At the beginning, Lenora had tried to write that down, but had quickly given up as Milton went along. “So a googolplex is the largest number?” she asked.
“Oh, no,” laughed Milton. “Not even close.”
“Well then, what is it?”
Milton said. “I don’t know. As I said, the great numbers are far beyond me.”
Lenora’s head was spinning at the thought of all this, but Lucy had her chin in her hand, deep in thought. “Why don’t we just go talk to them, then? They could tell us.”
“Talk to them?” said Lenora and Milton together. Lenora wasn’t sure about this, and Milton looked alarmed as well. These large numbers were sounding more dangerous all the time. Lenora wondered if the Forces of Darkness hadn’t been right to stay away. Still, she had no choice but to get an answer for her patron. She’d already let one patron down on Plato’s Republic, and she didn’t plan on that happening again. “Good idea, Lucy. Let’s do it. Is that all right with you, Milton? Can you take us to them?”
Milton looked uncertain, but he nodded. “I can. But you must proceed carefully. You are to the great numbers as a top quark is to you.”
“A top what?” said Lucy.
Lenora was very glad she had read Your Friends, the Subatomic Particles over the summer. “A top quark is an extremely tiny particle that lives for less than a trillionth of a trillionth of a second.”
“Yes,” said Milton. “And to the large numbers, you are little different from that. So to meet them, we must get large ourselves. Very large indeed. Give me your hands.”
They did. And then they grew—very, very, very, very large indeed.
CHAPTER NINE
Lenora and the Numbers
Lenora had once seen the glory of the stars from outer space when she had been tossed through the open door of a rocket ship. She recognized them again, but saw them so briefly it hardly counted, before she was staring down at a double-armed disc of stars disappearing beneath her feet—the Milky Way galaxy, dwindling to a speck. Around her, Lucy, and Milton were clusters of other galaxies, which in turn became smaller blurs of light until they couldn’t be seen at all.
Lenora could scarcely believe it, but she, Lucy, and Milton were zooming up, larger and larger, the trillions of galaxies streaking past like shooting stars, and then they were beyond even those, and now below her Lenora could see one collection of lights, all the universe in something like a bubble, but … different. She thought, but couldn’t be sure, that there were other bubblish things nearby, but her mind was too rattled to be sure of any of it. And then all that vanished away into nothing, also.
Lenora looked over at Lucy, whose eyes and mouth were wide with wonder. It seemed she, too, could understand what had happened, that they were larger, far larger now, than the universe, or perhaps many universes. Lenora’s brain trembled at the thought.
“Here we are,” said Milton. “This is where the large numbers live.” He was perfectly calm, though Lenora was on the verge of telling him to take them back to normal size. For something in her bones told her: Humans are not supposed to be here.
She held her tongue. Lucy looked thrilled, Milton probably did this all the time, and Lenora had a patron who needed an answer. She did want to get this over with as quickly as possible, though, and so she asked, “What now?”
Milton thought for a moment. “Let’s meet Graham’s number. He might be willing to speak with us. Not all of them are.” And then, though she could not tell how, they began moving, flying really, toward one of the lights that still surrounded them.
As they flew, Lenora remembered the third task Malachi had given her. And so she asked, “By the way—do you know who Zenodotus is?”
“Of course!” said Milton. “He was the first head librarian of the Library of Alexandria.”
“Oh!” said Lenora.
“What’s that?” said Lucy.
“It was considered the greatest library of the ancient world, founded in Egypt long ago,” said Lenora. And then, to Milton: “Do you know where Zenodotus is? I have to find him.”
“No,” said Milton, “I have not seem him in quite some time. But I remember him as a dashing man with a long, curled mustache, full of energy and life.”
Lucy spoke up. “Wouldn’t it be easy to find him? Let’s just go to this Library of Alex-whatever-ia and see if he’s there.”
“It’s not there anymore,” said Milton. “I’m not sure what happened, but I heard it was accidentally burned down in 48 BC by Julius Caesar.”
“What a dummy,” said Lucy.
Lenora scribbled L of A destroyed by Caesar’s fire—maybe in her notebook. Then she saw they were coming swiftly toward one of the lights, and soon Lenora could make out a man sitting on a chair amid a brilliant gleam. He wore a flat-brimmed straw hat and an elegant old striped suit. He sat with one leg crossed over the other and took no notice of them at all. He seemed deep in thought, and though his lips did not move, Lenora could hear a whispering coming from him.
The three stopped in front of the man, and Milton bowed low. Lenora and Lucy looked at each other, and then Lenora bowed deeply, too, while Lucy executed an elegant curtsy.
“Sir,” said Milton, “may we please speak with you for a moment? This librarian has a question.”
The man did not respond, still gazing at something faraway, still whispering.
Lenora whispered, too. “Who is this?”
Milton spoke low, as though he did not want to disturb the man. “This is Graham’s number. He is the result of certain calculations concerning the edges of many-dimensional cubes. He was once the largest number ever produced by a mathematical proof. But that record has since been broken.”
At this, the man’s head turned slowly toward them, and Milton immediately went silent. Graham’s number regarded each of them in turn for what seemed to Lenora like a terribly long time. First Lucy, then Lenora, and then his gaze, which was not a friendly one, landed on Milton.
“Why have you disturbed me?” he asked in a soft voice with just a hint of menace. “I am engaged in several very important conversations.”
“I apologize, sir,” said Milton, bowing again. “But this librarian is searching for the largest number. I thought you might be able to direct us.”
The man uncrossed his legs and looked hard at them. “Am I not large enough for you? What use could you possibly have for anyone larger?”
Lenora spoke up. “Sir, if I may ask—how large are you, exactly?”
Graham’s number looked at her, and his gaze softened slightly. “A librarian. I would like to tell you how large I am. However, there is nothing your mind can understand, nothing I can be compared to, that will aid you in understanding my vast size. I am far beyond the realm of your imagination.”
Lenora wondered how bold she dared be. “Thank you, sir.” And then she hesitated before saying, “Milton has told us there are larger numbers than even you. Perhaps you can tell me the largest of you?” She hoped this would not offend.
Graham’s number turned his gaze back to whatever he had been doing before. “Ask TREE(3), if it will speak to you. It is the next number that humans—you are human, are you not?—were able to discover beyond me.” And then he went back to his whispering. Lenora had a feeling he would not speak to them again.