January 16, 2014

And Now for Your Moment of Math Zen: The sum of 1 + 2 + 3 + 4 + 5 + ... until infinity is somehow -1/12


We know its not mathematical hocus-pocus because this sums shows up all the time in physics and in physics we don’t get infinite answers.

"What's fascinating is that this idea that the sum of all natural numbers is -1/12 actually popped up way back in 1735.

B ut seeing all those numbers actually come out to -1/12 is a whole 'nother story. So watch physicists Tony Padilla and Ed Copeland from the University of Nottingham walk through the process of getting -1/12. The video by Numberphile is fascinating because it's mind-blowing but also because you can see the real joy from the wonderful people proving this. I love it. I love them. I like math a little more. " Chasy Chan at The Sploid

He's right. This is a highly lucid and very rewarding seven minute tour of mathematical thinking. Take it.

Posted by gerardvanderleun at January 16, 2014 7:01 PM
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The interesting thing is that they are working with simple 1st grade math problems using very creative problem solving. I wish I'd seen math like this when I was younger. I might not have hated it so much.

Posted by: Jewel at January 16, 2014 7:55 PM

Less hand wavy explanation at TRF. What is going on is that a growing part of the series is canceled (for physical reasons) leaving behind -1/12.

Posted by: chuck at January 16, 2014 8:11 PM

And a more "philosophical" explanation at TRF here.

Posted by: chuck at January 16, 2014 8:22 PM

It must be why so many people wanted a base 12 numeric system instead of the base ten.

(We already have 12/24 hours/12 months etc)

If you want to learn more about base 12 (dozenal/duodecimal) click my name for a youtube video.

Posted by: Potsie at January 17, 2014 3:48 AM

That made everyone better dressed, richer and more handsome.

Posted by: Vermont Woodchuck at January 17, 2014 4:15 AM

So the sum of all natural numbers is a rational number. By any chance is the sum of all rational numbers also -1/12? The sum of all irrational numbers? (Not trolling; I'm mathematically challenged.)

Posted by: BillH at January 17, 2014 8:56 AM

That just proves that my aversion to higher math was and is totally justified. Once you get to the square root of minus one it's obviously bullshit all the way down no matter how useful it may be.

Posted by: Old Surfer at January 17, 2014 2:25 PM

It's the Judas Principle. He was the negative one out of the twelve.

Posted by: Joan of Argghh! at January 17, 2014 3:57 PM

*sigh* If it's not just a joke, a send-up, then they are dim-witted boobs. Never let physicists try to do a mathematician's job.

Posted by: Grizzly at January 17, 2014 6:04 PM

I first thought it was a hoax, then I saw that there is a lot of support for it, so it might be a very widespread hoax. The problem isn't that the result is counter-intuitive but that it is illogical. You cannot add ever larger numbers to a sum and get a smaller result without changing the definitions of "add" or "sum" or "larger". So, it seems that this is the essence of "mathematical hocus pocus". Something is hidden here.

Lewis Carroll demonstrated that 2+2=5 but he divided by zero to make it so. Perhaps something like that is happening here. Mathematical "sleight of hand".

Or, like the non-Euclidians showed that parallel lines do intersect, but they have to warp the plane to make it so, maybe the zeta function changes the meaning of numbers.

I am probably showing my ignorance here. Somebody teach me!

Posted by: BroKen at January 21, 2014 3:46 AM

I first thought it was a hoax, then I saw that there is a lot of support for it, so it might be a very widespread hoax. The problem isn't that the result is counter-intuitive but that it is illogical. You cannot add ever larger numbers to a sum and get a smaller result without changing the definitions of "add" or "sum" or "larger". So, it seems that this is the essence of "mathematical hocus pocus". Something is hidden here.

Lewis Carroll demonstrated that 2+2=5 but he divided by zero to make it so. Perhaps something like that is happening here. Mathematical "sleight of hand".

Or, like the non-Euclidians showed that parallel lines do intersect, but they have to warp the plane to make it so, maybe the zeta function changes the meaning of numbers.

I am probably showing my ignorance here. Somebody teach me!

Posted by: BroKen at January 21, 2014 3:46 AM

OK, my initial reaction seems to be the right one. The first sum of alternating zeros and ones does not converge so its result is NOT 1/2. And there seems to be a problem of adding a coverging series with diverging ones. It is inconsistent.

Here are a couple of links:

http://scientopia.org/blogs/goodmath/2014/01/17/bad-math-from-the-bad-astronomer/

and a simplier synopsis:

http://freethoughtblogs.com/pharyngula/2014/01/17/the-sum-of-all-natural-numbers-is-not-112/

I guess the bottom line is that you can't add ever larger numbers and get a smaller result. It isn't just bad math, it is bad logic.

Posted by: BroKen at January 22, 2014 11:15 AM

BroKen,

Yeah, that's my first thought. The initial postulate is where I have a problem. Is infinity even or odd and does that question even make sense? Taking an "average" of the even/odd results seems to me where the mistake actually is.

but I'm not a mathematician.

Posted by: pdwalker at February 3, 2014 8:32 AM
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