The Phantom Tollbooth Chapter 16 Summary
by Norton Juster

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Chapter 16 Summary

A Very Dirty Bird

Milo climbs the stairs to Infinity but realizes he is no closer to the top than when he began—and not much farther from the bottom than when he started. He says he is certain he will never get there. A voice says he would not like Infinity much anyway; it is a very poor place that can never manage to make ends meet.

Milo looks up to see a half a child, neatly divided from top to bottom, standing next to him. Milo says he has never seen half a child before. The boy says it is .58 “to be precise.” His family is quite average: mother, father, and 2.58 children. He is the .58, of course.

The boy is never lonely because every family has a .58 for him to play with. Milo objects that averages are not real, but the boy says they are quite useful. For example, if Milo had no money and was with four friends who each had ten dollars, each of them would have an average of eight dollars. The boy gives more examples, but they only confuse Milo.

The boy patiently explains that one of the best things about mathematics (and many other things one learns) is that many things that can never be, are. Infinity is like that. Everyone knows it is there but no one knows quite where it is; not being able to reach it does not mean it is not worth looking for, either.

Milo walks back down the stairs. As he leaves he smiles warmly, something he does an average of forty-seven times a day.

Milo thinks everyone in Digitopolis knows more than he does; he will have to get much better at thinking before he will be able to rescue the princesses. At the workshop, Milo explains that everything in Digitopolis is much too difficult for him, and the Mathemagician gently assures him that the only thing that can be done easily is to be wrong, which is “hardly worth the effort.”

Milo wonders why even things that are correct do not always seem to be right, and the question makes the Mathemagician sad. He tells Milo things have been this way ever since Rhyme and Reason were banished. Suddenly he is furious, blaming the stubborn King Azaz for everything. He sent Azaz a letter just last month and never received a reply. Milo looks at the letter and sees that it is nothing but a series of numbers; he suggests that perhaps Azaz does not understand numbers.

Everyone understands numbers, claims the Mathemagician, because they mean the same thing in every language. Tock asks permission to rescue Rhyme and Reason, but if Azaz approved, the Mathemagician would never do so for the two of them will never agree. Milo says that if both men agree that they will never agree with the other, they are actually in agreement. Defeated by this logic, the Mathemagician allows them to rescue the princesses.

He warns Milo to watch for the demons; there is something worse, but he can only tell Milo when he returns. He transports the travelers to the edge of Digitopolis. The car will not be able to climb the...

(The entire section is 804 words.)