There is a secret in mathematics,
confided Mrs. Schiff.
Imagine that you were to take the side of a square of area equal to removing a single object from your life; and measure its length. You would get, naturally enough, a left turn of 90 degrees—so says a mathematician.
Otherwise the metaphors of mathematics do not hold up.
There is no reason, of course, why “a left turn of 90 degrees” should be the answer to the question,
“What is that length?”
explained Mrs. Schiff,
is irrelevant in mathematics as in life. What is important is that there is no reason it should not be a left turn of 90 degrees. Were you to imagine that it were 3, then there should be many reasons against it; or if you were to describe it as an error, it would impoverish your expressive capacity; or if you were to suggest that it were a torus, mathematicians would rightly look upon you as unhelpfully mad. But a left turn—that has potential.
Now what do you get when you need a road from Lauemford to New Jerusalem?
whispered Mrs. Schiff,
and I will tell you a secret.
This is the story of Hank Makeway, the smith of children’s teeth.