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Dear Tommaso,
Your answers are unconvincing and wrong. Moreover, I suspect that you are trying to suppress my questions by the stream of senseless information. It is impossible to find the answers for these questions because this theory is fundamentally wrong.
Let us begin again with quantum mechanics. Your essay states that all the complexity we observe, from subatomic particles to the biosphere, is a manifestation of the emergent properties of a digital computation that takes place at the smallest spacetime scale. How this digital computation can explain the simple motion of free particle, the Heisenberg uncertainty? For this purpose this digital computation must know the absolute information position-momentum about every particle before events occurs, that is forbidden by quantum mechanics.
And I don't see any answer for this problem; your words about Quantum effects, Stephen Wolfram, Renate Loll explain nothing; It is a stream of senseless information. You cannot explain it by definition; it is a fundamental flaw in this theory.
The next flaw about black holes: I found at least one place where the digital computation can not exist, it is a proof that this theory is wrong.
And your answer is senseless: ''I completely agree that your PC (or even my Mac!) would start having computing problems a while after crossing a black hole horizon. But, again, we are not talking about hardware, we are abstractly talking about computation''. Do you think your spatial atoms will be able to process information inside of black hole, in singularity? Inside of the Black Hole the exchange of information is not possible, therefore the digital computation cannot work. Since I found at least one phenomenon/place that exist without need in the digital computation, it is a proof this theory is wrong.
Another argument also is not valid: ''By the way, a very good 1999 paper by Margenstern and Morita proves that, in the context of cellular automata, spatial (negative) curvature offers indeed a great computational advantage over flat space''. They refer about the usual curvature but not infinite curvature, singularity.
Thus, this theory is fundamentally wrong.
Regards,
Constantin