Toward a Noncomputatiod Cognitive

Gordon G. Globus University of California Irvine

Abstract Downloaded from http://mitprc.silverchair.com/jocn/article-pdf/4/4/299/1754995/jocn.1992.4.4.299.pdf by guest on 18 May 2021 The near universally accepted that the pro- information processing is developed in which the brain permits cesses information persists in current neural network theory and supports “participation” of and other as constraints on where there is “subsymbolic” computation (Smolensky, 1988) the dynamically evolving, self-organizing whole. The noncom- on distributed representations. This theory of brain information putational process of “differing and deferring” in nonlinear processing may suffice for simplifying models simulated in dynamic neural systems is contrasted with Black’s (1991) ac- silicon but not for living neural nets where there is ongoing count of molecular information processing. State hyperspace chemical tuning of the input/output transfer function at the for the noncomputational process of nonlinear dynamical sys- nodes, connection weights, network parameters, and connec- tems, unlike classical systems, has a fractal dimension. The tivity. Here the brain continually changes itself as it intersects noncomputational model is supported by suggestive evidence with information from the outside. An alternative theory to for fractal properties of the brain.

INTRODUCTION neural is so widespread and automatic that it begins to appear less like an innovative leap than The theory that the brain performs computations is so like a bandwagon phenomenon, of the sort often ob- widespread in cognitive neuroscience, and so strongly served in the sociology and history of . held, that its status is “paradigmatic” in Kuhn’s (1976) (Daugman, 1990, p. 15) strong sense. It is difficult to even think of brain com- putation as a “theory” until alternatives are seen, so Emboldened by Daugman’s caveat, an alternative theory deeply rooted is the information processing idea in cur- that brain functioning is not computational is proposed rent thought. Thus this journal’s stated purpose is to here. This alternative theory is a “radical” form of con- publish papers that “bridge the gap between descriptions nectionism (neural net theory). of information processing and specifications of brain The alternative is labeled “radical” because current activity.” Indeed “computational neuroscience” is consid- connectionism fully accepts the computational view. The ered to be a subdiscipline (Schwartz, 1990), whose “ul- neural nets of the brain are performing computations, it timate aim” is to “explain how electrical and chemical is thought, though not like desktop computers do. There signals are used in the brain to represent and process is no programmed logical processing of information in information” (Sejnowski, Koch, & Churchland, 1988, real neural nets; the processing is differently performed. p. 1299). But nonetheless there is a computation going on, a “sub- Daugman (1990) reminds us, however, that computa- symbolic” computation, as Smolensky (1988) argues, not tion is a metaphor of brain function. a symbolic one, as Fodor and Pylyshn (1988) think. This computation is naturally expressed by the mathematics Surprisingly, given the pervasive popularity of this of linear algebra (Jordan, 1986), in which the computa- metaphor, there remains today no well-established tion is thought of as the mapping of an input vector to evidence of symbolic manipulation or formal logical an output vector. rules at the neurobiologicdl level in animal physiol- The meaning of “computation” requires some com- ogy. . . . while the computational metaphor often ment, since it is so central to what follows. In their seems to have the status of an established fact, it discussion, “What is computational neuroscience?,” should be regarded as an hypothetical, and historical, Churchland, Koch, and Sejnowski (1990) consider a conjecture about the brain. . . . Today’s embrace of physical system “in a most general sense” to compute a the computational metaphor in the cognitive and hnctionflx) when there is

0 1992 Massachusetts Institute of Technology Journal of Cognitive Neuroscience Volume 4, Number 4

Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/jocn.1992.4.4.299 by guest on 23 September 2021 (1) a mapping between the system’s physical inputs logical vacuum” and computational models that are “par- and x, (2) a mapping between the system’s physical ticularly impoverished compared to biologically based outputs andy, such that (3)f(x) = y. (p. 48) brain function” (p. xii). Shepherd (1990) observes, This is a very general account of cornputxion in terms One must conclude that there is at present a consid- of competence, and a “weak” sense of computation. But erable mismatch between neural networks and the they also give “a suitably broad notion of computation” real . A case could very well be made in terms of perjGormance. that the networks could hardly be less neural; that most of the properties believed to be neural are in It is useful , . . to class certain functions in the brain fact not so or are only remotely so, and that many as computational because nervous systems represent properties are introduced that are explicitly not and they respond on the basis of the representations. neural. (p. 92) Nervous systems represent the external world, the

