Why should "e" exist?
September 9, 2012 12:16 AM Subscribe
Why is the number "e" so...
I get that its important and that it comes up everywhere, in interesting integrals, differential calculus, statistics, everything. So I'm not asking about what cool places this number pops up, but rather why it should pop up in so many of these places. Philosophically, I guess, why should a number like e exist?
For example, Pi has a very intuitive explanation: the circumference of a circle divided by its diameter. And the fact that it comes up in non-geometric problems, I guess, can be explained by the concept that these geometries are fundamental parts of the physical and mathematical universe, and "pi" is a fundamental part of those.
But what about "e"?
What universal concept or physical property of the universe does it represent. What reason is there that it should be so pervasive and important.
BONUS: under different conditions (more dimensions in our universe, or the presence/absence of string theory, or some other sci-fi universe) would math exist as we know it, especially - would the number "e" exist or have the same value?