SUO: Re: Standard Treatments Of Common Knowledge In Descriptive, Empirical, Research Ontologies
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STOCKIDERO. Note 13
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I will make a few observations above the relevance of
this material for some of our ever-ongoing discussions.
The distinction between graphs, by any name, and labeled graphs,
by any other name, is a standard item of technical knowledge in
many applied fields. There are physical problems whose natural
coefficients are given by the sequences that enumerate families
of labeled graphs. These are typically the easy problems, and
most of them were solved ages ago. But there are perhaps more
physical problems whose natural coefficients are given by the
sequences that count families of (unlabelled) graphs, which
may be regarded as the symmetry group reduced enumerations
of their labeled cousins. These are typically much harder
to settle. Many of them only started to be solved in the
last half century, and many of them are as yet unsolved.
The hard fact is that Nature doesn't always care about
all the distinctions that we make when we try to sift
her phenomena through our coordinate sieves, and so
it frequently happens that the physical invariants
that constitute the hard scientific realities in
many settings are the group reduced versions of
of what only wishful thinking deceives us into
thinking that we have the freedom to impose
on Nature.
Jon Awbrey
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