[Inquiry] Re: Prospects for Inquiry Driven Systems

[Jon Awbrey]

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PRO.  Note 30

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1.2.2.1.  Papyrus, Parchment, Palimpsest

Starting from the standpoint of systems theory a sizable handicap
must be overcome in the quest to figure out:  "What's in the brain
that ink may character?" and "Where is fancy bred?" (McCulloch, 1965).
If localized deposits of historical records and promissory notes are all
that can be found, a considerable amount of reconstruction may be necessary
to grasp the living reality of experience and purpose that underlies them still.
A distinction must be made between the analytic or the functional structure of the
phase space of a system and the anatomical structure of a hypothetical agent to
whom these states are attributed.  The separation of a system into environment
and organism and the further detection of anatomical structure within the
organism depend on a direct product decomposition of the space into
relatively independent components whose interactions can be treated
secondarily.  But the direct product is a comparatively advanced
stage of decomposition and not to be expected in every case.

This point draws the chase back through the briar patch of that earlier theory
of complexity, the "prime decomposition" or the "group complexity" theory of
finite automata, along with that of their associated formal languages or
transformation semigroups (Lallement, ch. 4).  This more general study
requires the use of "semi-direct products" (Rotman, 1984) and their
ultimate extension into "cascade products" or "wreath products",
together with with the corresponding notions of decomposition,
divisibility, or factorization (Barr & Wells, 1990, ch. 11).
That theory appears to have long ago reached a baroque stage
of development, either too difficult to pursue with vigor,
too lacking in easy and immediate applications, or just
falling short of some essential insight.  It looks
like another one of those problem areas that will
need to be revisited on the way to integrating
AI and systems theory.

Jon Awbrey

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