Hi Nebullis!
I loved this remark from Gill, from the link you give:
"...Perhaps... the world was built 'according to quantum mechanics but quantum mechanics itself prevents us from ever being sure.'"
I imagine that our putative prime mover may simply be a set of initial conditions plus an algorithm that states the rules of evolution of the universe. In this sense, it is "deterministic." But the interesting thing that Wolfram demonstrates is that (for Class 4 cellular automata at least, such as his "universal emulator," Rule 110), given a simple set of initial conditions, the iteration of even very simple rules over indefinitely long time periods can "spontaneously" generate systematic behavior that appears to be quite random.
I gather it all has to do with the ability of earlier iterations to convey information to later states of the system. If at later iterations we find that information has been "lost" along the way, apparent randomness is the result in at least parts of the total system.
The system as a whole will display local ordered structures throughout its evolution (which structures cannot be precisely anticipated or predicted with certainty), like little islands of order in a sea of apparent chaos. These "islands" preserve information and transmit it to future iterations. Now these little islands may themselves become attenuated, or they may themselves die out. But if all they are is "attenuated" (and not extinct) then they may cast forth a little thread into the future (so to speak), and at some later stage, bloom forth as yet another little island of order -- amid a roiling sea of chaos.
What we have is extraordinarily complex behavior, evolving from "simple" initial conditions and a fairly "simple" instruction set (i.e., algorithm.)
I probably haven't explained this very well. And things are about to get worse:
In any case, to the extent that natural selection seems to depend (at least in part) on the preservation of information and its transmission to "later iterations" of the system, perhaps Wolfram's insight that its role may not be the decisive role is analogous to whether we, as observers, "encounter" an island of order or a patch of apparent chaos at any given iteration of the systemic evolution, which is essentially unpredictable. And we don't occupy an "Archemedian point" outside the system from which we can view it in toto, so as to see "where is the order" and "where is the apparent randomness".
I gather that's why Wolfram sets such store by his cellular automata -- they let us see what the evolution of a system in toto "looks like," even if our "viewing" is only an imaginary act.
Take a look at the Rule 110 cellular automaton. It's the "picture" I'm trying to describe.
I would like to add this prediction to your analysis:
It appears that very large structures can be directly related to the very tiny: Stability and Size of Galaxies from Planck’s Constant (PDF). We can look back so far in history, that we are able to see the Harmonics in the Early Universe.
As time passes, our ability to discern information from the cosmos should increase, IMHO, exponentially.
The information gathered from such efforts (e.g. Cosmological Patterns and Galaxy Biasing (pdf)) - will converge with the findings of the experiments by High Energy Particle Physicists and the entire collection will mulled over by the Mathematical Physicists.
Correlations between quantum and astronomical will surely not be missed, and since the cosmos is a record of the early universe – IMHO, some of that missing information just might be found after all.
Do you mean complex? I think what you are getting at is that the rules appear to us to be random when they are, fact, quite simple. There is no way to model the system from a top-down, macroscopic point of view, but only in a reductionist way, by teasing out the simple rules. However, the initial conditions can be random.