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    COGNITIVE SC IENCE Vol21 4) 1997, pp. 461-481 ISSN 0364-02 13Copyright 0 1997 Cognitive Science Society, Inc. All rights of reproduction in any form reserved.

    The Dynam ical ChallengeANDY CLARK

    Washington niversity

    Rec ent studies such as Thelen and Smith 1994), Kelso, 1995), Van Gelder,199~3, Beer, 1995), and others have presented a forceful case for a dynam-

    ica l systems approach to understanding cognition and adaptive behavior.These studies call into question some foundational assumptions conc erningthe nature of cognitive scientific explanation and in particular) the role ofnotions such as internal representation and computation. These are exc itingand important challenges. But they must be handled with c are. It is all tooeasy, in this debate, to lose sight of the explanatorily important issues and totalk at cross-purposes, courtesy of the surprisingly) various ways in which dif-ferent theorists often conceive the key terms. The primary goal of the presentpaper is thus a modest one: to begin to c larify just what is at issue and to high-light some of the most central and pressing conc erns. In so doing, we mayhope to develop a constructive framework for future debate. In addition, I tryto open up a space of intermediate options-ways in which dynamica l andrepresentational/computational understandings may sometimes afford com-plementary rather than competing) perspec tives on adaptive success.

    1. A NASCENT SCEPTICISMThese are exciting times for Cognitive Science. Once-unchallenged ideas concerning thenature of internal representational systems have been upset by the explosion of interest inconnectionist and neural network mod els. Mo re recently still, even the bedrock notions ofinternal representation and computational explanation themselves have been subject toincreasing critical scrutiny. In particular, several theo rists concern ed to do justice to thespecial nature of embod ied intelligent systems have endorsed versions of a rather radicalclaim which goes something-like this:

    The Radical Em bodied Cog nition Thesis: Structured, Symbolic, Representational andCom putational views of cognition are mistaken. E mbo died cognition is best studiedusing non-computational and non-representational ideas and explanatory schem esinvolving e.g. the tools of Dynamical Systems Th eory.

    Direct all correspondence to: Andy Clark, Philosophy/Neuroscience/Psychology Program, Department of Philos-ophy, Washington University, St. Louis, MO 63 130; E-Mail: [email protected]

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    462 CLARK

    Versions of this thesis can be found, for examp le, in recent w ork in developmental psy-chology (Thelen & Smith, 199 4, Thelen, 199 5), work on real-world robotics and autono-mous agent theory (Smithers, 1994 , Broo ks, 199 1), in philosophical treatments such asWh eeler (1994 ), and in some neuroscientific and neurobiological appro aches such as Mat-urana & Varela (198 0), Skarda and Freeman (1987 ). Mo re circumspect treatments whichnonetheless tend towa rds scepticism about compu tation and internal representation includeBeer and Gallagher (1992 ), Beer (1995 ), Kelso (1995), Van Gelder (1 995), V arela,Thom pson and Ro sch (19 91), and essays in Port and Van Gelder (1995 ). Historical prece-dents for such scepticism are also in vogue and include especially Heideg ger (1927: 1965 ),Merleau-Ponty (1945: 196 2), and the wo rk of J.J. Gibson and the ecological psycholog ists(e.g. Gibson, 197 9).

    The Radical Emb odied Cognition Thesis constitutes, I believe, one of the most impor-tant and challenging developments in contempo rary cognitive science. But it is a develop-ment wh ose genuine value is easily obscured by terminological misunderstandings (thewo rd representation being an especially slippery case ) and knee-jerk reactions (its justbehaviorism, or, on the other side, cartesianism). The goal of the present paper is to clarifythe nature of the genuine, open, em pirical questions that are at issue and to develop aframew ork for constructive future debate. In addition, I shall try to open up a space of inter-mediate options-ways in which dynamical and representational tools may afford comple-mentary (not competing) perspectives on adaptive success.

    The strategy is as follows. I next (section 2) outline four ways in which the slippery termrepresentation may be used. Of these four, only the last two constitute substantive, empir-ically significant options. Section 3 pursues some case studies of dynamical explanationand tries to identify a few guiding ideas. In section 4 I identify some assumptions that mayseem to bridge the large prima facie gap between these ideas and the thesis o f radicalembod ied cognition. I question these assumptions and, as a result, the relevance of theguiding ideas to the radical conclusions. Wh at emerg es, I hop e, is a clearer sense of wha treally distinguishes the dynamical approach-namely a deep difference in explanatoryemph asis (roughly, it is the difference between aiming to explain patterns and aiming tounderstand architectures). Section 5 pursues this difference, asks how the two projectsinterrelate, and suggests some ways in which they may ultimately prove complementary toone another. The concluding section draws the se threads together to paint a picture of themain issues, and to (hopefully) clarify the space for future d ebate.

    2. UNPACKING REPRESENTATIONThe term internal representation has long stood firm as part of the basic infrastructure ofcognitive scientific research and experimentation. Connectionists, it is true, diverged fromtradition by putting their faith (for the most part) in a more implicit style of representing:they replac ed the stable, simple, highly-manipu lable symb ols of classical Artificial Intelli-gence with numerical vectors and operations of vector completion and transformation. Butthough the computational profile differed, the basic commitment to a vision of intelligentbehav ior as involving the creation and use of internal represe ntations remained inviolate.2

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    DYNAMICALCHALLENGE 46

    Contem porary critics of representational approa ches tend, as we shall see, to distrustboth classical and connection&t species of representationalism, though they typicallybelieve the connectionists to be on the right track-see e.g., (Wheeler, 1994 ), (VanGelder, 1993 , (Thelen & Smith, 199 5) and others. O ur immediate task, then, is to begin toclarify the (clearly quite general) sense of internal represen tation that look s to be at issue.

