An analogy is a raft you use to cross a river

In this Better Explained video, how the right analogies can make math joyful. "Numbers are like rocks." But what happens when the number is 0 or -1? The analogy breaks down. "OK, numbers are like points on a line," with zero at the center. But where on the line does the square root of -1 go? "OK, let's add another line at 90 degrees to the other number line, where imaginary numbers go."