With Virginia gone, the place was less lively; with Livia gone, less stormy. Vincenzio remained as uninspiring as ever. Galileo’s spirits began to flag as it became clear to him that the celatone was even more of a failure than the compass had been. As it turned out, no one would ever buy a single one.
He began to fall ill again. Months passed in which he seldom left his bed, seldom even said a word, as if Livia had put a curse on him. Salviati asked Acquapendente to come over from Padua to have a look at him, to attempt a diagnosis, but he had little success.
“Your friend is very full of all the humors,” he told Salviati afterward. “I have bled him a little, but he doesn’t like that, and sanguinity is not the problem anyway. He is melancholy again, and when a choleric shifts into melancholy, it tends to be a black melancholy. Such people often suffer greatly from exaggerated fears, and Galileo it seems to me now is almost in a state of omninoia.”
“It probably doesn’t help that he has a lot of real enemies who are trying to do him harm,” Salviati said.
“True. These only make him more fearful.”
Indeed, published attacks on Galileo were appearing more and more frequently. He could not reply, and everyone knew it. Astronomical attacks from ambitious Jesuits were constant. Rumors that Galileo was making rash private rebuttals were everywhere, and it was quite true that his fellow Linceans wanted him to make such a reply. When Galileo read these well-meaning but ill-advised letters of encouragement, he would howl on his bed. He began to drink more and more wine. When he was drunk enough, he would often fall into a sweaty delirium. “They want to burn me at the stake,” he would assure people with deadly seriousness, eyes locked on theirs. “They literally want me burnt alive, like the heretic Bruno.”
Thus when three comets arrived in the skies at the same time, injecting triple the usual air of doom and controversy they brought into human affairs, Galileo was at first irritated, then, it seemed, terrified. He retreated to his bed again, and refused to answer any letters that brought up the subject, or to receive any callers. When absolutely pressed, he told people that he had been so sick that he had not been able to make any observations of the phenomenon. Luckily the comets soon disappeared from the night skies, and though the controversies continued to swirl, including very often veiled or open attacks against Galileo’s astronomy, and even his knowledge of basic optics, he resolutely refused to respond.
“They’re out to get me,” he moaned to La Piera and the other servants, throwing letters and books across the room. “There’s no other explanation for arguments this stupid! They’re trying to goad me into speaking out by writing this idiotic stuff, but I’m not fooled.” One book, by a Father Grassi, a Jesuit astronomer, caused him particularly sharp distress, as it accused him of incompetence, mendacity, an inability to comprehend the heavens, and a habit of contradicting the ban on Copernicus. It seemed certain that it would call the Dogs of God down onto him again.
One day he snapped. “Get me Cartophilus,” he said to Giuseppe, voice grating. When the ancient servant arrived, Galileo closed the door of his room and took the old man by the arm.
“I need to go back up there,” he said. He had lost a lot of weight; his eyes were bloodshot, his hair greasy and lying in hanks on his head. “I want you to get me to Hera, do you understand?”
“Maestro, you know I can’t be sure now who’s going to be at the other end of the thing,” Cartophilus warned him in a low voice.
“Get me back there anyway,” Galileo ordered, pinching the old one’s upper arm like a crab. “Hera will find me once I’m there. She always does.”
“I’ll try, maestro. It always takes a little while, you know that.”
“Quickly this time. Quickly.”
One night soon thereafter, Cartophilus came to Galileo in his bedroom. “Maestro,” he said in a low voice, “it’s ready for you.”
“What?”
“The entangler. Your teletrasporta.”
“Ah!” Galileo heaved himself to his feet. He looked shabby and thin. Cartophilus encouraged him to dress, to comb his hair. “It’s colder there, remember. You’ll be meeting strangers, no doubt.”
At the edge of the garden he had set a couch with blankets on it. Beside the couch on the ground was a metal box. It looked like pewter.
“What, no stranger? No telescope?”
“No. I’m the one in charge of this device. He was always just your courier, or guide. He came to get you. But now he has gotten himself in trouble on Callisto, as you’ll find out. Apparently I’m sending you to Aurora, who has been given the care of his entangler. She has agreed to see you again.”
“Good.”
“I think Hera will not be pleased.”
“I don’t care.”
“I know.” Cartophilus regarded him. “I think you need to learn what Aurora has to teach. Remember.” And he tapped the side of the pewter box.
CHAPTER ELEVEN
The Structure of Time
Imagination creates events.
—GIOVANFRANCESCO SAGREDO, LETTER TO GALILEO, 1612
HE STOOD BY THE RECLINING CHAIR he had taken his tutorial in, high in Rhadamanthys Linea, the Venice of Europa. Aurora was indeed there to greet him. “You look unwell,” she said, staring at him curiously.
Galileo said, “I am fine, lady, thank you. Please, may we continue your tutorial where we left off? I need to understand better how things work, in order to alter my life away from a bad result. You said when we parted that I was only at the beginning of your science. That there was some kind of reconciliation that would solve the paradoxes we were mired in. That I am mired in.”
