How do complex adaptive systems move towards the edge-of-chaos regime (cf. Part 81), and then manage to stay there? Per Bak (1996) supplied a clear answer in terms of his important notion of self-organized criticality (SOC).
This is a very powerful idea in complexity science. In fact, according to
Bak (1996), SOC is so far the only known general mechanism to generate 'robust'
complexity.
Bak defined a complex system as that which
consists of a large number of components, has large variability, and the
variability exists on a wide range of length / time scales. According to him,
large 'avalanches', not gradual change, can lead to qualitative changes of
behaviour, and may form the basis for emergent phenomena and complexity. A
surprisingly large number of phenomena, processes and behaviours can be understood in terms of this very basic feature of complex systems.
We can
understand the essence of the SOC idea by considering the very simple sandpile
experiment. Imagine a tabletop on which grains of sand are drizzling down
steadily. To start with, the flat sandpile just grows thicker with time, and
the sand grains remain close to where they land. A stage comes when the sand
starts cascading down the sides of the table. The pile gets steeper and steeper
with time, and there are more and more sandslides. With time the
sandslides (avalanches or catastrophes) become bigger and bigger,
and eventually some of the sandslides may span all or most of the pile. The
average slope now becomes constant with time, and we speak of a stationary state.
This is a
system far removed from equilibrium. Its behaviour has become collective. Falling of just one more
grain on the pile may cause a huge avalanche (or it may not). The sandpile is
then said to have reached a self-organized
critical state, which can be reached from the other side also by starting
with a very big pile: the sides would just collapse until all the excess sand
has fallen off.
The state is self-organized because it is a property
of the system and no outside influence has been brought in. It is critical because the grains are
critically poised: The edges and surfaces of the grains are interlocked in a
very intricate pattern, and are just on the verge of giving way. Even the
smallest perturbation can lead to a chain reaction (avalanche), which has no
relationship to the smallness of the perturbation; the response is
unpredictable, except in a statistical-average sense. The period between two
avalanches is a period of tranquillity (stasis)
or equilibrium; punctuated equilibrium is a more appropriate description of the
entire sequence of events.
Just like the constant input drizzle of sand in that system, a steady
input of energy, or water, or electrons, can drive systems towards criticality,
and then they self-organize into criticality by repeated spontaneous pullbacks
from super-criticality, so that they are always poised at or near the edge
between chaos and order. The openness of the system (to the
inputs) is a crucial factor. A closed system (and there are not many around)
need not have this tendency to move towards an SOC state.
Nature operates at the SOC state. As in the
sandpile experiment, large systems may start from either end, but they tend to
approach the SOC state.
Biological and
other types of evolution are nothing but examples of self-organization. The
constant influx of information-carrying energy (or rather Gibbs free energy)
leads to the evolution of higher and higher levels of complexity and order.
Bak (1996)
theorized that even life is a self-organized critical phenomenon. Similarly, in
biological evolution, mass extinctions, as also punctuated equilibria, can be
understood as SOC phenomena.
In general,
complex behaviour is exhibited mainly by open systems far from equilibrium. For
closed equilibrium systems, complex universal behaviour can arise only under
some very specific conditions. 'Critical phenomena' (cf. Wadhawan 2000) at
continuous phase transitions in crystals are an example of this. At the
critical point, the system passes from a disordered state to an ordered state.
The important point is that the system has
to be brought very close to the critical point to observe complex
behaviour, namely scale-free fluctuations of the order parameter, giving
transient ordered domains of all sizes. Such complex criticality is not robust; it occurs only at or very
near the critical point, and not at other temperatures (Bak 1996).
According to
Bak (1996), chaos is another such example of nonrobust criticality, and
therefore chaos theory cannot explain complexity completely. Chaos theory
explains how simple, deterministic systems can sometimes exhibit unpredictable
behaviour, but complex-looking behaviour occurs in such systems only for some specific range of values of
the control parameter; the complexity is not robust.
A third
example of criticality which is not self-organized, and therefore not robust,
is that of a nuclear-fission reactor. The reactor is kept critical (neither
subcritical nor supercritical) by the human operator, and cannot, on its own,
tend towards (and be stable around) a state of self-organized criticality.
Robustness is
an essential feature of SOC. Fragile criticality is not conducive to the
adaptive evolution of a complex system.
good stuff. reminds me of the edge of criticality found in evolutionary systems. power laws are found in extenctions and species radiative explosions as well. Kauffman defined natural systems as non predictive exploring possibility spaces. The trends are towards an increase in entropy producing capability phi(m) which gives them a Popperian propensity or trned..
ReplyDeleteThanks Nick. I had thought of writing about Kauffman's idea of the 'adjacent possible', but then decided to keep things simple and brief. Kauffman had, in fact, proposed a fourth law of thermodynamics for self-constructing biospheres. This is what the law said: 'Autonomous agents will evolve such that causally local communities are on a generalized "subcritical-supracritical boundary" exhibiting a generalized self-organized critical average for the sustained expansion of the adjacent possible of the effective phase space of the community'.
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