    Let us begin with the weak est possible sense-one with which no one takes issue,except to note th at it is so weak as to be totally uninformative. This is just the bare idea o finternal state. It is agre ed on all sides that flexible, adap tive, intelligent behav ior oftenrequires a creature to respond to current situations in ways informed by past experience,on-going goals and the like. Systems that merely react, in a pre-determined way, to imme-diate stimuli (that will always react the same way to the same stimulus) are unable toachieve this flexibility. Wh at is needed is, at a minimum, the use of inner state to allow theagent to initiate and organ ize behav ior witho ut immediate environmen tal input, to antici-pate future environmental inputs, and so on. In short, merely reactive agents are clearlyinadequate to the full range of intelligent adaptive behaviors exhibited by biological organ-isms. Com plex persisting and updatable inner state is thus at the heart of many (probablyall) genuinely cognitive phenom ena. This much must be comm on ground to both fans andsceptics about internal representation. The existence and importance of comp lex inner stateis thus not at issue.3

    Moving up a notch from the bare notion of inner state, we encounter the only slightlyless vacuous notion o f environmentally-correlated inner state. On its own, how ever, thisrequirement of correlation adds little to the bare idea of inner state. It would, after all, bealmost m iraculous if some kind of correlations between adaptively useful inner states andadaptively relevant environmental param eters did not exist. Mo reover, correlation comesche ap (mappings can alway s be artificially defined ) and is not necessarily even function-ally illuminating. Thus Churchland & Sejnowski, (1992 , pp. 185-1 86) describe a neuralnetwork in which certain hidden unit activities correlate rather nicely with the presence ofedges-but the systemic role of these units is, in fact, not to do edge d etection at all but tohelp extract curvature from shade d im ages. In sum, the bare idea of correlations betweeninner states and worldly features does not provide a substantial and illuminating sense forthe term internal representation.The crucial m oment in the transition to a genuinely substantive reading com es, instead,when we abandon the focus on mere inner state and/or correlation and replace it with afocus on the relation mo st usually gloss ed a s standing-in. All substantive notions of inter-nal representation, I am willing to assert, have at their heart some idea of inner states (orprocesses) wh ose real functional role is to stand-in for other (usually extra-neural) objects,events, actions o r states of affairs. Thus the philosoph er John Haugeland insists (rightly)that representation-using systems are ones that achieve some kind of coordination withenvironmental features by the special m ethod of having something else (in place of a signaldirectly received from the environment) stand-in and guide behavior in its stead (Haug e-land, 199 1, p. 144).

    It is immediately apparent, how ever, that this notion of standing-in must now be treatedwith caution. For it can easily collapse back into the (too weak) notion of correlated inner

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    DYNAMICAL CHALLENGE 465of weak-substantive internal representation. Bu t it is not really capab le o f mod eling itsworld in the stronger sense mentioned above. To see wh at is missing, consider Maze-run-ner 2.

    Maze-runner 2 is very like Maze-runner 1, but it includes some extra circuitry. Thisextra circuitry allows the agent to reason about maze-running off-line. Thus, confronted bya new way into the maze, the agent can deploy a tactic of vicarious exploration (see Cam p-bell, 19 74) to determine a viable route in advance of actual physical action. T o supportsuch functionality, the system uses distinct inner states as stand-ins for distinct fe atures ofthe maze, and is set up (by learning, evolution or hand-coding) so that the relations betweenthes e inner states mirror the actual relations (of distance, accessibility, etc.) between real-world maze-features. Notice, then, that all that need ultimately distinguish such a case fromany similarly articulated case of weak-substantive internal representation is the capacity toaccess such inner structures off-line and thus to suppo rt planning and problem-solving inthe absence of rich on-going environmental exchang e.

    This description of strong internal representation is deliberately vagu e concerning theactual mechanisms involved (for a wo rked exam ple involving the capacity to stronglymodel potential motor activity, see Grush, 199 5). For it does not matter wh at the mecha-nisms are (neural nets, object-oriented program s, expert system s, etc.) as long as they dis-play certain key features. First, they must involve inner states or processes wh osefunctional role is to coordinate the systems activity with its world (no mere correlations).Second, we must be able to identify specific inner states or processes with specific repre-sentational roles-we must be able to isolate, within the system, the inner parameters orprocesses that stand-in for particular extra-neural states of affairs (otherwise we confrontonly com plex inner state implicated in successfu l agent-environment coordination). Andlastly, the system must b e capable of using these inner states or processes so as to solveproblems off-line, to engage in vicarious explorations of a domain, and so on. It is this lastcapacity that distinguishes the genuine model-using agents from the rest6 Strong internalrepresentation is thus of a piece w ith the capacity to use inner mod els instead of real-worldaction and search. Inner states and processes that function as stand-ins in such mod els are,I suggest, genuinely representations for the agent and not simply useful glosses im posedfrom outside.

    3. THE DYNAMICAL CHALLENGEThe Radical Em bodied Cognition Thesis (see section 1) is motivated, in part, by a numberof recent demonstrations spanning a variety of disciplines and appro aches including devel-opmental psycholog y, robotics and autonomous agent theory, and the general study ofdynamic pattern formation. The comm on ground of these various investigations is (veryroughly) th e idea that certain target phenomena-including some cognitive and psycholog-ical ones-are best understood as the emergent produ cts of the comp lex, often non-linearand temporally rich, interplay between a variety of forces. This interplay can be whollyinternal or (mo re frequently) can involve, as equal partners, internal, bodily, and environ-mental factors. Wh ere target phenomena depend on such comp lex interactions (internal or

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    DYNAMICALCHALLENGE 467

    space may exhibit notable properties. An attractor is a point or region such that any trajec-tory passing close by will be drawn into the region (the area of such influence being knownas the basin of attraction). A repellor is a point o r region that deflects incoming trajectories.A bifurcation is a point at which a small change in parameter values can re-shape the flowwithin the state space and yield a new landscape of attractors, repellors and so on. Dynam-ical systems appro aches thus provide a set of mathematical and conceptual tools that helpdisplay the temporal and spatial order in the evolution of specific systemic param eters. Ournext example illustrates this and introduces a second guiding idea viz. the use of collectivevariables.

