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?

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