On Sat, Oct 20, 2012 at 07:07:14PM -0400, Stephen P. King wrote:
> On 10/20/2012 5:45 PM, Russell Standish wrote:
> >A UD generates and executes all programs, many of which are
> >equivalent. So some programs are represented more than others. The
> >COMP measure is a function over all programs that captures this
> >variation in program respresentation.
> >
> >Why should this be unique, independent of UD, or the universal Turing
> >machine it runs on? Because the UD executes every other UD, as well as
> >itself, the measure will be a limit over contributions from all UDs.
> Hi Russell,
>     I worry a bit about the use of the word "all" in your remark.
> "All" is too big, usually, to have a single constructable measure!
> Why not consider some large enough but finite collections of
> programs, such as what would be captured by the idea of an
> equivalence class of programs that satisfy some arbitrary parameters
> (such as solving a finite NP-hard problem) given some large but
> finite quantity of resources?
>     Of course this goes against the grain of Bruno's theology, but
> maybe that is what it required to solve the measure problem. :-) I
> find myself being won over by the finitists, such as Norman J.
> Wildberger!

This may well turn out to be the case. Also Juergen Schmidhuber has
investigated this under the rubrik of "speed prior".

I should have a chat with Norm about that sometime. Maybe if I see him
at a Christmas party. I didn't realise he was a finitist. I knew he
has an interesting take on how trigonometry should be done.



Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au

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