Context Dependency in Human Performance: Balance Tasks and Cognitive Development, Lecture notes of Psychology

Download Context Dependency in Human Performance: Balance Tasks and Cognitive Development and more Lecture notes Psychology in PDF only on Docsity! CHAPTER 12 Kloos, H. & Van Orden, G.C. (2009). Soft-assembled mechanisms for the grand theory. In J.P. Spencer, M. Thomas, & J. McClelland (Eds.), Toward a New Grand Theory of Development? Connectionism and Dynamics Systems Theory Reconsidered, (pp. 253- 267). Oxford University Press. Soft-Assembled Mechanisms for the Unified Theory Heidi Kloos and Guy C. Van Orden Do connectionist and dynamic-systems models converge on a unified theory? The answer depends on the kind of mechanism that the two models attempt to unravel. Two views of mechanism avail themselves to contemporary scientists. One view of mechanism represents cognitive activity as reducible to a cognitive architecture of separate cognitive components. Another view sees cognitive activity as emergent and highly dependent on fine details of the con- texts in which behavior emerges. We will argue in this chapter that connectionist and dynamic systems models complement each other and collectively move toward a unified theory of development if they subscribe to the second view of mechanism, one that treats behavior as soft assembled in the immediate context. The chapter organization is as follows. In section Where Models Converge in Stalemate, we address why models aimed at reducing behavior to cognitive components cannot make clear headway. The argument is that a reduction of behavior requires human performance to be relatively context free. Yet, as we show with the example of balance task performance, human performance is highly context dependent, even in the sterile laboratory context of balance experiments. In section Taking Context Effects Seriously, we elaborate on what such context dependence could mean. While not conclu- sive on its own, strong context dependence is consistent with the idea that cognitive activ- ity is softly assembled to suit the immediate task environment. Soft assembly offers a plau- sible alternative to hard-assembled cognitive functions—functions that exist prior to and independently of the task context. We review more pointed evidence for soft assembly and discuss why models that take soft assembly seriously—connectionist or dynamic systems— anticipate the unified theory. WHERE MODELS CONVERGE IN STALEMATE At the center of the argument is strong con- text dependency in human performance. We develop this argument around well-studied examples from developmental psychology, in particular children's performance on balance scale tasks. However, our points pertain to cog- nitive modeling more generally. Balance Scale Performance and Associated Models Picture a child in a balance scale experiment. The balance scale straddles a fulcrum and has pegs along its surface on which to set weights (see Fig. 12.1). The experimenter sets some weights and asks the child to predict the behav- ior of the scale. Will it stay balanced, will the right side tip, or will the left side tip? To per- form correctly in every case, the child must take into account the number of weights on each side of the bar, the distance of each weight from the fulcrum, and their product. Different children give different kinds of answers to balance scale problems of this sort, but four kinds of answers seem reliable and systematic (Siegler, 1981). (I) One class of answer appears to reflect an exclusive focus on 253 254 REACTIONS FROM THE OUTSIDE . Figure 12.1. Schematic illustration of a balance scale apparatus The balance scale apparatus depicted has four pegs on each side; the number of weights on each side varies during the balance scale task. the amount of weight on each side of the ful- crum. Children who answer this way consis- tently expect the side with the most weights to tip. When there are equal numbers of weights on each side, children in this group expect the balance scale to stay level, ignoring distance from the fulcrum. (II) A second class of answer appears to take into account distance from the fulcrum, but only when weights are equally dis- tributed on both sides. Children who produce this kind of answer predict that the heavier side will tip. But when both sides have the same numbers of weights, they predict that the side with weights furthest from the fulcrum will tip. (Ill) A third class of answer takes into account both weight and distance from fulcrum, but does not suggest a systematic integration of the two dimensions. Children who produce this class of answers correctly predict the effect of weight when the distances are the same, and they correctly predict the effect of distance from fulcrum when the number of weights is equal. However, when both weight and distance from fulcrum differ, then these children simply guess. (IV) A final, fourth class of answers appears to take into account both relevant dimensions (number of weights and distance from the fulcrum) and integrate dimensions appropriately when the two dimensions are pit- ted against each other. A variety of models have been proposed to explain the four kinds of answers and the transition from one type of answer to the next more sophisticated. Production-rule models suggest that children's performance derives from rule-like algorithms or strategies that