On 10/21/2012 3:48 AM, Russell Standish wrote:
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.

Cheers

Hi Russell,

    I will look at Juergen's stuff again. ;-)

--
Onward!

Stephen


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