    Case Two: Rhythmic Finger M otionIn the case of the BZ reaction, a useful low-dimensional description was achieved byfocusing on one actual produc t of the ongoing reaction-the concentration of bromideions. Sometim es, how ever, the search for pow erful low-dimensional descriptions requiresthe experimenter to actively define new collective variables. These are variables that do nottrack properties of simple physical parts but instead track higher-level properties that mayinvolve e.g., relations between measured values of physical parts. Thus consider the case(Kelso et al, 198 1), (Kelso, 199 5, Ch.2 ) of rhythmic finger m otion.

    Human subjects, asked to move their two index fingers at the same frequency in a side-to-side wiggling motion, display two stable strategies. Either the fingers m ove in phase (theequivalent muscles of each hand contract at the same moment), or exactly anti-phase (onecontracts as the other expands). The anti-phase solution, how ever, is unstable at high fre-quencies of oscillation-at a critical frequency it collapses into the phased solution.

    Ho w should we explain and understand this patter of results? One strategy (a version ofthe BZ strategy displayed above) is to seek a more illuminating description of the behav-ioral events. T o this end, Kelso and his colleagues plotted the phase relationship betweenthe two fingers. This variable is constant for a wide range o f oscillation frequencies but issubject to a dramatic shift at a critical value-the mom ent of the anti-phase/phase shift.Plotting the unfolding of the relative phase variable is plotting the values of a collectivevariable since relative phase is determined by a relation between the behaviors of morebasic system components (finger motions). The values of this collective variable wereobserved to be fixed by frequency of motion, which thus acts as a so-called control param-eter. The dynamical analysis is then fleshed out by the provision of a detailed mathem aticaldescription-a set of equations displaying the space of possible tem poral evolutions of rel-ative phase as governed by the control parameter. This description fixes, in detail, the statespace of the system: the attractors, repellors, bifurcation points and so on. Haken et al(198 5) uses such an analysis to display the different patterns of coordination correspondingto different values o f the control parameter. Som e noteworthy features of the resultingmodel are 1) its ability to account for the observed phase transitions without positing anyspecial switching mechanism-instead, the switching emerges as a natural product of thenormal, self-organizing evolution of the system , 2) its ability to pred ict and explain theresults of selective interference with the system (as when one finger is temporarily forcedout of its stable phase relation), and 3) its ability to generate accurate predictions of e.g..

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    the time taken to switch from anti-phase to phase. (For a nice review of the model, seeKelso, 1995 , p. 54-61 ).

    The dynamical explanation is thus perched midway between wha t, to a more traditionalcognitive scientist, may at first look like a (mere) description of a pattern of events and areal explanation of why the events unfold as they do. It is not a mere d escription since theparame ters need to be carefully chosen and the resulting model has predictive force: it tellsus enough about the system to know how it would behave in various non-actual circum-stances. But it differs from more traditional cognitive scientific explanations in that it usescollective variables to abstract aw ay from the behavior of individual systemic compon ents.This tendency toward s collective-variable style abstraction constitutes the second guidingidea I wish to highlight.

    Case Three: Treadmill SteppingConsider the phenomena of learning to walk. Thelen and Smith (19 94) sho w, quite con-vincingly, that these phenom ena (in human infants) demand explanations which invoke amultiplicity of facto rs spanning brain, body and local environment. Suc h explanation s dif-fer markedly from certain traditional schemes in which such progressive changes aredepicted as the inexorable playing out of a set of prior instructions encoded in e.g. a genet-ically specified central pattern generator or neural control system (Thelen & Smith, 1994 ,pp. 8-20, 263-2 66). The difference lies principally in the way the problems themselves areconceiv ed, and the resulting multidimensional nature of the solutions viz. a multi-dimen-sionality in which the organic compon ents and the context are equally causal and privi-leged (Thelen and Smith, op. cit., p. 17).

    In the case of learning to walk, Thelen and Smith a ddress the following pattern of devel-opmental transitions:1. New born infants, held upright, produ ce efficient, coordinated stepping movements.2. These movements disappear at about 2 months of age.3. The movements reappear at about 8 to 10 months of age when the infants begin to sup-

    port their weight on their feet.4. Finally, at about 12 months, the first independent steps are observed.

    One explanation of these regular transitions would be to posit a detailed developmentalplan or blueprint encoded in the central nervous system w hich (perhap s for reasons steepedin the idiosyncratic evolutionary history of the specie s) co nstrains the infant to display thisparticular sequence of intermediate forms. By contrast, Thelen and Smith argue, convinc-ingly, that walking .. .is not controlled by an abstraction , but in a continual dialogu e withthe periphery (op. cit., p. 9). To illustrate this, the authors report some striking data whichshow s how stepping motions are soft assembled out of a comp lex combination of neural,bodily and environmen tal influences.

    For examp le, Thelen and Smith report that stepping motions can be induced evenbetween stages 2 and 3 above (i.e. during the period in which held erect stepping is absent)if the infant is held upright in warm w ater. Moreover, non-stepping 7-month infants heldupright on a slow motorized treadmill pe rformed highly co-ordinated alternating steps,

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    DYNAMICAL CHALLENGE 469

    adjusted step speed to comp ensate for increased treadmill speed, and even made asymmet-rical leg adjustments to maintain rhythmic stepping on two belts driving opposing legs atdifferent speed s Other environmental manipulations (such as adding weigh ts to the legs)were able to inhibit stepping in infants wh o normally displayed it. Such results (describedin detail in Thelen and Smith, op. cit., Ch. l& 4) show that the behavioral repertoire of theinfants is highly sensitive to bodily and environmental parameters such as the effectiveweight of the legs. Such observations lead the authors to conclude that there is no essenceof locomotion either in the motor cortex or the spinal cord . Indeed, it would be equallycredible to assign the essence of walking to the treadmill than to a neural struc-ture...(Thelen and Smith, op. cit., p. 17).

