The Phantom Tollbooth

Partway up the stairs to Infinity, Milo realizes his climb will never end. Tired, he sits. Another boy appears, but he consists only of his own left side, or 0.58 of a person. He belongs to a typical family, and average families have 2.58 children; he’s the .58 part. Milo protests that averages are imaginary; the boy responds that they’re useful nonetheless. He gives the example of someone with no money in a group of five people, four of whom have an average of $10 each: All five members thus average $8 apiece, so the broke person now has some cash.

The .58 boy offers other examples, like a rat cornered by nine cats who, given the number of creatures involved, averages 90% cat. Milo objects that these are impossibilities, but the boy counters that even impossible things can be calculated, and sometimes they’re useful to know, like the properties of infinity. Realizing he has much to learn before he can rescue the princesses, Milo returns downstairs.

To the Mathemagician, Milo asks why some things that are correct seem nevertheless not to be right. The Mathemagician, with tears in his eyes, agrees and says it’s been that way since

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