Le 22-août-06, à 08:36, Tom Caylor a écrit :
> I believe that we are finite, but as I said in the "computationalsim > and supervenience" thread, it doesn't seem that this is a strong enough > statement to be useful in a TOE. It seems that you cannot have YD > without CT, but if true I would leave Bruno to explain exactly why. > I am not sure I have said that YD needs CT. CT is needed to use the informal "digital" instead of the "turing", "java" "python" seemingly restriction. For someone not believing in CT, "digital" could have a wider meaning than "turing emulable". Now CT needs AR. CT is equivalent with the statement that all universal digital machine can emulate each other. To make this precise (or just to define universal machine/number) you need to believe in numbers. (But just in the usual sense of any number theorist). Recursion theory is really a branch of number theory, although few number theorist would accept this joyfully. Well a notable exception is Yuri Manin. He wrote a beautiful (but advanced) book on number theory which has a impressive chapter on recursion theory (the theory of the Wi and Fi). Well, thanks to Matiyasevitch, few number theorist would seriously argue that recursion theory has nothing to say about numbers in the sense that you need recursion theory and even Church thesis to say that the 10th Hilbert problem has been solved negatively. By using compute science (alias elementary recursion theory), Matiyasevitch has indeed shown that there is no algorithm (this makes sense only with CT) for the resolution of diophantine equations (polynomials with integers coefficient and with integers or natural number for the variables or unknowns). Bruno http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
