On Sat, May 04, 2019 at 05:25:54PM -0700, glen∈ℂ wrote: > Right. But that's the point, I think. To what extent are semantics invariant > across these supposed "levels"? My argument is that "levels" are figments of > our imagination. The best we can say is that iteration constructs something > that we find convenient to name: "level". But what reality is actually doing > is mere aggregation and the meanings of the primitives are no different from > the meanings of the aggregates.
I don't think levels are just figments of imagination. Compression algorithms replace explicit descriptions with generative algorithms (like procedures of functions) that when called with appropriate parameters reproduce the original data. These generative descriptions have a tree-like structure, which is exactly the heirarchical structure you're after. Obviously, there is no unique compression algorithm, nor even a unique best algorithm. But I suspect that the best compression algorithms will probably agree up to an isomorphism on the heirarchical structure for most compressible data sets (note that this is already a set of measure zero in the space of all data sets :). I don't have any data for my hunch, though. -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Senior Research Fellow [email protected] Economics, Kingston University http://www.hpcoders.com.au ---------------------------------------------------------------------------- ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