can change rather suddenly as a result of experience (e.g., Klahr & Siegler, 1978; Langley, 1987; Sage & Langley, 1983; Schmidt & Ling, 1996). Connectionist models, on the other hand, suggest that children's performance is not a function of explicit rules but rather a grad- ual adaptation to statistical relations between balance scale appearance and response (e.g., McClelland, 1989, 1995; Shultz, Mareschal, & Schmidt, 1994; Shultz, Schmidt, Buckingham, & Mareschal, 1995). Finally, dynamical systems models capture developmental changes as sud- den jumps in the cusp catastrophe—a rule-like response looses stability and changes suddenly in a phase transition or bifurcation to a new rule (e.g., Van Rijn, Van Someren, & van der Maas, 2003). The condensed overview of these mod- els indicates some disagreement among them about the causal mechanism that could under- lie balance performance. One solution to the disagreement has been to evaluate the degree to which the output of a model can capture human performance overall (Van Rijn et al, 2003). For instance, one could find a way to calculate overall fit across models in a single score and conclude that the model with the best score must be using the correct mechanism—the mechanism that best mimics the underlying cognitive architec- ture. On the grounds of this logic, production- rule models might receive a low score because they have difficulty capturing the developmen- tal transition to a more sophisticated rule. And connectionist models might receive a low score because they do not capture rule-like human performance unless the rules are part of the sta- tistical relations in the training set (Raijmakers, van Koten, & Molenaar, 1996). SOFT-ASSEMBLED MECHANISMS FOR THE UNIFIED THEORY 257 other effects. In this case, one could legitimately partition out task context as an independent source of variation in data. In a model, task context would then become a fixed parameter. But task and context effects rarely combine so straightforwardly, in balance performance or any other developmental phenomenon. As our review illustrates, children tested in a balance task do not simply perform better or worse. They exhibit different qualities of performance in different task contexts. Still another way to treat contexts effects is to equate different effects with separate compo- nents of the mental architecture. Successful per- formance in one context might reflect implicit knowledge, for example, while performance in a different context reflects explicit knowledge. This solution may appear clear-cut when tasks differ conceptually. For instance, tasks that require a physical action such as balancing a rod can appear conceptually different from tasks that require a verbal judgment of balance (c.f. Kirst, Fieberg, & Wilkening, 1993; Levin, Siegler, & Druyan, 1990). A physical action might shed light on implicit knowledge, while verbal action might shed light on explicit knowledge—two distinct forms of representation. However, even if we ignore stalemates that have emerged over supposedly clear-cut distinctions (Cleeremans, 1997; Farah, 1994), this approach runs aground when tasks are conceptually alike. For example, it is not clear how a balance scale task with a small number of weights and pegs differs con- ceptually from balance scale tasks with a large number of weights and pegs. Both should entail the same knowledge; so finding a difference in performance leaves one guessing intuitively about what the separate components might be. But to merely equate effects with components, what has been called the effects = structure fal- lacy (Gibbs, 2006; Lakoff, 1987), yields a theo- retical enterprise that is unpredictable, circular, and likely to end in stalemates among compet- ing intuitions. Finally, the most widely practiced response to task effects is to argue about which context is more transparent to mental functions, or equiv- alently which task context produces more pure data than another. In the example of the balance scale performance, Siegler (1981) defends the highly structured and methodologically pre- cise task context of his assessment procedure, and Wilkening and Anderson (1982) justify the legitimate expansion of task contexts to explore the task space. But in truth, there is simply no empirical basis on which to decide which task context is best. All task effects refer equally to changes in outcome measures of performance. Distinctions among task effects are supported only by intuitions about competence based on convention or esthetics, but not evidence. Consider, however, that task effects might not be superficial aspects of performance, but rather that context is always and fundamentally con- stitutive of children's performance. Arguments about the purity of data have not fared well in other domains. Conventional studies of adult cognition have virtually run to stalemate on the question of which task's data best reveal the architecture of cognition. Details of apparent stalemates have been described for perception (Uttal, 1990, 1997), language and reading (Goldinger & Azuma, 2003; Van Orden & Kloos, 2005; Van Orden, Pennington, & Stone, 2001), and memory processes (Watkins, 1990; Weldon, 1999). Similarly, functional neu- roimaging of adult cognition shows signs of running to stalemate because subtle changes in task context cause cognitive functions to be in different parts of the brain (c.f. Cabeza & Nyberg, 2000). In sum, we have reviewed how task con- text effects determine our laboratory pictures of children's knowledge. Such context effects demonstrate that a child's performance is an interaction of the child's knowledge and the specific task constraints within which they act. The solutions discussed so far hold onto the idea that context-free performance exists and should be given priority for a reduction to spe- cific cognitive components. But these solutions have also, so far, led to stalemates about which tasks can separate context from components most successfully. In the next section, we dis- cuss a more conservative solution to context sensitivity—one that takes context sensitivity at face value and accepts that context is constitu- tive of human behavior. 