body they inhabit, and, in some instances, parts of Despite these strong doubts on the neurobiological side, Downloaded from http://mitprc.silverchair.com/jocn/article-pdf/4/4/299/1754995/jocn.1992.4.4.299.pdf by guest on 18 May 2021 the nervous system itself. (p. 48) neural net modelers remain confident that The performance of the computation makes uses of rep- if the computational model is firmly based on the resentations. Furthermore, the explanation of state tran- available experimental data, it can evolve along with sitions in the performance of the computation “describes the experimental program and help to guide future the states in terms of the information transformed, rep- research directions. (Sejnowski, Koch, & Churchland, resented and stored” (p. 48). So “computation” in the 1988, p. 1305) strong sense of performance is tantamount to informa- tion processing, whereas in the weak sense the term We shall see below that simplifying models serve to sustain the theory that the brain computes whereas bi- vacuously skirts the issue of how the computation is done ologically realistic models open toward the possibility of and thus is divorced from neuroscience. The term “com- a noncomputational neuroscience. putation” accordingly will be used in the strong perfor- Simplified nets consist of formal or richly mance sense in what follows. interconnected “nodes.”Signals fan in on the nodes and This presentation of a radical connectionism in which signals fan out from the nodes; the nodes open both the brain does not actually perform computations begins ways to the whole. There are input/output transfer func- with a critique of simplified neural net models. It is tions at the nodes. Connections between nodes (“con- shown that simplified silicon nets can be thought of as nectivity”) are excitatory or inhibitory and there are but biologically realistic nets are noncom- variable weights on the connections. There are also net- putational. Rather than structure sensitive rule governed work parameters such as signaunoise ratio, excitation/ operations on symbolic representations, there is an evo- inhibition ratio, and decay time that affect signal pro- lution of self-organizing nonlinear dynamic systems in a cessing. The net is layered into an input layer on which process of “differing and deferring.” Then a comparison an activation pattern is impressed from the outside, a is made between a biologically realistic molecular infor- hidden layer where distributed processing occurs, and mation processing model (Black, 1991) and the noncom- an output layer that transduces signals to the outside. putational model. Finally, studies of hypothesized fractal During the operation of simplified nets, the connec- properties of the brain are considered that provide some tivity, the connection weights, transfer functions at the preliminary empirical support for the noncomputational nodes, parameters, and input are kept constant. The net model. evolves as a dynamic system and settles into a state that optimizes satisfaction of the various constraints; the set- SIMPLIFIED NEURAL NETS tlement is self-consistent. This process is not pro- grammed but is self-organizing. The settling time Simplification of neural net models is thought to be demarcates an event or “interval.” When nets learn, the unproblematic and consistent with strategies successfully connection weights are changed before the next trial; applied elsewhere in science. Simplifying models “ab- the weight changes constitute a trace. Connec- stract from the complexity of individual neurons and the tivity, transfer functions, and network parameters are typ- patterns of connectivity in exchange for analytic tract- ically held constant from trial to trial; their settings can ability” (Sejnowski, Koch, & Churchland, 1988, p. 1301). be thought of as static traces. Connection weights mod- Crick (1989), in contrast, is dubious about the simplifying ified by learning provide dynamic traces in the simplified approach. “Most of these neural ‘models’ are not . . . model. really models at all, because they do not correspond The operation of simplified nets is typically described sufficiently closely to the real thing” (p. 131). Getting as computational. (1989), similarly, talks of “crude network models” that are “still barren in comparison with biological systems” In a typical connectionist model, input to the system (p. 200), and Black (1991) speaks of “a virtual cell bio- is provided by imposing activation values on the in-

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/jocn.1992.4.4.299 by guest on 23 September 2021 put units of the network; these numerical values rep- chemicals (neurotransmitters, neuromodulators, second resent some encoding, or representation, of the messengers). For example, the chemically modulated input. The activation on the input units propagates bag cell neurons of Aplysiu show a profound transfor- along the connections until some set of activation mation of electrical properties during which the cells values emerges on the output units; these activation fire repetitively and their action potentials undergo sig- values encode the output the system has computed nificant increases in height and width (Strong & Kacz- from the input. (Smolensky, 1988, p. 1) marek, 1987). Thus there is chemical modulation of the input-output function. There are at least four distinct Information is processed by the computation in that “in- ionic conductances modulated for amplitude and kinetics formation provided as an input vector flows through the by two different second messenger-protein kinase sys- network, one layer at a time, to produce an output vec- tems (Strong & Kaczmarek, 1987), and all this affects the tor” (Churchland & Sejnowski, 1989, p. 28). transfer function. Even in the case of simplified nets simulated in silicon, however, the understanding of what counts as compu- Since repetitive firing properties reflect the expres- Downloaded from http://mitprc.silverchair.com/jocn/article-pdf/4/4/299/1754995/jocn.1992.4.4.299.pdf by guest on 18 May 2021 tation is severely stretched. For the computational theory sion of the underlying ionic conductances, moduka- of , representations and combinatorial rules for tion of the ionic conductances will alter the input/ transforming them provide a complete account of syntax output relationship of a cell . . . The effects of modu- (Chomsky, 1980; Fodor, 1980; Pylyshn, 1980). All syntact- lators covers the range of intrinsic properties, includ- ical operations are on local tokens (symbols). In simpli- ing increased or decreased excitability, the fied nets, however, the whole must be taken into account modulation of spike frequency adaptation, the en- in explaining the transformation of input to output. The hancement of post-inhibition rebound, the induction representation is processed in distributed form. Since of plateau potentials, and the expression of intrinsic the explanation of change in representations must detour bursting. (Getting, 1989, p. 198) through the self-organizing whole, “holistic ” So whereas in simplified nets, the transfer function at seems a more appropriate description than “local trans- the nodes is held constant, in biologically realistic nets formation”-which threatens to deform the of the transfer function is chemically modulated in exquisite computation as the tradition conceives of it. [But see the fashion moment to moment without trace. defense of the tradition by Clapin (1991).] The issue The connection weights of simplified nets are equiv- becomes moot, however, when we consider living nets, alent to the “synaptic ” between living neurons. which are essentially noncomputational, i.e., do not rely In learning there are structural changes so that synaptic on rules and representations. efficacy improves (the weight is increased). For example, Lynch (1986) proposes that postsynaptic receptors buried in the cell membrane are excavated in learning. The BIOLOGICALLY REALISTIC NETS increase in receptors available for ligand effectively in- Although silicon simulations of complex biologically creases synaptic efficacy. This structural change in which realistic nets are just beginning (Adamopoulos & Anni- a memo y trace results is modeled by changing the con- nos, 1989; Alexandre, Guyot, Haton & Burnod, 1991; nection weights in simplified nets. Bush & Sejnowski, 1991; Carpenter & Grossberg, 1990; In real nets, however, synaptic efficacy is also depen- Horn & Usher, 1990) we know enough of the relevant dent on moment to moment chemical modulation of properties to consider the possibility that something transmitter synthesis, release, transport, and reuptake other than computation is going on. In living nets every- (Zucker, 1987; Shepherd, 1990) which controls the thing is continually fluctuating: connection weights, amount of ligand available. There is no memory trace transfer functions, parameters, input, and even the very here. The connection weights qua synaptic efficacy of connectivity, without leaving any traces of the fluctuation. biologically realistic nets change fluidly, unlike simplified As Getting (1989, p. 194) states, “the functional organi- nets. zation of many neural networks appears to be under Network parameters are also modulated moment to dynamic control, changing in accordance with the con- moment by chemical means. For example, noradrenalin ditions at the moment.” Black (1991) emphasizes that the is thought to improve signahoise ratio (AstonJones & fluctuation is of structure (hardware), as well as the Bloom, 1981a, 1981b; Woodward et al., 1979; Sessler, functional organization. “Extensive evidence indicates Cheng, & Materhouse, 1988; Servan-Schreiber, Printz, & that the brain is not an immutable series of circuits of Cohen, 1990) and certain amino and GABA control invariant elements; rather it is in constant structural and excitatiodinhibition ratio (Douglas & Martin, 1990). So functional flux” (p. 3). Thus biological nets are chemi- important network parameters, too, fluctuate in realistic cally tuned moment to moment in many respects, some nets, which changes their functioning. Of course, input details of which will now be discussed. also is in continual flux in the ordinary unsimplified The input-output transfer function at the node de- ecological case. pends on ion channels that are exquisitely controlled by The very connectivity of realistic nets varies fluidly in

