Friday, January 17, 2014

1 + 2 + 3 + 4 + ⋯ = -1/12

This is making the rounds and I think this is the first time I've seen this. Apparently, the infinite sum 1 + 2 + 3 + 4 + ⋯ is -1/12. Really. And this value is useful in physics (well string theory and some other things). And I feel good because even the Bad Astronomer can't quite wrap his head around it.

This is the video going around...

After that one bothers you goto the followup page they posted with two more videos with some more details, Thanks for the messages. Each had a few bits that helped me.

There are some comments on Quora of people trying to help explain this non-obvious result. This one was useful.


Richard said...

This one ruined (brightened?) my Sunday. It did make me look up a bunch of articles and remember how much math I don't remember. It is internally consistent. I think the video guys flub the assumptions a little bit so it appears to be magic.

Howard said...

Scientific American weighs in and isn't happy with the video,

Also the Bad Astronomer followed up.

Skull in Stars walks through it and then gives a physics example involving Casimir force where it works.