    The treadmill stepping task, thus provides an especially useful window onto the dynam-ical construction of infant walking, as it highlights the comp lex and subtle interplaybetween intrinsic dynamics, organic change and external task environment. In fact, thetreadmill looks to be acting as a real-time control parameter that prom pts the phase shift, inthe 7 month olds, from non-stepping to smoo th alternating stepping motions. To test andrefine this hypothesis, Thelen & Ulrich, (199 1) focused on the alternation of steps (thetreadmill response that seemed m ost suggestive of mature locomotion patterns). T hey usedthe relative phasing of the two legs as a collective variable, since this distinguishes truealternation from other possible leg actions that have less in commo n with mature locom o-tion strategies (in mature stepping the two legs are at .S relative phase i.e., 180 out ofphase-one leg is 180 through its cycle when th e other initiates its motion). In their study,Thelen & Ulrich plotted relative phasing in treadmill stepping in infants from one to eightmonths o f age. The authors plotted month-to-month performance (infant by infant) andalso observed the effects of varying treadmill speed both between and during individual tri-als. When held on the treadmill, infants could display a variety of responses (no action, sin-gle step, double step, parallel step, alternating step). In the early months, all these werefrequently observed. But alternation steadily b ecame the preferred response: in dynamicterms, the multi-stable states of single, do uble, parallel and alternating were replaced bythe singular state of alternation, the attractors both dissolving and evolving over the first 8or 9 months (Thelen & Smith, 199 4. p. 103). With a large body of data to hand, the nextstep was to try to discover possible control parame ters (organic or environmental) toaccount for the detailed profile of the onset o f treadmill stepping. Out of a host of options,one factor coordinated especially well with the data: the orientation of leg and foot in rela-tion to the treadmill. Poor stepping was correlated with high degrees of leg flex and inwardrotation of the foot. Goo d stepping was correlated with flat-foot belt contact (rather thantoe contact). And flat-foot contact itself was negatively correlated with high leg-flex. Thusimagine that the leg, when stretched out, acts like a spring-at full stretch, the energyimparted to the spring is released and swings the leg forward . Recep tors in the musclesrespond to the uncoiling of the leg and this information is used to control relative phasing.On such a scenario (see Thelen & Smith, op cit., p. 11 I - 12) it is crucial that the leg be fullystretch ed back , by the treadmill action, to initiate alternating stepping . Still treating infantlegs like mass springs, we can now see that if the intrinsic tension of the leg is too high, thetreadmill won t manage to produ ce the back-stretch needed to activate the receptors and

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    47 CLARK

    initiate pha sed stepping. Increasing treadmill spee d will, in som e borderline cases , yieldthe necessary stretch. Y oung infants, it is observed, have high flexor b ias in the legs-theyare coiled up and only relax over several mo nths. The authors con clude that:

    . the relative flexor (very tight) or extensor (more loose) tendencies of the legs, in thiscase as indexed by several postu ral c haracteristics, acted as the control para meter toengender the shift into stable alternate stepping. As a control param eter, flexor toneconstrained the interacting elements, but did not prescribe the outcome in a privilegedway...the emergence of coordinated treadmill stepping m ust be a multi-determinedprocess. Wh ile it seems likely that the pathway s essential for treadmill-stepping patternproduction can function by 1 month of age, central neural pattern generation is likelynot the developmental control parameter in this case. Rather, the behavior itselfemerges only when the central elements coop erate with the effecters-the muscles,joints, tendons-in the approp riate physical context (Thelen & Smith, 1994, p. 113).

    The third (and final) guiding idea to emerge from o ur case studies is thus the image ofsoft assembly in an extended (brain/body/world) system- an image that leads us to depictdevelopment as the successive creation and dissolution of attractors in a distributed systemwho se organic and environmental componen ts are changing over time.

    4. REPRESENTATION REVISITEDHo w does all this bear on the issues concerning internal representation and computational-ist theorizing? The question is difficult because, at first sight, the relevance can appea rsome what marginal. The specific problems addressed seem far removed from more tradi-tionally cognitive topics such as planning, speech, story-understanding and so on. Thevocabulary and method ology do indeed seem very different. But it is hard to avoid the sus-picion that these differences stem largely from this difference in topic (basic m otor skillsversus real thinking).It is thus not immediately clear how the ideas bear on the muchmore general thesis of radical embo died cognition. Non etheless, there can be no real doubtconcerning the authors intentions. We read, for examp le, that:

    Explanations in terms of structure in the head-beliefs, rules, concepts and sche-mata-are not acceptable.. .Our theory has new concepts at the center-nonlinearity,reentrance, co upling heterochronicity, attractors, mome ntum, state spaces, intrinsicdynamics, forces. T hese c oncepts are not reducible to the old ones. (Thelen & Smith,1994, p. 339). (My emphasis).We posit that development happens because of the time-locked pattern of activityacross heterogeneous components We are not building representations of the world byconnecting temporally contingent ideas. W e are not building represen tations at allMind is activity in time.. .the real time of real physical causes (Thelen & Smith, 1994,p. 338). (My emphasis).The thesis here is that the hum an brain is fundam entally a pattern-forming, self-orga-nized system governed by non-linear dynam ical laws. Rather than compute, our braindwells (at least for short times) in metastable states...(Kelso, 199 5, p. 26). (Secondemphasis mine).

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    DYNAMICAL CHALLENGE 47

    Linking the investigations and guiding ideas just rehearsed and the more general andradical thesis are, I suggest, three bridging assumptions. First, there is an (often explicit)hypoth esis of continuity*-a claim to the effect that all of cognition is continuous with itsmoto r and developmental foundations, and hence that the shape of solutions (emergent, sit-uated, soft-assembled) to these problems will be recapitulated in all supposedly higher cog-nition domains (see e.g., Thelen & Smith, 199 4, p. xxiii). Second, there is an assumptionabou t the objectivist nature o f any putative internal represen tations. And third, there is anassumption about the kind of behavior control systems implicated in computationalaccounts. All three bridging assumptions bear discussing, and I will address each in turn.