258 REACTIONS FROM THE OUTSIDE TAKING CONTEXT EFFECTS SERIOUSLY In the remainder of this chapter, we describe a path to circumvent stalemates about cogni- tive components and task contexts and thereby situate connectionist and dynamical systems models within a unified theory. The argument rests on the distinction between soft-assembled and hard-assembled cognition introduced by Turvey and Carello (1981). In what follows we describe this distinction in more detail and show how soft assembly provides a new way to think about context and behavior. We then return to the issue of modeling and discuss how connectionist and dynamical systems models can complement each other and point toward a new unified theory. Soft- Versus Hard-Assembled Mechanisms Most of the research discussed so far is grounded in the assumption that cognitive activity is based on hard-assembled mechanisms. These mechanisms exist off-line in some form of inac- tive or dormant state and are activated in a par- ticular task. Going back to the balance scale research, a hard-assembled mechanism could be a child's rule about what makes a balance beam tip, a recurring strategy that a child pur- sues in order to figure out the answer, or simply a child's knowledge about the effects of relevant dimensions. Hard-assembled mechanisms are independent of the immediate task context, they reveal themselves across multiple contexts, and are therefore discovered in context-independent performance. By contrast, soft-assembled mechanisms emerge in contextually constrained, collec- tive action of the brain and body. They come into existence with enaction, and they are only realized within the immediate context of enac- tion. An example of a soft-assembled system is the kinematics of a limb in a particular action. The mind and body in context will together cre- ate unique kinematics, and if the movement is repeated, each repetition will reveal unique kinematics (Berkinblit, Feldman, & Fukson, 1986; Bernstein, 1967). Looking across repeated movements, one sees a family resemblance, but no context-free mechanism exists to tie these movements together. Of course muscles and ten- dons and neuropil continue to exist throughout, but the instantaneous play of emergent control is realized in the movement itself, an enacted limb movement that is unique in each instanta- neous context (Turvey, 1990). Self-organized criticality is proposed as the mechanism that underlies soft-assembled cognitive activity (Juarrero, 1999; Turvey & Moreno, 2006; Van Orden, Holden, & Turvey, 2003), a concept borrowed from physics (Bak, 1996; Jensen, 1998). Criticality refers to a pre- paratory state of a system, also referred to as critical state, that emerges immediately before a response occurs. This preparatory state con- sists of several potential responses, all of which are contextually appropriate, although maybe not accurate. In the balance scale example, the potential responses will include the kinematics of indicating whether the scale will stay bal- anced, tip to the right, or tip to the left. Self-organized criticality is brought about by local interactions among processes of the sys- tem. Those interactions that satisfy contextual constraints are strengthened, and thereby recruit other processes to their configuration. As a result, these local interactions extend to the periphery of the body and create interdependence among all component processes. It is this interdepen- dence that allows components to act together, to express one of a potential set of contextually appropriate outcomes. Thus soft assembly creates poised, situated, state dynamics across the brain and body. Immediately prior to action, the final contextual contingencies of the trial, including the stimulus, will collapse the critical state to one response option, the response that the child will enact (c.f. Jarvilehto, 1998). Two features make self-organized criticality ideal to explain context effects. First, as noted, a critical state is a situated state, meaning that it is directly linked to the immediate constraints of the task context. Preparative cognition stays in the loop, so to speak, to create continually updating, contextually appropriate, critical states ready for action. This situated cognitive activity ensures that the child will respond appropriately (though not always accurately) SOFT-ASSEMBLED MECHANISMS FOR THE UNIFIED THEORY 259 with the response options that the experimenter allows. A cognitive act within an arbitrary con- text requires a situated preparatory state to anticipate the situated future—for instance, a child poised to stay on task in