Hi Douglas,
we had already an exchange in your thread (it is hard to keep track of everything here!). Thanks for reading my essay, and for your comments. I just react to one of them, appearing in square brackets [...]. Often is has been observed that descriptions of the universe, across history, have been influenced by the current technology - from the clockwork universe of Pascal, Newton, Leibnitz, to the computing universe of our times, and this of course invites some skepticism about such technology-biased views. However, while computers are certainly the representative technology of the last few decades, the notions of algorithm and computation are much older (by millenia). The computational universe conjecture (Zuse, Fredkin, Wolfram, Lloyd and others), in its boldest form, claims that the universe is discrete (spacetime being a giant causal set - as also suggested by the Causal Set Programme physicists - Bombelli, Sorkin, Rideout, Henson, etc.) that is animated algorithmically. When mentioning `software` as the engine that fuels everything by algorithmic steps, the idea is not to provide a metaphor based on one`s area of expertise (like a football coach would do), but to provide the actual, infinitely accurate description of everything (if, ontologically, the universe is discrete and finite, albeit possibly growing unboundedly, infinite accuracy is conceivable). God created only Natural numbers; men invented the Reals.
In the dialogue among Tomas, Tommy and Alice (no Bob around), I`ve illustrated how the views by Wolfram, Chaitin and Tononi (to pick three representative scientists) can fit under a rather unifying picture of three diverse components of our universe: Prelife, Life, and Thought (using Teilhard`s terminology). The unifying factors are: discreteness and algorithmic evolution.
Differential equations, fields, path integrals, and all the tools of continuous mathematics, are extremely powerful for providing approximated descriptions of physical reality, and any computation-oriented account of the world must eventually be able to replicate the results obtained by them (as the Causal Set people are well aware of).
A crucial argument here (to make a long story short) is the typing monkeys: their output is a messy universe of characters, too messy to look like ours. But if you feed this digital mess to a universal Turing machine (i.e., you take it as a program), then the output you get is a mix of order and disorder (Levin`s distribution) that resembles what we see around us.
Best regards
Tommaso
PS - I know that the deadline is approaching. I did rate your essay, a few days ago, after commenting. You write that you hope to find more time to give a more thorough reading to my work. If this means that you have not yet rated it, please do. Rating here is definitely a complex system. I`ve been for a long time in the top 15, but a couple of days ago, probably due to a malicious antipodal butterfly, I jumped to around rank 30 in one shot, which looks strange to me under both a continuous and a discrete mathematical viewpoint.