“Where are you taking me?” he said.

“To a person who may be able to answer your questions. Or maybe you would call it a machine.”

“A machine? So none of you know?”

“No no, this person is a kind of … composite. A person quite like you, in fact—a physicist and mathematician, quite famous.”

“Good,” Galileo said. “I want some explanations.”

They came to a lake, and stepped down into a long low boat, like a gondola. When they were settled in its bow, a boatman cast off and they hummed slowly over clear blue water, leaving a wake that ran in a clean curl that was slower than it would have been on the lagoon. Greenish blues pulsed overhead and in waves around them, and Galileo could not tell how deep the lake might be, as the many subtle shades of creamy blue bobbed darker and lighter, but always opaque. Royal blue, sky blue, azure, turquoise, aquamarine—all these bounced against each other in long bands, and it also seemed that waves of cobalt were passing through the other blues, staining them as it pulsed by, as if they boated through the veins of a beating blue heart. The buildings behind the broad fondamenta to their left looked like clean blocks of ice, painted in pastels that held their color manfully even in the omnipresent green-blue glow, contradicting what Galileo thought he knew of color theory. The sight of one curving row of waterfront buildings reminded Galileo strongly of the Grand Canal, and he saw the city was a kind of Venice carved in ice. “Why doesn’t it melt?”

“It’s all cladded. Sheathed in diamond, in fact.”

People promenaded on the fondamenta just as they would have at home. Some of them looked out on the water, but not at Ganymede and Galileo; theirs was only one watercraft among many. All the wakes on the water created a fine curvilinear slow-motion cross-chop. The ice ceiling overhead was thicker in some places than in others, judging by the differences in the green-blue. Pulses most definitely were running through it.

“What are those waves of color running through the roof?” he asked.

“The other moons exert tidal forces against the tug of Jupiter proper. We shine a type of light through the ice to reveal the stresses in it, so we can see these tides’ interactions.”

“How do you keep these canals and lakes liquid?”

“We heat them,” Ganymede said patiently. “In places you will see steam. In other places we will break through a skim of ice as we progress along certain canals.”

“But you don’t know how the water is heated, do you?”

“That is not one of the more difficult accomplishments of our technology believe me.”

Their boat hummed up to a fondamenta made of something like black stone. As they climbed out of the boat, Galileo asked, “Where do you get rock?”

“From meteorites, called here dropstones. One or two big ones will supply enough material for an entire city, as it just supplements the local ice.”

“How many people live in this Venice of yours?”

“This is Rhadamanthys Linea. About a million people.”

“That many! And how many cities like this are there on Europa?”

“Maybe a hundred.”

“A hundred millions!”

“It’s a big moon, as you know.”

Overhead the broad crossing arcs of cobalt and violet pulsed from before them to behind them. Galileo said, “The patterns of light are so complicated, it seems there must be more than four influences.”

“All the Jovian moons pull a bit on the rest.”

“But are there more than four moons?”

“There are about ninety.”

“Ninety?”

“Most are very small. Some are out of the plane of the rest. In any case they all have a pull, no matter how slight, and with the ice overhead charged as the locals have charged it, every change in tug registers piezoelectrically.”

“Why do they charge it that way?”

Ganymede shrugged. “They like the way it looks.”

They were now walking down a broad crowded street flanked by long low buildings. Low carts moved at a running pace, without anything pulling them. Before them a cluster of very tall angular buildings reached right up to the ice ceiling.

“It must be the Tower of Babel,” Galileo said.

“Well, there is a great deal of confusion inside it, to be sure. And people who want it to fall.”

Soon they reached these tall buildings, and outside one they entered a glass antechamber, which then rose on the outside wall so fast that Galileo’s ears popped, surprising him. He always had a small earache in his right ear, and now it throbbed unhappily. So it seemed that in some sense his body was here too. “If I am here, how am I also back in Italy, lost in one of my syncopes?”

“You are here in a complementary potentiality.”

The glass antechamber stopped and a door opened on its inner side. They stepped out on a smooth broad roof terrace the color of malachite, just under the ice ceiling. Ganymede led Galileo to a small group of people congregated against a railing that overlooked the city. From here Galileo could see far down the canal; it developed a mirror surface in just the place a waterblink would have appeared on Earth, about halfway to the horizon. From there on it looked like a silver road through undulant blue buildings. Venice had looked just so on certain moony nights, and again Galileo wondered if he were dreaming.

Ganymede said, “This is Galileo Galilei, the first scientist, here in a proleptic entanglement.”

“Ah yes,” said a tall old woman at the center of the group. “We heard you were coming. Welcome to Rhadamanthys.”

Though old she was still straight, and stood a head taller than Galileo. Pendulant silver earrings emerged directly from her ear holes and then curved and seemed to dive into her neck. He bowed to her briefly, looked to his guide, muttered, “And where is the mathematician?”

Ganymede indicated the old woman. “This is she. Aurora.”

Galileo tried to conceal his surprise. “I thought you said it was a machine,” he said to cover himself.

“That’s partly true,” the willowy crone said. “I am interfaced to various artifactual entities.”

Galileo kept a straight face, although the idea struck him as monstrous, like jamming one of his military compasses through an ear into one’s brain. And in fact there were those earrings.

“Come with me,” Aurora said, taking him by the arm and moving him down the altana railing a short distance. Low creaks and hums that seemed to come from the ceiling kept them from being able to hear the other conversations on the terrace.

“It’s a pleasure to meet you,” the ancient woman said politely. She had a voice like Ganymede’s, hoarse and croaky, and her Latin had the same odd accent. “You are often called the first scientist.”

“That would be an honor, but I was not the first.”

“I agree with you. But you were the first mathematical experimentalist.”

“Was I?”

“So it seems from what we read in history, and see in the entanglements. One must always make assumptions, of course. And the past is always changing. But as far as we can tell, you tried only to assert what you could demonstrate and describe mathematically. This is science. Wasn’t it you who said that? That the world is written in mathematics?”

“I like that,” Galileo admitted. “If it’s true.”

“It’s partly true.” Although she looked troubled. “Reality is mathematical, as long as you understand that uncertainty and contingency can be mathematically described, without them becoming any more certain.”

“Teach me,” Galileo said. “Teach me how you breathe here, and what these tides of color are, and—teach me everything. I want to know everything! Teach me everything you have learned since my time.”

She smiled, pleased by his effrontery. “That would take a while.”

“I don’t care!”

She glanced at him curiously. “It would take years, even for one of your intelligence.”