novel or famil- iar stimulus conditions and to make a balance scale response. Perpetually changing relations among context, brain, and body situate cogni- tive activity within an oncoming task. Second, self-organized criticality ensures coordination across multiple scales of time and space. Even aspects of the artifactual bal- ance scale environment change at different rates. Trial-by-trial changes in the distribution of weights occur on a relatively fast timescale, whereas the static laboratory backdrop changes on a much slower timescale. In another exam- ple, millisecond changes in the acoustics of a conversation co-occur with second-by-second, minute-by-minute, and more drawn out scales of change in structure, content, contextual backdrop, shared knowledge, turn-taking, and other facets of the conversation. Likewise there are many scales of change entailed in the optical flow of a walker, from nearby bumps in the road to landmarks or scenery, flowing by at different rates depending on relative size and proxim- ity, to meandering detours and even changes of destination, to name just a few. Perpetual coor- dination of cognition is necessary because the environment changes perpetually on multiple timescales. The brain, the body, and other biological sys- tems are likewise organized on hierarchies of timescales (Soodak & Iberall, 1987). Each hier- archy spans faster and slower changes in neural activity and other physiological processes, time- scales of change in limb and torso movements, and in fascia and skeletal movements. Self- organized criticality organizes the processes of the brain and body to act together, simulta- neously, across their various scales of space and time. This organization across the brain and body allows context to work simultaneously at all scales, to fully and subtly situate the brain and body within the changing environment (Kello, Beltz, Holden, & Van Orden, 2007). Local interactions among embodied pro- cesses on different timescales weave the intrinsic fluctuations of the component processes into a coherent fabric of flux, despite inherent tenden- cies of the different processes to vary at their own different rates (on their own timescales). Competitions among local rates of change strike a precise balance with globally emerging cooperative activity. In the precise balance of (or near) the critical state, they produce a long- range correlated, aperiodic pattern of change or flux in behavior—a complex fractal pattern of long-range correlations. The aperiodic flux is called 1/f noise, pink noise, 1/f scaling, fractal time, and other names, and is a generic predic- tion of systems in critical states. Evidence for Soft Assembly What is the evidence that human cognition is soft assembled? As discussed above, soft- assembled processes have two characteristics that come from self-organized criticality: (1) pre-preparedness of critical states, rather than a dormant system that is merely reactive to a stimulus, and (2) long-term coordination and correlation of processes, rather than indepen- dent and static components. We present evi- dence next for these two features. Pre-prepared critical states. Findings of ultrafast cognition provide evidence that cog- nition is pre-prepared. Take for example the results of Grill-Spector and Kanwisher (2005): The time it takes a participant to know that a picture was flashed on the screen is sufficient to know whether the picture showed a bird or a car. Perceivers apparently required no more time "for object categorization than for object detection" (Grill-Spector & Kanwisher, 2005, p. 157). Such ultrafast cognition has been found even when participants are asked to categorize novel pictures on the basis of animacy (i.e., ani- mate versus inanimate), an archetype of high- level cognitive activity (Fabre-Thorpe, Delorme, Marlot, & Thorpe, 2001). Ultrafast cognition is surprising and unex- pected from the perspective of hard-assem- bled cognition. If cognition begins only after a stimulus onset, then substantial information processing remains to be completed prior to a categorization response. If cognition were one part of a hard-assembled chain of events that 262 REACTIONS FROM THE OUTSIDE assembly, context is causally entwined with the measurement of behavior (Van Orden, Kello, & Holden, in press). Consequently, measured outcomes differ in quality from the embodied processes from which they emerge. On-coming contingent details of task demands and imme- diate task contexts are constitutive of behav- ior. Contingent details, as fluid changes in constraints, change the interaction among the component processes from which behavior emerges. Context Constrains the Body We have argued in previous sections that con- text effects are not simple add-ons to so-called real effects. Instead, pervasive context effects indicate different design principles altogether. This argument expands upon a famous descrip- tion of development by connectionists—namely, that development entails "interactions all the way down" (Elman et al, 1996). Elman and col- leagues use a newly hatched duck to illustrate how preparative constraints set up the poten- tial for imprinting that is subsequently deter- mined by the interaction with the environment. Beyond nature and nurture, a duck, or a child, is pre-prepared for developmental milestones, and the milestones are realized in interactions with the