Measures of Complexity

[phil henshaw]

Seth,
 
Here's my suggestions to add to your measures of 'complexity', largely
expanding on a couple of the last items in your list.    I realized on
rereading your introduction that you were speaking as if having a
growing number of measures might indicate confusion.    I think the
opposite is more generally the case for science, that being able to
measure something in different ways shows it's starting to come into
focus.    I guess we'll see!    My list is thematic,  but I'm sure there
are other themes.   If someone was thinking to fill out such a list
comprehensively that would be interesting.
 
...2nd ed.   Glad I saved this for a day.  I ran across the wonderful
1969 list by E.P. Odum again (from The Strategy of Ecosystem
Development) of mostly measurable characteristics of complexity in
ecologies, and it reminded me of all the other lists collected by people
from each of the several 'failed' general theories of complex systems
that have come and gone since .    Maybe they should all be collected
and thrown into a heap so see what grows?   I think they probably all
have real value, even if not all quite set up as measures in the
normally expected sense.
 
----------
- add under:
Measures and indicators to assist in complex system identification,
location and structural mapping
 
Statistical scales of complex order
        Ascendancy (Ulanowicz - growth & development, general models of
association)
        Attribute interaction & dependence (Jakulin -data mining,
general measures of association)
 
Measures for any kind of self-organizing or adaptive system developing
by growth;
        Physics of Happening (Henshaw -general observation method w/
various borrowings)
 
I. From Shapes identifiable in time-series data curves:

0) continuity, data curves having math and/or visually recognized
flowing shape
1) continuity along with growth (????.?), stabilization (.?? ?) ,
destabilization ( ? `?.) and decay (`?.??)
       mathematically definable as periods when all implied derivatives
are of same sign
2) fluctuation, often with nested scales, indicating and locating
homeostasis
3) divergence, indicating and locating structural imbalance with
developing instability
4) inflection points of (1) indicating developmental structure
transformation
5) trends of (1) in comfort or frequency of adaptive demands or adaptive
delays
6) trends of (1) in 'dark matters' for system response (ballooning
unknowns & distractions)
7) discontinuity between continuities, intrusion of outside systems
 
+masc..
8) isolated transient fluctuation =? local reversal of a flow direction
9) segments of (1) appearing in isolation =? reflects a larger system
10) repeated overshoot & collapse =? structural vulnerability, stuck in
the past
11) all the particular measures unique to each kind of emergence

II. Environmental features:

resources (opportunities in general) appearing in successively larger or
successively smaller units
resource pools allowing 'any-old-time' exchange or requiring
'just-in-time' exchange
emergence/changes-of-kind, diverse lasting changes occurring quickly at
the same time

* tracing progressions of scale & kind in causal loops connecting points
in a sequence *
    (cobbling dimensions)

once is an accident, twice and experiment & three times a habit (with a
niche)

III.  Structural indicators:


distinguishing causal links of opportunity vs. ones of necessity
identifying passive resource pools as structural elements facilitating
exchange
impetus and limits originating from switching gears inside vs. forcing
and constraints from outside

the co-evolving mirror images of a system and its niche, with an
identifiable boundary
system boundaries defined by the extent of growth system loops and what
they envelop
playfulness vs. disorder, resilience vs. rigidity

 
IV. As a parent:

when things get too quiet it's time to see what's happening!

 
 
- all comment welcome -
 
 

Phil Henshaw                       ????.?? ? `?.????
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e-mail: pfh at synapse9.com          
explorations: www.synapse9.com <http://www.synapse9.com/>    
 
re:  <http://web.mit.edu/esd.83/www/notebook/Complexity.PDF>
http://web.mit.edu/esd.83/www/notebook/Complexity.PDF
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