gunnarsen invited me to talk to his students sometime this summer for about a week or ten days... so i should try to plan out stuff to do / talk about ...
he suggested connecting with material about modular curves... child's drawing viewpoint ... which seems somewhat reasonable, i think ... though i was originally idly imagining "galois theory" (in very general sense ...) as topic... might fit together pretty well, perhaps ... ??....
??
covering spaces ... advent ... bread crumbs ... "structure vs symmetry" ... ... and so forth ... ???...
(??what about something about ... ??my experience with ... ??at first thinking that 2-sphere might have some weird covering space ... ??or something ?? ... ???also my experience with ... ??at first thinking that "any symmetric object must be bilaterally symmetric" or something ... yes, that one seems to have been particularly stupid, but ... ???... ??something about my maybe not even really having precise understanding of the question at that point ... ??or something ??...)
???branch points ???? ...... ????? .... ??"moduli ... ? " ... ???...
???sa kuga ... "galois's dream" ... island picture ... ??... !!woozle ... asf, os... something about my woozle experience; see something about "advent" somewhere here...
??"...as an added bonus, each of these methods of problem-solving can also be used as a way of screwing up situations really badly when misapplied ... " ... ??or something ... ??...
??just happened to think of a possibly interesting minor example of "symmetry reasoning" ... sa "wear/carry" vs "ser/estar" ... ???or something ... ???and so forth ... ??? something about vague idea of "broken symmetry" here, maybe?? ... something about ... abstract pattern with perfect symmetry ... concrete manifestations of it with less ... ??or something??? ... hmmm ...
??try thinking of other examples like this?? ...
??something about bit about ... ???microscope ... "double blind" ... ??something about "respect group" of a partition ... ??or something ... and so forth ... ???... ??hmm, maybe relating also to something about "separate but equal" ???? or something ??? ... ... ????... ??hmm, in weird ways ... ???or something ...
??something about integration of functions with symmetry properties... or something... and so forth ... ??something about "overkill" here ???... ??or maybe i'm just over-reacting to what that one guy said that time ... ??... ??hmm, something about hints about _continuous_ groups here ... ???and so forth ... ???...
!!!special relativity ... ???...and so forth ... ???....
??something about vague general phenomenon of ... ??"z/2 as test case / launching platform / or something "... ?? ... ?? here i'm conflating "mirror symmetry as prototypical symmetry" with
??something about "hall of mirrors" and "kaleidoscope" ... ??and so forth, or something .... ????maybe something about non-abelianness here ??? .... or something ... ??something about bug/feature aspect of this ... complicated/fun ... ??or something ... (??what about slightly meta- idea here ... "one person's bug is another person's feature" ... role reversal there ... ??...) ??something about "coming into focus" ...?? ... as angle between mirrors varies ... ??or something ... and so forth ...
??hmm, something about weird memories that i have about playing with mirrors when i was a kid ... also something about that album cover ... ??maybe i should bring some mirrors ?? ... or something ... and so forth ... ???what about where to get kaleidoscopes ??? ... ??a2 vs b2, and so forth ??? ...
(??something about my experience with hall of mirrors ??...)
????hmmm, so what _about_ something about ... ????actually linking together stuff like ... a2 kaleidoscope (and some others...) and "actual galois theory" (...) and covering spaces and modular curves and so forth ... ????what _about_ something about mystery of branch points here ??? .... and so forth ... (something about arnold ... ?? ... ??hmm, something about "singularity" here ... ??)
(??something about ... ??even if you to some extent think that it's a good idea to avoid too much focus on branch points, might get dragged into it to some extent because of something about ... ??understanding how "child's drawing" works ... ??? or something ... ?? ...)
??something about ... "they're as afraid of you as you are of them" ... (or something ... and so forth ...) ??perhaps good as example of symmetry principle that's genuinely useful and powerful where applicable, but then also dangerous where not, as for example in case of man-eating tiger or something ...
religious examples ... ??hmmm, besides "permutations on class of religions" (and so forth...) stuff, there's also ... ???something about ... group theory ideas _in_ some religions ... ??something about ... reincarnation ... golden rule ... relationship therebetween ... "whatsoever you do unto ... " ... ??or something ... and so forth ... ??? ????something about ... cake-cutting ... mule ... and so forth .... ???....
nation examples ...
