Tuesday, June 7, 2011

summer course ...

"power of observation" (asso0ciated games ... ??? ...) vs "decoration" .... ??? .... ??? .... ???? ....

cubic reciprocity mathematica program ... ??

?? hyperlemniscate ...

20th roots of unity ... table of galois groups ... ??? ...

?? maybe try "square lattice" cheating proof of 2 squares theorem ... challenge to find flaw ... ??? ... after trying to actually trick them ?? ....

???? escher ... ????? .....

?? "double coset" interpretation of certain moduli spaces ... ???? ..... (and / or stacks ... ????)

?? "sprinkle fairy dust in kaleidoscope" and ... "theta series" ..... ????? ..... ?????? ...... ??? "gauss sum" .... ????? .....

?? "covering space" idea as arguably mere way of putting more fundamental idea in "geometric" form ??? ....

??? my experience ... mostly getting only chance to talk about stuff i _don't_ understand, and really wanting chance to talk about stuff i _do_ understand .... continued pressure even here (... ??? ...) to lean in direction in which i don't understand .... tension .... ?? perhaps see some mixture of both tendencies ... not sure which mixture ... more in one direction or another .... ???? ....

?? also my own uncertainty about what is it that i understand .... ?? actual fluctuation (at the very least) in both directions .....

?? tying in these uncertainties with general uncertainties about ... ?? lots of other stuff??? .... ???aiming too high vs aiming too low .... ????? relationship to possibilities of just completely flopping in all sorts of ways ....

??? still viewing big punchline (?? ...) of course (pun?) as ... ??? bit about ... "lagrange extrapolation" as "say anything", justifying "converse" aspect of "galois theory" .... ??? ..... ???? no idea if it'll actually work out that way though .... ???? ....

??? puzzle ... can you define this in terms of that ?? ....

this = less than on N ; that = addition on N ..

this = less than on N ; that = mult on N ... ??? ....

and so forth ....

??? "there's not enough information in multiplication of natural numbers to tell you about the (...) order structure on the natural numbers .... it can't tell you, because _it doesn't know_ !!!!!! ......" ....

??? "more powerful power of observation" =?= "more desctructive (??? ...) graffiti" .... ????? ... ??? "vandalism" .... ???? .... ??? ....

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