Comments on: Carry bits and group cohomology

By: Primary School Arithmetic and Group Cohomology « Mathematics under the Microscope

Thu, 25 Dec 2008 09:36:09 +0000

[...] that he had been speaking prose all his life. I was recently reminded (by Mikael Johanssons’ blog) tha tall my life I was calculating 2-cocycles.Indeed, a carry in elementary arithmetic, a digit [...]

By: More math education « The Unapologetic Mathematician

More math education « The Unapologetic Mathematician — Sat, 14 Apr 2007 14:36:00 +0000

[...] manipulations for any student to understand why before how. I only just recently found out (via Michi’s blog) that place-value addition “really” arises from group cohomology. Did my not knowing [...]

By: Michi

Michi — Wed, 14 Feb 2007 07:52:36 +0000

increpation: You are, of course right, in general. For the full Hochschild cocycle condition, you’ll want the last term to be right multiplied by c as well.

The clou here is that in the group cohomology ring
H(G,Z/10)
in which we’re doing all of this, we end up actually viewing Z/10 as a trivial module; thus vanishing all the left and right actions outside the f.

By: increpatio

increpatio — Tue, 13 Feb 2007 18:57:25 +0000

By comparison with the planetmath and wikipedia entries on group cohomology, should the cocycle condition

f(b,c)-f(a*b,c)+f(a,b*c)-f(a,b)=0

have the first term multiplied by a?

Of course, then it’s wrong; unless you’re defining some sort of trivial action I’m not seeing.

(I would like to get the example clear in my head; I don’t know enough group cohomology : ( )

Thanks,

By: Per Vognsen

Per Vognsen — Thu, 19 Oct 2006 00:46:35 +0000

Good stuff. If you go to Google Groups and search for old posts by James Dolan you’ll find a handful of posts where he talks about this connection in quite some detail.

By: Alexandre Borovik

Alexandre Borovik — Mon, 28 Aug 2006 14:49:34 +0000

A nice one. It is one of those observations which deserve to be much wider known. I have no Knuth on hands, it would be interesting to check whether he mentions this property of carries in his “Art of computer programming”.

By: sigfpe

sigfpe — Sat, 26 Aug 2006 00:06:51 +0000

Part of this was originally presented to me as a joke. You can only tell it to someone who’s a good enough mathematician to understand basic group cohohmology but who hasn’t actually studied it yet. (This must count as the smallest demographic for a joke – but I was roughly in it at the time.) You say “I bet you’ve been doing group cohomology since you were a kid” and when they deny it you start describing the 2-cycle above and wait for them to get it. While not particularly funny, it does have the unique virtue of being a joke, not about mathematics, or mathematicians, but completely *in* mathematics.