Dear Pavel and Dmitry,
Thanks for your appreciation and your interesting question in my blog - where I tried to answer.
I read you essays with great interest and you made me appreciate the algorithmic approach to physics. So a few questions remain for me and I hope these might be interesting for you:
1. You seem to accept unchangeable fundamental laws, that are not algorithmic. Why do you need these? Is the aim of your approach just to describe emergent mesoscopic laws (which of course is also very interesting).
2. You seem to have two kind of times. One in the fundamental laws and one in the algorithmic laws. How are they connected to each other?
3. Is the areal set constant trough time? Meaning it contains all possible states the universe or some system can ever take. Or can it change and is open to evolution? If yes is this change also described by some algorithm?
4. The areal set structure seem to correspond to a classical boolean logic. How does quantum mechanics plays into this. In QM the boolean logic comes into play, when measurements come into play or/and when contexts are set. In this domain only probabilistic laws can be formulated. If one wants deterministic laws, the unitary evolution of the wave function has to be considered. But there the boolean logic does not apply.
Hope these questions make sense to you.
Best luck in the contest.
Luca