Here is a famous post by two physicists that obtains the holy grail--it makes those whiney mathematicians cry. (Physics math is so much cooler than math math because we do what is obviously correct and we don't get bogged down worrying about those tedious proofs. *)
Yes, it is the famous proof (actually used in String Theory!) that the infinite sum of the natural numbers is -1/12. Yes that's right:
1 + 2 + 3 + 4 + 5 + .... = -1/12
Don't believe me? Check it out.
* This is true. Usually what we do (such as treating the dy and dx in the derivative dy/dx like algebraic variables in a fraction, and quickly obtaining results that take mathematicians months) works because mathematicians worry incessantly along the lines of "but what about misbehaved functions?" The physicist's response to such concerns is: "meh." Because the real world, at least for the most part, is built on well-behaved functions. Nature doesn't divide by zero.
Well, -1/12 being any kind of sum of the natural numbers doesn't seem to be common sense, to coin a phrase.
ReplyDeleteI couldn't see this one until now, either.