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 ha
d 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 t
here 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.