Michiel de Jong wrote: >Jesse Mazer writes: > > What are people's ideas about the problem of a global measure on > > "everything?" > >If I summarize correctly, you give the following 4 possibilities: > >1) there is no global measure >2) "one distinct structure, one vote" >3) only one measure is consistent with some other more basic assumptions >4) work backwards from the computations occurring _inside_ a universe > >I suggest to distinguish a 5th: > >5) although there is no global measure (as in option 1), Solomonoff's >universal prior allows us to make predictions _as_if_ there were one, >because it approximates any candidate measure within O(1). > >Do you feel this is distinct from option 1? > >For me, the importance is in the distinction between choosing the >universal prior as _the_ measure, and taking it as an approximation of >_any_ measure.
I hadn't heard of the universal prior before, but I found a short description on Russell Standish's site: http://parallel.hpc.unsw.edu.au/rks/docs/occam/node2.html It seems to me that this is still a measure of sorts, based on dividing the set of turing machines into equivalence classes and then adopting a rule of "one equivalence class, one vote" (correct me if I'm wrong on this). What do you mean when you say it approximates any measure? Do you mean that any algorithmically generated measure will be approximated by the universal prior in some limit? Russell Standish's page also mentions another option I hadn't thought of: an observer-relative measure. Different types of information-processing SAS's might have different preferred measures depending on what type of UTM they are...although this would not solve the problem of why I find myself as this type of SAS rather than some other, or why I find myself in this type of universe as opposed to a completely different kind, it could at least allow for future predictions and an elimination of the white rabbit problem. But we'd still need a single rule to tell us which SAS's should use which measure. Jesse _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com