??what _about_ historical vs contemporary examples here... ??especially something about difference between boundary between them for me vs for my audience .... ???...
??"political philosophy" examples, or something ?? ...
??"social situation" examples ... (which i already hinted at somewhere above i think ... see "man-eating tiger" or something ... ??...)
??see (??for context ? ...) bit i mentioned about big julie's "dice with no spots" somewhere ...
????something about "cutting problems down to size" ... and so forth ... ??or something ... ??something about "dual" ways this can happen?? ... (?? something about "n birds with one stone" vs "don't bother with the non-symmetric birds" ... ??? or something ... and so forth ...) ...or something ... and so forth ... ???something about relationship to "mathematical induction" ... ??something about orbits (??as fewer of them to worry about than of elements ... ???or something ... ) ... ...and so forth ...
??other places to check for where i may have written down relevant examples / ideas ?? ... and so forth ... ??...
??something about _me_ learning... ??something about modular curves os, asf os???...
??something about galois's usage of terminology "group" ... and so forth ... ???.... ??sa lack of time ... (??to perfect terminology, for example ??? ...) .... ???something about "ambiguity" bit .... ???.... ...my translation career ... ??? ...
??also something about "abstract vs concrete" ...
??soemthing about "logic" (and so forth ... "structure" ...) interpretation of cayley diagram (since gunnarsen mentioned something about them.... ?? ...)
??something about ... "keeping track of levels of structure" .... "varying reality" ... ???something about "imaginary numbers" here ??? well, maybe don't try to push that metaphor _too_ hard, since ... ???something about "imaginary" vs "non-real" ?? .... os... asf os... ????might still be able to push it a bit, though ?? ....
ok, i'd like to start with a game...
(most of my games will probably end up being too easy, or too hard, or both simultaneously... or something ... ???... ??something about me being out of practice ... ????...)
i guess this is really a whole bunch of games that are all pretty similar to each other... not sure that i have a name for this game / these games... maybe i should call it "mathematical 3-card monte" or something like that ...
??variations on game ...
???defining one thing in terms of another... "syntactically" ... ??then also something about "semantic" comparison ... ??and so forth .... ????....
??sa summer course ... sa religion ... meta ... os...asf os... sa reincarnation asf ... ???... golden rule ... ??os... asf os... ??sa cake-cutting ... ??...
???sa... "when i was here last time we discussed (or something...) this puzzle about how to express one rational function in terms of another that's at least as asymmetric... in a sense everything that i want to tell you about now is an attempt to explain the secret behind the solution to this puzzle ... which as it turns out is the secret behind the solution of a _lot_ of puzzles ..." ??? ... ???....
??something about "hedgehog" ... (???"hedgehog theorem" ??? ...???) ... ??? ...
??"theory of ambiguity" ... ?? ..."theory of undefinability" ... ??? .... ??nominally (??...), "ambiguity" as "about" word, "undefinability" as "about" thing, but ... ???sort of describing same idea ... ??... ??"irreducible ambiguiity" ... "irreparable" ... ?? ... "inherent" ... "inherent ambiguity of word as related to indefinability of thing under its umbrella" ... thing can't be characterized by word ... ??? .... ???? .... ??"umbrella term" ... "inherently an umbrella term" ... ???"who's buried in x's tomb?" ... ???_is_ that where i first started with the "galois theory = ambiguity theory" slogan ??? ... ... ???"tomb-mate" ... ???.....
??"galois'sprinciple" .... as ["x is definable in terms of y" = "y breaks symmetry more than x" ... with slight subtlety about meaning of "more" here... "qualitative rather than quantitative" ... ?? ... ??also my tendency to often get the principle backwards ... ???probably avoid psychoanalyzing me too much in this respect, for fear of infecting others... ??...]
