Let us define the number i as equal to the square root of -1.  So i cannot be positive or negative, but all real numbers are positive or negative—so i is imaginary.  I am pretty much the farthest thing from a mathematician, but i strikes me as being something that we think we have some understanding of, but we really don’t, similar to saying “There is either a red square-circle or there is not a red square-circle.”

But the funny thing is, we can perform operations with i:

(2i)(4i) = (2 · 4)(ii), which equals (8)( i²), which equals (8)(-1), which equals -8.

So from something that doesn’t really make sense, namely “i = the square root of -1,” we get something that makes perfect sense.  How much of philosophy is like this?