On 12 October 2013 10:46, Russell Standish <li...@hpcoders.com.au> wrote:

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> 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?
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