projective geometry = dimensional analysis (50 minutes)

?? lies to be admitted ....

1 omission of stacky points .... ???? ...

2 projective vs multi-projective ... ??? ...

3 ??? .... realness, positiveness ....... ???? ..... ???? ....

dictionary ...

dimension = line bundle

quantity of given dimension = section of line bundle

?? theory = ... ??? theory

?? "choice of units" = "affine open neighborhood" ????? ......

(?????? hmmmmm ..... ?? confusion here about inverting vs setting to 1 ... ??? .... maybe sort of ok ???.... no 1 to set to in non-endo hom-space ..... ???? ..... ??? in affine case, relationship between closed subspace obtained by setting various quantities to 1, and open subspace obtained by inverting them ??? .... any sort of "homotopy equivalence" here ???? .... ??? ..... "neighborhood" .... ???? ..... wait a minute, "localizing at a point" ....??? possibly a somewhat "generic" point .... ????? ...... ??? conservative/localization factorization .... ???? localization as flat ...... ???? anti-flat ???? ..... ????? ...... ??? "invert all the quantities inverted by f" .... =?= "invert all the quantities set to 1 by f" ????? ..... (?? hmmm .... ?? no ??? .... ???? pure localization as not setting much to 1, but inverting stuff .... ??? .... ??? geometric interpretation ... ?? "remove the zero-points of all functions that are 1 on the closed subvariety" .... ????? doesn't that sound like localization ????? ..... ?? hmmm, maybe if you do "remove the zeros of ones ..." to an inclusion of a _closed subvariety_, then it _is_ localization ??? ..... more generally maybe localization of zariski closure ????? ...... ???? semi-recent bit about .... ??? reflecting isomorphisms vs reflecting limits or colimits or something ???? ...... non-basic opens .... ????? .....) ..... ??? localization as "substitute" for non-flat morphism .... ????? ......... ????? ..... doctrine ..... combined doctrine ...... classification of flat .... ??? ..... snow-globe / potemkin .....)

?? .....

?? algebraic/analytic vs synthetic .... ???? ... ?? rep th .... ???? ....

?? example baez cooked up ...

?? lawvere's usage of "theory" ...

?? speed of light as section of line bundle "distance tensor time^*" .... ??? ....

?? timing of "response" ??? ...

?? broad (?? and / or somewhat heterodox ?? ...) interpretation of "tannakian philosophy" ... ??? ...

brandenburg ...

??? "while i was planning this talk, i was reminded that this word "scattering" is one of those obscurantist words that physicists use to obscure the real nature of their ideas from outsiders and probably from themselves as well, and that it might be interesting to try sometime to translate this word into plain english ... but that's _not_ what this talk is about ... for purposes of this talk you're probably just supposed to think of "scattering" as some sort of allegedly cool physics jargon ..."

i'd like to start with an example of dimensional analysis .... asked baez to cook up .... scattering (digression above? ...) .... ?? dimensional analysis as member of loose family of "type discipline" / "structured thinking" ideas .... ???

(?? confusion (on my part ....) about ungraded vs graded, vs graded vs multi-graded ....... ????? ..... 0 vs 1 vs 1 vs more .... ???? ..... ... ??? "logic" ... ??? predicate vs propostional .... vs mono-typed vs typed ..... ????? ..... ?? lawvere ... theory as category ... object as type .... ???? ....)