Against the Day: First Last thoughts

[robinlandseadel at comcast.net]

My first last thought is that AtD left most of y'all exhausted, 
and can we blame you for that? The manner in which 
characters and events are folded into the novel is about 
as confusing as OBA could cook up. I think this 'feature' 
of the novel is tied into the maths on display in the book.

The quarter dropped for me when I saw the computer animation
of Quaternions. The computer animations are based on the 
complex numbers of fractals:

          Fractals are produced using an iteration process. This 
          is where we start with a number and then feed it into a 
          formula. We get a result and feed this result back into 
          the formula, getting another result. And so on and so on...

          Fractals start with a complex number. Each complex 
          number produced gives a value for each pixel on the 
          screen. The higher the number of iterations, the better 
          the quality of the image

http://www.intmath.com/Complex-numbers/fractals.php

The Julia set is a fractal. Computer animations of Quaternions
are often based on Julia sets.

          Introduction

          Quaternion Julia fractals are created by the same principle as 
          the more traditional Julia set except that it uses 4 dimensional 
          complex numbers instead of 2 dimensional complex numbers. 
          A 2D complex number is written as z = r + a i where i2 = -1. 
          A quaternion has two more complex components and might 
          be written as q = r + a i + b j + c k where r, a, b, and c are real 
          numbers. There are slightly more complicated relationships 
          between i, j, and k

                              i2 = j2 = k2 = -1
                              i j = k	j k = i	k i = j
                              j i = -k	k j = -i	i k = -j

          For more details on quaternion maths (how to add and multiple) 
          see the reference given in the header above.

The math is beyond me, but the computer visualizations show patterns in
growth over time. We have developed so many overlays on reality that it 
makes describing reality difficult. Watching:

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

I was struck by several things. First off, how "Art Nouveau" these
animations appear. Second, watching the news last night, seeing 
the computer animated Logo for "Hardball" I realized we [who
consume popular media] are being inundated by quaternions
without realizing it. "Hardball's" logo consists of a 2d representation
of 3d surfaces, moving in time [that fourth 'd'] on rolling surfaces 
such as those on display in that demonstration of Quaternion Julia Set 01.

But the main thing is the sense that the evolving cyclic phenomenon
on display in these computer animations—concentric circles revolving,
morphing into different associative relations over time is a different 
model of reality than Newtonian/Rube Goldberg cause and effect.

Or maybe I just need less coffee.

Seriously, though, it does seem as though events in Against the Day
emerge far more from synchronicity and similarity than good old 
cause and effect.