Scott: I am bad at math.

Jonah: You are good at math.

Scott: No, I really am bad at math.

Jonah: No, you really *are* good at math.

Nisan: Esteemed colleagues, it is no use! If you continue this exchange, Scott will continue to believe they are bad at math, and Jonah will continue to disagree — forever!

Scott: Thank you for the information, but I still believe I am bad at math.

Jonah: And I still believe Scott is good at math.

Scott: And I *still* believe I am bad at math.

Nisan: Esteemed colleagues, give it up! Even if you persist in this exchange, neither of you will change your stated beliefs. In fact, I could truthfully repeat my previous sentence a hundred times (including the first time), and Scott would *still* believe they are bad at math, and Jonah would still disagree.

Scott: That's good to know, but for better or for worse, I still believe I am bad at math.

Jonah: And I still believe Scott is good at math.

Scott: Ah, but now I realize I am good at math after all!

Jonah: I agree, and what's more, I now know exactly how good at math Scott is!

Scott: And now I know that as well.

Sure, I understand the identity now of course (or at least I have more of an understanding of it). All I meant was that if you're introduced to Euler's identity at a time when exponentiation just means "multiply this number by itself some number of times", then it's probably going to seem really odd to you. How exactly does one multiply 2.718 by itself sqrt(-1)*3.14 times?

You simply measure out a length such that, if you drew a square that many meters on a side, and also drew a square 3.1415 meters on a side, they would enclose no area between the two of them. Then evenly divide this length into meters, and for each meter write down 2.7183. Now multiply those numbers together, and you'll find they make -1. Easy!