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 -- ---------------------------------------------------------------------------- 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 ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
