tilted off to the right. His big eyes gleamed in the stairwell’s dim light. “When you achieve a power of magnification of twenty or thirty times, you will find it really interesting. After that, I will visit you again.”

Then they reached the ground floor of the campanile, and walked together out onto the Piazzetta, where they were interrupted by the Doge himself, waiting there to escort Galileo back to the Signoria: “Really, my dear Signor Galileo, you must do us the honor of returning with us to the Sala del Senato to celebrate the incredible success of your extraordinary demonstration. We have arranged a small meal, some wine—”

“Of course, Your Beneficent Serenity,” Galileo said. “I am yours to command, as you know.”

In the midst of this exchange the stranger had slipped away and disappeared.

Unsettled, distracted by the memory of the stranger’s narrow face, his black clothing, and his odd words, Galileo ate and drank with as much cheer as he could muster. A chance meeting with a colleague of Kepler’s was one thing; a second encounter, deliberately made, was something else—he wasn’t sure what.

Well, there was nothing to be done now but to eat, to drink more wine, and to enjoy the very genuine and fulsome accolades of Venice’s rulers. Two full hours of the celebration of his accomplishment were marked by the giant clocks on the sala’s walls, before the lookouts on the campanile sent word down that they had spotted a fleet approaching San Niccolo. The room erupted in a spontaneous cheer. Galileo turned to the doge and bowed, then bowed again to all of them: left, right, center, then again to the doge. Finally he had invented something that would make money.