Aurora smiled. She had in her gaze the glow that her name led Galileo to expect, even though she was obviously aged. “There is a reconciliation,” she said. “But it will require you to go much further than we did before. That session took you through four centuries, as I said. To get to the theory of the manifold of manifolds, you must keep going for a thousand more years. And mathematical progress has often accelerated in that time. Indeed there is one century called the Accelerando.”
“I like those in music,” Galileo said, climbing into the tutorial chair. “Was it then followed by a ritard?”
“Yes, it was.” She smiled as the Aurora of myth would have at old Tithonius. “Maybe that’s part of the definition of an accelerando.”
Warmed by her glance, anticipating with pleasure another flight with her into the future of mathematics, Galileo said, surprising them both, “I never knew a woman mathematician.”
“No, I suppose you didn’t. The power structure in your time was not good for women.”
“Power structure?”
“Patriarchy. A dominance system. A structure of feeling. We are cultural creatures, and what we think of as spontaneous and natural emotions are actually shaped in a culture-made system that changes over time, as with arranged marriages to romantic love, or vengeance to justice. There are of course enduring hormonal differences in brains, but they are minor. Any hormonal mix can result in someone good at math. And everyone is a mathematician.”
“Maybe in your world,” Galileo said, remembering some of his more hopeless students with a little snort. “But please, give me the preparation, and let’s be on our way. And I think it might go better for me this time, if you were to help the machine more often than you did before.”
Aurora looked amused that he would presume she was at his service. But he was too hungry for knowledge to be concerned about courtesy, and perhaps she could see that too. “I’ll listen in,” she said. “If I feel I can help, I’ll speak up.”
Her assistants brought the wiry helmet to him, and the alchemical preparation.
Humans sensed only a small part of reality. They were as worms in the earth, comfortable and warm. If God had not given them reason, they would not by their senses know even a minim of the whole.
As it was, however, by the cumulative work of thousands of people, humanity had slowly and p
ainfully built a picture of the cosmos beyond what they could see. And then had found ways to use that knowledge, and move around in the cosmos.
Galileo flew again in the space of ideas, as if through patchy white clouds, following the construction of mathematics’ monumental edifice step by step through the centuries. He was thankful for the velocinestic, because he needed to be quick to apprehend what the machine was saying, and what Aurora added to its speech. This heightened apprehension now took him speedily beyond thought as he was used to it, into some larger realm of understanding, full of feeling and movement, something like a bodily music. He did not just see or sing the music, but became it. Math was his body. Words, symbols, and images all formed in the vague enormous clouds inside him, all moving in a continuous dance of equations and formulas, operations and algorithms, together melding into an ongoing polyphonic chorus. He was singing along and being sung. This meant taking certain things on faith, hoping that his performance of them indicated a subsequent firmer understanding that would grow and hold.
Here Aurora helped him to hew to the main line, reassuring him that he was proceeding just as all the rest of them had at one point or another, enduring confusions to follow a line through them. “No one can know everything,” she said. Galileo found this hard to accept. But in order to keep flying he ignored the bitter taste of his ignorance, of his faith in things he had not mastered. There were more important matters at hand than his sense of complete understanding. Apparently no one got to have that but God.
And so he flew on, diving into the new fields and methods, gauge theory, chromoelectrodynamics, symmetry and supersymmetry, multidimensional topology, manifolds, on and on it went, smaller and bigger, more complex and simpler—and after an extended protraction of his mind he found the long looked-for reconciliation of quantum mechanics and gravity physics. It came only very late in the story, when they got down into the very finest grain of things, regarding sizes that were so small that Galileo marveled there could be any knowledge of them whatsoever. But apparently it had been done.
As the generations of scientists had succeeded each other, each step of comprehension had served as scaffolding on which to stand and erect the next level. At every step of the way, quantum mechanics had proved itself accurate and useful. And so one aspect of it, Pauli’s exclusion principle, could be combined with the speed of light to establish minimum lengths and times: these were true minimums, because further division would break either the speed of light or the exclusion principle. The minimum width established by this principle turned out to be of a meter, and traveling at the speed of light a photon would cross this distance in of a second—a second being about the equivalent of a pulse, which Galileo measured as the speed of his calm heart beating. The ultimate minim of time, in other words, was a billionth of a billionth of a billionth of a billionth of a heartbeat, more or less. That was brief! The universe was very fine-grained indeed. Just thinking about it gave Galileo a shiver. It was stunning to feel in himself that fine grain, the dense texture of the glossy plenum—to sense in that density also God’s sense of artistry, His meticulousness or pulitezza. His love of math.
He flew on, doing his best to catch up to Aurora, who was continuing as if the minimum units were not stupendously, unimaginably small. She was used to the idea of them, and moving on to the question of how physicists had dealt with the idea that all space and time might be created out of the vibration of objects of the absolute minimum size and duration. Their most powerful experimental machines would have to be 1020 times more powerful than they were to be able to investigate these minimal particles or events; in other words, an accelerator ring large enough to create the energies needed would have to be as big around as the galaxy. The particles they sought were so small that if one of them were expanded to the size of the Earth, the nucleus of an atom, to stay proportional, would have to be expanded to ten times the size of the universe.
Galileo laughed at this. He said, “It’s the end of physics then.”