(sa proverbial shop teacher with missing finger ... might in fact be able to learn from them how not to lose your finger ... or at least, one way not to lose it ... ??unfortunately .... "way to not lose it" vs "way not to lose it" ... ??? ... ??? .... ????? .......)
??so what _about_ which versions of game to start with / middle with / end with ... ????... ??? ... ???....
??? ..."breadcrumbs" ... "structure as breadcrumbs" .... "featureless expanse ..." .... advent ... piglet ... ??as "stupidest person in world" .... undercurrent of nastiness .... ??? .... ... ............ .... ....kuga .... island ... ???"conceptual un/wrapping" ... ????"imagination vs knowledge" .... ????.....
??advent as _punchline_ here??? ... my turn ....
volleyball .... reincarnation ... "my/your/their turn"
???cartoon ... tom biting own tail ??? .... ??? .... .... cake-cutting ....
????double coset interpretation of "moduli space ... " ... cartesian product of homogeneous spaces as non-homogeneous .... (????"separate but equal ...." ..... ?????? .... ???? "diagonal ..." .... "degenerate ... " .... ????....) .... homogeneous components thereof ... ??? ... "classify" ... ?????.... "joint ... " ... ??? ....
???? "at first it seems like they're completely different from you / in a completely different situation ... but then suddenly you realize that if just one little (??? ...) thing is changed .... ???"switched" .... ??? ..."shift of perspective" .... ??? ... then they(??or their situation ... ??? ...)'re really the same ... ???.... ?? ... then you can use this information in different ways .... example : [1["i understand what they're thinking / feeling / experiencing, so we should be able to live in harmony ..."] vs 2["i understand what they're thinking / feeling / experiencing, so i should be able to trick them ..."] ... ] ... another example : [1["you find a complete stranger lying hurt in the middle of the street (??road??? ...), and you think : if this were my friend, ..."] vs 2["you find your friend lying hurt in the middle of the road, and you think : well, if this were a complete stranger i might just leave them lying here, so probably it's ok if i just leave my friend lying here ..." ...]] ..... ???in such examples, either way is a characteristically human way of thinking (... ???...) ... ????and the secret of math (???? ....) is to take this characteristically human mode of thought and exploit the hell out of it in extreme (??? ....) ways .... ??? .... ???? .....
????choosing "bad" symmetry group ... ??? "ok, today i'll try permuting good and evil " .... (???"there are some episodes of the tv show "seinfeld" sort of like that ..." ... ????too dated, or maybe not ??? ...) ???"too big" ??? ... "inappropriate" .... ????not a symmetry of certain particularly relevant structure (??despite counterpoint about how non-symmetry permutations / groups thereof (??? ...) can be very useful in certain ways ... "broken symmetries" ... ???? ....) .... ???? .... ???"in fact good/evil (??also true/false ??? ...) switching is a pretty good (perhaps prototypical ??? .... ???....) example of a "symmetry" probably broken for most practical purposes, but nevertheless often interesting and even potentially useful to think about, though of course (???) dangerous ... ???prototypical (??? ...) example of situation where you should think before you act" ???? ..... .... ???? ..... ??"misere transform" of a "game" ... ??? ... ???? .... funny tendency as to how strategies are affected ... ???idle speculation of mine about "intrinsic / invariant (??under "change of goal") "powerfulness" ("position of control ..." ... ???) of move" ... ???? .... ??? ....
???symmetry as the more useful for you "the more exciting your life is" ... "the more you face the unknown" ... ???os?? ... ????sa "entropy" ??? ....
???... ?? people who say stuff like "it's a dead field ... everything's already been discovered ... all that's left is calculating the nth decimal point ..." ... as idiots .... ???? ...
?? experience of ... ??generation who think they had it hard trying to sympathize with next generation but not quite appreciating how much (or at least in what ways... ??) harder things have gotten...
??? kummer's chemistry analogy ??? (???connection to hilbert(??)'s rng (??) analogy that gunnarsen told me about ??? ...) ...
???kronecker's youth-dream ... ??? "turning ideal numbers into actual numbers" ... ??? ....
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