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Complexity and Chaos

New -- December 15, 2003

This page is, among other things, a "Side-Bar" to the Annals of Earth (specifically Episode III).  But it can also be read as an adjunct to Chaos Theory.  In any case, it is designed for those destined to rush in where angels fear to tread.

The science of Complexity happens somewhere between totally ordered and totally random systems.  This transition point is termed The Edge of Chaos.  (Chaos, in this regard, is considered a subset of complexity.)  Complex systems are denoted by the fact that they may be generated by a relatively simple set of subprocesses -- a few things interacting, but producing tremendously divergent behavior.  As Nobel laureate Murray Gell-Mann phrased it: “Surface complexity arising out of deep simplicity.”  One might also call this: deterministic chaos; in other words, it appears random but isn’t. 

[And if one follows the thread, one can conclude as Chris Langton did:  “If the theory of complex systems is not some kind of seductive illusion [which it may well be!].  And if the brain can be described as a complex adaptive system; then, yes, consciousness can be explained.”  --  quoted from the book, Complexity, by Roger Lewin]

Some theorists suggest that the Cambrian Explosion may have been due to the occupation of a “vacant ecology”.  In other words, the early Earth was an environment which was available and receptive to evolutionary experimentation.  But such vacant ecologies had occurred before and have arisen since, and yet there have been no other geologic, evolutionary moments of such an explosive character.  Furthermore, the degree to which specialization followed experimentation, with many specialists going the way of the Dodo Bird, has not occurred with such a vengeance before or since. 

Keep in mind that having recently evolved from a few common ancestors, the various species of the Cambrian would have had to have been interacting with each other quite closely.  This factor strongly promotes the finding of a niche in the ecology by each species, or rather quickly teaching the failing species the concept of no room at the inn.  Extinction, is forever, and in addition, the re-evolution of extinct major forms requires the concatenation of too many improbable events for it ever to occur.

The pattern of the Cambrian Explosion, nevertheless, is fundamental in evolution, even if it’s the most extreme example.  As one specialist in complexity/chaos theory phrased it: “You get an initial scatter of new forms, and then it gets harder and harder to improve upon them.  You see it in biology, industrial economics, maybe even in the evolution of social complexity.” 

It also leads us back to the concepts of nonlinearity and system self-organization, aspects of complexity-chaos theory and other ingredients, mentioned in Episode IThe Cambrian Explosion is the quintessential representation of nonlinear and self-organizing systems.  Nonlinear systems provide for small inputs (such as the first time two cells joined together to form a multi-cellular organism), which then lead to dramatically large consequences.  At this point, very slight differences in initial conditions (such as would have existed at the end of the Precambrian Era) produce very different outcomes (variations in Phyla out-the-kazoo) -- the latter the basis for the unpredictability of nonlinear systems. 

It becomes painfully obvious that self-organization is a natural property of complex genetic systems.  [Well, maybe not obvious, but definitely painful.]  It can, in fact, be shown that there is a spontaneous crystallization of order out of complex systems, and that this spontaneity can occur with no need for natural selection or any other external force.  I.e. you don’t need a theory of evolution!

Global structure emerges from local activity rules, a characteristic of complex systems.  The biological membranes are at the edge of chaos, and that’s no accident.  The edge of chaos is where information gets its foot in the door in the physical world, where it gets the upper hand over energy.  Being at the transition point between order and chaos not only buys you exquisite control -- small input generating big change -- but it also buys you the possibility of information processing becoming an important part of the dynamics of the system.  Systems adapt toward the edge of chaos.  Complex adaptive system not only moves toward the edge of chaos, but also hone the efficiency of its rules as it proceeds.  (Arising from this factor is the curious fact that the number of cell types in any organism is roughly the square root of the number of genes.  It’s a strange, but mathematical, world.)

Genes, as it turns out, are arranged as networks, known as random Boolean networks.  [These networks arise from Boolean Algebra, which is totally arcane and esoteric (“for the few”), but whose very name implies great legitimacy amidst a universal sense-of-humor in naming things.]  A Boolean network proceeds through a series of so-called states.  At a given instant, each element in the network examines the signals arriving from the links with other elements, and then demonstrates activity or inactivity, according to its rules for reacting to the signals.  The network then proceeds to the next stage, whereupon the process repeats itself.

Under certain circumstances a network may proceed through all its possible states before repeating any one of them.  In practice, however, the network at some point hits a series of states around which it cycles repeatedly.  This repeated series of states is an attractor in the system. 

