“U-g-g-g-h-h-h,” gasped the bug, suddenly realizing that he was twenty-three times hungrier than when he started, “I think I’m starving.”
“Me, too,” complained Milo, whose stomach felt as empty as he could ever remember; “and I ate so much.”
“Yes, it was delicious, wasn’t it?” agreed the pleased Dodecahedron, wiping the gravy from several of his mouths. “It’s the specialty of the kingdom—subtraction stew.”
“I have more of an appetite than when I began,” said Tock, leaning weakly against one of the larger rocks.
“Certainly,” replied the Mathemagician; “what did you expect? The more you eat, the hungrier you get. Everyone knows that.”
“They do?” said Milo doubtfully. “Then how do you ever get enough?”
“Enough?” he said impatiently. “Here in Digitopolis we have our meals when we’re full and eat until we’re hungry. That way, when you don’t have anything at all, you have more than enough. It’s a very economical system. You must have been quite stuffed to have eaten so much.”
“It’s completely logical,” explained the Dodecahedron. “The more you want, the less you get, and the less you get, the more you have. Simple arithmetic, that’s all. Suppose you had something and added something to it. What would that make?”
“More,” said Milo quickly.
“Quite correct,” he nodded. “Now suppose you had something and added nothing to it. What would you have?”
“The same,” he answered again, without much conviction.
“Splendid,” cried the Dodecahedron. “And suppose you had something and added less than nothing to it. What would you have then?”
“FAMINE!” roared the anguished Humbug, who suddenly realized that that was exactly what he’d eaten twenty-three bowls of.
“It’s not as bad as all that,” said the Dodecahedron from his most sympathetic face. “In a few hours you’ll be nice and full again—just in time for dinner.”
“Oh dear,” said Milo sadly and softly. “I only eat when I’m hungry.”
“What a curious idea,” said the Mathemagician, raising his staff over his head and scrubbing the rubber end back and forth several times on the ceiling. “The next thing you’ll have us believe is that you only sleep when you’re tired.” And by the time he’d finished the sentence, the cavern, the miners, and the Dodecahedron had vanished, leaving just the four of them standing in the Mathemagician’s workshop.
“I often find,” he casually explained to his dazed visitors, “that the best way to get from one place to another is to erase everything and begin again. Please make yourself at home.”
“Do you always travel that way?” asked Milo as he glanced curiously at the strange circular room, whose sixteen tiny arched windows corresponded exactly to the sixteen points of the compass. Around the entire circumference were numbers from zero to three hundred and sixty, marking the degrees of the circle, and on the floor, walls, tables, chairs, desks, cabinets, and ceiling were labels showing their heights, widths, depths, and distances to and from each other. To one side was a gigantic note pad set on an artist’s easel, and from hooks and strings hung a collection of scales, rulers, measures, weights, tapes, and all sorts of other devices for measuring any number of things in every possible way.
“No indeed,” replied the Mathemagician, and this time he raised the sharpened end of his staff, drew a thin straight line in the air, and then walked gracefully across it from one side of the room to the other. “Most of the time I take the shortest distance between any two points. And, of course, when I should be in several places at once,” he remarked, writing 7 ? 1 = 7 carefully on the note pad, “I simply multiply.”
Suddenly there were seven Mathemagicians standing side by side, and each one looked exactly like the other.
“How did you do that?” gasped Milo.
“There’s nothing to it,” they all said in chorus, “if you have a magic staff.” Then six of them canceled themselves out and simply disappeared.
“But it’s only a big pencil,” the Humbug objected, tapping at it with his cane.
“True enough,” agreed the Mathemagician; “but once you learn to use it, there’s no end to what you can do.”
“Can you make things disappear?” asked Milo excitedly.
“Why, certainly,” he said, striding over to the easel. “Just step a little closer and watch carefully.”
After demonstrating that there was nothing up his sleeves, in his hat, or behind his back, he wrote quickly:
4 + 9 ? 2 ? 16 + 1 ? 3 ? 6 ? 67 + 8 ? 2 ? 3 + 26 ? 1 ? 34 + 3 ? 7 + 2 ? 5 =
Then he looked up expectantly.
“Seventeen!” shouted the bug, who always managed to be first with the wrong answer.
“It all comes to zero,” corrected Milo.
