Crazy math result

[thecynic]

This link proving that sum of natural numbers i.e. 1 + 2 + 3 + .. = -1/12 was posted to my twitter feed. I figured many here would find it interesting as well:

 

 

Apparently the result is used a lot in modern physics. This definitely undermines my faith in theoretical physicists.

[Hielko]

Assuming I understood the video correctly this kind of math is also used to explain the casimir effect, and other quantum mechanics related stuff. That's not theoretical physics anymore, but actually phenomena that have been measured and proven.

[randomep]

 

I didn't have the patience to sit through the video but what if I can prove that the result is infinity, then who is right?

 

Anyway, my point here is actually that now I have that much more respect for Jeff Gundlach; I read that he dropped out of his mathematics PhD program because he wanted to prove infinity doesn't exist. OMG could he be right?

 

 

[thecynic]

That's not theoretical physics anymore, but actually phenomena that have been measured and proven.

You are right. Perhaps the universe is so strange that strange results are needed to make sense of it. Maybe we'll have some theories in future which don't have to rely on positive numbers adding up to a negative number.

[ericd1]

I think with a little online checking you will find there's an error in the math.  :)

[thecynic]

 

I didn't have the patience to sit through the video but what if I can prove that the result is infinity, then who is right?

 

Anyway, my point here is actually that now I have that much more respect for Jeff Gundlach; I read that he dropped out of his mathematics PhD program because he wanted to prove infinity doesn't exist. OMG could he be right?

According to wikipedia the self taught number theory genius Ramanujam  http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%8B%AF also thought the sum was -1/12. I'm thinking that one can prove the sum is infinity or -1/12 depending on different assumptions. I am not a mathematician but I do not trust the analytic continuation step which is key to the result in the video.

 

If there is no infinity how would that change our understanding of the world? I guess that'd make for a good dissertation.

[constructive]

It's not regular summation - the addition and equals sign here are misleading since they don't mean regular addition and regular equals. It's Ramanujan summation.

 

http://en.wikipedia.org/wiki/Ramanujan_summation

[thecynic]

I think with a little online checking you will find there's an error in the math.  :)

Before I saw the video I thought the proof was going to be a complete leaky one involving cancelling infinities on both sides of the equation. But I did some online checking and found but the result is still good and accepted by many of the physicists/mathematicians: http://math.stackexchange.com/questions/633285/is-the-sum-of-all-natural-numbers-frac112

 

Apparently, the result is ok because it can be used explain observed physical phenomenon.

[thecynic]

It's not regular summation - the addition and equals sign here are misleading since they don't mean regular addition and regular equals. It's Ramanujan summation.

 

http://en.wikipedia.org/wiki/Ramanujan_summation

 

Thanks, very interesting. Perhaps that's what I'm missing, the original result is just too bizarre.

[johnpane]

This summation has very useful applications to representing risk in investing. The left hand side represents diligent savings of pennies over a lifetime, and the right hand side represents accumulated wealth after a market crash.