AtDTDA: [38] p. 1078 Zermelo's Axiom of Choice

[robinlandseadel at comcast.net]

     Zermelo's Axiom of Choice: 
     Let X be a set whose members are all non-empty. 
     Then there exists a function f, called a "choice 
     function," whose domain is X, and whose range is 
     a set, called the "choice set," each member of which 
     is a single member of each member of X. Since the 
     existence of a choice function when X is a finite set 
     is easily proved from axioms 1-8, AC only matters for 
     certain infinite sets. AC is characterized as noncon-
     structive because it asserts the existence of a choice 
     set but says nothing about how the choice set is to be 
     "constructed." Much research has sought to characterize 
     the definability (or lack thereof) of certain sets whose 
     existence AC asserts.

     http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory

[and, yeah—that went over my head like a paper glider, 
tossed from a window three flights up]

     Kit discovered the Scottish Cafe and the circle of more and less 
     insane who frequented it, and where one night he was presented 
     with a startling implication of Zermelo's Axiom of Choice. It was 
     possible in theory, he was shown beyond a doubt, to take a sphere 
     the size of a pea, cut it apart into several very precisely shaped 
     pieces, and reassemble it into another sphere the size of the sun. 

     "Because one emits light and the other doesn't, don't you think." Kit 
     was taken aback. "I don't know . . . ."

     "But staggering subsets, fellows-you see what this means don't you? 
     Those Indian mystics and Tibetan lamas and so forth were right all 
     "along, the world we think we know can be dissected and reassembled 
     "into any number of worlds, each as real as 'this' one." 

I asked before if Professor Heino Vanderjuice was really Professor 
Hubert J. Farnsworth of "Futurama", mainly on the basis of his 
speaking voice and the nature of the character. While it is clearly
a silly concern on my behalf, it is not so silly as to be off the map
for Pynchon:

   "Gweetings, gentlemen, on this Glowious Twelfth!"
    AtD, p. 757

Staggering subsets indeed:

http://www.math.vanderbilt.edu/~schectex/ccc/choice.html

Kit locates Professor Heino Vanderjuice: 

          now strangely youthful, his hair dark again

. . . .seemingly having a successful one-way ride on one of 
those time machines.

          "With so many dead," the Professor reflected after a bit, 
          "it seems disrespectful to them-but I'm glad Scarsdale 
          Vibe is now among their number. Though the company 
          is too good for him. My only regret is that it wasn't I who 
          finally plugged him." 

Kit's somewhat staggered by this subset, having seen the Professor's
work for Scarsdale Vibe.

          "Had a crack at him once, must've been after you'd left for Germany."