A Refereed Journal
By
Stephen Shucart
Akita Prefectural University
INTRODUCTION
Linguistics, like most sciences, has traditionally started at the top, viewing language as a complex machine, and has worked its way down analyzing a hierarchy of component parts. Analysis means ‘ the separation of an intellectual or substantial whole into constituents for individual study’. (Langton, 1996). But there’s more to language than mere mechanics, there is also dynamics. The principles of dynamical self-organization are rarely touched upon by traditional analytical methods, and the reason for this is simple; self-organization is a fundamentally non-linear phenomenon. Non-linearity depends on the interactions between parts, and this non-linearity disappears when the parts are analyzed in isolation from one another.
Language is a Complex Adaptive System (CAS), as is Life, Consciousness, Culture, and the Tokyo Stock Market. Of course such things are beyond the modest scope of this paper. What I propose is to use insights from Complexity Science in such fields as evolutionary biology, artificial life, and computer science to present a model of second language emergence within the group dynamics of a classroom setting. I have divided this paper into four main sections. In Part One, ‘Wolfram Classes/Language Classes’, I shall apply work done by the mathematician Stephen Wolfram on the four universality classes of cellular automata and research in the field of Artificial Life by Christopher Langton to present the basic framework of classroom dynamics. In Part Two, ‘Chasing the Red Queen’, I shall use the research of Dr. Stuart Kauffman on co-evolving fitness landscapes and auto-catalytic sets plus the work of Physicist Per Bak on Self-organizing Criticality to expand on the earlier framework. Part three, ‘Language Emergence’; will present research by the computer scientist, John Holland, and Nobel Laureate Murray Gell-Mann on Complex Adaptive Systems and Emergence to add depth and perspective. Finally, in Part four, the Terraced Labyrinth, I draw on recent work in evolutionary computation by Chaos pioneer James Crutchfield to synthesize a new model for second language acquisition.
Diane Larsen-Freeman, in her groundbreaking 1997 paper for the journal Applied Linguistics, ‘Chaos/Complexity Science and Second Language Acquisition’, listed ten key terms which apply to Complex Systems. Since these features will be mentioned throughout this paper, I think it best to define them at the outset. I will present her original description, and, sometimes, add a comment of my own.
1) Dynamic - Constantly changing over time.
2) Complex – Many components or agents whose behavior emerges from the interactions between them.
3) Nonlinear – A system in which the effect is disproportionate to the cause.
4) Chaotic – Here I take exception to her definition. She states: "Chaos refers simply to the period of complete randomness that complex nonlinear systems enter into irregularly and unpredictably." This is the layman’s idea of ‘Chaos’. Better is Kumai’s (1999) definition: "seemingly random, yet with deep structural patterns."
5) Unpredictable – Outcomes cannot be determined in advance. To me this is merely a feature of nonlinearity.
6) Sensitive to Initial Conditions – The famous ‘Butterfly Effect’. "Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?"(Lorenz, 1979). Again, this is a feature of a Nonlinear Strange (Chaotic) Attractor.
7) Open – An open system allows information and/or energy to flow in from the outside. This energy is necessary for the emergence of greater complexity. On the contrary, a closed system is subject to the 2nd Law of Thermodynamics, i.e. Entropy.
8) Self-Organizing – Structure or patterns form on their own. Or, as Kauffman (1996) puts it: ‘Order for Free.’
9) Feedback Sensitive – Feedback acts as a cybernetic governor to regulate the rate of change.
10) Adaptive – The agents do not simply respond passively to events, but
actively learn from environmental changes and responds to take the maximum advantage.
(Larsen-Freeman, 1997)
I – WOLFRAM CLASSES/LANGUAGE CLASSES
The concept of ‘Phase Space’ is one of the most powerful inventions of modern science. It is a way to turn numbers into pictures, and give a flexible roadmap of all the possibilities of a dynamic system. Before the invention of powerful computers physicists could only model linear differential equations in phase space. There are only two attractors that can be pictured with linear dynamics, the Fixed-Point and Limit-Cycle attractors. On a two-dimensional phase space picture, a Fixed-Point Attractor is just that. After a short time the system settles into a straight line. This is equilibrium, the 2nd law of thermodynamics, or entropy. A Limit-Cycle Attractor looks like a wavy line repeating itself. It can have two, three or more waves, but it always repeats.
A Strange or Chaotic Attractor is created by solving a nonlinear differential equation. It is both deterministic and dynamic; a fractal. Fractals, a term coined in 1975 by Benoit Mandelbrot, describe a seeming impossibility – a fractional dimension. It is an infinitely changing pattern, never repeating, self-similar across scales. When it is pictured in two dimensions it merely appears as a ragged line, just random noise. At least three variables are needed before the pattern takes on its distinctive shape; owl’s eyes, or the wings of a butterfly. It is infinite change confined within the finite box of phase space(Gleick, 1987).
Stephen Wolfram was a mathematical prodigy, receiving his Ph.D. from Yale at the age of 20. While doing post-doctoral work at Caltech he decided to investigate Cellular Automata (CA). By 1984 he discovered that he could classify the long-term behavior of CA into four distinct types, no matter which local rules he started from.
