AtDTDA: [38] pgs. 1079, 1081 "Talk about anomalies in Time!"

[robinlandseadel at comcast.net]

Things are about to get a whole lot more fictional. The infinite whorls of 
possibility, all the the possible insinuated fictions come into play from 
here on to the end of the novel, expressed as joy in possibility.

The Professor, having reconnoitered with Kit in the Scottish Cafe:

          . . . .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." 

          He spent awhile contemplating this. Zermelo had been a docent 
          at Gottingen when Kit was there and, like Russell, had been 
          preoccupied with the set of all sets that are not members of 
          themselves. . . .

From: Can a Mathematical Idea Have Political Import?
HYPOTHESES - A Matter Of Choice
By Jim Holt

          What is this much-invoked thing called the axiom of choice? 
          Is it really devoid of political significance, as Sokal and Bricmont 
          claim? Or could it turn out to pack an ideological punch beyond 
          the imagination of even the most wild-eyed Left Bank postmodern 
          theorist?
 
          To understand what the axiom of choice is, start with this homely 
          example, apparently thought up by Bertrand Russell. Suppose 
          you have an infinite number of pairs of shoes and you want to pick 
          out one shoe from each pair. There is an obvious rule for doing this: 
          Take the left shoe from each pair (or use the right-shoe rule—it 
          doesn't matter). Now suppose you have an infinite number of pairs 
          of socks and you want to select one sock from each pair. Since 
          socks in a pair, unlike shoes, are identical, there is no rule for 
          defining a set that consists of precisely one sock from each pair. 
          The choice for each pair would have to be arbitrary; and since 
          there are infinitely many pairs, that means an infinite number of 
          arbitrary choices. Here is where the axiom of choice comes to the 
          rescue. It allows one to assume the existence of such a "choice 
          set," even though there is no rule for constructing it. . . .
 
          . . . .Today, mathematicians are overwhelmingly pro-choice. 
          Without the axiom of choice, much of modern mathematics 
          would simply not exist. . . .
 
          . . . .But wait. Subversion lurks. Let us go back to the year 
          1924. The scene is the Scottish Café, in the city of Lvov 
          (then in Poland, now in Ukraine). Among the logicians 
          and mathematicians who haunt this bohemian spot are 
          Stefan Banach and Alfred Tarski. Together, using the axiom 
          of choice, they come up with a theorem that is literally incredible: 
          It is possible to take a solid sphere, dissect it into a finite number 
          of pieces, and then, without stretching or bending those pieces 
          in any way, reassemble them to form two solid spheres each 
          of which is the same size as the original. Equivalently, it is 
          possible to take a solid sphere the size of an orange, dissect 
          it into a finite number of pieces, and reassemble them to form 
          a solid sphere the size of the sun.
 
          The Banach-Tarski paradox, as this theorem came to be called, 
          certainly appears dangerous. It is a sort of mathematical miracle 
          of the loaves and fishes, one that threatens to abolish scarcity, 
          that linchpin of bourgeois economics, and usher in a postcapitalist 
          utopia rather like the one envisaged by Marx. (Just think of what 
          it would do to the gold market.) And it all hangs on the axiom of 
          choice. . . .

http://www.csub.edu/~mault/mathematicalideas.htm

The next Professor Vanderjuice episode is the purest of Dues ex machina
demonstrations, down to archetypical specifics:

          . . . .Then the dome of the courthouse began to lift, or expand 
          skyward, till after a moment I saw it was in fact the spherical 
          gasbag of a giant balloon, rising slowly from behind the dome, 
          where it had been hidden. Sort of that pea-and-sun conjecture 
          again, only different. Of course it was the Chums of Chance, 
          not the first time they'd come to my rescue-though usually it 
          was from professorial inattention, walking off cliffs or into 
          spinning propellers .... But this time they had rescued me from 
          my life, from the cheaply-sold and dishonored thing I might have 
          allowed it to become. . . .

As someone once said:

          ". . . .there's still time to change the road you're on. . . ."

And it appears that Lvov might well be Kit's personal Shambhala:

          "What just happened?" Kit feeling dazed. He looked around 
          a little wildly. "I was in Lwow-" 

          "Excuse me, but you were in Shambhala." He handed Kit the 
          glass and indicated one stamp in particular, whose finely-etched 
          vignette showed a marketplace with a number of human figures, 
          Bactrian camels and horses beneath a lurid sun-and-clouds effect 
          in the sky.
 
          "I like to look at these all carefully with the loupe at least once a 
          week, and today I noticed something different about this ten-dirhan 
          design, and wondered if possibly someone, some rival, had crept 
          in here while I was out and substituted a variant. But of course I
          found the change immediately, the one face that was missing, your 
          own, I know it well by now, it is, if you don't mind my saying so, the 
          face of an old acquaintance .... " 

          "But I wasn't ... " 

          "Well, well. A twin, perhaps."
          AtD, p. 1081 

As regards bilocating Shambhala & Lwow, the evidence is in the stamps:

http://tinyurl.com/56wm5w

http://en.wikipedia.org/wiki/Lviv

http://against-the-day.pynchonwiki.com/wiki/images/e/ec/ATD_stamp.gif

. . . .there's three towers with a lion under in Lwow, the "Tibetian Chamber of
Commerce stamp has a lion under three Mountains. 

          Maybe it's not the world, but with a minor adjustment or two 
          it's what the world might be.