No, Godel never did that. Godel, most famously, proved that not all mathematical facts can be proven from a consistent set of axioms expressed in a language suitable for expressing all the mathematical facts.

He did have, unpublished, a version of the ontological proof for God's existence, but that is because he thought that argument worked.

Bertrand Russel worked out the proof that 1+1=2, much to the consternation of David Mitchell that wonders what would've happened if it hadn't been proven:

http://www.youtube.com/watch?v=BE657F9sqyQ

I think you are thinking of Pascal's Wager.

Wherein Pascal said that if you want to gamble a finite set (your years on earth) on either an infinite set of your years in heaven, or a null set of you just dying and being worm food, then you would be stupid if you didn't go all or broke.

That should say "subtract 1 + 1 + ... from itself with a shift".

It puts me to mind of imaginary numbers. You start by defining the impossible, sqrt(-1) = i. Then you can do all sorts of interesting and at times very useful operations using i ( hey I use complex number a lot! ). And some counter intuitive things arise, but only because at the heart of it is this impossible thing that we've put off by defining it in a way that makes it amenable to said manipulation.

I was wondering about the unaccounted-for infinitieth term myself. But that's infinity for you, you can't get there to see what's really going on.

But I'm not about to dispute the mathematical utility of the result, since it appears to be a real thing (albeit way above my pay grade).

In fact, why not use the same approach? ( mathematicians here, feel free to call me an idiot and explain... ).

So I define the Wildcationry number o, such that the sum of S1 is now o rather than 1/2. Then our sum S is a more intuitive o/6 rather than 1/12. Intuitive in the sense that it's clear we've done some redefinition of things to achieve the result.

Any calculator will tell you that infinity looks something like this:

8=======D ------ ( ͡° ͜ʖ ͡°)

(While I'm a mathematician, I'm only a topologist, so take this with a grain of salt.) The reason 1/2 makes sense for S1 is one of analytic continuation. The infinite series 1 + x + x^2 + x^3 + . . . converges to the function 1/(1-x) as long as |x| < 1. But 1/(1-x) is still defined for any x other than 1. So we can smoothly extend the identity 1 + x + x^2 + x^3 + . . . = 1/(1-x) for all x not equal to 1. In particular, x = -1, which gives us 1 - 1 + 1 - 1 + ... = 1/2.

The 1 + 2 + 3 + ... = -1/12 comes from the continuation of a different series, the Riemann zeta function 1^(-s) + 2^(-s) + 3^(-s) + ... for all (complex) s not equal to 1. When s = -1, you get the series in question.

Oscar Wildcat: I realize you probably understand this, but imaginary numbers are no more imaginary than negative numbers. Sqrt(-1) is no more "impossible" then 1 - 2. the i and -i axes are just rotated 90 degrees from the integer axes.

Presumably you mean |x|>=1? But I get the idea; that's a more compelling argument for 1/2 than the clip presents. I am also happy we have drug imaginary numbers into this with the Riemann Zeta function, because I'm just that kind of idiot (grin).

No, I meant |x| < 1 (If that is the place you're referring to). The geometric series only converges if -1 < x < 1.

You could have just said nothing.

So could you.

It's really late, so I can't watch this without waking room mates up.

But, I want to know, which infinity are they referring to? The countable or uncountable kind?

For misrepresenting Popper.

Ad hoc is Ad hoc. If I say the sky is always blue, I can't disprove someone who's seen the sun go down.

"I can't understand this, so it must make sense"

- Several other poeTV users.


So we define a sum S such that the summation of an infinite number of users opinions is undecided (1/2).

That makes sense to me.

"nerrrrrrrrrrds"
-Ogre

I'm going to go with

"I can't understand this because I have an eighth grade education, so maybe I'll just keep my mouth shut." XD

Can you perhaps answer something? That first series (1 - 1 + 1 ...) sure seems like it could benefit from the "clone, shift, and add" process, where you would quickly reach 2S = 1 and then S = 1/2, without the fishy recourse to "eh, let's split the difference". Is there some reason he didn't do that? It's not like he wasn't going to trot out that technique a minute later anyway.

Me? No, I was serious about the eighth-grade education thing.

http://youtubedoubler.com/bpM6

I was lucky enough to see exactly one scene from that video. A friend gave it to me in a WMV file, and I fast forwarded to a random scene -- the one where Armin Shimerman (DS9's Quark) is saying to Marlee Matlin: "If thoughts can do that to water, imagine what our thoughts can do to us."

That is everything I could have hoped to get out of that video, and more.

Given he also appeared in the Atlas Shrugged movies, I'm beginning to thing Alan Shimerman isn't too many degrees away from starting his own Art Bell/Alex Jones podcast.

It's got physicists showing why they shouldn't do heavy math.

@meme I analyzed your comment, and using the using the Urban Dictionary Series Shift, have managed to deduce your meaning. For the uninitiated:

"Matheesha is Amazing Boobs, and a diet coke so yeah basically IRYH physical domestic violence."

#arcane