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/jocn.1992.4.4.299 by guest on 23 September 2021 several senses. Whether or not an action potential spike NONCOMPUTATION IN BIOLOGICALLY initiated at the axon hillock propagates past a branch REALISTIC NETS point on the richly arborized axonic tree depends in part In simplified nets, as discussed above, the outside is re- on its shape-broader action potentials are more likely to propagate past branch points-and the shape of the presented inside and the distributed representation is transformed. It is the processing of representations that action potential is neuromodulated (Kaczmarek & Levi- qualifies simplified nets as computational. In realistic tan, 1987; Westerfield, Joyner, & Moore, 1978). Neuro- chemically modulated frequency also affects propagation nets, however, it is not the representations that are changed; it is the self-organizingprocess that changes via past branch points (Luscher & Shiner, 1990). chemical modulation. Indeed, it no longer makes sense A sharp distinction thus must be maintained between to talk of “representations.” the effective functional connectivity and anatomical con- Instead of representation, the input flux (both from nectivity, since there is aprobubiliy of transmitter release the environment and from endosomatic instinctual

at each anatomical synapse. Downloaded from http://mitprc.silverchair.com/jocn/article-pdf/4/4/299/1754995/jocn.1992.4.4.299.pdf by guest on 18 May 2021 sources) provides a shifting constraint on the self-orga- only a proportion (perhaps a few tenths) of the syn- nizing process, together with other flowing constraints apses in an active input array will release transmitter due to chemical modulation of connectivity, connection for a given presynaptic input. This suggests that, dur- weights, transfer functions, and parameters. The outside is not represented inside but participates on the inside ing natural , a is likely subject to ac- as a constraint on a self-organizing process. There is an tivity in a relatively small proportion of the synapses interaction between input qua other-tuning and self-tun- on it at any given time. (Shepherd, 1986, p. 95) ing, out of which a constraint-satisfying settlement ap- Thus the functionally effective connectivity fluctuates un- pears. [This is a connectionist version of Neisser’s (1976, der chemical control rather than remaining constant, as p. 9) dictum: is where and reality meet. In the present connectionist terms, cognition tunes happens in simplified nets. and the “meeting” is an “interval” leading to “settle- There is still another sense in which the connectivity varies. Multiple transmitters are colocalized in neurons ment.”] Once the theory of information processing is let and many of them are independently expressed, regu- go of, then an interaction between self and other in a lated, and used as a function of the environment. There nonlinear, dynamic, self-organizing process can be the- results a variable and differential expression of the genes matized. that encode transmitter molecules which “leads to con- tinuous change in the transmitters synthesized by any The Brain Permits Participation single neuron” (Black, 1991, p. 7). So as the relative proportions of colocalized neurotransmitters varies, the These nets are a place where the outside and the inside connectivity varies. meet and participate in a whole, a place where cognition, memory, and reality join. The outside’s influence is in Within a single (neuroanatomical) pathway, chemical the form of activation patterns on an input layer and circuits form, dissolve, and reform, in response to traces carried by the connection weights; the inside’s environmental cues. Changing chemical pathways are influence is in the form of recurrent input (Churchland, thereby impressed on a substrate of relative gross 1989) and self-tuning. Out of that intersection of “self” anatomic stability. (Black, 1991, p. xiii) and “other” the dynamic whole evolves in its sponta- neous, unexpectedly bifurcating manner. So the brain Thus both the functibnal connectivity and the chemical does not compute; it permits and supports “participation” pathways fluctuate in biologically realistic nets. between self and other in the evolving whole. “Trophic molecules” also cause a slower chemical modulation of the connectivity that leaves a trace. For STATE SPACE FORMULATION example, nerve growth factor (NGF) molecule regulates “the development, maintenance, and normal function of The difference between computation in simplified nets specific, responsive pathways” (Black, 1991, p. 117). Neu- and noncomputation in realistic nets can be presented rite outgrowth is regulated by , , in terms of “state space.” The state of the net is given by insulin, vasoactive intestinal (VIP), and other the activation value for each of its N nodes. The network molecules. state, then, is represented by a point in an N-dimensional To summarize, in biologically realistic nets the con- space and state change over time by a trajectory in state nectivity, connection weights, nodal transfer functions, space. State space additionally has a topography. States and network parameters can change fluidly under chem- that well satisfy the constraints lie in basins whereas states ical control: the nets are chemically tumble moment to that do not well satisfy the constraints lie on peaks. The moment, leaving no trace, only a fluctuating attunement. spontaneous tendency of the net is to move “downhill,”

