The pleasure of finding things out

Just something quick. Here's a link to a Horizon programme from the early eighties featuring Richard Feynman. Really great man who makes so much sense.

http://www.bbc.co.uk/iplayer/episode/p018dvyg/horizon-19811982-9-the-pleasure-of-finding-things-out

enjoy

more mathematics that just seems wrong

I've been really interested in ideas based around mathematics lately. I have to admit that in many cases I couldn't work the proofs out for these math items, but I do understand them when they are explained to me - I suppose it's a case of being able to follow ideas but not having the tools to solve the problems myself.

Anyway here's a little intrigue.

What is the solution to this problem?  1+2+3+4+5+6+ ... to infinite.

Well believe it or not the answer is  minus 1/12 (yes that's correct).

Now I know this seems completely wrong, but the use of this knowledge, especially in quantum theory shows that it is, until proven otherwise, correct. It is used to make calculations and predictions in quantum mechanics, all of which appear to correctly describe nature.

So how can that be when 1+2+3+4+5 clearly equals 15. Well as I understand it the minus 1/12 is correct for the whole sequence to infinite, but breaks down once we place a finite limit on the sequence. I'm not going to show the proof here, but if your interested look at this.

Youtube - numberphile video called

ASTOUNDING: 1 + 2 + 3 + 4 + 5 + ... = -1/12