Replying to John Warfield's observations about connectivity and
complexity...
John, You cut to the quick with the "Everything is connected to everything
else." quote... I recall being asked by a professor almost 30 years ago
what did I really believe in my heart of hearts, and I stated that same
sentence..... However, I much prefer the spin which Ted Nelson, the
harbinger of the home computer revolution, gave it in his underground
best-seller... Computer Lib/Dream Machines back in 75....
"Everything is deeply intertwingled."
Thanks for the examples on digraphs which you cited. In their context, I
would like to stress the distinction between connectivity as direct
relationship, and connectivity as indirect relationship. It takes a
surprisingly small number of average direct relationships in some system,
to produce a system that is almost completely connected via indirect
relationships (strong connectivity). Empirically, it seems to be PI/2.
Hence, with less than 2 direct connections apiece for individual
components, the whole system becomes almost completely connected
(indirectly). The high number of relationships in the form of coherent
sub structures when this happens, I believe qualifies such systems as
being complex.
Cheers, 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."