“But what I told him was the most danger—one of the most dangerous secrets in mathematics which is that the square root—the lowly square root—is the Psychedelic of mathematics. It opens up the Panic Room in your mind that you did not know you had.”

“How?”

“Well, if I say what’s the square root of four, you say two. Okay so an integer gets you to an integer. Now I say what’s the square root of two, it goes from an integer to an irrational number—but it’s an algebraic number. Now I say what’s the square root of -2—suddenly you’re in the complex numbers. So the real numbers are a one-dimensional system but the complex numbers are a two-dimensional—you just broke out of Flatland. Okay well, that’s pretty crazy. What’s the square root of a determinant? Something called the Pfaffian, which you’ve never heard of. What’s the square root of the Pontryagin class? Oh, it’s the Euler class. And now you’re just like: what’s the square root
of vectors and tensors? Oh it’s spinors—and you know objects that require 720 degrees of rotation to come back to normal—and you’re just thinking doesn’t 360 do it for everything?

So the square root is the most powerful Dangerous Drug imaginable.”

— Eric Weinstein