Vol 7, No. 3
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'POST-DARWINIAN DYNAMICS'  by Steve Shucart

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COMPLEXITY THEORY:
C@LL ON THE EDGE OF CHAOS
BY STEPHEN A. SHUCART

COLUMN #3 POST-DARWINIAN DYNAMICS

For most living systems equilibrium corresponds to death. The edge of chaos has also been referred to as persistent disequilibrium. Kevin Kelly sees it as " ... a continuous state of surfing forever on the edge between never stopping but never falling." Chris Langton describes open-ended evolution as a system that ceaselessly self-tunes itself to higher and higher levels of complexity, and Stuart Kauffman says that "The best exploration of evolutionary space occurs at a kind of phase transition between order and disorder."

The majority of mainstream biologists today can be typified as neo-darwinists in that they recognized Darwinıs theory of natural selection as the only force driving evolution, and hold that all new species build up through an unbroken line of gradual, independent, random variations. Lynn Margulis is most famous as the biologist who, along with James Lovelock, came up with the Gaia hypothesis that the geological, atmospheric and biological processes on the Earth are so interconnected as to act as a single, living, self-regulating entity. She is also one of the leading post-darwinists.

A growing number of geneticists, theoretical biologists, mathematicians, microbiologists, and computer scientists are attempting to move beyond darwinian natural selection. Before computers, science consisted of two facets, experiment and theory. First theory shapes an experiment, then the experiment proves or disproves the theory. Computers provide a third way - scientific simulations. A simulation is both a theory and an experiment. Since the advent of cheap, powerful computers the science of complexity has allowed for the exploration of post-darwinist dynamics.

Post-darwinists see the four dynamics of symbiosis, directed mutation, saltationism, and self-organisation as complements to the ruthless power of natural selection. In this paper I shall explore how these dynamics push the evolution of complex adaptive systems along the edge of chaos, and try to give specific examples and uses relevant to language classes in general, and CALL classes in particular.

*Symbiosis -two organisms merging into one, or two working, simple systems merging into a larger, more complex system. In biology this is best observed in lichen or microbes, but in language a good example would be the evolution from a pidgin to a creole to a standard language. Urdu, Swahili and Bahasa Indonesian are instances of the latter.

When multiple, simultaneous innovations are required by a complex system, then large scale symbiosis could be the driving force. Rather than competition, cooperation is the criterion. Symbiosis can be seen in Communicative Language Teaching(CLT) methodologies which try to provide opportunities for students to work together in groups to solve specific tasks.

In a CALL classroom situation the idea of symbiosis pushing the studentıs SLA along the edge of chaos could best be facilitated by having more than one student engage in a CALL task on the same computer, or by having the computers organized in small networks, and have the cooperating networks compete. In this way the students would have to use English to cooperate in completing the task, and the CALL software would act as a catalyst for the symbiosis.

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Directed Mutation - mutations spontaneously crafted in direct response to stresses in the environment. Lynn Margulis has called natural selection the editor, not the author, of evolution. Darwin only dealt with the origin of species, not the origin of individuals. This form of creativity is much easier to accept in terms of the evolving systems of the mind or language, than in the genetic code, where it takes on a heretical Lamarckian dimension.

Hypothesis testing and parameter resetting are standards in modern SLA theory, and directed mutation seems to support it. Under the proper stress to the language environment, i.e. a communicative or CALL instigated task, students, rather than generating language selected at random, will direct their attention to generating a hypothesis about the proper language use in context and try it out to see if it works. If it accomplishes the task, then the students reset their internal image of the L2 accordingly - Interlanguage as linguistic mutation.

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Saltationism - from the Latin saltare, to jump. Complex adaptive systems, be they organisms, economies or languages, are hierarchal in nature. Natural selection and 'survival of the fittest' only proceeds through small, gradual steps, but the creativity needed to overcome a rapid environmental change, or a major innovation needs a quantum leap.

Evolution at the edge of chaos employs two main images. One is a Fitness Landscape, and the other consists of Basins of Attraction. The most important point to remember is they are identical. One is merely the reverse of the other. A Fitness Landscape represents the entire field of possible fitness peaks in a system. The goal is the climb to the global maximum, which, in language, is Communicative Competence or fluency.

Wolfram Classes of cellular automata describe a one dimensional phase space, but Fitness Landscapes based on Boolean Networks can be used to model phase space in three dimensions. The universality classes are the same; A fitness landscape with no connections is a single 'Fujiyama' peak. A correlated fitness landscape in the ordered regime, with low, regular peaks, is in Wolfram Class II. A random fitness landscape - a chaotic moonscape of jagged, towering peaks and precipitous valleys separated by unbridgeable gulfs is in Wolfram Class III. The peaks of maximum fitness, rugged yet close enough together to continually climb, lies at the phase transition on the edge of chaos- Wolfram Class IV.

A basin of attraction represents all of those points in phase space which lead to an individual attractor- Fixed Point, Limit Cycle, or Strange. Keeping the landscape as a model, a basin of attraction could represent all of the streams and creeks draining into a central lake or main river. The key, of course, is to locate an attractor which represents a systemıs maximum fitness.

The search for maximum fitness is where saltationism comes in. Evolution doesn't merely proceed through gradual incremental steps, but jumps from level to level, from peak to peak, or from one basin of attraction to an even deeper one. Another idea to keep in mind, though, is that the landscape is constantly deforming in response to outside influences. The edge of chaos isnıt static, itıs an ever changing wave upon which the system, to co- evolve, must remain in constant motion.

The pedagogic implications for language classes and CALL classes remain the same as for directed mutation. The 'jumps' in saltationism being the leaps in Interlanguage hypothesis testing, and when the language patterns crystallize in the learnerıs mind, a quantum jump to a higher peak on the fitness landscape is made.

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Self-organization - development biased towards certain forms which then become pervasive standards. Emergence is another term for this, and life, itself, is an example of an emergent phenomenon. The organic seems to have crystallized from the inorganic. Ontogeny is the study of the development of an adult organism from a single-celled zygote. Roughly 260 cell-types formed from one fertilized cell.

Emergence explains why no little black box of Chomskian UG has ever been located. UG and language typologies are emergent phenomena, self-organized vortexes in the mind, basins of attraction which are set early in a childıs developmental life.

Per Bak, a physicist working at the Brookhaven Institute, invented the sandpile image for self-organized criticality. As more and more sand is piled onto a table it eventually self-organizes into a pile poised on the edge of criticality. The next grain of sand will trigger an avalanche. No one can predict whether the avalanche will be large or small, but the frequency will follow a power law. This image is also useful in an EFL/ESL situation. The teacher should provide an environment where the students minds are in a state of self-organized criticality and keep adding increments of language(i+1 input) until an avalanche of output cascades from the students. It is impossible to predict when or how much language will be generated. The key point is to tune the classroom to the edge of criticality, then the individual students with learn at their own paces.

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In conclusion, evolution takes place in a complex adaptive system poised on the edge of chaos. Deep evolution is an aggregate of the four dynamics all operating in parallel with natural selection to bring about a system of open-ended, sustainable creativity. Intelligence, language and communication are emergent properties of this community of dynamics. Successful language classes, especially those computer classes powered by the tools of carefully selected CALL software, utilize the patterns generated by activities balanced in the zone of Wolfram Class IV behavior - language acquisition, like life and consciousness, occurs on the edge of chaos.