Obviously, on the face of it, exponential growth is what you want out of your “exponential church.” But you need to think clearly about which exponent you want, not just that you want exponential whatever. Let me use the number 2 as a simple example.
- If your exponent is positive and greater than unity, you’ll get somewhere. Thus, 22 = 4 and 23 = 8 (you’re really on a roll when you can cube things.)
- If your exponent is unity, you’ll get nowhere, thus 21 = 2.
- If your exponent is zero, you’ll get unity and nothing else, thus 20 = 1, and you’ll be “back to square one” in every sense of the word.
- If your exponent is positive and the denominator is greater than unity, you’ll get a nice root, thus 21/2 ~ 1.414 (square root of 2) but you’ll end up with less than you started.
- If your exponent is negative, you’ll get a reciprocal of what it would be if it were positive, thus 2-2 = 1/4 and 2-3 = 1/8. In cases like these where the exponent is less than -1, you end up going in reverse.
- If you end up with someting like 21/0, things either go to infinity or blow up, depending on how you look at it.
The most interesting case, from a theoretical view, is -11/2 = i, the imaginary number.
So you can talk about exponential church all you want, but unless you pick your exponent carefully, the result may not be what you wanted!
I am confident that examples of all of these in the church world can be found.
And don’t be quick to disparage the imaginary number either; the whole world of complex analysis, with its use in electrical engineering and vibrations, was developed from it.