    First, the hypoth esis of continuity. The problem here (a familiar one to evolutionarybiologists) is that the simple notion of continuity covers a remarkably wide variety of pos-sible linkages, pathw ays and commo nalities. In the genetic case these include the ideas offairly sm ooth evolution with constant function (as in the case of the eye), smooth structuralevolution with radical functional change (as in the case of the role of thermo-insulatingfeathers in enabling flight) and symbiosis, in which v arious parts evolve quite seperatelyand are put together at a later date so as to usher in some brand new functionality. Fordetailed discussion of all these cases see Ridley (1985 ) p . 35-41. In a similar manner theontogenetic continuity posited by the dynamicist surely exists in some form or other. Butit hardly follows from this that the guiding ideas and vocabulary suited to e.g., the expla-nation of early moto r development will apply across the board.

    Consider, for examp le, the strongest representationalist thesis outlined in section 2above. According to this thesis, we sometimes solve problems by exploiting inner statesthat are designed (by learning or evolution) to function as off-line stand-ins for feature s o four real-world environment. In such cases (Maze-runner 2 was our examp le), we tempo-rarily abandon the strategy of directly interacting with our world so as to engage in mo revicarious form s of explo ration. It is certainly possible that such off-line problem-solving isperfectly continuous in a sense with various on-line highly environmentally interactive,mo tor control strategies. Thus Grush (1995 ) describes a piece of circuitry wh ose principalrole is the fine-tuning of on-line reaching. The circuitry, howev er, involves the construc-tion of an emulator loop that predicts sensory feedback in advance of the signals arrivingfrom the bodily peripheries. This loop, once in place, can later suppo rt the additional func-tionality of fully off-line deployment, allowing the system to rehearse moto r actionsentirely in its imagination. Such a case show s both a profound continuity between smoo thmotor control strategies and higher cognitive capacities such as off-line reasoning andimagination, and (simultaneously) a profound discontinuit?, in that the system, as describedby Grush, is now using specific and identifiable inner states as full-blooded stand-ins forspecific extra-neural (in this case bodily) states of affairs. These are internal represen ta-tions in the very strong sense defined in section 2. At such times the system is not contin-uously assembling its behav ior by balancing ongo ing neural, bodily and environmentalinfluences. It is, instead, modelling and representing its world. We thus preserve a kind ofarchitectural continuity, while abandoning the guiding idea of soft assembly in an extendedsystem (for a more detailed treatment of the implications of this case, see Clark & Grush,to appear).

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    The second bridging assumption concerned the nature (content) of any putative internalrepresentations. Here, it looks as if the target of a great deal of dynamicist scepticism is notinternal representation per se so much as a particular type of internal representation vizwha t are sometimes called objectivist representations-the kind that might feature in adetailed, viewpoint-independent, map-like model of some aspect of the world. Notice,then, a second (and I believe, highly significant-see Clark, 1995 , Clark, 199 7) way inwhich higher level cognition may be innocently continuous with its moto r and develop-mental roo ts. It may be continuous insofar as it involves internal representations (weak orstrong) wh ose contents (unlike detailed objectivist representations) are heavily gearedtoward s the suppo rt of typical or important kinds of real-world, real-time action. Such con-tents may (as in the previous examp le) sometimes be manipulated off-line-but they arenonetheless types of content (wh at I elsewhere call action-oriented contents) that are espe-cially su ited to the control and coordina tion of real action in real time. Cognition, on thismod el, need not always be actually interactive (involving brain, body, and world as equalpartners). But the inner econom y has still been sculpted and shaped by the real-time,task-specific, interactive needs of the organism.

    Mu ch dynamicist scepticism, on closer examination, looks to address only the specificnotion of objectivist (de tache d, action-independent, highly -detailed, static, general-pur-pose) internal representation. Thus Thelen & Smith (199 4, p. 37-44) question all thoseideas, suggesting instead that we treat know ledge as an action-guiding process continuallyorganized against a contextual backdro p that brings forth its form, content and use. Thesame set of emp hases characterize Varelas notion of enaction in which cognitive struc-tures are said to emerge from the recurrent sensorimotor patterns that enable action to beperceptually guided (Varela, T homp son & Rosch , 199 1, p. 173 ). To mark the difference,Varela, Thom pson and Rosc h define a sense for the term strong representation that spe-cifically associates strong representation with the disputed idea of an inner recapitulationof the objective features of a pre-given world (op tit p. 148). Such a sense of strong rep-resentation, it should be clear, places the emph asis on the kinds of content involved ratherthan the functional role of the inner states. In a similar vein, A gre (1 995) notes the impor-tance of wha t he calls indexical-functional representations (such as a few feet straightahead)-these are ideal for the cheap control of individual action and are to be contrastedwith objectivist map-like representations such as at latitude 4 1, longitude 13 . The pointI want to stress is just that many disputes in this area thus look to concern the content, notthe existence, of inner states wh ose ro le is to stand-in (in either the weak-substantive orstrong sense) for adaptively important extra-neural states of affairs. At a, minimum, themer e fact (if it is a fact) that biological agen ts rely heavily on indexical-functional, action-oriented and context-responsive kinds of know ledge does not, in itself, undermine the ideathat such know ledge may itself be internally encoded in ways that allow us to gain illumi-nating insight into the functional organization of the agent by seeking a representationalistunderstanding- that is to say, by associating quite specific inner states and processes withthe tasks of maintaining and manipulating such information. Of course, there is no guaran-tee that this will be the case-the know ledge may be so widely and complexly distributedbetween various inner subsystems and bodily and environmental factors that even the