John von Neumann, one of the fathers of modern computing, wanted to design a self-replicating machine. With the help of the mathematician Stanislaw Ulam, he designed the first Cellular Automata. CA are the simplest form of Artificial Life (Alife). They are a collection of cells performing computation in unison based on simple, local rules. The steps are discrete, but each step depends not just on the state of the individual cell, but also on its neighbors. They actually evolve over time (Coveney and Highfield, 1995).
After an exhaustive study Wolfram found that all cellular automata would eventually fall into a basin of attraction and settle into one of four universality classes (Wolfram, 1984). A basin of attraction is like a valley with a lake at the bottom. When it rains, no matter where a drop falls, it will eventually it find its way to the lake at the bottom. In this case, the lake symbolizes some form of attractor.
Wolfram Class I: CA which fall into this class of behavior either disappear over time, or become fixed. They reach a static, homogeneous state. The Class I attractor is a linear, Fixed-Point attractor - like a ball bearing rolling around in a funnel and eventually dropping out the bottom.
Wolfram Class II: In this class of CA the pattern will evolve to a fixed, finite size, and form orderly structures that will repeat indefinitely. The attractor for this state is a linear, Limit-Cycle attractor. It resembles a ball bearing rolling endlessly around a grooved pathway, or a child’s racing car rushing round and round the fixed lanes of a racetrack.
Wolfram Class III: Class III behavior is nonlinear. The pattern never repeats, yet still evolves by the rules. Deterministic Chaos, the Strange Attractor, is the symbol for this basin.
Wolfram Class IV: Complex patterns grow and contract in cascades of Chaos connecting islands of Order. This is the phase transition between Order and Chaos, the so-called "Edge of Chaos" where life, learning, and evolution all take place. Understanding Wolfram Class IV is one of the main goals of Complexity Science.
In 1984 Christopher Langton started work on his Ph.D. under the direction of Dr. John Holland. The subject he chose to investigate was the Wolfram Class IV behavior of cellular automata. Before he completed his work, he had virtually single-handedly founded the field of Artificial Life, and pushed the image of "The Edge of Chaos" to the forefront of Complexity Science.
Wolfram Class IV behavior is a phase transition. There are two types of phase transitions first-order and second-order. In a first-order phase transition the jump is sharp and precise. The molecules make an either/or decision; Water or Ice; Order or Chaos, it’s the phase transition we are most familiar with. A second order phase transition is much rarer, but it is the real life embodiment of Wolfram’s Class IV CA model. In Alan Guth’s Inflationary Model of the early universe a Higgs Field undergoes a second order phase transition from the symmetry of the Big Bang singularity to the broken symmetry of our current universe (Guth,1989). In a second order phase transition islands of order float on a sea of fluid that gradually changes to a continent of latticework solid dotted with lakes of fluid. Order and Chaos do a complex dance with intertwining submicroscopic arms and fractal filaments.
Langton realized that phase transitions, complexity and computation were all linked. Wolfram Class IV CA were universal computers. Class II CA were stable enough to store information, but there was no way to transmit it. Class III CA were too chaotic and signals would get lost in the noise. Only a computer at Class IV was stable enough to store information and fluid enough to transmit it. Langton said:
"Life is based on its ability to process information. It stores
information. It maps sensory information. And it makes
some complex transformations on that information to produce
action." (Waldrop, 1992, p.232)
Wolfram Classes are the simplest framework to model general classroom behavior. In real life, elements of all four classes can be found in the same teaching environment, but, for means of clarity, I shall exaggerate the overall effects.
Wolfram Class I – ‘Death in the Afternoon’:
Wolfram Class I behavior swiftly settles to a fixed-point attractor; equilibrium and entropy. This could easily be envisioned as a sarin gas attack leaving the students slumped over their textbooks or lying on the floor in various attitudes of death. A CALL class where students are electrocuted while inserting the CD-ROM can have the same effect. Less extreme examples would include a lecture so boring that the students fall asleep; low-crawl out the back door; or students in various states of catatonia from alcohol or mind-numbing drugs. Day dreaming to the point where all class content flows in one ear and out the other with zero retention is also a definite indication of Class I behavior. At its best, the language class is narrow-focused on memorizing an obscure grammar point, or engaged in a Grammar-Translation exercise with only one correct answer.
Wolfram Class II – ‘The Language Lab’:
Wolfram Class II behavior is marked by the limit-cycle attractor. The activities are linear in nature and very cyclic. The Audio-lingual language lab of the 1950’s and 60’s seems to be the best representative of this teaching style. The students merely listen and repeat patterns over and over until they are memorized. Another example is the Japanese ‘Juku’ or Cram School where students acquire the ability to pass rigorous College Entrance Exam multiple choice grammar tests, yet cannot hold a simple conversation.
The fossilization familiar from Interlanguage studies would also fall into Class II. The student has reached a level of fluency sufficient for his or her needs and becomes stuck. The student can handle the relatively easy class material, and lacks the incentive to push harder (Ellis, 1985). A CALL class in which the computer is used as an electronic blackboard to write the answers to textbook activities, or to post listening transcripts has a Class II attractor.
