John, I think it is important to make strong distinctions between
complexity and what you are calling a system and a situation, and to
obtain a generic statement independent of them. Complexity, to be a
useful term should not have a complex definition, or else it signals that
there are important intermediate distinctions to make.
By the way, I strongly support the Gibbs definition of system which I
thank You for giving. It is very similar to one which I have used for 20
years by Kristen Nygaard of Norway, the author of Simula 67 and the
grand-founder of the object-oriented paradigm. Sorry, I would quote it,
but it is in storage back in Adelaide, Australia (having recently moved to
Geneva). The thing I like most about the Gibbs and Nygaard definitions is
their explicit acknowledgment of our participation in the process. Systems
do not exist without our explicit participation.
Referring to a description the emergence of connectivity in random
networks, given in a posting on Chaos and Complexity, I would suggest the
following "simple" definition of Complexity for consideration:
"A system or situation is complex when the active relationships between
its components is sufficient that almost all components are strongly
connected."
Strongly connected is a term from graph theory which means that there is
at least an indirect path from all components (nodes) to all other
components. The words "sufficient" and "almost all" speak to the
behaviour of random graphs, where at a particular point of increasing
complexity, the graph jumps from low connectivity to high connectivity.
Hope this helps..... Doug Seeley
---------------------------------------------------------------------------------
-----------
Dr. Doug Seeley: compuserve 100433,133... Fax: +41 22 756 3759
InterDynamics Pty. Ltd. (Australia) in Geneva, Switzerland
"Integrity is not merely an ideal; it is the only reality."