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    point in their comm ents on schemata: general movem ent plans that do not dictate specifickinetic details-op. cit., p. 75). Thus consider the very idea of a program for performingsome task. The basic idea is indeed that of a set of instructions that, when followed, lead toa solution. But what is the difference between a set of instructions (a recipe) and a mereforce which, if applied, brings about a result? The h eat applied to a pan o f oil, at a criticalvalue, leads to the emergence of convection rolls (see Kelso, 199 5, pp. 6-8). Yet, it is not,intuitively, a recipe for such currents. One difference is that a recipe is written in som e lan-guage of arbitrary symbols. But another is that the guiding parameter, in the case of theheated oil, seems too simple and unarticualted to count as a program . It is more like plug-ging a comp uter in than running a piece o f software, as one of my students usefullyremarked . Non etheless (and here is wh ere things get murky), it seems clear that genuineprogram s can vary markedly in complexity. A short piece of software, written in a high-level language, will not itself specify how or when to achieve many sub-goals-these tasksare ceded to built-in features of the operating system or to the activity of a cascade oflower-level code. Mo reover, a program can perfectly well assume some necessary back-drop of environmental or bodily structures and dynamics. Jordan et al (1994 ) describes aprogram for the control of arm motions, but it is one that assumes (for its success) a lot ofextrinsic dynamics such as the mass of the arm, the spring of muscle and the force of grav-ity. My claim, then, is that we here confront not a dichotomy (program med versus unpro-gramm ed) but a continuum-the less detailed the specification required (the more wo rk isbeing done by the wider intrinsic physical dynamics of the system), the less value there isin treating the neural contributions as any kind of a program .No w it may be, of course, that so very mu ch is done by the synergetic dynamics of thebody-environment system that the neural contributions are indeed best treated, at all stages,as the application of simple fo rces to a comp lex but highly inter-animated system w hoseintrinsic dynamics then carry mo st of the load. But less radically, it may be that basic m otoractivity simply requires less in the way of detailed inner instruction sets than we mighthave supposed , courtesy of the existence of a small set of preferred collective states suchthat successful behavior requires only e.g., the setting of a few central p arameters such asinitial stiffness in a spring-like muscle system and so on. Such sparse specifications maysuppo rt comp lex global effects without directly specifying joint-angle configurations andthe like.

    The lack of a particularly detailed kind of neural instruction set does not then, establishthe total absence of stored programsSu ch a characterization is compelling only at the mostextreme (and perhap s basic motor-control specific) end of a genuine continuum. Betweenthe two extremes lies the interesting space of wha t I elsewhere (Clark, 199 7) call partialprogram s-minimal instruction sets that maxim ally explo it the inherent (bodily and envi-ronmental dynamics of the controlled system. T he real moral of much actual dynamical-systems-oriented research is, I suspect, that it is in this space that we may ex pect to encoun-ter many of natures own pro grams.There is, of course, a second way in which a program differs from an applied force. Aprogram is,in some surprisingly elusive sense, constituted by a set of comm ands or descrip-tions couch ed in some kind of code. T his notion of a code is intuitively one that involves

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    ideas of arbitrary symbols and some capacity for the concatenation and recomposition ofsuch symbols to express new contents. It is unclear, how ever, wh ether we should assimi-late the general vision of the brain as a computational device to this narrower vision of thebrain as a locus of such compositional coding scheme s. Many connectionists wh o do notsubscribe to the use of traditional compositional coding sch emes typically regard them-selves as nonetheless investigating the space of potential co mputational strategies thatmight figure in biological cognition (see e.g., McClelland, Rum elhart et al, 198 6, Church-land, 198 9, Smolensky, 198 8, Elman, 1994 ). One reason for this is clear. There is a senseof computation that is tied not so much to the stored pro gram image as to the idea of sys-tems that effect autom atic, semantically-sensible transformations betwe en internalrepresentations9. Recall now the weak-substantive sense of internal representation outlinedin section 2. In this sense, w e find internal represen tations wheneve r we can identify an iso-latable inner s tate or process with the functional role of standing-in for specific, usuallyextra-neural, states of affairs. Such states may, however, be found in connectionist systemsthat lack many of the usual features of classical code and symbol devices (for a review, seeClark, 1993 , Ch.3). In such cases the failure of the stored,coded,comp ositional programidea need not undermine the vision of the system as broadly computational in the sense justdescribed. If it is indeed the case (and this is open to question- see e.g., essays in Harnad,199 4 for some discussion) that we find computation whenev er we find automatic, seman-tically-sensible transitions between internal represen tations, then the question of wh ethe rthe brain really compu tes reduces to the prior question about internal representation. (Myown view, th ough I will not argue for it here, is that the notion does thus reduce-hence theemp hasis, in the presen t treatment, on issues concerning internal repres entation).

    All three bridging assumptions thus face serious difficulties. As a result, I can find noclean and compelling route from the various guiding dynamical ideas to the strong conclu-sions expressed in the Radical Emb odied Cognition Thesis. Instead, wh at looks to bestrongly suppo rted is a pair of very reasonable and important strictures that may usefullyinform both computationa list/representationalist and pure dynam ical investigations.They are:1. Bew are o f putting too much into the head. Adaptive behavior emerges from a comp lex

    balancing act that incorp orates neural, bodily, and environmen tal influences.2. Bew are of narrow visions of the form and content of putative internal representational

    system s. Such system s may involve indexical-functional (action-oriented ) contentsand may not require expression in the form of compositional codes and classical pro-grams.

    This more conservative message , how ever, should be coupled with the realization thatdynamical appro aches are genuinely successful in forcing a much-needed re-examinationof the explanatory goals, methods and expectations that inform much cognitive scientificresearch. Wh at our discussion indicates, I suggest, is that the real challenge lies not in thesuppo sed implications for notions of representation and computation but in the ideas con-cerning the dense spatial and temporal interplay between neural, bodily and environmentalfactors, and the kind of tools and construct (collective variables, control pa rameters and so

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    476 CLARKon) needed to distill illuminating order from this mass of burgeoning complexity. The truedynamical challenge thus lies in the imperative to shift our primary focus from the comp o-nential de tail of internal architectu res to the tine-grained structure of bodily and environ-mentally extended patterns. It is to this challenge that we now turn.