In fact, a network can be thought of as a complex dynamical system, and is likely to have many such attractors.  There may be a large attractor in morphogenetic space that results, for example, in a functional visual system for an organism.  I.e. eyes are the product of high-probability spatial transformations of developing tissues. 

Similarly, species are attractors in a space of morphogenetic parameters.  Instead of any kind of biological form being possible, within certain mechanical limits (as in Neo-Darwinism), the organizational dynamics of morphogenesis define a limited number of points in that space.  In effect, the possible range of biological form is restricted in some fundamental way.

There is also the specter of what is referred to as The Red Queen effect (Alice’s nemesis in Through the Looking-Glass).  This curious effect (things are indeed getting curiouser and curiouser) refers to the phenomena that predator and prey species appear to have to keep running hard (in terms of evolution) just to stay in the same place.  It is the classic and/or proverbial “rat race” -- where even if you win, you’re still a rat” [Lily Tomlin]. 

Individual species in a group may behave selfishly, and in the process adapt collectively with the group benefit being a goal (one of the wilder theories of Complexity).  Collective adaptation to selfish ends, in fact, produces the maximum average fitness, each species in the context of others.  Creatures get better at evolving in the midst of all the activity.  It’s Mini-Gaia [referring to Lovelock’s Gaia Hypothesis -- where the Earth itself has a sense of consciousness].  If connectedness among species within the system is low, then the effects of the initial perturbation will soon peter out.  This is when the system is near the frozen state.  With high connectedness, however, any single change is likely to propagate hectically throughout the system, with many large avalanches.  This is the chaotic state.  At the intermediate state, the edge of chaos -- with internal and between-species interactions carefully tuned -- some perturbations provoke small cascades of change, others trigger complete avalanches, equivalent to mass extinctions.  There is something deep about the world out there.  Very deep.

Species-poor communities (such as the last stages of the Precambrian) are easy to invade.  Newly-established species-rich communities (early Cambrian) are more difficult to invade than species-poor ones, but mature communities (later Cambrian) are even tougher.  Interactions among the species in the community create “an invisible protective network” that tend to repel potential invaders. 

In Hawaii, for example, the highland regions which are still pristine with native plants and birds, have allowed the invasion of relatively few species.  But in the lowland regions, human settlements have disrupted established communities and made them equivalent to immature communities and thus vulnerable to invasion. 

A global property of persistence arises from interactions among species, but not particularly any special grouping of species.  Reassemble a community from the beginning using the same species, and one finds they can’t do it, no matter what.  One simply cannot put a community back together again once it’s been taken apart (the old Humpty Dumpty analogy).  Persistent communities can be assembled only if, on the way to them, other species come in and out of the community, like stepping stones to a more stable state.  Natural communities during assembly bring themselves toward a critical state, the edge of chaos; where they act on the basis of internal dynamics, not in response to anything external.  This is the emergent property of a dynamical system.

Biological systems can’t avoid complexity; it emerges spontaneously, with complexity seeming to increase through time.  Great complexity flows from a simple set of rules.

Why? One possibility is that biological complexity has to do with the ability to process information.  Organisms are complex dynamical systems and what may be driving their evolution is increased computational ability; i.e. information processing being the mark of complexity.  Selection among organisms will thus lead to an increase in computational ability. 

The fossil record, for example, shows a dramatic increase in average brain size with the evolution of mammals from reptiles (230 million years ago), and again, when “modern” mammals evolved some 50 million years ago.  On the other hand... Of the 40,000 species of vertebrates, 25,000 are fishes (with no trends in increasing brain size), and 8,000 are birds (again, no increasing brain size trends).  Brains, in fact, may appear important only to a brain-centric culture such as ours.  The porpoise may in fact be having more fun!

Alternatively, dynamic systems, according to Herbert Spencer, have a tendency to become more concentrated and heterogeneous as they evolve.  Simple, or homogeneous, systems (“One World Orders” and other anti-diversity attitudes) are inherently unstable -- like a balanced scale, they inevitably becomes unbalanced due to rust, wind, too much Russ Limbaugh, or simply in response to Entropy.


Episode III -- The Evolution and/or Creation of Life

Chaos Theory         Connective Physics

Forward to:

Episode III -- The Evolution and/or Creation of Life

Episode IV -- In Search of Eve         Sonoluminescence


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