Hello Jeff,
I enjoyed your essay, and I went through it twice so I could be sure to grasp your intended meaning. I think you would greatly enjoy the book "Turbulent Mirror" by Briggs and Peat, which fleshes out some of what you left unsaid very nicely, and follows a similar theme. My main interest in that book is its focus on what I call the far shore of chaos. In my formulation, the presence of randomness comes from the accumulation of too much order in dissimilar patterns, which forces irregularity or roughness to appear, where the patterns are in conflict.
So in effect; chaos emerges from order. But on the other side of randomness, things become orderly again, so that there are regimes of order within chaos, if things are allowed to vary continuously. According to Noether, observed conservation laws are equivalent to symmetries, so the study of symmetry is very prominent in Physics. But as you say; entropy prevails given enough time and space to have its action, so this suggests the universe as a whole is asymmetric when considering its progression over time.
In terms of the patterning of the octonions, building of order is stage 4, the onset and increase of chaos is stage 5, and the far shore of chaos is stage 6 phenomenology. But this interplay is easily observed in the Mandelbrot Set, if we home in on any of its branching Misiurewicz points. A theorem of Tan Lei states that the symmetry becomes more and more exact the farther we zoom in, but the reverse is also true - where the structures bounding any Misiurewicz point are asymmetrical, reflecting the global asymmetry of M. So we see an interplay between exact local symmetries and global asymmetry - just like the universe.
I believe in everything you say Jeff, but I see much of the pattern and phenomenology as arising from pure Mathematics.
All the Best,
Jonathan
