On 17 February 2014 09:02, Bruno Marchal <[email protected]> wrote: May be I should not have, as we can use the intensional Church's thesis, > for the UD. But we can formally make a difference, and some can exploit it. > In fact the difference between computation and computability is more > general than between physical computation and physical computability. > Computability a priori concerns only the class of functions that we can > compute. > It has been proved that such class is the same for all know universal > system, from Babbage machine to the quantum computer. But each system > computes in a priori very different ways. Combinators are computed by > following two simple reduction laws (like Kxy = x, Sxyz = xz(yz)), > arithmetic computes by adding and subtracting one, register machine compute > by erasing or adding one in some register, quantum computations processes > on waves, etc. > But all systems can imitate all systems. Combinators and their reduction > can implement a program computing like a quantum processor (althou with a > superexponential slow down, which does not matter in the UD*, though). > > Now for some reason, I didn't get that immediately, and for a time I > believed that QC could violate the intensional Church thesis, notably due > to strict parallelization, use of arbitrary complex coefficients, and > entanglement. I was just wrong. > > In fact, even if some quantum computation was necessary for the mind to > exist, comp should still able to justify this, by a necessary back and > forth above and below the substitution level, which indeed must already > play some role in the stabilization of the histories (the measure). In fact > comp predicts already the existence, formally, of comp-quantum > computations. But it is an open problem if it is isomorphic to quantum > computation. Today, it is even an open problem if such > comp-quantum-computation violates Church thesis (which I find not quite > plausible, to be sure). >
OK, I see. Thanks. David -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
