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The Phantom Tollbooth | Study Guide

Norton Juster

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The Phantom Tollbooth | Chapter 15 : This Way to Infinity | Summary



The travelers have lunch with their hosts down in the mine, and the more they eat, the hungrier they get. Milo eats nine portions, and the Humbug eats 23 servings of subtraction stew. The Dodecahedron points out that in Digitopolis, they dine when they're full and stop eating when they're hungry. Eating when you're hungry is wrong, he says, just like sleeping when you're tired is wrong.

The Mathemagician draws a straight line in the air, then walks across it, explaining that he always takes "the shortest distance between any two points." When he needs to be in more than one place at the same time, he multiplies himself. Now there are seven Mathemagicians standing alongside each other.

The Mathemagician gives Milo some basic math lessons about numbers, division, and infinity.


Juster again uses opposites for comic effect in this chapter when Milo learns that in Digitopolis, you eat when you're full and not when you're hungry. Also, Juster again paints a literal picture of a figurative expression, when the Mathemagician demonstrates that "the shortest distance between two points is a straight line."

The math lessons remind Milo that there is much he doesn't know or understand. Over the course of his journey, Milo will come to realize the importance of learning, and he will look at the value of receiving an education in a different light.

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