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Complexity: The
Emerging Science at the Edge of Order and Chaos
by M. M. Waldrop
1992, Simon & Schuster, New
York, NY
ABSTRACT - The stories of a
few of the leading contributors (economist Brian Arthur, biologist Stuart Kauffman,
computer scientist Chris Langton) to the new science of complexity are nicely told. These
contributors come from a variety of disciplines and have come together through the Santa
Fe Institute.
Key Points: |
All complex systems are built up
from numerous components which constantly drive large and small scale change, through
common mechanisms, in the overall system.
The mutual dance of
interdependence among organisms is stressed as is the growing recognition of the central
role of cooperation in fostering survival as contrasted with reliance on competition.
Complex systems seem to operate
and survive best when they operate on the edge of chaos and order and when behavior is
organized from the bottom up.
To effect a systems behavior or
development one must appreciate its patterns and power, apply interventions judiciously,
and dont bet on a limited set of strategies.
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Master of
the Game |
Key Point:
All complex systems are built up from numerous components which constantly drive large and
small scale change, through common mechanisms, in the overall system. |
"Complex adaptive
systems."...all seemed to share certain crucial properties...
First...each of these systems is
a network of many agents acting in parallel...Furthermore...the control of a
complex adaptive system tends to be highly dispersed...If there is to be any coherent
behavior in the system, it has to arise from competition and cooperation among the agents
themselves...
Second...a complex adaptive
system has many levels of organization, with agents at any one level serving as the
building blocks for agents at a higher level...Furthermore, said Holland - and this was
something he considered very important - complex adaptive systems are constantly revising
and rearranging their building blocks as they gain experience...At some deep, fundamental
level, said Holland, all these processes of learning, evolution, and adaptation are the
same...
- Third...all complex adaptive systems anticipate the
future...
Finally, said Holland, complex
adaptive systems typically have many niches, each one of which can be exploited by an
agent adapted to fill that niche...Moreover, the very act of filling one niche opens up
more niches - for new parasites, for new predators and prey, for new symbiotic partners.
So new opportunities are always being created by the system. And that, in turn, means that
its essentially meaningless to talk about a complex adaptive system being in
equilibrium: the system can never get there. It is always unfolding, always in transition.
In fact, if the system ever does reach equilibrium, it isnt stable. Its dead.
And by the same token,...theres no point in imagining that the agents in the system
can ever "optimize" their fitness, or their utility...The space of possibilities
is too vast; they have no practical way of finding the optimum. the most they can ever do
is to change and improve themselves relative to what the other agents are doing." p.
145-148
What Holland wanted to know was
how evolution could explore this immense space of possibilities and find useful
combinations of genes - without having to search over every square inch of
territory...Indeed, thought Holland, thats what this business of
"emergence" was all about: building blocks at one level combining into new
blocks at a higher level. It seemed to be one of the fundamental organizing principles of
the world...Once a set of building blocks like this has been tweaked and refined and
thoroughly debugged through experience...then it can generally be adapted and recombined
to build a great many new concepts....And that, in turn, suggests a whole new mechanism
for adaptation in general. Instead of moving through that immense space of possibilities
step by step, so to speak, an adaptive system can reshuffle its building blocks and take
giant steps." p. 167-170
"Reproduction and crossover
provided the mechanism for building blocks of genes to emerge and evolve together - and,
not incidentally, provided a mechanism for a population of individuals to explore the
space of possibilities with impressive efficiency. By the mid - 1960s, in fact, Holland
had proved what he called this schema theorem, the fundamental theorem of genetic
algorithms: in the presence of reproduction, crossover, and mutation, almost any compact
cluster of genes that provides above-average fitness will grow in the population
exponentially." p. 174
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Peasants
Under Glass |
Key Point:
The mutual dance of interdependence among organisms is stressed as is the growing
recognition of the central role of cooperation in fostering survival as contrasted with
reliance on competition. |
"Any given organisms