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/jocn.1992.4.4.299 by guest on 23 September 2021 optimizing constraint satisfaction; peaks are “repellers” THE NONCOMPUTATIONAL PROCESS OF and basins are “attractors.” DIFFERING AND DEFERRING Now symbolic computation is not usually thought of The computational process is one of rule-governed trans- in state space terms but there is no impediment to doing formations of symbolic representations. The noncom- so. At every stage of the computation the N digital com- putational process described here is one of differing and ponents of the computer are in a particular state (on or deferring (which in another context, that of texts and off) and during the serial computation a trajectory is writing, Derrida (1974, 1982) calls d@&ance. See also traced in the computer’s state space. Given the input to Globus (1990, 1992)l. the computer and a program, the resulting trajectory is Given a net with uniform connectivity, connection fixed. This gives state space a peculiar topography in the weights, transfer functions, and parameters, the topology case of computation, in that the entire trajectory lies in of hyperspace is undifferentiated. Difference appears the deepest vertical canyon and everything else is on the when the connectivity, weights, transfer functions, and highest ridge. There is no “downhill,” hence no spon- parameters are tuned by input, learning, and/or self- Downloaded from http://mitprc.silverchair.com/jocn/article-pdf/4/4/299/1754995/jocn.1992.4.4.299.pdf by guest on 18 May 2021 taneity; the trajectory is externally driven. tuning. Differing is In the case of subsymbolic silicon computation, when especially striking in the fluctuations given the input and the constraints, the resulting trajec- of hyperspace topology. This process is not a transfor- mation of representations but an incessant and sponta- tory is not fixed but has a fixed probability. The topog- neous differing of itself. raphy here is “normal,” in that there are variegated peaks Deferring is very much a Freudian concept (Freud, and basins, and depending on which region of state space 1900, chapter seven). [The concept of differing owes the input shifts the net to, the net settles into one or much to the great semiologist, Saussure (1966).] Freud another basin. The trajectory here is spontaneously fol- distinguished between the “primary process” that pro- lowed. So in symbolic computation the result is fixed, ceeds directly to the pleasure of instinctual gratification given the input and program, whereas in subsymbolic and the “secondary process” that delays drive satisfaction silicon computation, the theoretical probability of the result is fixed, given the input and the constraints. Pro- under the reality principle, so that a “detour” is taken to gratification via thought. In state space terms, the attractor gram and constraints correspond in terms of exerting control, but the former’s control is absolute whereas the is the memory of the instinctual object and actions for latter’s control is probabilistic. attaining it. Under the primary process, the trajectory In the case of living nets where there is continual goes down hill directly to the instinctual attractor. Under tuning going on, not even theoretical probabilities are the secondary process, the trajectory is made to defer settling into the attractor. The deferral is accomplished fixed but change moment to moment, which gives an by tuning of the net; the local topology is adjusted so the autodynamic property. The topography is decidedly ab- trajectory takes a detour from what would otherwise be normal: it continually fluctuates. The network’s task is reverse Sisyphean: no sooner does the net settle into a the most direct path. In the case where the instinctual state than the topography changes so that that very state attractor is forbidden (e.g., Freud’s “incestuous object”), a permanent unbreachable barrier is maintained around may lie on a peak and it is downhill all over again. Horn the attractor; this is called the “defense” that is continually and Usher (1990) have modeled nets with dynamic thresholds that are autodynamic even in the absence of sustained by the so-called “countercathectic energies,” any external stimulus. which are reinterpreted here as self-tuning. So the noncomputational process continually differs from itself and defers itself, in a spontaneous and unpre- The network starts its dynamical flow from some ini- dictable self-organizing process under tunable con- tial condition and when properly tuned, goes on for- straints-which is anything but the strict march of the ever wandering around in pattern space [state space]. computational process. (p. 256, bracket added)

RESIDUAL SUEJECTMTY? Results, then, are not fixed but arise spontaneously out of the ever-changing interaction between the flow of The question might be asked: Who or what does the input to the net, the relatively static memory traces, and inner tuning in this account? If self-tuning requires a the net’s flowing attunement. It is not that something is tuner, something higher, a homunculus or Demiurge being done to something-not logical operations applied who keeps tweaking the net, a ghostly subject that goes to representations-but interaction in the form of partic- by the name “I,” then the theory will hardly do. ipation in the whole. In such participatory holistic co- To answer this question, an understanding of “hierar- operation and autodynamic movement the character of chy” in neural net terms is required. Thus far network computation as driven mechanical information process- nodes were conceived of as formal neurons organized ing is lost. into “hyperneurons.” Now suppose that these self-orga-