For it meant that a stupendous abyss lay between humanity and the fundamental reality that would explain things at all the larger scales. They couldn’t cross that abyss. Physics was therefore stumped.
And indeed, for a long time mathematical physics and cosmology skittered around and appeared to stall, as physicists struggled to concoct scaffolding that they could cast all the way across the abyss in a single throw—that would give them even questions to ask.
“To an extent we are still there,” Aurora said. “But a mathematician named Bao made a bridge that seems to have held, and allowed us to build from it. Let’s go there now.”
Before Bao’s time, Galileo saw, which was precisely the beginning of the period known later as the Accelerando, the goal of physicists was to explain everything. He recognized that; it was the reductio ad absurdum of science: to know everything. The unspoken desire in that urge was the hope that, knowing everything, humanity would also know what to do. The blank that was their sense of purpose would perhaps also be filled.
But to know everything was asking too much. “They want to be like God!” he said.
“Maybe God is only a prolepsis,” Aurora said. “Our image of what we could be, imagined by contemplating our future.”
“Which would make it an analepsis, no?”
She laughed as they flew. “You like paradoxes, but of course this one is just entanglement all over again. We are extensive in time. Fly on and you will see.”
So they flew. Progress in physics struggled on. Theories of what occurred at the minimum and in postulated extra dimensions were elaborated, considered, challenged, refined. Predictions were made that could sometimes be checked against observation, or involved findings just beyond the realm of current observation. Ideas thus drove technologies. Slowly progress was made. But the unbridgeable abyss made every theory speculative. The wind from Galileo’s flight could have knocked down some of these houses of cards, and the collapsed theories he flew through had perhaps been knocked down in just that way, by the offhand remark of some observer like Bao, surveying the whole landscape and taking a completely new line over it.
It wasn’t until the twenty-eighth century that a theoretical structure accomplished a substantial part of what had been begun so long before. It was a physics based on Bao’s bridge to the minim, and on experiments spanning the solar system—controversial experiments that had entrained significant portions of the system’s total potential energy. Bao’s work had clarified the ten-dimensional manifold of manifolds theory that had been proposed since the time of Kaluza and Klein. Bao’s version had created many cosmological and subatomic questions and predictions that had given them experiments to try, observations to make, the results of which then gave them corrections and surprises, but mainly confirmations, a sense that they were on the right track at last—and in some ways had been all along, if one made allowances for the usual eddies and dead ends. Each generation had served as scaffolding for the generations that followed, and the work continued through collapses and reversals, almost one might say mindlessly. “It’s like watching ants building a mound,” Galileo observed as he flew through the elaborations. “The mass just keeps grinding.”
“Yes, although it’s a strange thing to say about a process that has taken so much brain power.”
“Tell me more about the ten dimensions,” Galileo requested. “Something more than their math. What do they mean? What can they mean?”
Aurora flew next to him, so closely that he felt they were intertwined. He dipped and turned, dropped or soared, stooped or gyred, always trying to stay next to her, and he found that she could make writing appear as clouds, or red ingots in the air before him. His body was a flock of bannering thoughts, flying around her in a dance. The landscape under them was a mountain range made of symbols and numbers piled one on the next, gnarled tectonically.
“Recall the Euclidean space that you know and sense,” she said, “having the three dimensions of length, breadth, and height.
With Newton we added a different kind of dimension, which is time—”
“But I did that!” Galileo objected again. “Falling things accelerate as a square of the time passed! This I found out, and it meant time and space were bound together somehow.” Although, he recalled uneasily, the finding lay still unpublished, buried in his folios out in the workshop.
“All right, call it Galilean space,” Aurora said easily. “Whatever you call it, these four dimensions were understood as if they were an absolute, an underlying invisible gridwork through which physical phenomena moved. That’s when you have Laplace declaring that with a sufficient physics and database you could predict the entire past and future of the universe just by entering the numbers for the current moment, and running them through the equations either forward or back, as in an astrolabe. It was a thought experiment only, because no one would ever have the data set to do it. But the implication was that God, or something like it, could do it.”
“Yes. I can see that.”
“It implied a predetermined, clockwork universe that many found depressing to contemplate. We weren’t really choosing to do anything.”
“Yes. But your quantum mechanics destroyed all that.”
“Precisely.”
“Or imprecisely.”
“Ha, yes. With relativity and quantum mechanics we began to understand that the four dimensions we sense are artifacts of our perception of dimensions far more numerous than we knew. We began to see things that made it clear four dimensions were not adequate to explain what was happening. Baryons rotated 720 degrees before returning to their starting positions. Particles and waves both were confirmed even though they contradicted each other as explanations, as far as our senses and reason were concerned. In some cases our observations seemed necessary to make things exist at all. And something otherwise undetectable was exerting very marked gravitational effects, that if caused by a mass would outmass the visible matter of the universe ten to one. Then there appeared to be a kind of reverse gravity effect as well, an inexplicable accelerating expansion of space. People spoke of dark matter and dark energy, but these were names only—names that left the mysteries untouched. What they were was better explained by the existence of extra dimensions, first suggested by Kaluza and Klein, and then put to use by Bao.”
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