One bored mathematician (was: the mind of culture)

Eric Brunner (
10 Jul 1996 16:22:10 GMT wrote:
[Responding to yet another Firl-ism]

: > I will use this post to examine some of the interesting
: > questions which appear when we try to view a culture as a complex
: > adaptive system which interacts with similar systems; it processes
: > information, acts, reacts, and seems to operate as if it were a
: > semi-conscious (?) entity with something like a mind of its own.

Some questions are less interesting than others. There is an entire
literature on maths in social sciences, from the closed-form feed-back
approximational work to the more fashionable non-standard anaylsis of
the present. Only a few of the protagonists of such work evince much
sophistication as mathematicians and as theoreticians in the disciplie
to which some mathematical method is attempted. Since anyone trying to
be serious about such a theoretical framework, which "looks and smells"
rather processualist (biologically deterministic, New Archaeology) to
my canine probiscus, ought to know whether or not they are processual
(or whatever label appears to be a "best fit") before reaching too deep
into the maths tool kit, let alone reaching conclusions, this ought to
be "up front".

Firl is obviously a bio-det, given his mating-for-immuo-dollars fixation.
I hope others will self-identify at their earliest convience, it will
avoid some clutter of misunderstanding(s).

: This is one area where chaotic theories a certainly applicable. In fact,
: you seem to intuitively describe it as such: complex (non-linear) and
: adaptive (implies a dynamic system, changing over time). Chaos theory is
: also being applied to spatial systems which I think might apply. But
: this aspect of the theory is still under development.

Hmm. "Chaos theory" and "spatial systems"... Rattner's horocycle flow series
of papers? Sinai and Kolmogoroff's works? Marsden et al on attractors? I'm
scratching my head. Perhaps you can enlighten me on which "chaotic theories
a(re) certainly applicable", I can always read the journal papers.

: You state that it 'interacts with similar systems.' Actually, I can
: think of few systems which act completely independent of other systems,
: linear or non-linear. I would think it would be expected to see a high
: level of interaction between similar systems.

Hmm. Nothing substantial there.

: You define the system as processing, acting and reacting (all aspects of
: a dynamic system), and operating 'as if it were a semi-conscious enitity
: (this I assume you are referring to complex responses to environment
: rather than to self awareness?

Nore here, though the multi-week series of Len Piotrowski and Matt Hill in
ARCH-L was really interesting.

: You continue by describing the system in linear terms.

I hadn't noticed the alumina-chapeaued one using any mathematical terms,
linear or otherwise. What did I overlook?

: I thought that perhaps I might suggest that you examine chaos theories.
: A good book for those with no mathematical inclinations would be any
: book on fractals and especially one discussing strange attractors (this
: aspect of chaos theory is similar to the qualities you describe as a
: cultural mind, or a semi-conscious entity). The key is in remembering
: that while such a book refers to fractals, the concepts behind the
: theories are applicable to all complex dynamic systems.

Care to name one, "good book for those with no mathematical inclinations"
that is? I'll pass on the problem a non-mathematically sophisticated work
as a compendium of useful tools for social scientists presents, since that
problem was solved almost 100 years ago, when statistics entered into public
policy. Statistics-using social scientists are no longer afforded the
luxury of "no statistical or probablistic inclination" when attempting to
do useful work.

So, "(t)he key is in remembering that while such a book refers to fractals
(fractional dimensional Hausdorff spaces, properly speaking), the concepts
behind the theories are applicable to all complex dynamic systems." This
will come as a surprise to ergodic theorists and non-standard analysts.

: Just a thought.

Please enlarge.

Eric Brunner