----- Original Message ----- From: "Lennart Nilsson" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Sunday, June 15, 2003 9:14 AM Subject: Something for Platonists
> Here is something from David Deutsch for Platonists to contemplate...I think > > LN > > > > "We see around us a computable universe; that is to say, of all > > possible mathematical objects and relationships, only an in.nitesimal > 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 di.erence 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." > >
