AtdTDA: [38] pgs.156, 1080, 1084, 1085 Where he should really be [Re: Quaternion Julia Sets]

[robinlandseadel at comcast.net]

         grladams:
          OMG this is cool! Lot's o' little cliffs and crannies for spying 
          on other surfaces while the topography slips out from under 
          you, kind of like reading ATD!

http://www.youtube.com/watch?v=s27n3QzuE4E&feature=related

I got the same sense, themes and characters submerge, then reappear, 
joined by harmonizing themes and characters. Quaternions and the 
Axiom of Choice has everything to do with this book. I don't quite 
understand it quite yet, but I feel just like Miles Blundell. The Against 
the Day Pynchon Wiki has a good, short, squib on Quaternions with 
a lot of good links:

          130; In mathematics, quaternions are a non-commutative 
          extension of complex numbers. They were first described by 
          the Irish mathematician Sir William Rowan Hamilton in 1843 
          and applied to mechanics in three-dimensional space. At first, 
          quaternions were regarded as pathological, because they 
          disobeyed the commutative law ab = ba. Although they have 
          been superseded in most applications by vectors, they still find 
          uses in both theoretical and applied mathematics, in particular for 
          calculations involving three-dimensional rotations. James Clerk 
          Maxwell first published his famous theory describing electricity 
          and magnetism as a set of twenty equations, but he was later 
          able to reformulate it as four equations using quaternions. 
          Heaviside translated these into four vector equations, the form 
          typically taught in basic physics classes today. Heaviside's 
          vector version is compatible with Einstein's special relativity, 
          but the quaternion form is not. . . .

http://against-the-day.pynchonwiki.com/wiki/index.php?title=Q

http://www.youtube.com/watch?v=To_FmzOoJe8&feature=related

http://www.youtube.com/watch?v=lwB7KzG9awk&feature=related

It's a of mapping of simultaneity in time, displaying features of 
synchronicity: a whole lot of the same thing seems to be happening, 
and it all seems to be in harmony:

          "Popular fellow, this Rinehart," Kit remarked. 

          "A Harvard pleasantry from a few years back," explained 
          Scarsdale Vibe, "which shows no sign of abating. Uttered in 
          repetition, like this, it's exhausting enough, but chorused by a 
          hundred male voices on a summer's evening, with Harvard Yard 
          for an echo chamber? well ... on the Tibetan prayer-wheel principle, 
          repeat it enough and at some point something unspecified but 
          miraculous will come to pass. Harvard in a nutshell, if you really 
          want to know." 

          "They teach Quaternions there instead of Vector Analysis," 
          Kit helpfully put in. 
          AtD p. 156

Someone capable of seeing these patterns of repetition, the cyclic nature of 
time—well, most likely they end up in Against the Day, scrying toilets or 
something like that.

The Quarterninon visualizations not only display the profound complexity of 
these time cycles, but also explain such things as the Supendica's bifurcation, 
the point where history's time tracks split off. We're stuck on another 
parallel time track with the oil guys winning and lighter than aircraft off the 
table. But back to those Julia sets; at the bottom of these Quarterninon 
visualizations are mathematical equations that describe certain natural 
growth patterns, the patterns of growth observed in nature:

          Because they appear similar at all levels of magnification, fractals 
          are often considered to be infinitely complex (in informal terms). 
          Natural objects that approximate fractals to a degree include clouds, 
          mountain ranges, lightning bolts, coastlines, and snow flakes. 
          However, not all self-similar objects are fractals—for example, the 
          real line (a straight Euclidean line) is formally self-similar but 
          fails to have other fractal characteristics.

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

http://www.youtube.com/watch?v=-oJaE-iBIvA&feature=related

http://www.youtube.com/watch?v=GZ0MAx-30C0&feature=related

http://aleph0.clarku.edu/~djoyce/julia/julia.html

More than anything else, Pynchon, like the Alchemists, is looking deeply 
into the charecteristics of physical stuff, seeking the spiritual element 
within. Those visualizations of growth patterns through time expressed 
as quarterninons would help explain the episodic and cyclical nature of
Against the Day. Strange to think that Scarsdale Vibe gave Kit his greatest 
gift, and yet it was the head Vibe that aimed Kit towards where he really
should be:

          Since Tuva, where he had heard such unaccountably double-jointed 
          singing. . .   . . .Kit had found himself making down in his throat a 
          single low guttural tone, as deep as he could reach, as long as 
          breath would allow. Sometimes he believed that if he got this exactly 
          right it would transport him to "where he should really be," though he 
          had no clear picture of where that was. After he had done this for 
          long enough he began to feel himself enter a distinctly different 
          state of affairs. . . .

For whatever reason Kit, knowing enough about vectors to know when he's 
headed straight to hell, goes back to lessons learned on the road to 
Shambhala, like Tuvan throat singing, the shamanic roots of Buddhist overtone 
chant, major league mojo, if you ask me. Note well that somehow, that place
where Kit is supposed to be seems to be on a parallel track with the missing
final page of the Crying of Lot 49.

          It was like the convergence of a complex function. He would come to 
          for brief intervals, and then go back inside a regime of starvation 
          and hallucinating and mental absence. He didn't always know 
          where he was, or-especially unsettling for an old Vectorial 
          hand-which direction he was going. . . . .

http://www.youtube.com/watch?v=5iiZZdksuqY&feature=related

http://www.youtube.com/watch?v=X845Xm8qqmU&feature=related

http://www.youtube.com/watch?v=PgbxaNNbZiI&feature=related

          . . . .to the astonishment of onlookers he was turned to shimmering 
          transparency, dwindling into a sort of graceful cone and swept through 
          its point into what appeared to be a tiny or perhaps only distant 
          window of bright plasma. Kit, on the other hand, found that he had  
          remained the same size while the luminous opening began to grow, 
          until it had flowed around and wrapped him in antique rusts and 
          reds. . . .

http://www.youtube.com/watch?v=QMOlAGMGNPU&feature=related

                    If I ventured in the slipstream
                    Between the viaducts of your dream
                    Where immobile steel rims crack
                    And the ditch in the back roads stop
                    Could you find me? 
                    Would you kiss-a my eyes? 
                    To lay me down
                    In silence easy
                    To be born again
                    To be born again

                    Van Morrison, Astral Weeks

http://www.youtube.com/watch?v=Q5hD4rNVkmM&feature=related

http://www.youtube.com/watch?v=2tRdLD6vh3g&feature=related

          . . . .awed impressions of a ship exceeding the usual three 
          dimensions, docking, each time precariously, at a series of 
          remote stations high in unmeasured outer space, which together 
          form a road to a destination-both ship and dockage hurtling at 
          speeds that no one wishes to imagine, invisible sources of gravity 
          rolling through like storms, making it possible to fall for distances 
          only astronomers are comfortable with-yet, each time, the 
          Inconvenience is brought to safety, in the bright, flowerlike heart 
          of a perfect hyper-hyperboloid that only Miles can see in its 
          entirety. 

http://www.youtube.com/watch?v=9LjmS-v0EOs

http://www.youtube.com/watch?v=kcD4iRjWNLY&feature=related

          Bekah:

          Oh too cool.   Thanks.