Does the Square Root of Negative One Exist? (Does God Exist?)

Two short acts. I have tried to write this several times. The current version comes across to me as condescending, but I cannot figure out how to fix that. If you find this writing lacking, please accept my apologies.

Although this is nominally a conversation between a mathematician and a non-mathematician (whom I call an "amathematician") the real point is that it could be a conversation between a theist and an atheist, who are talking about God, not an imaginary number. As it comes out in the following, it is difficult to say whether or not imaginary numbers actually exist. However, it is clear that imaginary numbers are useful to some people, but not to others. Also clear, I think, is that whether or not a person uses imaginary numbers is not an indicator of the quality of the person: a mathematician, scientist, or engineer, is no better nor no worse than a poet, artist, or lawyer.

Likewise, the idea is that whether or not God exists in a physical sense may be irrelevant. What is more important to note is that God makes sense for some people, but not for others. I argue that whether or not a person believes in God is not an indicator of the quality of the person -- and that the world would be a better place if we learned to understand and accept, as equals, those who differ from us on the God issue.

Act I

Amathematician: How can you possibly believe in an imaginary number such as i, the square root of negative one?

Mathematician: What's so hard about that?

Amathematician: Well, if i is a number, is it bigger than 0 or less than 0? Is it more or less than 10, or 100, or 1000?

Mathematician: None of those--it's different. That's not really the right question to be asking.

Amathematician: If i isn't comparable to any number, why do you maintain that it exists?

Mathematician: The number i doesn't exist anywhere on the real line. It is in a different dimension. Do you see?

Amathematician: No, I don't. Look, if you believe in i, but it isn't real, what's the point?

Mathematician: It is very real to me. It helps me to do the things I do. Without it, I'd have a very hard time.

Amathematician: Believing in a number that isn't real helps you live your life? You sound like a sap.

Mathematician: Ah, but i is so beautiful and intuitive and necessary--how do I explain? Let's see....
     Okay, this isn't really the way I think about it, but perhaps it'll make some sense to your kind of thinking. The number i is like a useful abstract concept or, perhaps, a well-defined word in a language.
     With some problems I am trying to tackle, if I can figure out how i fits into the problem, I can then immediately draw on a vast amount wisdom, and use it in my attempts to work toward a solution.
     Not only that, when talking with others like me on how I would tackle the problem, references to i allow them to draw on the same knowledge, to more clearly and more quickly understand the approach I am taking.

Amathematician: I'm starting to understand what you're getting at.... But I get along just fine without the number i. It can't be necessary.

Mathematician: I don't understand how you do that. If you avoid i and the associated body of knowledge, don't you have to reinvent the wheel every time? Won't things be unpredictable? Won't you make mistakes?

Amathematician: No, I do just fine. Although I don't really think of it this way, your metaphor works--I have a language I use to speak about the world, and to speak with others like me.
     The language I use is different from yours. I don't yet fully understand your language, but it may be the case that my language is neither better nor worse than yours.

Act II

Happy ending? This is way to simplistic and way too brief. Perhaps the idea comes across anyway?

Amathematician: You know, although we think in different languages, we often come up with the same conclusions. I suppose that's because, regardless of language, we are both human and both live in the same world. Perhaps, my suspicion that your reliance on i shows a narrowness of focus is misplaced.

Mathematician: Yes, and perhaps I too am mistaken in my suspicion that your avoidance of i indicates a dangerous and unpredictable departure from accepted wisdom.

Amathematician: Perhaps we should work on learning each other's language. If I promise to try using the number i will you give a try to going without it?

Copyright 2005, Lee Newberg. All rights reserved.