On Fri, Oct 11, 2013 at 10:07:58AM -0700, meekerdb wrote:
> On 10/11/2013 2:28 AM, Russell Standish wrote:
> >On Thu, Oct 10, 2013 at 06:25:45PM -0700, meekerdb wrote:
> >>So there are infinitely many identical universes preceding a
> >>measurement. How are these universes distinct from one another?
> >>Do they divide into two infinite subsets on a binary measurement, or
> >>do infinitely many come into existence in order that some
> >>branch-counting measure produces the right proportion? Do you not
> >>see any problems with assigning a measure to infinite countable
> >>subsets (are there more even numbers that square numbers?).
> >But infinite subsets in question will contain an uncountable number of
> >elements.
>
> 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?
Cheers
--
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Prof Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics [email protected]
University of New South Wales http://www.hpcoders.com.au
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