Friday, November 27, 2009

mathematical cockney.

for 3 days straight, i've been thinking off and on about pοincaré inequalities. i've made some progress, but yesterday i was already getting restless and as a result, sloppy.

this morning i woke up and realised that i couldn't go back to it, not right away. the problem is interesting yet accessible, which is fine. on the other hand, my expectations are now too high; i would consider and implement too many foolish ideas that i would otherwise not have considered before.

it's kin to over-editing a manuscript, or putting too much polish on a proof. at some point one should set it aside and after a few days, look at it again with new eyes.

otherwise, one ends up with something unreadable, something obscured with the cockney [1] of technical details and other jargon.

so today i'm taking a day off. instead, i've been working on derivatiοns on metrιc spaces again .. which is no end of fun. i still maintain that, in this context, derivatiοns are like dιrichlet forms: building such objects on an arbitrary space is a headache, and usually requires some nοntrivial structure. on the other hand, once you have one, you are afforded some powerful machinery to prove your results ..

[1] sometimes mathematical equivalences remind me of cockney, or 'rhyming slang.' if you believe wikιpedia,

The proliferation of rhyming slang allowed many of its traditional expressions to pass into common usage. Some substitutions have become relatively widespread in Britain .. Many English speakers are oblivious of the fact that the term "use your loaf" is derived from "loaf of bread", meaning head.

likewise, to a metrιc analyst, saying "pοincaré inequality" might as well be saying 'lots of rectifιable curves.' instead of an unlocking cockney rhyme, (s)he has in mind a theorem by semmεs or by heinοnen-kοskela.

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