    5. PATTERN, ARCHITECTURE EXPLANATIONThe notions of patterns and of self-organization dominate much dynamical research. Wehave seen these notions in action in all the case studies reported in section 3. Closelyrelated notions include those of coupling and of circular causation. These latter notions areespecially useful in describing and analyzing the patterns that emerge in ongoing organ-ism-environment interactions. Two sources of variance (the organism and the environ-ment) may be depicted as a single coupled system wh ose evolution is specified by a set ofinterlinking equations. Thus consider two pendulums mounted close together on a wall.The pendulums tend to becom e swing synchronized over time courtesy of vibrations run-ning through the wall (see Salzman, 199 5). This synchronization admits of an elegantdynamical explanation in which the motion equation for each pendulum includes a termthat is fixed by the others current state. As each system (each pendulum) moves throughits state space, it effectively alters the shape of the state space of the other system. Thesealtered dynamics simultaneously transform the state space of the first system. The largercoupled system thus displays a kind of circular causation (see Merleau-Ponty, 194 2, Varelaat al, 1991 , Kelso, 199 5, Ashby, 1956 ) in which each subsystem is continuously influenc-ing, and being influenced by the other. This kind of comp lex interplay is wha t I call con-tinuous reciprocal causation (Clark, 1997)-it can lead, in many cases, to large-scaleemergent behaviors who se quality and complexity far exceed s that which either subsystemcould display in isolation.

    The notion of coupling (see e.g., Beer, 199 5, Van Gelder, 199 5) thus provides a mathe-matically elegant w ay to display and understand the sometimes very comp lex interplay thatcharacterizes systems that both affect and are continuously affected by their surroundings.Biological systems, it seems clear, are a case in point. Perception and action, as Merleau-Ponty long ago pointed out (see also Varela et al, 199 1 and, in a computational vein, Bal-lard, 199 1) are bound together in just such an intimate loop. Our perceptions guide actionsthat alter perceptions that guide further actions and so on. Mo reover, this same kind of cir-cular complexity may characterize even purely internal relations such as those that obtainbetween distinct neural and bodily subsystems-see e.g., Cohen s (19 92) wo rk on heterar-chical control structure s linking brain, spinal cord, muscles and limbs, or Knierim and VanEssens (1992 ) wo rk on hierarchical influences in visual processing. Such dense and recip-rocal interactions pose special analytic problems-ones that may well require the use ofdynamical tools to display salient low-dimensional regularities in the comp lex web ofinteractive influence.When such comp lex interactivity is present, it seems likely that some kind of explana-tory priority should be given to attempts to discover (via the use of collective variables,coupled dynamical equations, control parame ters and so on) the (perhaps temp orarily) sta-

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    DYNAMICALCHALLENGE 477

    ble global states that such comp lex exchang es support. Notice, h owev er, that complexitiesthat turn only on ongoing organism-environment interactions cannot support a case againststrong representation, since this (by our definition) crucially involves a potential de-cou-pling between the inner representational system and the stream of immediate environmen-tal input. The immediate point, how ever, is that there is no inherent opposition between theproject of giving explanatory priority to the understanding of patterns in the behavior ofcoupled organism-environment systems and the project of understanding how specificinner architectures contribute to adaptive success. It is agreed on all sides that certaindynamical stories, qua low-dimensional takes on a higher dimensional reality, may obscure(or at least fail to reveal) im portant details concerning the actual physical mechanisms thatare at work . This is just the price we pay for the explanatory insights they provide concem-ing the higher level patterns that emerge in comp lex, self-organizing systems. Thus twoprominent theorists studying the BZ reaction using dynamical tools comm ent that suchappro aches aim at revealing the mathem atical essence of the experimental periodicityand are of limited use for understanding the chemical mechanism that generates the com-plexity (Gyorgyi & Field, 1993 , p, 55). Similarly, Thelen & Smith, immediately after theirilluminating discussion of collective variables and control parameters in treadmill step-ping, note that the resulting story is clear about th e general processes of change throughthe loss of stability of coherent dynamic organization, but completely uninformed aboutthe more precise m echanisms of changing attractor stability (Thelen & Smith, 199 4, p.129 ). In response to this need, Thelen & Smith go on to pursue issues concerning thedynam ics of the underlying neural organization s. Kelso , likewise, insists on a tripartiteschem e in which full understanding requires an analysis of the task itself, a high-leveldynamical account pitched at the collective variable level, and an account pitched at thecomponent level-see Kelso (1995 , p. 66). He also cautions, importantly, that wh at countsas a component or a collective variable depends to some d egree on our current explanatoryinterest. Non-linear oscillators, he notes, may be treated as compon ents for some purposes.Yet such oscillation is itself a collective effect that emerges from the interactions of stillsimpler compon ents. Randall Beer, in a series of careful and progressive attempts to under-stand the operation of neural network controllers for embod ied action in insect-like agentshas also stressed the need to pursue the dynamical understanding all the way down. Hisproject targets the detailed dynamics of individual neuron-like units, then coupled pairs ofunits, then pairs of units coupled with simple bodies, and so on (see Beer, 199 5). There is,it seems, a quite general recognition that the explanatory aspirations of cognitive sciencerequire us to move, at some point, beyond the collective-variable style depiction of grossemergent patterns and into the realm of inner architectures, compon ents and organizations.There is thus a clear space for complementary investigative activity spanning high-leveldynamics and more detailed, compo nent-oriented research. T he question is really one ofexplanatory priority, with fans of embo died and situated approaches advocating greaterattention to the large-scale, ecologically crucial patterns to wh ich inner neural organiza-tions contribute as more or less equal partners with bodily and environmental factors.

