Arrow of Time Explained? Emergence = Intelligence = Entropy = Hypercomputation

From an earlier post: “Today, I viewed a recording from FQXi 2014 where Scott Aaronson from MIT talks about the Physical Church-Turing Thesis. He brought up irreversibility. That made me think about the claim made by one paper I’d recently talked about [by AI researcher Ben Goertzel] that consciousness may be hypercomputational. Aaronson drew the link for me between hypercomputation and irreversibility. Hypercomputation implies irreversibility because, by definition, you cannot enumerate the sequence of instructions of a hypercomputation. If you don’t know how something was done, how could you undo it?”

From another previous post, the undecidability of the spectral gap verifies that there are, in fact,  hypercomputational aspects of nature. This falsifies the Physical Church Turing Thesis. To be a hypercomputational process means to be emergent, i.e. the sum is greater than the parts, otherwise the process could be fully described by its components and would not be hypercomputational. As noted above, hypercomputation implies irreversibility. The verified existence of hypercomputational, emergent phenomena in nature explains why we have the arrow of time. Furthermore, this irreversibility is shown to be linked with intelligence by Wissner-Gross’s Entropica simulation. From statistical mechanics, entropy is the measure of irreversibility and it is also apparently the measure of emergence and hypercomputability. We already know that theromodynamic entropy and Shannon entropy are duals and that  maximization of Shannon entropy (i.e., compression) is an objective of artificial intelligence algorithms. I speculate that if we equate Tononi & Koch’s measure of integrated information, phi, with thermodynamic entropy we may reveal precisely how the arrow of time arises from the fact that hypercomputational, emergent intelligence is a fundamental operating basis of nature. To explain the first-person experience, “consciousness,” is a separate issue- we should refer to the works of, e.g., Bruno Marchal or Max Tegmark.