In "The Universal Numbers. From Biology to Physics" Bruno writes "The universal dovetailing can be seen as the proofs of all true Sigma_1 propositions there exists x,y,z such that P_x(y) = z, with some sequences of such propositions mimicking the infinite failing or proving some false Sigma_1 propositions."
This is something I was thinking about recently in the context of universal Diophantine equations. It seems more correct to me to say these equations don't themselves represent the execution traces of the programs, but rather represent proofs of the outputs of programs. This can be seen from the fact that the work of verifying a Diophantine equation requires only a finite and constant number of arithmetical operations, while the computation itself could involve much more work, in terms of arithmetical steps. So is it right to say that the proof of the result of some computable function is different from the computable function itself? In other words, a fixed Diophantine equation, regardless of the values of its variables, does not itself yield conscious mind states, though it points to the existence of another object in math (the universal machine) whose operation would yield the conscious mind states? I am just trying to develop a more clear picture in my mind of the relation between arithmetic, proofs, computational traces, and mind states. Jason -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CA%2BBCJUizGA5wN9KOLynozbovu0KpJjgf%3DA6jf24fMXdcr1fVTg%40mail.gmail.com.