Wolfram Class III – ‘The Butterfly Knife Effect’:
Class III behavior is nonlinear. The strange attractor shows wild results from small changes to the initial settings. The class is Chaos confined by the phase space of the classroom. A simple activity quickly degenerates into students gossiping in their first languages, answering calls on their cell phones, or butterfly knife fights at the back of the class. The noise level increases, students shout and wander in from other classes, or refuse to remain seated. Discipline is nonexistent. A CALL class finds students reading about Pop idols on L1 websites, playing solitaire, downloading hardcore pornography from Nasty Jack’s Smut Shack (www.nastyjacks.com) or playing QUAKE III deathmatches. A peanut butter sandwich in the hard drive would not be unusual.
Wolfram Class IV – ‘Life on the Edge’:
Class IV is balanced at the phase transition on the Edge of Chaos. The attractor is Self-Organized Criticality (See Part Two – Chasing the Red Queen). Classroom language is at the optimal i+1 Level proposed by Krashen (Krashen, 1978), and the interactions are within Vygotsky’s ‘Zone of Proximal Development (ZPD)’. He states:
" We propose that an essential feature of learning is that
it creates the zone of proximal development; that is,
learning awakens a variety of internal development
processes that are able to operate only when the child is
interacting with people in his environment and in
cooperation with his peers. Once these processes are
internalized, they become part of the child’s independent
developmental achievement." (Vygotsky, 1978)
A classroom in Wolfram Class IV could be organized into many pairs or small groups engaged in meaningful communication to complete a task with a specific goal. The language should be structured, yet still remain open enough to include an element of fluidity or creativity. A CALL example would be the Internet Scavenger Hunt, where teams of students cooperate in a race to complete a task sheet provided by the teacher. Through the use of computers, the students use language and critical thinking to organize their goals, and attempt to accumulate the most points within a time limit.
II – CHASING THE RED QUEEN
"It takes all the running you can do to keep in the same place.
If you want to get somewhere else, you must run at least twice as fast…"
-The Red Queen, in "Through the Looking Glass" by Lewis Carroll.
Dr. Stuart Kauffman is a medical doctor and tenured professor of biology at Dartmouth College, but he spends much of his time in New Mexico, at the Santa Fe Institute, where he devotes his life to the search for the laws of Self-Organization and Complexity. To facilitate his research he has adopted the image of the Fitness Landscape from the evolutionary biologist Sewell Wright . Picture a rolling landscape of peaks and valleys encompassing all of the possibilities of phase space. The highest peak symbolizes maximum fitness. Kauffman wanted to move beyond the basics of Langton’s CA model of an individual agent evolving on the edge of chaos. He was interested in the behavior of a collection of agents coevolving, which is why he brought the landscape image from predator/prey relationships in an ecosystem.
When he set up his N-K model of a fitness landscape (N refers to the fact that each species has N genes, and their fitness depends on K other genes, K being the number of connections) he found that the results of his computer simulations fell into the exact same Wolfram universality classes as Langton’s CA. The N-K landscape modeled a single species, but species do not exist in isolation. To model the even more complex interactions of multiple species he used an NKCS Landscape. The C stands for connections, and the S stands for the number of species. When he ran these computer simulations he found that the different species all evolved to one of three different sections of the landscape, i.e. an Ordered Regime, a Chaotic Regime, and/or an Edge of Chaos phase transition (Kauffman, 1996). The agents in the Ordered Regime reached what Game theory calls Nash Equilibrium, or what biology refers to as an Evolutionary Stable Strategy (ESS). They all reach relatively low peaks and, by cooperating, they all feel no need to improve or climb higher. The basins of attraction are limit-cycle attractors. The Chaotic Regime is sometimes called the Red Queen, after the character in Carroll’s ‘Through the Looking Glass’. All of the agents are running as fast as they can just to stay in the same place. The peaks are high and jagged, and the agents are competing so ferociously that none can climb very high before being knocked off. The landscape, itself, is deforming faster than agents can improve their positions. Here the basins of attraction are Strange Attractors.
The Coevolutionary Edge of Chaos is the phase transition between the two. This is the realm of the highest mean fitness, a balance between cooperation and competition. This is the regime of the most successful agents in an ecosystem. What kind of attractor is found at the Edge of Chaos?
Per Bak, a Danish born physicist at Brookhaven National Laboratories, along with his colleagues Chao Tang and Kurt Wiesenfield, came up with a theory called Self-Organized Criticality while studying the condensed-matter physics of charge-density waves. They soon found that that it could also explain such diverse phenomenon as earthquake distribution and the vagaries of city traffic (Bak, 1998).
The now classic image of self-organized criticality is the sandpile model. If you pour a steady stream of sand into a tabletop it will form a higher and higher cone until it reaches its maximum height, adding more sand causes an avalanche. The pile is self-organized in the sense that it reaches the critical angle by itself. Its state is critical in the sense that the grains of sand are barely stable, the addition of even one more random grain will trigger an avalanche. It is impossible to predict the size of the avalanche, perhaps only a few grains will slide down, or perhaps a chain reaction will send a massive cascade of sand showering off the face of the pile. Only one thing is certain, the statistical frequency of the avalanche size follows the mathematical principle known as a power law, i.e. the average frequency is inversely proportional to some power of its size.
