On 12 Oct 2013, at 00:14, 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?

It cannot. For the same reason that the partial computabe functions is immune to diagonlaization. That is why it is "universal". But as I said, you forget to take into account the 1p/3p distinction. You are forgetting step 7.

Bruno


http://iridia.ulb.ac.be/~marchal/



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