On Sat, Oct 12, 2013 at 11:14:32AM +1300, LizR wrote:
> On 12 October 2013 11:12, LizR <lizj...@gmail.com> wrote:
> > On 12 October 2013 10:46, Russell Standish <li...@hpcoders.com.au> wrote:
> >
> >> On Fri, Oct 11, 2013 at 10:07:58AM -0700, meekerdb wrote:
> >> > I don't think being uncountable makes it any easier unless they form
> >> > a continuum, which I don't think they do.  I QM an underlying
> >> > continuum (spacetime) is assumed, but not in Bruno's theory.
> >> >
> >>
> >> UD* (trace of the universal dovetailer) is a continuum, AFAICT. It has
> >> the cardinality of the reals, and a natural metric (d(x,y) = 2^{-n},
> >> where n is
> >> the number of leading bits in common between x and y). ISTM, this
> >> metric induces a natural measure over sets of program executions that
> >> is rather continuum like - but maybe I'm missing something?
> >>
> >> I always assumed the UD output bits - i.e. not a continuum, but a
> > countable infinity of symbols - but maybe I'm missing something?
> >
> Am I missing diagonalisation? i.e. Can the UD output be diagonalised?

The UD doesn't output anything. If it did, then certainly, the output
could not be an uncountable set due to the diagonalisation argument.

Rather UD* is like the internal view of the operation of the
dovetailer, like the sum of all possible experiences of the Helsinki
man being duplicated to Washington and Moscow that is being discussed
rather a lot lately.


Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au

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