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/jocn.1992.4.4.299 by guest on 23 September 2021 nizing hyperneuronal networks are themselves nodes in resentation in this account that is processed while it hides a “higher” net, and that this nesting recurs for many out in the whole. Instead there is a spontaneous dynamic iterations. At the highest level these higher nodes would process that is variously constrained by the environment, be of a complexity that they could be described as self- the internal milieu of the body, learning, and cognition organizing “modules” that are nodes of a supernet. These (understood as holistic self-tuning). The system of net- modules variously activate, inhibit, and tune each other works evolves under all these constraints (and more, as they drop in and out of participation in the whole e.g., linguistic constraints). Information of the world is supernet which flowingly evolves. The supernet state of not represented in the nets and processed but partici- attunement arises spontaneously out of the whole. pates in the whole with other constraints, enfolded to a So “what” does the tuning is the whole, which is not whole self-organizing process. higher but has wider participation and thus increased The equations that best capture these nets apply to the complexity. The attunement intersects with samples of evolution of nonlinear dynamic systems, which are prone the surround and the whole net evolves along its unpre- to deterministic chaos. The evolution of such equations Downloaded from http://mitprc.silverchair.com/jocn/article-pdf/4/4/299/1754995/jocn.1992.4.4.299.pdf by guest on 18 May 2021 dictably bifurcating path through state space. (See Pri- can be thought of as a trajectory in a high-dimensional gogine & Stengers (1984) on the tendency for state space or hyperspace that is studded with attractors nonlinear dynamical systems at far from equilibrium con- and repellers. These prominent features in the state ditions to shift unpredictably into states of increased space topology are not static, as we have seen, but fluc- complexity.) tuate with self-tuning; in effect the network self-tuning This noncomputational process should also be distin- biases for certain attractors as the net intersects its input guished from conditionlaction mechanisms, which are flux. The exosomatic and endosomatic environment is in computational. The rules of conditionlaction give con- flux and the network attunement is in flux; out of their ditions of satisfaction and when the representation of mutual participation and settlements a trajectory evolves. input meets those conditions, a certain action is taken The settlements in that trajectory at the superlevel of the (perhaps a recognition signal, recall of a memory, or recursively organized neural system comprise the stream search for another input). For conditiodaction, instead of . Such participatory, unpredictably har- of the rules transforming representations, the rules spec- monizing self-evolution is not easily conceived of as in- zfi representations that satisfy the conditions and the formation processing; there is a scientific paradigm computation calculates a correlation of some kind, i.e., difference at work here which opens toward the possi- the match between input and specifications. The non- bility of a noncomputational cognitive neuroscience. computational process, in contrast, does not detect matches but produces global settlements under tuned constraints. The noncomputational process is productive MOLECULAR INFORMATION (not selective, as Edelman (1987) would have it). One of the launch points for the present discussion is the great discrepancy between the silicon simulations of REVIEW bench connectionism and the actual living neural case According to conventional connectionism, information (Black, 1991; Crick, 1989; Getting, 1989; Shepherd, 1990). flows through neural nets. The representation of input Black, in addition, goes on to elaborate a theory of mo- is processed in distributed form in the hidden layers. lecular information processing that far transcends silicon Indeed, “hidden” layers is an easily misunderstood ex- implementation and is grounded in the achievements of pression. It is true that there is an input layer in which neuroscience. Since Black’s molecular computationalism the impinging stimulus information is represented in and the present noncomputationalism diverge sharply network terms-transduction is accomplished-and an from an initial point of critical agreement, a comparison output layer in which a transformed representation ap- is instructive. pears that commands output; input and output layers are It is easy to forget that “information in the brain,” even superficial and mask the “hidden” layers within where in “a molecular perspective,” is a theory. [The quotes are distributed processing occurs. But also the representa- the title and subtitle of Black’s (1991) book.] The neu- tion is itself “hidden”within the hidden layer, distributed, roscientist deals operationally in the physical measure- “subsymbolic,”as Smolensky (1988) says. Where conven- ment of chemicals, electrical spikes, and the like. The tional connectionism expands on the tradition is in en- idea that molecular mechanisms might “receive, trans- larging the notion of representation to include duce, encode, store, retrieve, and express information distributed representations; otherwise it remains com- about the real world (p. 14), however, is purely theo- putational. retical. An alternative theory is that the readings on the What I have called “radical connectionism” denies that neuroscientist’s measurement devices have to do with there are representations altogether, whether local or influencing and being influenced, i.e., withpartic$ation distributed; hence there is no computation. Something in a nonlinear dynamical system that is self-organizing, very different is going on, There is no distributed rep- self-tuning, and autodynamic. The difference between

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/jocn.1992.4.4.299 by guest on 23 September 2021 these is so fundamental that we can properly in the nervous system. (Black, 1991, p. 45, first italics speak of “paradigm difference.” added) We shall consider this paradigm difference in a specific case discussed by Black (1991, p. 55) in the section Here there is slippage from “regulation” to “represen- “Communicative symbols and transducer molecules,” tation,” whereas we can alternatively think of regulation which he illustrates with a detailed discussion of as tuning of a process. hydroxylase as a rate-limiting enzyme in Another specific case discussed by Black (chapter 8) biosynthesis. Black begins with the claim that “[clertain is disconnexion syndromes (Geschwind, 1965). At the molecules within the nervous system are capable of act- most complex levels of brain functioning there are func- ing as transducers, converting one form of information tional modules that intercommunicate. When the com- to another” (p. 55). An alternative theory is that infor- munication is severed-in the extreme case, right and left do not directly communicate-peculiar syn- mation & converted to Constraints on apvocess. dromes result. For example, even though a patient may

