Study Guide

The Phantom Tollbooth Chapter 15

By Norton Juster

Chapter 15

This Way to Infinity

  • The characters all have lunch inside the mine.
  • Milo, Tock, and the Humbug are all super-hungry. So when they're done with their soup they have seconds – and then thirds, and so on.
  • The more they eat, the more they want to eat.
  • When the soup is taken away, they're even hungrier than they were to start with.
  • The Mathemagician explains that in Digitopolis, people only eat when they're full. It's the opposite of what Milo and the other two are used to. Once again, we have to look at things a little differently.
  • All the details about the way people in Digitopolis eat are really an excuse for a math lesson about negative numbers and zeros. We're onto you, Mathy.
  • Then, the Mathemagician helps them magically travel to his office, which he does by erasing everything with his magic wand (which is an enormous pencil).
  • Surprise surprise, The Mathemagician uses his wand to do more magic/math.
  • Then Milo has a few questions. He tries to ask what the biggest number ever is, but has a hard time explaining what he means. Tock steps in.
  • The Mathemagician answers that however large a number Milo can think of, there's always going to be one that's even bigger. The same is true for the tiniest number ever. There will always be one that's tinier – and on and on into infinity.
  • In fact, Infinity is a place, and the Mathemagician tells Milo how to get there. He can follow a line or go up some stairs.
  • Milo is too curious to resist, so he tries out the stairs, just to get a taste of Infinity.