How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

Usually, when someone announces they’re a “nonlinear thinker” they’re about to apologize for losing something you lent them.

Dividing one number by another is mere computation; figuring out what you should divide by what is mathematics.

This didn’t faze Tversky, who relished a good fight, whatever the outcome. “I’ve been in a thousand arguments over this topic,” he said. “I’ve won them all, and I’ve convinced no one.”

In the Bayesian framework, how much you believe something after you see the evidence depends not just on what the evidence shows, but on how much you believed it to begin with.

Indeed, it’s a general principle of rhetoric that when someone says “X is essentially Y,” they generally mean “X is not Y, but it would be simpler for me if X were Y, so it’d be great if you could just go ahead and pretend X is Y, sound good?”