Jason, Interesting and important questions. Unfortunately today I have family duties … , I will answer in the evening or tomorrow. (Same for possible other posts),
Best, Bruno > On 12 Aug 2019, at 23:36, Jason Resch <[email protected]> wrote: > > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CA%2BBCJUizGA5wN9KOLynozbovu0KpJjgf%3DA6jf24fMXdcr1fVTg%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CA%2BBCJUizGA5wN9KOLynozbovu0KpJjgf%3DA6jf24fMXdcr1fVTg%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- 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/378149E3-D089-434A-BC61-17D5B9711F18%40ulb.ac.be.