When Kauffman met Bak at the Santé Fe Institute a crucial piece of the edge-of-chaos puzzle fell into place. Self-organized criticality turned out to be the missing attractor, the Edge of Chaos Attractor, and the picture became clear. It also provided a scale of measurement. When a system is at the Edge of Chaos, critical state waves of changes emerge, and this emergence invariably follows a power law.
Fitness landscapes are probably the best way to model the complex interactions that occur in a language classroom. Unfortunately the extremely high number of possible variables and the nonlinearity inherent in the system make it almost impossible to extract the empirical data necessary for replicable experiments. A classroom can have students and /or groups of students moving between any of the regimes of the fitness landscape. It is the teacher’s job to provide the correct level of input, and encourage the students to climb to their points of maximum fitness.
Students deep in the Ordered Regime could be said to be experiencing fossilization. They are on mutually consistent peaks, but the peaks are in the foothills. The students learn a few simple ways to say something, enough to accomplish basic communication tasks, but they endlessly repeat the same patterns with no creativity. These students are often well behaved and cooperative, but much too passive. They are afraid of making mistakes, thus they never experiment. When the tasks are too easy, and the language patterns have already been internalized the students have low motivation and are content with their language level. They can pass their tests and thus have no incentive to improve.
When students are in the chaotic regime a simple mistake can multiply exponentially, causing more and more confusion. The material being presented is usually too advanced for the students to comprehend. Instead of i+1 level input, it is i+10. The assigned task might be too complex or the rules of a game too difficult to understand. Perhaps the task is open -ended, without a clear goal or finish. Students can never reach the fitness peaks because they keep kicking each other off before they get close. Often the noise-level is high, or the teacher’s instructions unclear. The overall fitness of this class is low and the peaks are jagged and massive – a moonscape with cliffs and overhangs that mutate as they climb. Students give up in despair, and discipline becomes a problem. See the examples cited under Wolfram Class III in part one for some other types of behavior experienced in this regime.
Students in the Ordered Regime need more fluidity, more challenge, and those in the Chaotic Regime need more structure or discipline. In between the two the aggregate fitness has reached maximum. Here the fitness peaks are the highest, the information flow is smooth and fast. Students balance cooperation with competition, both pushing and pulling each other to higher levels of fluency. Self-organization is one of the key images for the Edge of Chaos. The input is just a little beyond their comprehension, but they are in Vygotsky’s Zone of Proximal Development. The teacher tunes the complexity of the tasks to the students needs, and higher levels of fluency emerge spontaneously. Activities are both interesting and fun. This causes student feedback, creative input and spontaneous conversations. These types of classes almost run themselves.
III - LANGUAGE EMERGENCE
In 1959 John Holland was awarded the first American Ph.D. in Computer Science, and he is the originator of the genetic algorithm. Most recently he has been working on the question of Emergence in Complex Adaptive Systems (CAS). He is attempting to find the answer by breaking the system into its basic constituents. So far he has isolated seven basics, three mechanisms and four proprieties, common to all CAS. It is important to understand that he doesn’t see these seven as absolutes, other possibilities are a matter of context pertaining to the specific CAS being studied. Though he maintains that all of the other ‘basics’ can be derived from his seven with the appropriate combination. He organizes them in such a way as to emphasize their interrelations (Holland, 1995).
1. AGGREGATION (Property) – This is the standard way of simplifying a CAS. First decide which details are important to the model, these are the agents and meta-agents. Complex, large-scale behavior emerges from the aggregate interaction of the less complex agents.
2. TAGGING (Mechanism) – This mechanism facilitates the formation of aggregates. Tags are the mechanism behind hierarchical organization and lead to the emergence of meta-agents. They provide the basis for filtering, specialization and cooperation. A flag or banner used to rally an army to one side or the other is a tag. A message header on an Internet discussion group is a tag.
3. NONLINEARITY (Property) – The aggregate actions are nonlinear in that the ultimate behavior cannot be predicted by summing or averaging the parts.
4. FLOWS (Property) – A CAS flows over a network of nodes and connections which vary over time. Nodes and connections appear and disappear as agents adapt or fail to adapt. Tags define the network by delimiting the critical interactions, the major connections.
5. DIVERSITY (Property) – The persistence of an individual agent depends on the context provided by the other agents. If we remove one agent from the network a cascade of adaptations results in a new agent filling the niche. Diversity is a dynamic pattern of a CAS, persistent and coherent, like a standing wave. Perpetual novelty is a hallmark of CAS.
6. INTERNAL MODELS or SCHEMA (Mechanism) – The models are used for anticipation and prediction. The schema are interior to the agent. The schema are the patterns selected from a torrent of input, then converted into changes in the internal structure. The changes in the structure of the model enable the agent to anticipate the consequences that will follow when a similar pattern is encountered again.
