As I’ve mentioned before, I am utterly thrilled by the concept of imaginary numbers. An imaginary number is defined as the square root of negative one, which is an impossibility, because any number squared has to be positive.
During algebra class a couple of weeks ago, I caught myself literally choking back tears of joy over the fact that such a thing could exist. I realize this makes me the biggest geek in three counties, but really: How could any thinker fail to be delighted by the existence of something that can’t exist? The mind reels.
More wonderful was my instructor’s explanation. He told how imaginary numbers got their name: The word “imaginary” was a derisive term used to ridicule the theoretical mathematicians who had come up with the concept. The name stuck — a circumstance my instructor found unfortunate. An imaginary number, he explained, is just as real as any other number; the problem is that we simply haven’t figured out a practical application for it.
His explanation delighted me almost as much as the concept itself. I couldn’t put my finger on why I liked it so much until a few days later, when it came to me that imaginary numbers are perfect expressions of God, who is sometimes mistaken for (or derisively — and inaccurately — described as) a figment of someone’s imagination simply because our limited human perception hasn’t yet expanded sufficiently to grasp the nature of infinity.
Like God, an imaginary number is incorporeal. We can’t see it, touch it, or offer tangible proof of its existence. Matter can’t define it. Yet when we use it correctly in a problem, it always leads us to the right answer.
Isn’t it wonderful to think of such a thing?