At other places, however, the two theories come close Downloaded from http://mitprc.silverchair.com/jocn/article-pdf/4/4/299/1754995/jocn.1992.4.4.299.pdf by guest on 18 May 2021 together. have normal hearing, reading, and writing, the spoken word cannot be understood when Wernicke’s area is Specific communicative symbolic molecules convert severed from auditory input (p. 139). Tactile aphasia environmental or internal information into altered occurs when Wernicke’s area is severed from somesth- neural function and behavior. (p. 60) etic sensory input and disconnection of Wernicke’s area from motor centers results in an inability to execute Here informution converted to altered function. The is commands (apraxia). In disconnexion syndrome the le- prment noncomputational theory agrees, interpreting sion blocks communication. “altered function” to mean “the tuning of constraints on But disconnected “communication” has at least two a self-organizing process.” With regard to the information interpretations here. In Blacks, what is communicated to behavior conversion, the two theories completely to the module housed in Wernicke’s area is information, agree. Here the issue is competence, the conversion of a message. When Wernicke’s area is cut off from auditory an input vector to an output vector. But how that is information, for example, the Wernicke’s module is un- accomplished within the “black box” and whether that able to compute the meaning of spoken words, unable performance has anything to do with information, ought to process the auditory information, even though hear- to be an open question. ing, dependent on other modules, is intact. The written “Neurotransmitters , . . are quintessential communi- word, however, “communicates” with Wernicke’s module cative symbols in the nervous system” (p. 55). Again, through intact visual pathways, and the written word is Blacks idea that there is communication going on is meaningful. theoretical; alternatively, a process is influenced by neu- On an alternative interpretation, Wernicke’s area is a rotransmitters. The notion of “symbols” is also theoreti- complex node whose settlements provide the meaning cal. of spoken and written words. The Wernicke’s node is Although their [neurotransmitters’]communicative tuned by auditory and visual inputs (among others) and functions have long been apparent, their symbolic is accordingly constrained in its self-organizing process. functions have not been recognized. Yet these mo- When the changing auditory influence is disrupted in lecular signals are known to change in highly spe- disconnexion syndrome, the settlements become free of cific ways in response to environmental events. constraint in this regard, while the influence of particular (Black, 1991, p. 55) written words on the Wernickian self-organizing process continues to constrain the settlement process toward Here Black distinguishes between the communication of certain attractors. information between neural systems and the “symbolic” Despite the information processing emphasis, a dy- representation of the world. He is surprised that the namic model peeks through at various places in Black’s symbolic function has not been recognized because the presentation. molecules change specifically in response to environ- mental events. Rut a covariation between environmental the neuron and the synapse are emerging as unex- events and molecules does not necessarily imply that the pectedly dynamic entities that change from milli- molecules symbolically represent the environment. It is second to millisecond . . . Indeed conceptions of the equally possible that the molecules are influenced by very nature of neural information are undergoing the environment and these influenced molecules partic- marked changes. (p. xii) ipate in the self-organizing dynamical process. Again, the statement is made, Extensive evidence indicates that the brain is not an immutable series of circuits of invariant elements; Neural structures that are regulated by specific envi- rather it is in constant structural and functional flux. ronmental stimuli, that change function in response The digital computer analogy is fatally misleading. to those stimuli, may represent those external stimuli (P. 3)

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/jocn.1992.4.4.299 by guest on 23 September 2021 There is no place to stand in such a dynamical evolu- which the present noncomputational theory can be fruit- tion-no origin (arche), no end (telos),no center (echo- fully compared. Following a contrastive method, Baars ing Derrida [ 1974]), only a dynamic interplay. summarizes the capabilities of conscious processes and unconscious processors on the basis of the research Environmental stimulus, mental state, behavior, and literature. He provides a table (Table 1) (Baars, 1988, molecular are in constant interplay. p. 75), which Global Workspace Theory is designed to (P. 167) explain. And Black closes his book with this trenchant statement: Global Workspace Theory posits a global workspace in which specialized processors may participate. When The essence of life systems may involve the central specialized processors do not participate, they continue fact that high levels continually transform the lower, functioning in parallel, each processing the information elemental levels upon which the high levels are that comes to it in an independent fashion. But when based. Appreciation, description, and analysis of this

participating in the global workspace, specialized pro- Downloaded from http://mitprc.silverchair.com/jocn/article-pdf/4/4/299/1754995/jocn.1992.4.4.299.pdf by guest on 18 May 2021 ubiquitous phenomenon may represent one of the cessors gain access to global messages and can send fundamental tasks of the life sciences. (p. 181) global messages. The emerging dominant message When the higher transforms the lower which transforms among competing messages is the content of conscious- the higher, there is no ground or center or foundation. ness. The table can be explained with this communica- Blacks statement can be construed as a roundabout de- tion model as follows. scription of the spontaneous and unpredictable holistic Nonparticipating processors are adapted to the mes- evolution of recursively organized nonlinear dynamic sages they receive and so the computations proceed very systems. efficiently and in parallel, without regard for inconsis- That a tacit dynamic conception underlies Black’s in- tency. Participating processors are subject to the emer- formation processing approach is also apparent in his gence of a dominant message, which takes time and all blurring of the distinction between “hardware” and “soft- of the global workspace’s resources. Participating pro- ware.” cessors are doomed to seriality and a consistent product in virtue of participation in a global process of cooper- the brain can no longer be regarded as the hardware ative and competitive communication. But the gain for underlying the separate software of the mind. Scru- participating processors is flexibility through the infor- tiny will indicate that these categories are ill framed mation exchange via the global workspace. Through par- and that hardware and software are one in the ner- ticipation, processors get into the information loop and vous system. (Black, 1991, p. xiii) have a voice in the process that produces a dominant global message, which is the conscious content. Baars the molecules, the transformations of biochemistry, summarizes: and the principles obeyed are both hardware and software. These terms, however, fail to capture the In conclusion, we can now replace all of the facts nature of neurologic function. (Black, 1991, p. 5) described [in the table] with a rather simple model: But information processing is a computation that de- pends on structure-sensitive rules (program, software) Table 1. Capabilities of Comparable Conscious and acting on hardware representations. Since the distinction Unconscious Processes between rules and representations is not maintained Capabilities of conscious Capabilities of unconscious when “hardware and software are one,” there is no basis proceses processes for speaking of information processing. Furthermore, there are various mechanisms “by which the molecular 1. Computationally inefficient: 1 Highly efficient in their High number of errors, own tasks: Low number of structure, the ‘hardware,’ of neurons changes over time, low speed, and mutual errors, high speed, and altering function” (p. 7). There is nothing comparable to interference between little mutual interference this in computation; the hardware is “hard’ precisely in conscious computations its invariance, in contrast to the changeable program. So even when we turn from the impoverished silicon 2. Great range of different 2 Each specialized processor contents over time: great has limited range over neurobiology implementable at the bench to the rich ability to relate different time: each one is relatively neurobiology displayed by Black (1991), information conscious contents to each isolated and autonomous processing remains theoretical and an alternative theory other; great ability to relate of evolving nonlinear dynamic neural systems is con- conscious events to their ceivable, against the tradition. unconscious contexts At the cognitive level, too, well-established empirical 3. Have internal consistency, 3 Diverse, can operate in data support alternative computational and noncompu- seriality, and limited parallel, and together have tational interpretations. Baars’ (1988) Global Workspace capacity great capacity Theory of consciousness is a computational theory with