Holland says:
"There are two kinds of internal models, ‘tacit’ and ‘overt’. A
tacit internal model simply prescribes a current action, under
the ‘implicit’ prediction of some desired future state. An overt
internal model is used as the basis for ‘explicit’, but internal,
explorations of alternatives, a process often called ‘lookahead’
(Holland, 1995,p33)
7. BUILDING BLOCKS (Mechanism) – CAS can be decomposed into reusable elements, i.e. limited samples of perpetual novelty. Experiences can be parsed into the repeated use of the same building blocks, though never in exactly the same combinations. For instance, quarks can be combined into nucleons and nucleons into atoms, then molecules/organelles/cells . . . level on top of level. Building blocks at one level can be reduced to the interactions and combinations of building blocks at a lower level. Higher level laws derive from laws of lower level building blocks.
The Nobel Laureate Murray Gell-Mann approaches CAS from the viewpoint of information and how it reaches the system in the form of data. He focuses on sorting the patterns into schema, then comparing the schema with real-world data and using feedback on the viability of schema in predictions among competing variants. This viewpoint is one of the alternative combinations discovered by Holland’s seven basics. One interesting point Gell-Mann makes, though, is the role of deterministic Chaos. He regards Chaos as a mechanism that can amplify the indeterminacy inherent in quantum mechanics to the macroscopic level (Gell-Mann, 1994).
Professor Jean Aitchison of Oxford, makes some interesting observations in her book on language evolution which I think is quite relevant in contrasting the Fitness landscape model and the CAS model of language. She states that ‘components within the language system . . . interacted with usage of the system in a complex way."(Aitchison, 1996;p.215) She points to the fuzziness of human concepts as a prerequisite for leaps of restructuring. This sounds awfully close to ‘Random Walks on a fitness landscape’ which is the mechanism for moving between varying peaks in different regimes. If we consider a CAS to describe the evolving structure of language, and the Fitness Landscape to model language processing, then we can envision the dichotomy between the two frameworks.
Holland ordered his seven basics to emphasize their interrelationships, but to understand their use in language I think that they should be grouped first into mechanisms, then the properties. Here’s how I see it:
MECHANISMS
TAGGING: Tags form the boundaries of a CAS and allow for aggregation. They break symmetries and enable us to observe and act on properties previously hidden by the symmetries. Holland gives the image of a pool table full of white cue balls. It’s virtually impossible to track the actual cue ball in such a situation, but if you tag it with a red stripe it’s easy to follow. This facilitates selective interaction, allowing agents to select among agents or objects that would otherwise be indistinguishable.
At a deep level, tagging could be setting the language typologies, i.e. SVO rather than SOV, and breaking the symmetry of UG. Communication becomes possible and linguistic separation occurs. Tagging appears to be more syntactic than semantic in nature. In a classroom situation this could be equated with a ‘Focus on Form’, where a teacher ‘tags’ grammatical forms so that the students can be more aware of them within the communicative task.
BUILDING BLOCKS: These are the nuts and bolts of language: The sounds; words; parts of speech and grammar; the subjects, verbs and objects; nouns and articles, etc. Building blocks generate schema, and these are the components that change during hypothesis testing.
SCHEMA: Schema are the archetypal scripts of communicative interactions: restaurant language; hotel language; the giving directions scenario; etc. (Schank and Abelson, 1977). These are most often models based on actual experiences in the Real World. Schema allow for prediction and anticipation. Learning can often come from ‘anticipation failure’ and hypothesis testing (Schank, 1988). Gell-Mann says:
"The process of learning grammar also demonstrates the other
features of a complex adaptive system in operation. A schema
is subject to variation, and the different variants are tried out
in the real world. In order to try them out, it is necessary to
fill in details, such as the ones that were thrown away in
making the schema. That makes sense, since in the real world
the same kind of data stream is encountered again as that from which
the schema was abstracted in the first place. Finally, what happens in the real world influences which variants of the schema survive."
(Gell-Mann, 1994, p.54)
PROPERTIES
AGGREGATION: This is the hierarchical or nested-network nature of all CAS. In language this would be the progression from sound to word to sentence to paragraph to discourse and/or internal speech to monologue to dialogue to group interactions to speech community to all L1 speaker to the global community of L1 and L2 speakers of a language. Perhaps even Interlanguage could qualify as the emergence of higher and higher level aggregates the steps on the path to fluency.
NONLINEARITY: This resonates with the very deepest recesses of language. Small changes in the jump from UG to parameter setting trigger a Butterfly Effect, or an avalanche of switch settings. Chomsky comments:
"Change in a single parameter may have complex effects,
with proliferating consequences." And " A few changes in
parameters yield typologically different languages."
(Chomsky, 1981;p.6 and Chomsky, 1986;p.152)
Small changes at the beginning of the semester or class can trigger unpredictable changes in the results. The nonlinearity of language emergence is a hallmark of a class climbing towards the peaks of maximum fluency, and it is intrinsic to all of the models present here.
FLOWS: A network of nodes and connections. The nodes being the agents or students, and the connections are the messages and ideas flowing between students or between the teacher and students. The teacher controls the flow in a classroom and adjusts it for maximum information; the Krashenite i+1. Tags define the networks by delineating the critical interconnections. This could explain the success of ‘Focus on Form’ exercises to raise the comprehension level of the input and output. Adaptive processes select for tags that cause communication and against the tags that cause misinformation.
