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 Boccacio, three storeys of rooms all over-occupied, and every person there dependent on Galileo and his salary of five hundred and twenty florins a year. Of course the nineteen students boarding in house paid a tuition fee 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 period in house on the Via Vagnali, 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 house boys 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 money to help support him and his large family in Munich, where he was trying to make a living as a musician. Their father’s failure in that same endeavour, 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, and it was a family obligation. 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. 520 florins a year 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 escape 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, kicked one of the boys in order to tip the balance of their judgement toward flight. ‘Mazzoleni!’ he bellowed. ‘MAT! ZO! LEN! EEEEEEEEEE!’
Well, 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, 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.’
‘Yes yes.’
This was Mazzoleni’s stock phrase for such situations. Galileo nodded absently, putting the box down on the work-shop’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 mouldering 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 in 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 arbour 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 work book. 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