Complexity

Jeff Prideaux (JPRIDEAUX@GEMS.VCU.EDU)
Wed, 24 May 1995 23:43:24 -0400


Of course Rosen defines complexity in the following way: (excerpts
from LIFE ITSELF).

Analytic does not equal synthetic
Semantic does not equal Syntactic
Direct product does not equal direct Sum
external description does not equal internal description
fabrication does not equal physiology

and

A complex system contains a non-simulable model (something that
cant be done on a computer)...

A complex system is non-fractionable

Complex systems contain impredicativities (self-references)... It can't
be defined without referring to itself...

There is no (mechanistic) largest model (that explains everything)

The categories of causation in it cannot be segregated into discrete,
fixed parts, because fractionability itself fails.

No state set built up synthetically from the states of minimal models.
This takes us out of dynamical system's theory...

------------

Of course, now, to understand these definitions, one has to understand
these concepts (referred to by these terms)...

One hint on a possible strategy to find a realization...Rosen implies that
complex systems may interact with different observables than we measure. Even
though we may not be able to directly perceive these observables, we may be able
to know under what circumstances these different observables exist...and then
put certain appropriate subsystems together so that they can interact using
these observables... If these subsystems then interact in a way that is
substantially different than anything our dynamical system's equations can
predict, then we MAY have a complex realization.

Of course, the reductionists would then just call this a new force and go on
their merry way...It would then be interesting if a Godel-like theorem (for the
physical world) could be developed that showed that a new complex system
(interacting with new observables) could be developed for each "new force" added
to the reductionist repertoire.