“What a shame," signed the Dodecahedron. "They're so very useful. Why, did you know that if a beaver two feet long with a tail a foot and a half long can build a dam twelve feet high and six feet wide in two days, all you would need to build Boulder Dam is a beaver sixty-eight feet long with a fifty-one-foot tail?""Where would you find a beaver that big?" grumbled the Humbug as his pencil point snapped."I'm sure I don't know," he replied, "but if you did, you'd certainly know what to do with him.""That's absurd," objected Milo, whose head was spinning from all the numbers and questions."That may be true," he acknowledged, "but it's completely accurate, and as long as the answer is right, who cares if the question is wrong? If you want sense, you'll have to make it yourself.”

“Why, did you know that if a beaver two feet long with a tail a foot and a half long can build a dam twelve feet high and six feet wide in two days, all you would need to build Boulder Dam is a beaver sixty-eight feet long with a fifty-one-foot tail?""Where would you find a beaver that big?" grumbled the Humbug as his pencil point snapped."I'm sure I don't know," he replied, "but if you did, you'd certainly know what to do with him.”

“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.”

“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.”

“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.”

“As the cheering continued, Rhyme leaned forward and touched Milo gently on the shoulder. "They're cheering for you," she said with a smile. "But I could never have done it," he objected, "without everyone else's help." "That may be true," said Reason gravely, "but you had the courage to try; and what you can do is often simply a matter of what you *will* do." "That's why," said Azaz, "there was one very important thing about your quest that we couldn't discuss until you returned. "I remember," said Milo eagerly. "Tell me now." "It was impossible," said the king, looking at the Mathemagician. "Completely impossible," said the Mathemagician, looking at the king. "Do you mean----" said the bug, who suddenly felt a bit faint. "Yes, indeed," they repeated together; "but if we'd told you then, you might not have gone---and, as you've discovered, so many things are possible just as long as you don't know they're impossible." And for the remainder of the ride Milo didn't utter a sound.”

“It has been a long trip," said Milo, climbing onto the couch where the princesses sat; "but we would have been here much sooner if I hadn't made so many mistakes. I'm afraid it's all my fault.""You must never feel badly about making mistakes," explained Reason quietly, "as long as you take the trouble to learn from them. For you often learn more by being wrong for the right reasons than you do by being right for the wrong reasons.”