DIVERSITY: The cooperation/competition balance in the classroom/student /consciousness that encourages emergence. Evolution is diversity; a dynamic pattern – the standing wave of language. Diversity is the product of progressive adaptation to new situations/expectations/schema refining. Adaptation equals changes in structure based on experience. Diversity and adaptation is the reason why a teacher needs to constantly adjust the cooperation/competition balance of his lessons to promote maximum opportunities for greater levels of fluency to emerge.
These seven basics of a complex adaptive system, when applied to the
language classroom environment, point out the variables and mechanisms which drive the students across the fitness landscape image from part two. The goal is to raise the teacher’s awareness of the mechanisms of language emergence.
In Complexity Science the term emergence denotes the unpredictable, spontaneous reorganization of the components of a parallel distributed network at a higher level (Holland, 1998). The meta-agent emerges from the network of agents. This can be seen all around us. A living cell emerges from a network of chemicals; organs emerge from a network of cells; a human being emerges from a network of organs; and society emerges from a network of human beings.
Language and the modern mind emerge from the interplay of a number of networks. In the purely physical realm, brain modules emerge from a network of neurons, consciousness emerges from this network of modules, but what about language. Professor Merlin Donald (1991) speculates that it was a side effect from transition of different forms of memory that gave rise to language and the modern mind. He divided memory into several different styles, each one emerging from the previous. Episodic memory is common in higher animals, apes and early man. Mimetic memory separated Homo Erectus from the less complex earlier forms, and primitive forms of Homo Sapiens evolved a mythic memory. Proto-Language began in the Mimetic realm, but didn’t take on its final shape until the emergence of longer blocks of coherent discourse in the form of myth (Donald, 1991).
PART IV – The Terraced Labyrinth
The Terraced Labyrinth model originated in the field of Evolutionary Computation as an alternative to the standard fitness landscape model. Language evolution and acquisition, along with other dynamical systems, exhibit epochal evolution – "…behavior in which long periods of stasis in an evolving population are punctuated by sudden bursts of change." (Crutchfield and van Nimwegen, 1999,p. 1) The Terraced Labyrinth differs from the usual fitness landscape in that it utilizes a subbasin and portal architecture to model emergence as a phase transition between levels within a multidimensional framework. An understanding of the separation of scale is necessary to comprehend the place of Second Language Acquisition (SLA) in the current model. Acquisition is a form of emergence, a phenomenon that seems to have a fractal presence in our space-time continuum. Painted in broad strokes, it stretches from the Big Bang instant when Planck-length superstrings began to sing out existence in 11 dimensional Calabi-Yau shapes (Green, 1999), through the coalescence of hydrogen and helium, the flash of nuclear fusion, the formation of solar systems, and the jump from inorganic to organic. Narrowing the focus to our earthly biosphere, life emerged, and adapted under the random variables of gravity, atmospheric composition, and catastrophic collisions with cosmic debris to the tune of epochal evolution. Mammalian, primate, then hominid minds coevolved with social systems through the Peircian levels of Iconic, Indexical, and Symbolic consciousness until reaching today’s post-modern level of language and culture (Deacon, 1992; Mithen, 1995; Noble and Davidson, 1996). Sausaurre referred to langue and parole, Chomsky discussed performance and competence, and Hymes talked of linguistic competence versus communicative competence.
Language, Evolution, and the Human Mind
The first concepts which need to be clarified in this model of language acquisition are genotype and phenotype. Genotype is the code, the DNA, the basic set of rules for an operating system. The phenotype is what emerges when those rules are followed. The phenotype is susceptible to outside variables and random mutation. In the case of human language, there is no separate genotype in hominid DNA which corresponds to language, rather, the genotype which generates the organ called the human brain co-evolved with language as we made the emergent step from Homo Erectus to Homo Sapiens (Deacon, 1992). Exaptation describes a structure that emerges in evolution before the function it now performs. Stephen J. Gould (1991) calls the human brain ‘ the best available case for predominant exaptation’. There has been a consistent and identifiable pattern of increased brain size for the past 3.5 million years. Brain casts from two million-year-old hominid fossils show a region corresponding to Broca’s Area, one of the sections of the modern brain devoted to language processing (Noble and Davidson, 1996).
Language rules do not have a physical existence in the structure of the human brain. Language rules exist in the minds of linguists who take random examples of natural language production and dissect it. In the spirit of Western, reductionist science, they kill a piece of living language, mount it on a board and cut it into pieces. They then examine these individual pieces under their microscopes, and write learned papers on rules that constrict the patterns that these pieces can form. This linear science is correct as far as it goes, but it fails to take into consideration the nonlinear, living whole that emerges from the interactions between the connected parts.
Such diverse scientists as the biologist Terrence Deacon (1992), the psychologists Donald Merlin (1991), and William Noble (1996), and the archaeologists Iain Davidson (1996) and Steven Mithen (1995) all use the cognitive system devised by the American philosopher Charles Peirce in their models of the co-evolution of language and the modern mind. They talk of the three levels: Iconic, Indexical, and Symbolic, as the stages through which language and mind progressed to reach our current level of cognition. Stephen J. Gould and Nils Eldredge (1977) developed the concept of Punctuated Equilibrium to explain the lack of transitional forms in the fossil record. These emergent jumps from Iconic to Indexical to Symbolic seem to mirror external archaeological evidence for epochal evolution (Mithen, 1995). The Neo-Darwinist model of evolution; i.e. gradual change and adaptation via the mechanisms of mutation and natural selection; has had to accept the modification of punctuated equilibrium. The Terraced Labyrinth model explains the details underlying this epochal evolution.
