Galileo's Dream (46 page)

Again, this was contra Aristotle, but that was no surprise anymore. More important, it was interesting in its own right.

There was so much that was interesting in what they could see with this apparatus. They started dropping balls freely and letting them hit an inclined plane, then a horizontal plane. Other times they sent balls rolling off the end of a horizontal plane, and watched them fall in a quick curve to a bed of sand they had set on the floor, so the balls would leave a mark that could be measured precisely. Very interesting! Different distances, angles, therefore speeds, and all of them timed proportionally, by the weight of water. These various setups divided motion into parts of different kinds, when before motion had been all mixed together in nature, and thus difficult to study. He had been working on these problems for almost twenty years, and never
had he been able to articulate differences like he could now. By manipulating the variables one could measure different things, and establish that there were relations—just as one would have expected, but could never before create and measure. Relations of past speed, present speed, future speed.

And so now they were sure, at last, after twenty years of various formulations that had not worked, that
the downward acceleration of a ball increased as the square of the time elapsed in its fall
. It was as simple as that.

Galileo showed the equations to Mazzoleni: “See? See? Acceleration is a very simple ratio! Why should it be true? Why? God made it that, that's why! God likes mathematical ratios. He must! He puts them there for all to see.”

“For you to see, maestro. Has anyone else ever seen this?”

“Of course not. Archimedes would have seen it, if he had had such a fine apparatus. But no. I am the first in the world.”

The gap-toothed grin. When God created the cosmos, He had had just that grin. He had put it on Mazzoleni to show Galileo how He had felt.

Combined results began to accrue. When a rolling ball fell off a horizontal plane into the air, the curve of its fall was a mix of two motions—first, the uniform speed of the horizontal motion, which did not diminish just because the ball left the tabletop, and second, the accelerating speed of its vertical fall, which was
precisely the same as if it were falling without any horizontal motion
—something they established by repeated testing. So the horizontal speed was uniform, while the downward speed was increasing as the square of the time elapsed, as already demonstrated. And the combination of those two was, by definition, half of a parabola. One could therefore describe the motion with a simple parabolic equation.

He stood looking at these equations he had written down, and at the numbers and sketched diagrams on the pages before it. His 116th work folio was almost completely filled.

“MAT-ZO-LEN-IIIIIIIIIII!”

The simian face of the ancient one. “Something good?”

“PAR-A-BO-LAAAAAA! Let me show you. This is something even you can understand.”

But first he had to dance around the table, out into the garden and back again, feeling bell-struck. All the world struck, all the world ringing inside him.
Gong! Gong! Gong!

Black space; Hera's face.

“So. Do you see what you did?”

“Yes. I remember.”

“Do you understand the power of your apparatus, of your method?”

“You could seek the mathematics inside nature, and find it.”

“Yes. This is what you loved. This is what gave you joy.”

She sat back, watching him closely. “The inclined plane apparatus,” she went on, “allowed you to create events that in nature were compound, but now were teased apart. You had independent variables under your control. Each experiment was unique, but when the variables were the same, the results were the same. It was as if you were enacting the calculus in advance of the mathematics of the calculus—doing calculus as if it were geometry, or even mobile sculpture.

“And these events you staged—if anyone else were to stage them in the same way, they could not help but get the same results. You could take the various descriptions of motion that were competing in your time, and put them to the test, and the event itself would determine which of the explanations matched the results. Then, with your mathematical description in hand, you could predict what would happen in new situations. When you were right, this was something no one could ever revise. If we were to do it here and now, it would be just the same.”

“Well, but there is no pull downward here.”

“You know what I mean.”

“Yes yes. It was a way of seeing the truth.”

“Not so fast. It was an accurate description of events at that scale. It was an abstraction with a concrete referent, which meant that no one could logically deny it. If someone were to assert that there was a different description for motion, then you could put it to the test, and show that they were wrong and you were right. You could in fact withdraw, and let motion speak for itself. Motion then speaks, and your rivals in explanation are silenced, without you having to say a word.”

“I liked that,” Galileo admitted. “I liked that very much.”

“Everyone does. And so we still speak of Galilean motion. We still have inclined planes in physics classrooms.”

“I like that too.”

“It was your chief joy.”

“Well, maybe,” Galileo temporized, thinking of all the other things he had enjoyed. He realized that he had loved his life.

“No. It
was
your chief joy, as revealed by your own mind. Remember that the mnemonic is a brain scanner that locates your most powerful memories by identifying and stimulating the largest coordinating clusters in the amygdala. The strongest memories make the biggest clumps, and they are always entrained with the strongest emotions, in particular the strongest pleasures and the strongest pains. The emotional component is determinative for intensity and permanence of memory. Thus, sexual release can be memorable or forgettable, depending on if it is attached to more complex feelings. To joy, for instance—that feeling you describe as being rung by a bell. And then physical pain, all your many ailments, most of which originated with the poisoned cellar that killed your weaker companions—pain leaves a mark, especially at first, when accompanied by dismay and fear. But much more powerful is shame—perhaps the strongest of the negative emotions. Although fear, humiliation … well. The point is, we have very emotional memories. So I have just been visiting your strongest memories, that's all. This is what we find among the most pleasurable of your memories.”

“Not the telescope?”

“Of course not! That's just the thing that Ganymede gave you. And by so doing, he bent your whole life in a new direction, until what you were martyred for and remembered for was a drama that overshadowed your real contribution, which was the inclined plane work. Your telescopic discoveries were just what anybody would see when they look through such a glass. And your astronomical theories were usually wrong.”

