© | Dror Bar-Natan: Talks: CMU-1504

# Talk Video

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0:26:15  So, by renaming the nails, you get a bijection from $[[x,y],z]$ to e.g. $[[y,z],x]$. Is this obvious without considering the visual? Isomorphismes (talk) 19:39, 19 October 2015 (EDT)

- I don't think I said that. "Dropping a nail" is the same as setting $x=e$ or $y=e$ or $z=e$, and it is easy to convince oneself that any one of these substitutions maps $[[x,y],z]$ to $e$. (And the same is true for further-iterated commutators, such as $[[[w,x],y],z]$, etc. --Drorbn (talk) 19:55, 19 October 2015 (EDT)

0:33:11  ah! I didn't know Boas Katz was your student! I saw that video too and tried to make an R script of Arnol'd's proof: http://isomorphism.es/post/113720283271/commutator

I'm thinking of redoing it as HTML + Javascript, where users can click-and-drag either the coefficients or the roots...

Either way, I think middle-school & high-school students would like to see this, or play with your Mathematica file in general (if their school has mathematica ---- an upside of R is that it's a) free and b) runnable online without an install (http://www.r-fiddle.org/#/fiddle?id=Ggh3OHmt&version=1)). Isomorphismes (talk) 22:12, 20 October 2015 (EDT)

-- Anybody's free to play with my code, it is available from the parent page of this video (Talks/CMU-1504) as "Commutators-Slides.nb", with more under the "pensieve" link. Though I wrote the code for me to use, and it is very finicky. An improved stable version in a free and browser-executable platform would be terrific! --Drorbn (talk) 06:46, 21 October 2015 (EDT)