“There are other advantages," continued the child. "For instance, if one rat were cornered by nine cats, on the average, each cat would be ten percent rat and the rat would be ninety percent cat. If you happened to be a rat, you can see how much nicer it would make things.”

“How can you see something that isn't there?" yawned the Humbug, who wasn't fully awake yet. "Sometimes, it's much simpler than seeing things that are,"he said. "For instance, if something is there, you can only see it with your eyes open, but if it isn't there, you can see it just as well with your eyes closed. That's why imaginary things are often easier to see than real ones.""Then where is Reality?" barked Tock. "Right here,"cried Alec, waving his arms.”

“Is everyone with one face called a Milo?""Oh no," Milo replied; "some are called Henry or George or Robert or John or lots of other things.""How terribly confusing," he cried. "Everything here is called exactly what it is. The triangles are called triangles, the circles are called circles, and even the same numbers have the same name. Why, can you imagine what would happen if we named all the twos Henry or George or Robert or John or lots of other things? You'd have to say Robert plus John equals four, and if the four's name were Albert, things would be hopeless.""I never thought of it that way," Milo admitted."Then I suggest you begin at once," admonished the Dodecahedron from his admonishing face, "for here in Digitopolis everything is quite precise.”

“...I'll continue to see things as a child. It's not so far to fall.”

“Don't you know anything at all about numbers?""Well, I don't think they're very important," snapped Milo, too embarrassed to admit the truth."NOT IMPORTANT!" roared the Dodecahedron, turning red with fury. "Could you have tea for two without the two — or three blind mice without the three? Would there be four corners of the earth if there weren't a four? And how would you sail the seven seas without a seven?""All I meant was—" began Milo, but the Dodecahedron, overcome with emotion and shouting furiously, carried right on."If you had high hopes, how would you know how high they were? And did you know that narrow escapes come in all different widths? Would you travel the whole wide world without ever knowing how wide it was? And how could you do anything at long last," he concluded, waving his arms over his head, "without knowing how long the last was? Why, numbers are the most beautiful and valuable things in the world. Just follow me and I'll show you." He turned on his heel and stalked off into the cave.”

“Outside the window, there was so much to see, and hear, and touch — walks to take, hills to climb, caterpillars to watch as they strolled through the garden. There were voices to hear and conversations to listen to in wonder, and the special smell of each day.And, in the very room in which he sat, there were books that could take you anywhere, and things to invent, and make, and build, and break, and all the puzzle and excitement of everything he didn't know — music to play, songs to sing, and worlds to imagine and then someday make real. His thoughts darted eagerly about as everything looked new — and worth trying."Well, I would like to make another trip," he said, jumping to his feet; "but I really don't know when I'll have the time. There's just so much to do right here.”

“But that can never be," said Milo, jumping to his feet."Don't be too sure," said the child patiently, "for one of the nicest things about mathematics, or anything else you might care to learn, is that many of the things which can never be, often are. You see," he went on, "it's very much like your trying to reach Infinity. You know that it's there, but you just don't know where — but just because you can never reach it doesn't mean that it's not worth looking for.”