The Phantom Tollbooth Chapter 15 Summary
by Norton Juster

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Chapter 15 Summary

This Way to Infinity

Seven of the strongest miners bring a huge, bubbling cauldron into the cave, and soon a tantalizing aroma fills the space. The travelers watch hungrily as each miner fills his bowl from the steaming pot. The Mathemagician gives each of the travelers a heaping bowlful, and all three of them eat every bit of what they had been given. The Mathemagician fills their bowls again and again and again, and Milo wonders why he grows hungrier with every portion he eats.

Milo eats nine servings, Tock eats eleven, and the Humbug eats twenty-three without ever looking up from his bowl. The Mathemagician blows his whistle and the pot is removed from the cave and the miners return to work. The Humbug is now twenty-three times hungrier than he was before and thinks he is starving. The Dodecahedron says they just ate the specialty of the kingdom, subtraction stew.

In Digitopolis, the more one eats, the hungrier one gets; the citizens have their meals when they are full and eat until they are hungry. This way, if a person does not have anything at all, he always has more than enough. It is a simple thing: the more one wants, the less one gets, and the less one gets, the more one has. It is simple math. The Mathemagician finds it curious that Milo only eats when he is hungry and wonders if he then only sleeps when he is tired.

Suddenly the travelers are transported to the Mathemagician’s workshop; he explains that the best way to get from one place to another is to erase everything and begin again. It is a strange, circular room with sixteen tiny arched windows which correspond exactly with the sixteen points of the compass. Everything is numbered by its height, weight, width, and depth. Any tool used for measuring hangs from the ceiling next to a giant notepad set on an easel.

Milo asks if the Mathemagician always travels that way, and their host says he usually takes the shortest distance between two points. If, however, he has to be in several places at once, he simply multiplies. He shows his guests how to make things disappear by a mathematical formula whose answer is zero, and Milo asks to see the biggest number there is. He shows Milo the largest number he has ever seen: a giant number 3, twice as tall as the Mathemagician. Milo says he meant the longest number ever, and the Mathemagician shows him a huge number 8, nearly as wide as the 3 is high.

Milo looks to Tock for help, and Tock asks the Mathemagician to...

(The entire section is 663 words.)