Re: [Swarm-Modelling] general question on complexity

[glen e. p. ropella]

Jacob Lee wrote:
> Is the complexity of a system strongly correlated to the computational
> complexity of a model of that system?

If I ignore the word "computational" in your question, I answer as
follows.  Two clusters of work that I find interesting in relation to
possible invariants in the model<->reality map are:

1) the "law of requisite variety" -- a.k.a. Shannon's 10th theorem,
which states:

"If the correction channel has a capacity equal to H_y(x) it is possible
to so encode the correction data as to send it over this channel and
correct all but an arbitrarily small fraction of the errors.  This is
not possible if the channel capacity is less than H_y(x)."

Paraphrased:  A controller must have equal or greater variety than
whatever it controls.

Obviously "variety", "uncertainty", and "complexity" are assumed to be
related in this context.  It may not be obvious how control relates to
the type of modeling we do to understand or predict system behavior.  If
not, I'm sure the people on this list can throw many words at that topic.

2) Robert Rosen's thesis that a system is complex if and only if one or
more of the models of that system are noncomputable.  Caveat emptor re:
Rosen, though.  [grin]  He had private definitions for lots of words,
particularly "complexity" and "model".


If by "computational complexity", you mean a _particular_ measure, then
the answer depends entirely on which measure you pick and which system
you're modeling.

-- 
glen e. p. ropella, 971-219-3846, http://tempusdictum.com
This is patently absurd; but whoever wishes to become a philosopher must
learn not to be frightened by absurdities. -- Bertrand Russell