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Thursday, January 29, 2004

Finished a first read of DFW's infinity/Cantor book a couple days ago. Two things I hope to go back to: The part about limits of point-sets, which is the motivating link between continuity and the less analysis-heavy (and easier for me) material on transfinite nos., reals v. rationals, and cardinality. Also the last few pages on infinite ordinals, which may actually be too compressed to get the inuitive arguments out of properly. It's depressing to realize that I've known certain things about this subject for decades now -- understood the Diag Argument via Martin Gardner in HS, maybe even earlier -- but haven't deepened my understanding since; if nothing else, I got out of this, finally, a clear grasp of why there are as many points on/in a square/cube/n-manifold as a line (segment).

Main thing I like about the book: Despite constant apologies for the difficulty of the material, there are none for its intrinsic interest, which is, I suspect, anethema to a lot of his fiction readership. Which is too bad, because I think he achieves the effect of balance between precision and talkiness more efficiently than in -Infinite Jest-. (Side note: Though he never comes out and plumps for Platonism, his obvious excitement about Cantor's results -- calls one 'nape-tingling' -- suggests leanings that way; would he dig it so much if he thought it was 'just a game'?)

Complaints: I was prepped for him saying misleading things about discontinuities in functions by the review in -The New Yorker-, which was quite correct on this score. (He associates them too closely with undefined points on a given function.) Also, I have a quibble w/ the following:

"If the above [paragraph] seems shifty or convoluted, we can reduce the argument to a simple syllogism: 'Since (1) all numbers are definable by decimals and (2) all decimals are definable by sequences, (3) all numbers are definable by sequences,' which happens to be 100% valid." (221)

Valid, yes, but not an example of any syllogistic form I know of. There's no general valid form that runs: xRy, yRz, therefore xRz. Argument depends (plausibly) on the transitivity of 'definable.'

recently --

Tuesday: 50 Ft Wave @ Silverlake Lounge
Wednesday: Pretty good diss workday
Thurs: Stavroula's practice job talk @ UCLA

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