“What do you mean?” Galileo demanded.

“Your explanation of the comets? Your theory of the tides?”

“Well, but that isn't fair,” Galileo objected. “The real explanation for the tides is ridiculous. That the Earth's water moves because space itself is bending? It's inexcusable.”

“And yet real.”

Gallileo sighed. “Maybe we need to be able to forget more than we need to remember,” he said, thinking of what she had said about emotions. About shame, and his catalog of bad looks.

“You need to remember what helps you, and forget things that don't help you. But you have not achieved that. Few people have, I've found.”

“You did this to many people, I take it?”

“It was my work.” She shook her head unhappily. “It's what I did, before this thing in Europa drew us all down into its maelstrom.”

“Is the creature really such a problem?”

She looked grim. “The debate over what to do about it is the problem. We are the problem. But the problem is tearing us apart.”

“As bad as that?”

She gave him one of her sharp looks. “You know better than most how people can fight over an idea.”

“Indeed. That's what Aurora said too.”

“Fights over ideas are the most vicious of all. If it were merely food, or water, or shelter, we would work something out. But in the realm of ideas one can become
idealistic
. The results can be deadly. The Thirty Years' War, isn't that what they called the religious war that Europe was fighting during your time?”

“Thirty years?” Galileo exclaimed, dismayed.

“So I seem to remember. And here, now, it may be happening again.”

For a while they flew to Europa in silence, both of them locked in their thoughts. By now the equivalence of change of speed and the physical sensation of weight was firmly established in Galileo's body and mind, so when he felt pressed back into his chair, he came out of his reverie.

“You're speeding up?”

“Yes.” She was grim again. “Apparently Ganymede and his group are already there. Four ships in a tight orbit, just over the ice. There's no good way to stop them now.”

Ahead of them bulked the white ball of Europa. Hera muttered viciously in a language he did not know, tapping hard at her control pad. “Come on!” she complained.

You must be patient, Galileo prevented himself from saying. Instead he asked, “Why does Ganymede want me to be burned at the stake, do you think? What difference would it make? Aren't there so many potentialities that they all happen or not, cancel each other out or not, so that any one doesn't matter?”

She looked at him with the expression he had seen before that he could not decipher. Pity? Affection? “All the temporal isotopes have effects downstream. Think again of the braided channels of a river. Say you kick the bank of one stream so hard it crumbles, and the stream wears away the bank until it breaks into a nearby channel, and they both become so strong together that they cut a straighter line, take water from some channels, reroute others…. Well, so, Ganymede thinks you are at a crucial point, a big bend. He's been obsessed with changing that bend for a long time. He keeps going back to it, I think. And I wonder if he doesn't want the change he causes to be so profound it alters things even in our time too. I wouldn't be surprised.”

“But say I am burned—what's different?”

“Maybe the more accurate question would be, what would be different if you weren't burned?” She glanced at him, sensing his shudder. “After you, there is a deep divide between science and religion. A war of two cultures, two worldviews. And with you burned at the stake for stating an obvious physical fact, religion is thereafter discredited, even disgraced. The intellectual innovators of the world are secularized, science rises to dominate human culture, religion is seen as an archaic power system, like astrology, and it fades away.”

“But that's not good. Why would anyone want that? That's no different than these bastard priests who are attacking me!”

She regarded him carefully. “Interesting to see again the structure of feeling you grew up in. To us it seems clear that your religion was a kind of mass delusion, serving the powerful by justifying their hierarchy.”

Galileo shook his head. “The world is sacred. God made it all, as an expression of mathematical playfulness, perhaps, but however that may be, He did it.” She shrugged at this and he went on. “Besides, how can you say that science dominating civilization is such a good thing? Didn't you tell me that your histories have been nightmares, that most cultures in most times, including your own, have been to one degree or another insane? Where's the great advantage in that?”

“The question,” she said carefully, “is whether the alternatives are not even worse.”

This was sobering. Galileo thought it over. “Do you have a tutorial for the history of human affairs between my time and yours, like the one Aurora had for mathematics?”

“Of course,” Hera said, still brooding. “There are many. They describe different potentialities, or attempt to show the whole wave function. But there's no time for that now. We're approaching Europa.”

And in fact Europa stood directly before them, growing rapidly larger, blossoming like a white rose, its surface crackled like the ice on the Po just before it broke up in the spring. It was striking how for the longest time in their flights, their objectives remained at the same small size, only growing incrementally, and then in a final rush bloomed to the size of an entire world.

Now Hera was cursing again.

“What's wrong?” he asked.

“They're landing,” she said, and pointed. “Just over the north pole.”

Galileo did not have a sense of orientation to apply to this. “You can see them?”

“Yes. There.” She pointed, and Galileo saw a cluster of tiny stars, very close to Europa's white surface, swirling down toward it. “They're landing, and the Europans are trying to stop them, but …”

“They don't have cannons to fire at them?”

“Weapons have been forbidden, as I told you, but there are things that can be used as weapons, of course. Power systems, construction tools, field generators …” She shook her head as she watched her screen and listened to her interlocutors. “I wish they would generate a small black hole in their midst and suck them out of existence!” She cursed in the language that didn't get translated.

A streak of brilliant white light shot down out of the quartet of firefly ships onto the surface of Europa, and she stopped in her tirade.

“What was that?” Galileo said.

“I don't know. Possibly one of their ships flew right into the moon, like a meteorite. I don't know how that could have happened, though. The pilot systems wouldn't have allowed it, so there must have been an override, or …”