environment. Development reflects local details of the environment as a consequence. Likewise cognition itself is preparative and real- ized in local interactions with the environment (Turvey & Fitzpatrick, 1993). Currently, dynamical systems and con- nectionist models address context effects by accounting for children's performance in more than one context, usually by additions to their architectures. For example, the dynamical sys- tems model of Van Rijn and colleagues (Van Rijn et al., 2003) simulates rules I-IV, as well as the torque effect described by Ferretti and col- leagues (e.g., Ferretti et al., 1985). McClelland's (1989) connectionist model can account for a dif- ference in salience between weight and distance that could explain the discrepancy in perfor- mance when children are given propriocep- tive information about weight versus distance. These attempts are insufficient in the present light, however. And this not only because they fail to capture the addition rules proposed by Wilkening and Anderson (1982) or the idiosyn- cratic rules discussed by Kliman (1986). Even if a model could be rigged to account for chil- dren's behavior in all the discussed contexts, it will not anticipate the inevitable next round of context effects. Context effects are not exhausted at the level of the larger task contexts illustrated in the first part of this chapter. Context effects permeate the brain and body well below the level of trial judgments in particular tasks. That is to say, the context effects discussed in previous sections are just tips of icebergs, so to speak, and soft- assembled icebergs are context sensitive all the way down. Below the iceberg tips, each instanta- neous muscle flex and each pattern of rhythmic cortical firing creates a context for every other muscle flex and every other pattern of neural firing (c.f. Belen'kii, Gurfinkel, & Pal'tsev, 1967; Freeman, Holmes, Burke, & Vanhatalo, 2003; Marsden, Merton, & Morton, 1983; Raichle & Gusnard, 2005). Take, for example, the coordination of speech after an unexpected pull to a person's jaw (Kelso, Tuller, Vatikiotis-Bateson, & Fowler, 1984; Shaiman & Gracco, 2002). Articulation com- pensates with movements in the upper and lower lips to preserve the flow of speech such that a lis- tener cannot distinguish between perturbed and unperturbed speech. The compensation entails cortical interactions, the fluid matrix of neuro- muscular interactions in the lips, modulation of the force of breath and the pace of respiration, and all else that makes up speech. Most impor- tant, the fluid compensation stays within the limits of contextual constraints. Context in this case equals the unfolding of a spoken word as co- articulated speech. This context of constraints, specific to the particular co-articulation, exists in a particular configuration at the point at which the experimenter perturbs the jaw. This configuration constrains the fluid compensa- tion, limiting potential compensations to those that insure intelligibility, all the way down. The example illustrates how global and local context are embodied in local interactions as limits (or constraints) on cascading interactions among excitable neuromuscular media. These SOFT-ASSEMBLED MECHANISMS FOR THE UNIFIED THEORY 263 limits are demonstrated widely in motor coor- dination and also in the neuroscience of per- ception and action. In laboratory experiments, brain and body demonstrably reconfigure, in an instant, to accommodate local changes in the task environment. For example, a slight change in a motor coordination task—increasing the stimulus pace of the coordinated movements— leads to a new pattern in behavior in a virtually instantaneous phase transition across brain and body (Kelso, 1995). To accomplish this, active constraints must anticipate the phase transi- tion, and must define a potential set of changes in concurrent interactions among excitable media. Active constraints maintain perpet- ually updated, context-specific potential sets of actions, which anticipate which actions are appropriate, necessary, and possible. Human and nonhuman animals prefigure how to act to satisfy their contexts of action. They must do so to keep apace of perpetually changing relations between actors and environments. In effect, brain, body, and context combine constraints to poise the actor perpetually ready for action. IMPLICATIONS FOR MODELING________ Contemporary models do not usually repre- sent context as a source of constraints. Context is usually implemented as activation or some other causal force. The pace at which activation is updated defines the primary timescale of a model's dynamics, and activations from context and other sources are usually integrated on this single timescale. A typical connectionist model will also include a second timescale of change in connection weights, but the model is always limited to a definite (usually small) number of timescales. This is true of dynamical systems models as well if they equate parameters and variables with hard-assembled mechanisms. Parameters and variables amount to a few explicit timescales of hard-assembled dynam- ics. However, for all their strengths, contempo- rary models grossly underestimate the number of temporal scales on which cognitive activity is actually assembled. Actual cognitive activity unfolds across an indefinite number of timescales in a coordinated fractal pattern