ability to survive and reproduce depends on what niche it is filling, what other organisms
are around, what resources it can gather, even what its past history has been. "That
shift in viewpoint is very important," says Holland. Indeed, evolutionary
biologists consider it so important that theyve made up a special word for it:
organisms in an ecosystem dont just evolve, they co-evolve. Organisms dont
change by climbing uphill to the highest peak of some abstract fitness landscape...(The
fitness-maximizing organisms of classical population genetics actually look a lot like the
utility-maximizing agents of neoclassical economics.) Real organisms constantly circle and
chase one another in an infinitely complex dance of co-evolution." p. 259
...he wanted to understand a deep
paradox in evolution: the fact that the same relentless competition that gives rise to
evolutionary arms races can also give rise to symbiosis and other forms of
cooperation...It was a fundamental problem is evolutionary biology - not to mention
economics, political science, and all of human affairs. In a competitive world, why do
organisms cooperate at all? Why do they leave themselves open to "allies" who
could easily turn on them?" p. 262
In a computer simulation game on
competition versus cooperation, a tit for tat strategy (seek cooperation with your
competitor, if reciprocated, keep cooperating; if cooperative approach is met by
competition, compete back, if approach changes to cooperation, reciprocate) beat all other
strategies repeatedly. "The conclusion was almost inescapable. Nice guys - or more
precisely, nice, forgiving, tough, and clear guys - can indeed finish first." p. 264
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Waiting for
Carnot |
Key Point: Complex
systems seem to operate and survive best when they operate on the edge of chaos and order
and when behavior is organized from the bottom up. |
"The most surprising lesson
we have learned from simulating complex physical systems on computers is that complex
behavior need not have complex roots...Indeed, tremendously interesting and
beguilingly complex behavior can emerge from collections of extremely simple
components." p. 279
"...the way to achieve
lifelike behavior is to simulate populations of simple units instead of one big complex
unit. Use local control instead of global control. Let the behavior emerge from the bottom
up, instead of being specified from the top down. And while youre at it, focus on
ongoing behavior instead of the final result." p. 280
"Living systems are actually
very close to this edge-of-chaos phase transition, where things are much looser and more
fluid. And natural selection is not the antagonist of self-organization. Its
more like a law of motion - a force that is constantly pushing emergent, self-organizing
systems toward the edge of chaos." p. 303
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Work in
Progress |
Key Point: To
effect a systems behavior or development one must appreciate its patterns and power, apply
interventions judiciously, and dont bet on a limited set of strategies. |
"You can look at the
complexity revolution in almost theological terms, he (Arthur) says. "The Newtonian
clockwork metaphor is akin to standard Protestantism. Basically theres order in the
universe...The alternative - the complex approach - is total Taoist. In Taoism there is no
inherent order... The universe in Taoism is perceived as vast, amorphous, and
ever-changing... So we are part of this thing that is never changing and always changing.
If you think that youre a steamboat and can go up the river, youre kidding
yourself. Actually, youre just the captain of a paper boat drifting down the river.
If you try to resist, youre not going to get anywhere. On the other hand, if you
quietly observe the flow, realizing that youre part of it, realizing that the flow
is ever-changing and always leading to new complexities, then every so often you can stick
an oar into the river and punt yourself from one eddy to another." "Notice that
this is not a recipe for passivity, or fatalism," says Arthur. "This is a
powerful approach that makes use of the natural nonlinear dynamics of the system. You
apply available force to the maximum effect... The idea is to observe, to act
courageously, and to pick your timing extremely well." p. 330 - 331
"What has happened is that
were beginning to lose our innocence, or naiveté, about how the world works. As we
begin to understand complex systems, we begin to understand that were part of an
ever-changing, interlocking, nonlinear, kaleidoscopic world. So the question is how you
maneuver in a world like that. And the answer is that you want to keep as many options
open as possible. You go for viability, something thats workable, rather than
whats optimal. A lot of people say to that, Arent you than
accepting second best? No, youre not, because optimization isnt
well-defined anymore. What youre trying to do is maximize robustness, or
survivability, in the face of an ill-defined future." p. 333 - 334
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