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.## Advertising

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!`

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