“Don’t be too sure,” said the child patiently, “for one of the nicest things about mathematics, to anything else you might care to learn, is that many of the things which can never be, often are. You see,” he went on, “it’s very much like your trying to reach Infinity. You know that it’s there, but you just don’t know where–but just because you can never reach it doesn’t mean it’s not worth looking for.”

The Dodecahedron man in The Phantom Tollbooth

So says the .58 child in Norton Juster’s masterpiece children’s book The Phantom Tollbooth (the child is part of an average family with a mother, father, and 2.58 children–he’s the fractional son). I’ve written about The Phantom Tollbooth before because it’s so full of wonderfully odd explanations of concepts. Milo, the main character, and his retinue make it to Digitoplis where numbers are mined and sent around the world (though they are highly valuable it’s alright when a few numbers drop to the ground because the broken ones can be used for fractions).

They also eat subtraction stew–the more you eat, the hungrier you get. When Milo asks to see the biggest number in the kingdom, he is shown an extremely large 3–it took 4 miners to dig it out. He tries to explain that he wants to see the number of greatest magnitude. The Mathmagician (ruler of the land of Digitopolis) tells him to think of the biggest number possible, and then add one. And then add one again.

“But when can I stop?” pleaded Milo.

“Never,” said the Mathemagician with a little smile, “for the number you want is always at least one more than the number you’ve got…”

Sometimes I wonder if reading The Phantom Tollbooth at a young age gave me a head start on my math career. Thank you, Milo.