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/jocn.1992.4.4.299 by guest on 23 September 2021 the idea of a set of specialized processors, each well revealed in the geometry of state hyperspace. Let’s first equipped to handle its own special job; all the spe- consider a classical dynamic system. cialists can communicate with the others through a The state hyperspace attractors for classical systems global workspace. In this way they can cooperate and are typically points, limit cycles, and tori. Classical sys- compete with each other, to strengthen or weaken a tems that follow dynamic equations are in principle pre- global message. dictable (e.g., as with the prediction of eclipses). Suppose one narrows the initial state of the classical system to a Like consciousness itself, this system works best small region of hyperspace. (Because of unavoidable when routine tasks are directly delegated to the best small measurement errors we cannot be certain of the expert that is ready to solve it, and the use of the exact point.) Knowing the initial state and the evolution blackboard is reserved for just those problems that equation, it is possible to predict the final state within cannot be solved by any expert acting alone. When an equivalently small region of hyperspace. This pre- the cooperating processors discover a single algo-

dictability is consistent with the idea of computation. But Downloaded from http://mitprc.silverchair.com/jocn/article-pdf/4/4/299/1754995/jocn.1992.4.4.299.pdf by guest on 18 May 2021 rithm able to solve the problem, that algorithm can nonlinear dynamic systems are nonclassical, and unpre- again be handled by a single expert, freeing up lim- dictable like the weather (Lorenz, 1963). ited global capacity for other unsolved problems. For even very simple nonlinear dynamic systems with (Baars, 1988, p. 92) only a limited number of variables, the attractor can be But the same data are consistent with the noncomputa- chaotic and the geometry “strange” in that state hyper- tional model and its metaphors. space for such systems has a fractal dimension. Any un- Noncomputationally, participation does not mean get- certainty about the location of an initial state is ting into the information loop with its global blackboard. exponentially amplified so that the final state is unpre- Participation instead means constraining by tuning a dictable in principle. Nearby trajectories diverge expo- spontaneous global dynamical process. The process pro- nentially rather than remaining confined to a small ceeds within the context of the resulting attunement. region of state space. Nonparticipating processors are settled into solutions Thus the initial uncertainty in the specification of the that well adapt them to their input. These mutually in- system is eventually smeared out over the entire at- consistent processors proceed in parallel and with great tractor and all predictive power is lost, i.e.,all causal joint capacity. Participating processors are subject to the connection between the present and the future is lost. self-organizing process of the global whole that produces This is referred to as sensitive dependence on initial consistent serial settlements that utilize total capacity. conditions. (West, 1990, p. 13) Global participation of many processors in the self-or- ganizing process ensures flexibility, a wide range of po- This uncertainty is “fundamental to the system dynamics tential settlements, and because of the stochastic nature and gathering more information will not reduce the de- of the process, a quirky unpredictability. gree of uncertainty” (West, 1990, p. 8). So in comparing the computational and noncompu- The rate of divergence of initially nearby trajectories tational models, we again find empirical data nondis- in dynamic systems manifesting chaos can be quantified criminating. The computational inefficiency of conscious- by means of Lyapunov exponents and the rate at which ness, the great range of its contents, its self-consistency, the system becomes unpredictable can be quantified by seriality and limited capacity-as well as the opposite the Kolmogorov entropy (Schuster, 1984). These quan- properties of unconscious processes-can be explained tities have been calculated for EEG time series, and as by the theory that information is being processed by a we shall see in the next section, appear to increase from brain with a global information exchange and also by coma and NREM sleep to waking (Gallez & Babloyantz, the theory that an unpredictable, self-organizing, dynam- 1991). In any case, the difference between computational ical process is spontaneously generated by the brain, a and noncomputational models can be well-posed, in that process that is continually tuned and thereby constrained the hyperspace geometry of the latter has a fractal di- in its evolution. At levels of complexity from the neuronal mension. [For a model of fractally configured neural node of the hyperneuron to the supernet whose nodes networks, see Merrill & Port (1991).] are highly complex self-organizing modules, one theory Computation as understood by the tradition is not envisions the processing of information and the other en- performed by chaotic systems. Computer computation is visions influence on a self-generating dynamic evolution. not sensitively dependent on initial conditions. Small fluctuations in digital components do not effect the result of silicon information processing. A system which in THE FRACTAL GEOMETRY OF principle gives unpredictable results is not computing. STATE ‘HYPERSPACE So if it could be empirically demonstrated that brain Thus far the emphasis has been on the computational functioning shows sensitive dependence on initial con- and noncomputational models as alternative explana- ditions, then the brain is not computing, at least in the tions. The focus now discriminates between them, as strong sense of performing information processing. And

