[FRIAM] More on levels of sequence organization

[Russell Standish]

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.


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Principal, High Performance Coders
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