Why the Number Line Freaks Me Out

Math with Bad Drawings

One of my favorite quotes about mathematics is from John von Neumann:

“In mathematics you don’t understand things. You just get used to them.”

On one level, this runs against everything I believe as a teacher. Mathematics should not be an intimidating collection of inscrutable methods! It should be a timidating collection of scrutable methods! We should accept nothing on authority. Everything in mathematics is there to be understood.

And I do believe that.

But I also know that mathematics is full of startles and shocks. I know that even the simplest objects can bury deep secrets.

Take the number line.

20161205084636_00018

Boring, right? Nothing could be more prosaic.

Well, that’s only because you’ve gotten used to it. To my mind, the number line merits only one possible reaction:

20161205084636_00019

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