that hard assembly does not anticipate. We have explained this fact keeping in mind a picture of cognition that has a primary preparative function (c.f. Raichle & Gusnard, 2005). In the concrete terms of a lab- oratory experiment, cognition situates a person to participate. Contemporary models do not capture the situated behavior of participants and thereby fail to reveal the situated mecha- nisms of behavior. Instead, the most widely practiced modeling strategies have emphasized regularities across participants, central tenden- cies in data, or gross features of developmental change. These phenomena, though legitimate, do not reliably define a mechanistic level of explanation. A different target for theory, modeling, and explanation is a level of emergent control, above the component details of enacted mechanisms. This strategic reduction captures causal prop- erties of systems that are not transparent in component causes. A theory of emergent con- trol makes progress so long as there actually are general principles of control to be discov- ered. This point about general principles takes a lesson from dynamical systems models. The cusp catastrophe, for example, is a very gen- eral account of control and qualitative change (Gilmore, 1993). And the search for empirical flags of the cusp catastrophe illustrates how one goes about establishing that cusp princi- ples of control actually apply (van der Maas & Molenaar, 1992). However, if one grounds the ensuing model in hard-assembled components, then the paradoxes we have described come along for the ride. At the level of emergent control, task con- text effects are equated with task constraints in a model's control parameters (Van Orden, Holden, Podgornik, & Aitchison, 1999). A con- trol parameter is a ratio among constraints. Values of the ratio will favor one or another of the probabilistic outcomes. Control parameters are most often associated with dynamical sys- tems models, but they are also discussed in the context of connectionist models (Kello, 2003; Kello, Sibley, & Plaut, 2005; Rueckl, 2002). For example, the ratio of weight to distance trials in a balance scale task could be conceived as a 264 REACTIONS FROM THE OUTSIDE control parameter. The values of the ratio that favor distance trials yield different rules than the values of the ratio that favor weight trials. In a connectionist model, the ratio of weight ver- sus distance trials is made explicit in the train- ing regime and implicit in the weight matrix. In a dynamical systems model, this ratio could appear explicitly as a parameter in a system of equations. In both cases, the ratio controls com- peting outcomes that live on opposite sides of a critical value. The critical value defines the point of equally distributed constraints, an imaginary point of no decision, a state of criticality, and a precisely balanced tug of war between equally compelling rules. This is a different view of modeling and con- trol compared to previous schools of psychol- ogy. Models do not stand outside of history, in the sense of a cognitive architecture, except in the principles of their design. Most impor- tant, they do not capture phenomena outside of history. Models capture and make explicit the control of behavior emerging in time. Previous schools of psychology relegated control of behavior to relatively static loci in the environ- ment (behaviorism) or the organism (cognitiv- ism). The new unified theory will locate control in the perpetually changing interaction of child and environment. CONCLUSION _____________________ Hard-assembled cognition must inevitably treat context effects after the fact or as methodolog- ical problems of experimental control. Context effects are either something to be explained later, once the basic architecture is in place, or something that undermines data that could otherwise be equated with cognitive compo- nents. Nonetheless, cognitive performance is unduly dependent on the particulars of con- text. A unified theory of cognition and cogni- tive development must find its beginnings in the particulars of context sensitive phenomena. As for modeling, mimicking the control structure of human behavior captures the available causal basis of behavior. Control of behavior, even qualitative changes in control structure, can be simulated in both connectionist and dynamical system models. Therefore, a unified theory of soft-assembled cognition and development may embrace both dynamic systems and con- nectionist models. These attractive possibilities, perhaps inevitabilities, can be achieved by dis- carding hard assembly, by accepting that per- formance is not transparent to hard-assembled competence. Fluid soft assembly of cognition is the essential human competence and per- formance is transparent to this competence. Competence as context sensitivity and perfor- mance as sensitivity to context are two sides of the same coin. ACKNOWLEDGMENTS _______________ We thank Michael Riley, Kevin Shockley, and the reviewers for comments and questions that improved this chapter. We also acknowledge funding from the National Science Foundation to Heidi Kloos (DRL # 723638) and to Guy Van Orden (HSD #0728743; BCS # 0642716). REFERENCES ________________________ Bak, P. (1996). How nature works: The science of self-organized criticality. New York: Springer. Bassingthwaighte, J. 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