Let me point you all to the work of Peter Wegner and his research on
[EMAIL PROTECTED] wrote:
> [EMAIL PROTECTED]:
> > Check out analytic TMs (Hotz, Vierke and Schieffer,
> > 1995) and R-Machines (Blum, Shub, Smale, 1989):
> > http://rapa.idsia.ch/~juergen/toesv2/node47.html The alphabet of
> > is indeed real-valued instead of binary. This is beyond
> > though. GTMs are at the extreme end of the constructive spectrum.
> > They are beaten by nonconstructive devices only.
> > But stuff describable by nonconstructive devices only does not even
> > Does it?
> But stuff indescribable by us ought to be constructible by observers
> with real-valued input, output and memory living in real-valued
> worlds. They might communicate identities of arbitrary real numbers
> as naturally as we refer to a points on a line, and execute analytic
> algorithms as easily as we fiddle with finite alphabets.
> Those observers may not be in reach of our analysis, but they are
> within the scope of their own.