[This is an email I sent to the reading group. It's title was:
Emergence, Chaos Envy, and Formalization of Complexity
I think that, rather than worrying about the existing concepts of
emergence, we would be far better off looking at the history of Chaos
and how they achieved amazing results in a short time, and how we
could similarly attempt formalization of complexity. One idea is to
simply look at the "edge of chaos" idea in more detail, thus placing
complexity as a field within chaos.]
Nick has started a seminar on Emergence based on the book of that name
by Bedau and Humphreys. This got me to thinking about the core
problem of Complexity: its lack of a core definition, along with lack
of any success in formalizing it.
Chaos found itself in a similar position: the Lorenz equations for
very simple weather modeling had quirks which were difficult to
grasp. Years passed with many arguing that Lorenz was a dummy: he
didn't understand error calculations, nor did he understand the
limitations of computation.
Many folks sided with Lorenz, siting similar phenomena such as
turbulent flow, the logistics map, and the three body problem. All
had one thing in common: divergence. I.e. two points near each other
would find themselves at a near random distance from each other after
short periods of time.
See: http://en.wikipedia.org/wiki/Chaos_theory
Complexity similarly arose from observations such as sand-pile
formation, flocking, ant foraging, and so on. Their commonality,
however, was not divergence but convergence, not chaos but order.
Typically this is coined "emergence".
I would like to propose an attempt to do what Poincare, Feigenbaum,
Layapunov and others have done for Chaos, but for Complexity.
Nick has hit the nail on the head, I think, in choosing Emergence as
the core similarity across the spectrum of phenomena we call "complex".
The success of Chaos was to find a few, very constrained areas of
divergence and formalize them into a mathematical framework. Initial
success brought the Rosetta stone: the Lyapunov exponent: a scalar
metric for identifying chaotic systems.
It seems to me that a goal of understanding emergence is to formalize
it, hoping for the same result Chaos had. I'd be fine limiting our
scope to ABM, simply because it has a hope of being bounded .. thus
simple enough for success.
You see why I included Chaos Envy?
-- Owen
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