Bruno says: "...the notion of computability is absolute."
David Deutsch says: "We see around us a computable universe; that is to say, of all possible mathematical objects and relationships, only an infinitesimal proportion are ever instantiated in the relationships of physical objects and physical processes. (These are essentially the computable functions.) Now it might seem that one approach to explaining that amazing fact, is to say "the reason why physical processes conform to this very small part of mathematics, 'computable mathematics,' is that physical processes really are computations running on a computer external to what we think of as physical reality." But that relies on the assumption that the set of computable functions -- the Turing computable functions, or the set of quantum computable operations -- is somehow inherently privileged within mathematics. So that even a computer implemented in unknown physics (the supposed computer that we're all simulations on) would be expected to conform to those same notions of computability, to use those same functions that mathematics designates as computable. But in fact, the only thing that privileges the set of all computational operations that we see in nature, is that they are instantiated by the laws of physics. It is only through our knowledge of the physical world that we know of the difference between computable and not computable. So it's only through our laws of physics that the nature of computation can be understood. It can never be vice versa." http://www.qubit.org/people/david/Articles/PPQT.pdf If it is only through our knowledge of the physical world that we know of the difference between computable and not computable, and I don´t see any flaw in David´s argument that leads up to that statement, then the notion of computability definitely is not absolute. LN --~--~---------~--~----~------------~-------~--~----~ 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?hl=en -~----------~----~----~----~------~----~------~--~---