    When the mo re inner oriented research is conducted using dynamical constructs andtools, however, an interesting possibility emerges. Even if there are no simple, static fairly

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    local states of the brain that can usefully be associated with representational roles (due, per-haps, to the presence of dense reciprocal connectivity and circular causal influences), theremigh t still be high er level dynamical regularities that are playing just such an adap tive role.The opportunity thus exists to use the distinctive analytic tools of dynamical theorizing(collective variables, attracto rs, trajectories and so on) to distill potential representation alvehicles from the burgeoning com plexities of internal neural activity.

    Such, indeed, is already the case in active research in artificial neural n etworks. Suchnetworks affo rd multiple po tential vehicles for internal represen tations, including states ofdistributed activity, attractors defined within the state space of units and weights, and tra-jectories in the state space (see e.g., Smolensky, 198 8, Elman, 199 1). Other dynamicalentities su ch as chao tic attra ctors, limit cycles, an d bifurcation structure s are equally capa -ble of playing the adaptive roles characteristic of either weak or strong representation, asdescribed in section 2. Mo reover, as dynamicists increasingly turn their attention to mo retraditionally cognitive and representation-hungry (the term is from Clark & Toribio,199 4) domains, such as long-term planning and decision-making, the need to press suchvehicles into representation al service grow s stronge r-this is clearly seen in e.g., the vari-ous essays in Port & Van Gelder (1995) Nehm zow & Smithers (1991), Amit (1989) VanGelder & Port (1994 ), Petitot (1 985), Miller & Freyd (1 993 ), and elsewhere. The door isthus open for some pow erful and complementary investigations in which dynamical pat-terns act as the spatially and temporally extended vehicles of specific representational con-tents. Such developmen ts, should they prove useful for understanding biological cognition,would not constitute a revision of the notion of internal representation itself (pace e.g. VanGelder, 199 5) so much as a revision of our ideas about the kinds of inner state and processthat might act as the vehicles of such representation. The root notion of internal represen-tation (weak-substantive or strong) remains unchanged, involving as it does only the ideaof identifiable aspects of inner processing wh ose real functional role is to stand-in for otherstates of affairs (for an extended defense of this claim, see Miller & Freyd, 1993 ).

    The putative change in our conception of likely representational vehicles is, how ever,profound and important. It constitutes a move away from the idea of static, text-like, spa-tially local, and atemporal vehicles to the much m ore challenging image o f temporally andspatially extended patterns as the key players in a who le new kind of inner econ omy.

    6. CONCLU SIONS: A SPACE FOR DEBATEThe dynam ical challenge, I conclud e, is substantive, important and all too easily misunder-stood. On the vexed issue of internal representation, we can return a null-verdict. Given atleast a weak-substantive notion of internal representation, it is an open empirical questionwh ether the construct will earn its keep in explanations of biological cognition. A positiveanswer will require the isolation of distinct inner states or processes wh ose functional-adap tive role, as describ ed in section 2, is to act as genuine stand-ins for extra-neural statesof affairs. W e saw that the contents of such putative representations need not be of theobjectivist, observer-independent variety but could instead focus on functional-indexical,action-oriented features. Non etheless, the project of isolating any such states is threatened

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    by the spectre of processes of continuous reciprocal causation criss-crossing organism,environment and inner neural sites. In this respect, strong internal rep resentation may ,somw hat surprisingly, fare better than wea k since (by definition) strong representation sup-ports episodes of environmentally de-coupled, off-line reasoning and is thus isolated fromat least one source o f causal complexity. The ubiquity of such off-line reasoning is, ofcourse, op en to question. The issues concerning representation thus reduce to questionsabout the isolability of inner content-bearing vehicles and the nature (wea k or strong) ofthe standing-in relation itself. It was noted, ho wev er, that the tools of dynamical analysismay themselves provide a means of unpicking comp lex causal webs and revealing tempo-rally and spatially extended entities as potential vehicles o f representation al content.

    The issues about computation are even less clear-cut. There are pow erful dynamicistconsiderations, at least in the area of mo tor control, that argue against any notion of com-plex, detailed, neural instruction sets and hence against a strong notion of stored inner pro-grams. But we here confront not a dichotomy (program med versus unprogram med) but acontinuum of possibilities linked to the amount and specificity of neural comm andsrequired to bring about a desired action. Mo reover, the stored program idea may not evenbe essential to the more general image of the brain as some kind o f computational device.Instead, all that may be require d is the presen ce of semantically sensible transitionsbetween representational states. Further resolution of these issues must thus wait uponmuch-needed progress in our general und erstanding of the nature of computation itself.

    The true heart of the dynamical challenge, how ever, lies elsewhere. It lies in the visionof the brain as, when all is said and done, just another participant in the construction of sit-uated action. From this vision proceed s an imperative: to give explanatory priority to thepatterns that characterize embod ied, situated action, to analyze tho se patterns (using thetools of collective variables, control p arameters, coupled equations and the like), andagainst this backg round to seek furthe r understanding of specifically internal contributions,architectures and organizations. The real dynamical insight thus turns on issues ofexplanatory privilege (should we focus almost exclusively on the brain?) and temporality(should we focus on static states or on temporally extended processes?). And the advice isclear: look harder at temporally extended processes that span brain, body and world. Th isgoo d counsel is the true fruit of the dynamical challenge.

    Acknowledgments: This paper has benefited enormously from discussions with RandyBeer, Tim Van Gelder, Esther Thelen, Melanie Mitchell, Scott Kelso and MichaelWh eeler. Thanks also to Franscisco Varela, E sther Thelen, Bill Clancey and an anonymousreferee for constructive and invaluable comm ents on an earlier version. I respectfully ded-icate this paper to the mem ory of Donald Campb ell.

    NOTESI. See e.g. McClelland, Rumelhart and the PDP Research Group (1986) vols. I and II; Clark (1989); P.M.

    Churchland (1989); Clark (1993).

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