“Precisely,” said the Mathemagician, making a very theatrical bow, and the entire line of numbers vanished before their eyes. “Now is there anything else you’d like to see?”
“Yes, please,” said Milo. “Can you show me the biggest number there is?”
“I’d be delighted,” he replied, opening one of the closet doors. “We keep it right here. It took four miners just to dig it out.”
Inside was the biggest
Milo had ever seen. It was fully twice as high as the Mathemagician.
“No, that’s not what I mean,” objected Milo. “Can you show me the longest number there is?”
“Surely,” said the Mathemagician, opening another door. “Here it is. It took three carts to carry it here.”
Inside this closet was the longest
imaginable. It was just about as wide as the three was high.
“No, no, no, that’s not what I mean either,” said Milo, looking helplessly at Tock.
“I think what you would like to see,” said the dog, scratching himself just under half-past four, “is the number of greatest possible magnitude.”
“Well, why didn’t you say so?” said the Mathemagician, who was busily measuring the edge of a raindrop. “What’s the greatest number
“Oh dear,” shouted Milo, holding his hands to his ears, “doesn’t that ever stop either?”
“How can it,” said the Mathemagician, “when you can always take half of whatever you have left until it’s so small that if you started to say it right now you’d finish even before you began?”
“Where could you keep anything so tiny?” Milo asked, trying very hard to imagine such a thing.
The Mathemagician stopped what he was doing and explained simply, “Why, in a box that’s so small you can’t see it—and that’s kept in a drawer that’s so small you can’t see it, in a dresser that’s so small you can’t see it, in a house that’s so small you can’t see it, on a street that’s so small you can’t see it, in a city that’s so small you can’t see it, which is part of a country that’s so small you can’t see it, in a world that’s so small you can’t see it.”
Then he sat down, fanned himself with a handkerchief, and continued. “Then, of course, we keep the whole thing in another box that’s so small you can’t see it—and, if you follow me, I’ll show you where to find it.”
They walked to one of the small windows and there, tied to the sill, was one end of a line that stretched along the ground and into the distance until completely out of sight.
“Just follow that line forever,” said the Mathemagician, “and when you reach the end, turn left. There you’ll find the land of Infinity, where the tallest, the shortest, the biggest, the smallest, and the most and the least of everything are kept.”
“I really don’t have that much time,” said Milo anxiously. “Isn’t there a quicker way?”
“Well, you might try this flight of stairs,” he suggested, opening another door and pointing up. “It goes there, too.”
Milo bounded across the room and started up the stairs two at a time. “Wait for me, please,” he shouted to Tock and the Humbug. “I’ll be gone just a few minutes.”
16. A Very Dirty Bird
Up he went—very quickly at first—then more slowly—then in a little while even more slowly than that—and finally, after many minutes of climbing up the endless stairway, one weary foot was barely able to follow the other. Milo suddenly realized that with all his effort he was no closer to the top than when he began, and not a great deal further from the bottom. But he struggled on for a while longer, until at last, completely exhausted, he collapsed onto one of the steps.
“I should have known it,” he mumbled, resting his tired legs and filling his lungs with air. “This is just like the line that goes on forever, and I’ll never get there.”
“You wouldn’t like it much anyway,” someone replied gently. “Infinity is a dreadfully poor place. They can never manage to make ends meet.”
Milo looked up, with his head still resting heavily in his hand; he was becoming quite accustomed to being addressed at the oddest times, in the oddest places, by the oddest people—and this time he was not at all disappointed. Standing next to him on the step was exactly one half of a small child who had been divided neatly from top to bottom.
“Pardon me for staring,” said Milo, after he had been staring for some time, “but I’ve never seen half a child before.”
“It’s .58 to be precise,” replied the child from the left side of his mouth (which happened to be the only side of his mouth).
“I beg your pardon?” said Milo.
“It’s .58,” he repeated; “it’s a little bit
“But maybe he doesn’t understand numbers,” said Milo, who found it a little difficult to read himself.
“NONSENSE!” bellowed the Mathemagician. “Everyone understands numbers. No matter what language you speak, they always mean the same thing. A seven is a seven anywhere in the world.”
“My goodness,” thought Milo, “everybody is so terribly sensitive about the things they know best.”
“With your permission,” said Tock, changing the subject, “we’d like to rescue Rhyme and Reason.”