Subbasins, Portals, and Constellations
Previous complexity-based models of language acquisition were based on the image of a Fitness Landscape. (Kauffman, 1995) But the Fitness Landscape model came from the field of evolutionary biology, and "patterns one sees in biology are not always found in other Complex Adaptive Systems." (Axelrod and Cohen, 1999)
James Crutchfield and Eric van Nimwegen, who grounded their model in the fields of evolutionary computation and statistical dynamics, were also unsatisfied with the fitness landscape image:
The evolutionary biologist Wright introduced the notion of "adaptive
landscapes" to describe the (local) stochastic adaptation of populations
to themselves and to the environmental fluctuations and constraints…
The basic picture is that of a gradient-following dynamic moving over a "landscape" determined by fitness "potential". In this view an evolving population stochastically crawls along a surface determined, perhaps dynamically, by the fitness of individuals, moving to peaks and very occasionally hopping across fitness "valleys" to nearby, and hopefully higher fitness peaks…the common interpretation of punctuated equilibria in evolving populations is that of a population being "stuck" on a local peak in a landscape, until a rare mutant crosses a valley of relatively low fitness to a higher peak. (Crutchfield and van Nimwegen, 1999, p.4)
The genotypes in the populations, or, in our framework, the different language subbasins, can be represented as bit-strings of a fixed length. A portal consists of a constellation, a subset of bits that is set to a particular configuration from which a new ability emerges. When the parameters of a specific constellation are set to specific values, the child’s language ability moves through the portal to a higher-level subbasin and can be said to have now acquired that language feature. A hierarchical tree is the easiest way to represent the constellations and their connections via portals, and "setting a constellation to a portal configuration leads one level up the tree" (Crutchfield and van Nimwegen, 1999, p.9).
We should perhaps note here that a Universal Language Tree – one constructed by overlaying all possible language trees, past, present, and future – must contain Chomsky’s Universal Grammar (UG) as a sub-section. Such a universal Terraced Labyrinth would contain all possible human languages. If a path could not be traced through the tree to a particular feature, then that feature could not appear in any human language. If a path could not be traced through the tree connecting any two features, than those two features could not coexist in a single human language.
A Terraced Labyrinth model of language acquisition alleviates the need to posit Chomsky’s mysterious Language Acquisition Device - a black box explaining the innate knowledge a child would need in order to achieve such rapid fluency without the seemingly necessary exposure to an impossible quantity of comprehensible input. The subbasin and portal architecture of the Terraced Labyrinth explains the fixed stages of interlanguage through which a child progresses by setting the portal constellations. It also provides a model of a mechanism for the coevolution of the brain and language.
Summary
Complexity-based frameworks for modeling language acquisition all offer more realistic pictures of this nonlinear, dynamic process than the traditional linear and reductionsist models favored by mainstream linguists. While these models are able to distill the patterns of language emergence and offer fresh insights from their various perspectives, they failed to include the multidimensional pattern of the hierarchical whole, especially across the major boundary between the mechanism of language emergence within an individual and the fractal jump in scale to language emergence in a social setting. By including these complexity-based frameworks in its subbasin, constellation setting, and portal architecture the Terraced labyrinth model eliminates these problems, as well as explaining the difference between learning and acquisition, the step-like pattern of punctuated equilibrium found in all language emergence, and the complexly entwined nature of the relationship between neurolinguistics, psycholinguistics and sociolinguistics. In relating the Terraced Labyrinth to epochal evolution, Crutchfield and van Nimwegen conclude:
We described this more general view of epochal evolution, attempting to clarify the connections to both statistical mechanics and dynamical systems theory. The result is a dynamical picture of a succession of "phase transitions" in which microscopic symmetries are broken and new macroscopic dimensions are discovered and stabilized. These new macroscopic dimensions then become the substrate and historical context for further evolution. (Crutchfield and van Nimwegen, 1999, p. 24)
PART IV – CONCLUSION
So what is the meaning of all this? Is Complexity Science the ‘Magic Methodology’ which will transform teaching? Unfortunately, I think not. At best Complexity offers a new framework to view the knowledge that we already have. An activity that works for one teacher or class often falls flat under different circumstances. Complexity Science is a way to let teachers view classroom dynamics from a higher perspective and analyze why a specific activity works. The main point to remember is that, based on long experience, most teachers already know what works best for their teaching styles and individual classes. Complexity, though, might help us to understand why, and thus help us to design new and improved activities along the same pattern.
