On 11 Oct 2013, at 23:46, Russell Standish wrote:
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.
From the first person views statistics.
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).
That would be a sort of measure on infinite programs, not so much on
the computations, which will need a sort of measure on experiences,
which needs the definition of "experiences" and thus of the knower
logic and semantics, and for this I use the (counter-intuitive)
arithmetic of self-reference.
Bruno
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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