Dear James Putnam,
your post triggers a number of reactions, probably (and unfortunately) more than I can put in a post here.
The first general point I need to clarify is that, in an attempt to be concise in writing the essay, I adopted a style, especially in the opening that you quote, which may indeed sound more 'assertive' than that of a stardard scientific paper. On the other hand, I believe that a bit of 'assertiveness' may be helpful for stimulating discussions, in a context such as the FQXi forum.
And in the sequel of the essay, in particular in Section 3 - 'Experimental validation', I do put my views in the right perspective.
I did not feel like using more space just for supporting the validity of the idea of working with discrete models such as causal sets, in light of the aboundance of solid papers that share that view as a very reasonable working hypothesis, to say the least.
You ask: By which means does a discrete spacetime grow?
Rideout and Sorkin [Phys. Rev. D 61, 024002, 2000] discuss classical dynamics for causal set growth, using *probabilistic* techniques.
Out of the several ways I have explored (by simulations) for obtaining causal sets by *deterministic algorithms*, the one that I personally consider most attractive consists in letting a 'stateless ant' walk on a trivalent graph G while applying, step by step, one out of two possible graph rewrite rules (known also in Loop Quantum Gravity, and used by Smolin, Markopoulou & friends). G can be equated to a growing space, while spacetime corresponds to the causal set of the computation being performed on it (the relevant references are [1-5], [8], [14] and [17]).
One of the two graph rewrite rules introduces a new node in G, so this rule would be responsible for the growth of space. But spacetime (the causal set) grows at *every* rewrite rule application, since:
1 rewrite rule application = 1 computation step = 1 node (event) added to the causal set (spacetime).
In this respect, my approach is indeed in contrast with the following statement from your essay:
"The universe evolves, but not because simplicity can generate complexity. Complexity can come only from pre-existing complexity. The greatest possible effects of complexity in the universe exist right from its start in a potential state."
I tend to disagree on that, based on the phenomenon of deterministic chaos, or algorithmic randomness. The best example of this is perhaps Wolfram's elementary cellular automaton n. 30: in spite of the elementary initial condition and the very simple rule (coded by a boolean function of three variables), the computation dynamics exhibit surpring pseudo-random character, as if information were continuously injected in the process from outside.
I like to believe (ideology again!) that our universe started from nothing, or almost nothing, and that space, spacetime, and complexity did increase: they were not 'already there' at the beginning, unless you mean that all the complexity of the mentioned rule 30 computation is 'potentially' present in the few bits that code its initial condition and boolean function.
I remember a workshop at the Phys. Dept. of the Padova Univ. (Jan 15, 2008) with lively discussions on String Theory vs. Loop Quantum Gravity. During the panel, Gabriele Veneziano and Carlo Rovelli did agree on one thing: they both were unable to point out a crucial validation/falsification experiment for their respective theories. I believe I am in good company in claiming that, in physics, both imaginative hypotheses and accurate experimental verification are necessary. If you call the former 'ideological', then I am afraid my essay has a lot of ideology in it. And, although I also provide simulation results (more in the references) that suggest interesting analogies with physical phenomena (e.g. the emergence of interacting objects!), my research on causal sets (as well as that of many others) is still very far from precise numerical predictions.
Since this is getting long, I answer to the remark on the self-modifying program in the next post. Looking forward to your comments after reading the essay. Thanks for your stimulating remarks!
Tommaso