The Phantom Tollbooth

“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.”

“Then perhaps you can help us decide which road to take,” said Milo.

“By all means,” he replied happily. “There’s nothing to it. If a small car carrying three people at thirty miles an hour for ten minutes along a road five miles long at 11:35 in the morning starts at the same time as three people who have been traveling in a little automobile at twenty miles an hour for fifteen minutes on another road exactly twice as long as one half the distance of the other, while a dog, a bug, and a boy travel an equal distance in the same time or the same distance in an equal time along a third road in mid-October, then which one arrives first and which is the best way to go?”

“Seventeen!” shouted the Humbug, scribbling furiously on a piece of paper.

“Well, I’m not sure, but——” Milo stammered after several minutes of frantic figuring.

“You’ll have to do better than that,” scolded the Dodecahedron, “or you’ll never know how far you’ve gone or whether or not you’ve ever gotten there.”

“I’m not very good at problems,” admitted Milo.

“What a shame,” sighed 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.”

“All three roads arrive at the same place at the same time,” interrupted Tock, who had patiently been doing the first problem.

“Correct!” shouted the Dodecahedron. “And I’ll take you there myself. Now you can see how important problems are. If you hadn’t done this one properly, you might have gone the wrong way.”

“I can’t see where I made my mistake,” said the Humbug, frantically rechecking his figures.

“But if all the roads arrive at the same place at the same time, then aren’t they all the right way?” asked Milo.

“Certainly not!” he shouted, glaring from his most upset face. “They’re all the wrong way. Just because you have a choice, it doesn’t mean that any of them has to be right.”

He walked to the sign and quickly spun it around three times. As he did, the three roads vanished and a new one suddenly appeared, heading in the direction that the sign now pointed.

“Is every road five miles from Digitopolis?” asked Milo.

“I’m afraid it has to be,” the Dodecahedron replied, leaping onto the back of the car. “It’s the only sign we’ve got.”

The new road was quite bumpy and full of stones, and each time they hit one, the Dodecahedron bounced into the air and landed on one of his faces, with a sulk or a smile or a laugh or a frown, depending upon which one it was.

“We’ll soon be there,” he announced happily, after one of his short flights. “Welcome to the land of numbers.”

“It doesn’t look very inviting,” the bug remarked, for, as they climbed higher and higher, not a tree or a blade of grass could be seen anywhere. Only the rocks remained.

“Is this the place where numbers are made?” asked Milo as the car lurched again, and this time the Dodecahedron sailed off down the mountainside, head over heels and grunt over grimace, until he landed sad side up at what looked like the entrance to a cave.

“They’re not made,” he replied, as if nothing had happened. “You have to dig for them. 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.