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Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/jocn.1992.4.4.299 by guest on 23 September 2021 if the brain does show sensitive dependence on initial intervals of spontaneously active neurons in the simian conditions as revealed by fractal properties, then this motor cortex and concluded that at least on occasion the brings a new “metaphor” [recalling Daugman’s (1990) neuronal activity is chaotic. Furthermore, the chaotic be- caveat] in which the brain evolves as a self-generating, havior of certain neurons had a low dimension, indicat- nonlinear dynamic system under tunable neurochemical ing comparatively simple dynamic behavior (i.e., few constraint, degrees of freedom are required in the dynamic law that specifies the neuron’s behavior). (See also Rapp et al., 1987.) Mpitsos et al. (1988) provided evidence that some EVIDENCE FOR FRACTAL PROPERTIES of the variability in the spike trains of motor neurons of OF THE NERVOUS SYSTEM the mollusc Pleurobranchaea californica can be attrib- West’s (1990) helpful discussion of fractal and uted to chaotic activity. chaos in discusses the three “guises” of the Furthermore, there is some reason to think that cog-

fractal concept. In the first guise, the fractal is geometric. nitive functioning correlates with the “correlation di- Downloaded from http://mitprc.silverchair.com/jocn/article-pdf/4/4/299/1754995/jocn.1992.4.4.299.pdf by guest on 18 May 2021 Here the complexity of ramifications in a tree-like struc- mension” of the EEG (Babloyantz, 1986; Babloyantz & ture is conserved with increasing number of branchings; Destexhe, 1986; Babloyantz, Salazar, & Nicolis, 1985; Gal- the pattern of branchings remains self-similar as one goes lez & Babloyantz, 1991; Mayer-mess & Layne, 1987; Ni- further and further out the tree. West reviews (chapter colis, 1985; Skarda & Freeman, 1987; Xu & Xu, 1988). two) evidence that the bronchial tree and the His-Pur- West (1990, p. 19) concludes that “the dimension of the kinje network of the heart are self-similar (fractal) in ‘cognitive attractor’ [underlying the EEG] decreases mon- their arborizdtions; that is, as the bronchial tree and the otonically as a subject changes from quiet, awake and His-Purkinje networks become more finely ramified, the eyes open to deeper stages of sleep.” Functionally speak- complexity remains (rather than finding the simplifica- ing, the hypothesis is that the dynamic behavior grows tions of primitive elements or a continuum). The more more complex with cognitive activity (On chaos and bushy the tree, the higher the fractal dimension. The cognition see also Freeman, 1987; Mandell, 1983; Nicolis, possibility that dendrites, too, form a branching tree with 1986; Nicolis & Tsuda, 1985; Skarda & Freeman, 1987, fractal properties has been investigated by Morigiwa, Tau- 1990.). This is a plausable hypothesis that invites further chi, & Fukudd (1989) and Schierwagen (1990). experimental investigation. Furthermore, there are pre- If the arborization of neural processes, both dendritic liminary reports that level of cognitive activity varies with and axonic, turns out to be geometrically fractal, then the degree of chaos, as measured by Lyapunov exponents this is of great functioiial importance. As already noted, and Kolmogorov entropy (Babloyantz, Salazar & Nicolis, the spike initiated at the axon hillock can be recorded 1988; Gallez & Babloyantz, 1991). at only a few tenths of the presynaptic terminals (Shep- So although we are far from being able to speak con- herd, 1986) and the extent of penetration of the initiated fidently of a “fractal brain,” there are at least the begin- spike into the arborization is controlled by both the nings of an experimental and modeling literature neurochemically modulated shape (Westerfield, Joyner, suggesting that nervous tissue has fractal geometric, sta- & Moore, 1978) and frequency (Luscher & Shiner, 1990) tistical, and dynamic properties and that there are fractal of the action potential. Thus functionally speaking, fractal correlates of cognitive activity. This literature is consistent geometric properties may be neurochemically tuned. with the noncomputational theory and inconsistent with Another guise of fractals is statistical self-similarity with the computational theory because the sensitive depen- magnification. “In a fractal stochastic process, not only dence on initial conditions for a state hyperspace with a does the process itself display a kind of self-similarity, fractal dimension spreads a principled uncertainty con- but so too does the distribution function characterized sistent with the noncomputational, but antithetical to the [sic] the statistics of the process” (West, 1990, p. 77). computational, theory. Since cognitive neuroscience is Teich et al. (1990) presented a relevant study of se- productive of a wide range of time series data, there is quences of action potentials recorded from adult-cat au- opportunity to distinguish what appears to be noise from ditory nerve fibers and lateral superior olivary units. They what may turn out to be deterministic chaos. Reports report that the firing rate remains self-similar when cal- that fractal properties of the EEG vary with level of cog- culated with different averaging times and further that nitive activity are especially intriguing and call for further the cluster distribution remains self-similar. These neu- study. Despite the present indiscernability of computa- rons thus show statistical fractal properties. tional and noncomputational theories with respect to The third guise of fractals discussed by West has to do much available data, cognitive neuroscientific study of with time series. For a recent example, Canavier, Clark, the hypothesized fractal brain properties should prove & Byrne (1990) modeled the R15 bursting cell in the decisive. abdominal ganglion of Aplysia. The model exhibits both Reprint requests should be sent to Dr. Gordon G. bursting and beating modes. But there is also a chaotic Globus, University of California, Irvine Medical Center, regime with a calculable fractal dimension between these Department of Psychiatry, 101 The City Drive, Rt. 81 Bldg. two modes. Rapp et al. (1985) studied the interspike 53, Orange, CA 92668.

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