In the centuries before microscopes and germ theory local shamans and medicine men would treat illness and injury with natural herbs and healing rituals. Many of those herbs now form the basis for modern pharmaceuticals. The shamans didn’t know why the herbs worked, they just did. In many ways we are the local shamans of language teaching. There are many theories as to why a methodology works, some correct, and some mere fantasy. The important point is that they do work. Modern chemistry has allowed scientists to extract the active ingredients to combine and create more effective medicine. This is the place I see for Complexity Science, extracting the patterns which are most effective at allowing the students to self-organized their minds to the edge of criticality, then over that edge in a cascade of creativity, to emerge at the next terrace level. The Terraced Labyrinth model allows teachers to hasten the exploration of subbasins, and reset their student’s language constellations in order to locate those portals.
Modern technologies of Corpus Linguistics, computer labs, CALL and the Internet are rapidly deforming the fitness landscape of language teaching, but I don’t really see teachers becoming extinct. Technology should only replace the gruntwork of repetition, and add incentive and student motivation. It’s still up to the teacher to guide their students through the labyrinth and find the portals so as to provide the maximum opportunity for language emergence. Complexity Science isn’t the Final Answer, but
it could describe one of the hidden laws of the universe.
END
References
AITCHISON, Jean (1996) THE SEEDS OF SPEECH, CUP:Cambridge.
BAK, Per, (1998) HOW NATURE WORKS, Springer-Verlag
BODEN, Margaret A. (ed.) (1996) THE PHILOSOPHY OF ARTIFICIAL LIFE, OUP:Oxford.
CHOMSKY, Noam (1981) LECTURES ON GOVERNMENT AND BINDING, Dordrecht:Foris.
--(1986) KNOWLEDGE OF LANGUAGE: Its Nature, Order, and Use, New York: Praeger.
COVENEY, Peter, and HIGHFIELD, Roger (1995) ‘FRONTIERS OF COMPLEXITY: The Search for Order in a Chaotic World’, Ballantine Books:New York.
DAVIES, Paul (ed) (1989) THE NEW PHYSICS, CUP: Cambridge.
Crutchfield, J. P., & van Nimwegen, E. (1999, February), ‘The Evolutionary Unfolding of Complexity’, Santa Fe Institute Working Paper 99-02-015.
Deacon, T. (1992) The Symbolic Species. New York: W.W.Norton.
DONALD, Merlin (1991) ORIGINS OF THE MODERN MIND, Harvard University Press: Cambridge, Mass.
ELLIS, Rod (1985) UNDERSTANDING SECOND LANGUAGE ACQUISITION, OUP:Oxford.
GELL-MANN, Murray, (1994) THE QUARK AND THE JAGUAR: Adventures in the Simple and the Complex, Abacus:London.
GLEICK, James (1987) CHAOS: Making a New Science, Penguin: New York
Green, B. (1999) The Elegant Universe. New York: Vintage
Gould, S. J., and Eldredge, N. ‘Punctuated Equilibria: The tempo and mode of evolution reconsidered. Paleobiology, 3:115-251, 1977
Gould, S. J. (1991) Exaptation. Journal of Social Issues, 47, 43-65
Guth, A. and Steinhardt, P. (1989) ‘The Inflationary Universe’ in Davies, Paul (ed.) THE NEW PHYSICS, CUP:Cambridge.
HOLLAND, John H. (1995) HIDDEN ORDER: How Adaptation Builds Complexity, Addison Wesley: Reading, Mass.
HOLLAND, John H. (1998) EMERGENCE: From Chaos to Order, Addison Wesley: Reading, Mass.
KAUFFMAN, Stuart (1995) AT HOME IN THE UNIVERSE: The Search for the Laws of Self-Organization and Complexity, OUP:Oxford.
KRASHEN, Stephen (1981) PRINCIPLES AND PRACTICE IN SECOND LANGUAGE ACQUISITION, Oxford: Pergamon.
Kumai, W. (1999) ‘Group Dynamics at the Edge of Chaos: Toward a Complex Adaptive Systems Theory of Language Learning’ Draft.
Larsen-Freeman, Diane, 1997 ‘Chaos/Complexity Science and Second Language Acquisition.’ Applied Linguistics 18/2: 141-165.
Langton, Christopher, (1996) ‘Artificial Life’, in BODEN, Margaret, (ed.) THE PHILOSOPHY OF ARTIFICIAL LIFE, OUP: Oxford.
Lorenz, E. (1979) ‘Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?’ address to the American Association for the Advancement of Science, Washington D.C.
Noble, W., & Davidson, I. (1996) Human Evolution, Language, And Mind. Cambridge: CUP.
Mithen, S. (1995) The Prehistory of the Mind. New York: Thames and Hudson
Peirce, C. (1978) Collected Papers. Vol. II. Elements of Logic. Cambridge, Mass: Belknap
SCHANK, Roger, (1982) DYNAMIC MEMORY, CUP:Cambridge.
SCHANK, R. and ABELSON, R. (1977) SCRIPTS, PLANS, GOALS AND UNDERSTANDING, Erlbaum: Hillsdale, N.J./
VYGOTSKY, L. S. (1978) MIND IN SOCIETY, Harvard University Press: Cambridge, Mass.
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WALDROP, M. Mitchell, (1992) COMPLEXITY: The Emerging Science at the Edge of Order and Chaos, Simon & Schuster: New York.
Wolfram, Stephen, (1984) ‘Cellular Automata as Models of Complexity’ in Nature 311, 419.