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“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.”

“Can’t you do it quickly? Give me the short version?”

“The short version doesn’t give you real understanding. It’s only a matter of metaphors, images that don’t really convey the situation. The mathematics is what you want, and that took a great number of people many centuries to develop. Now no one learns more than a small percentage of what there is, and even that takes many years.”

“Maybe not for me!”

“Even for you.”

Galileo shook his head. “I don’t want to take years. I don’t have years.”

Aurora seemed to consult the patterns of intersecting waves in their low ice sky. She said, “There is a drug complex we can give you that would enable you to learn faster. A synaptic velocinestic, it is called, made of a particular mixture of brain chemicals. With the help of it, one can accomplish a certain forcing. Networks bloom in the brain extremely rapidly. It’s useful in certain situations.”

“An alchemical preparation?”

“Yes, if you like.”

“Is it safe?” Thinking of the half-crazed alchemists he had met, pursuing something like witchcraft in their foul workshops, poisoned by their own hand.

“Yes, we think so. It is mildly carcinogenic, but it won’t kill you. Although some people have felt distressed afterward, I’ve heard. But I have taken it, and felt no such thing.”

This, from a machine mind. Galileo could not stop a snort from emerging, though he curbed his tongue. After considering it briefly, he said, “Give me this preparation of yours. And then who will teach me the mathematics? You?”

She gave him an amused look. “One of our machines.”

“Another machine?”

“It’s a standard curriculum, designed for use with the velocinestic. It will be faster than I could be, and clearer too. I will oversee the process.”

“Do it then. I want to know!”

Her people gave him a tight-fitting helmet, made of a mesh of metals in a dense weave. They insisted he sit down, and got him settled into what looked like a small throne tilted onto its back.

Recumbent in it, he stared at the ice ceiling. It was pulsing rapidly in dense interference patterns, waves from three directions tossing off brief glints of sapphire iridescence. These triple peaks formed their own moving pattern, like sunlight on windblown water. Even if there had been just the four big moons, the Galilean moons (such a good name), their tugging would of course create a very complex pattern. He had been so sure that the tides on Earth were the result of the ocean sloshing around in its basins of stone, shifting as the Earth both rotated and flew around the sun, creating differential speeds. But here they said it was not true. In that case, what caused tides? The tug of celestial bodies—but that was astrology all over again. And yet they seemed to be saying it was so. Was astrology right, then, with its celestial influences and its action at a distance, action without any mechanical forces applied? He hated such nonexplaining explanations!