Monday, February 24, 2014

The Sum Of All Positive Integers? That's Easy: It's - 1/12

I'll admit I was skeptical about this when I first heard about it, but it turns out to actually be true:

1 + 2 + 3 + 4 + 5 + ... (to infinity) = - 1/12

While it's a completely counter-intuitive result - how can adding a set of strictly positive values possibly end up in a negative sum? - a relatively simple proof of it shows that it's true.  I'm even more impressed by the fact, referred to in the linked video, that quantum physics appears to point in this same direction.  I love stuff like this!

I have to say this reminds me of an unrelated phenomenon in computer science: because of the way numeric values are stored, a positive value that's constantly increased by 1 will (barring intervention by the operating system to prevent it) eventually go from a very high positive value to a very small negative value because of the high order bit eventually flipping from positive to negative (from 0 to 1).  Who knew that was reflecting, in a bizarre way, a functionality of the real world where infinite values are concerned?

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