Mind as a Dynamical System: Implications for Autism

Mike Lesser and Dinah Murray

1998 Lesser, M.J. & Murray, D.K.C. “Mind as a dynamical system: Implications for autism”, Durham conference Psychobiology of autism: current research & practice

In the last twenty years there has been an intensive study of non-linear dynamical systems. [1,2,3,4,5] The flow of fluids, the collapse of engineering structures, the development of the phenotype from the genotype and human imagination are examples. These systems although subject to smoothly varying controlling parameters, exhibit sudden changes and even the emergence of formerly non-existent features.

Such revelations of formerly invisible qualities of a system mark – are – the spontaneous appearance of new information. We should beware of thinking of Information as a locally conserved quantity. There is no law of the conservation of information. We should expect to observe the spontaneous appearance and disappearance of information. Once there was no life on this planet. Once there was no planet. Now all this has emerged.

I. The Interest System.

We believe that mind models its environment, thus increasing the ability to predict. We assume that mind links sensation, both present and previous, with action. Our model provides a description of the underlying workings of Tolman’s cognitive map [6,7].

In our model we describe the link between experience and activity by an algebraic equation derived from ecological studies carried out by Peter Allen and Mike Lesser [8]. In the ecological model, a fundamental and limited resource, solar radiation, is competed for by a spontaneously arising hierarchy of life forms. In our model the fundamental and limited resource is mental attention. Mental events, which we describe as interests, using the word in its everyday sense, compete for and consume attention. Interests are emergent properties of the mental process.

Interests have the following properties:-

1.0 Interests may be more or less aroused.

1.1 The degree of arousal of an interest is a function of the magnitude of its emotional charge.

1.2 Interests are aroused in as many different ways as there are emotions, but to reduce the volume of computation, and simplify presentation, we only model attraction, a fundamental reduction of all other emotions.

2.0 Interests compete for attention, which they consume.

3.0 The arousal of interests is modified by sensation.

4.0 Interests arouse each other.

4.1 An individual’s personality is determined as much by the pattern of their interests’ inter-arousability as by the nature of the interests themselves.

5.0 The arousal of interests is autocatalytic.

6.0 Interests engender activity.

7.0 Interests are consumed by the activity they engender.

II. A Model of the Interest System

click here for diagram

The model is expressed as a pair of spatially discretised differential equations. Our mathematical model of the interest system is a densely interconnected and highly diffusive matrix. Nonetheless, the equations produce entities which are recognisably distinct both from one another and from their common background. That is to say, despite the equation’s strong diffusion terms, the model generates a landscape of distinct features. We refer to these distinct features as interests. Interests are dynamical objects, patterns of briefly stable flow, produced by fields of positive and negative feedback and the accidents of history. They have no independent existence. The particular role each one plays is dependent on the state of the entire system.

We model the environment of mind by a small perturbation in the value of each cell in the matrix at each time step. This is a strategy used in ecological mathematics to create a neutral environment. We use this strategy in the version of the model in the illustration in order to preserve its general features. In fact, we believe that the environment of mind is not neutral but information bearing. Information in the environment would be represented by a bias in the pertubation. Social transactions are modelled by using the output of one model to contribute to the bias of the input of another model with which it shares an environment.

II i The correspondence between model and mind.

The value of a model relies on both its conformity to and its difference from its object. Our model of mind differs from mind itself primarily in that it is happening in culture space, and in the circuits of a computer, rather than as part of our ideas about the functioning of a living person. The value of this difference is that repeatable experiments can be performed with the model. Clearly, however, what the model has to teach depends on the model’s correspondence to its object. I will now survey some of the salient features of this model’s conformity with the contemporary understanding of mind.

II i a Mental development.

We model the emergence of the landscape of everyday mind as a function of sensory input and the pertaining state of the system itself, which is effectively its past. We model three distinct learning processes. The result of each of these processes is that new interests become established in the system.

II i b

Interests occupy more than a single cell in the matrix. They are compound, various and multifaceted, rather than homogeneous or monolithic. They are gestalts rather than ideals. New interests enter the system as sub-components of existing interests, as differering aspects of the same thing.

II i c

Interests come into being in the model by a process of intermittent, rapid and crisp bifurcations. The creation of interests by bifurcation models the simple linear learning process that might be described as Pavlovian. Such interests are spatially associated within the model.

II i d

There is, in addition to simple association, another way in which new interests may come into existence within the system. The population of interests is occasionally augmented by the sudden emergence of clusters of new interests. Our growing ability to describe sudden emergence, that is, how new attractors suddenly appear in complex systems is illuminating many formerly obscure aspects of the development of natural objects. We are beginning to learn how complex systems undergo transformations of their fundamental identity. Furthermore our ability to describe complex and sudden emergence provides us with tools to describe the mechanisms that underlie inspiration, insight and intuition and to rebut the argument that mind is simple and linear. The equations develop smoothly but also generate discontinuities, modelling both systematic thought and spontaneous mental creativity.

II ii

The propensity of the system to harbour new interests, and the consequent density or quantity of interests present in the system at any one time is a function of the strength of the system’s inhibitory feedback fields. We believe that the density of interests sustained by the system is of fundamental significance in the understanding of the behaviours identified as and associated with Autism. We will return to this point shortly.

II iii

Our model maximises its symmetry when it is unperturbed. That is to say, whilst the model is not being perturbed, it spontaneously seeks to minimise its informational content. It does not do this by the simple extinction of interests (forgetting), but by minimising internal differences present in the entire interest system. If global symmetry acquisition is the sort of thing that happens to our minds when we sleep, then dreaming may be a vestigial awareness of the process.

II iv

The one dimensional Volterra-Lotke equation comes to a cyclic attractor at equilibrium. Our, spatialized, version of the equation can exhibit both micro and macro cyclic behaviour. We speculate, therefore, that cyclic behaviours such as the sleep waking cycle and the breathing cycle may be generated by similar mechanisms to rocking, flapping and tapping. Cyclic behavious of this kind may also be linked to such psychological cycles as adventure/reassurance and transgression/forgiveness. We speculate that cyclic behaviour may be part of the stage rather than part of the play.

In the very broadest of terms we might say that we feel there just is not enough room for all the stuff in our heads to go in straight lines. It seems easier to imagine that our minds go round and round. In more formal terms, we believe that the mental landscape is comprised of processes rather than states, and that these processes are bound by strange cyclic attractors rather than by point attractors.

II v

At this stage in the development of our equations we have attempted to map only essential mechanisms. Language and self are two areas of the proposed system which, although not specificaly modelled, require special mention. We believe that embedded within the general interest system most people have an elaborate sub-system of interests which is what they know of language. The manipulation of interest systems is an important function of language and a direct consequence of language as an amplifier of the imagination. Embedded within the language system is an elaborate sub-system which is what we think we know of ourselves. Language brings greatly enhanced detail, durability and communicability to the system of self interests, but these interests are identical in structure to the rest of the interest system.

Ego, ourselves to ourselves, is not the prime mover in our model. We believe that it is the alchemy of language which generates the apparently independent agent, transforming activity into transitive behaviour. We think that the idea of the doing and the done to is one way, just one amongst many ways, in which the world can be imagined. In our model, ego is the spontaneous emergence of a system of images of the imaginer in the imagination. Ego is an emergent property of language, far from the central machinery of mind. In our model, social actions emerge from the play of our interests, including self-interests, from our images of other people, and from the situation in which we find ourselves.[9, 10]

Computer graphic of development of interest system showing sudden events A. With added language system B and ego C .

II vi

Although this model owes little to Freud, we feel that a plausible model of mind should provide some account of the notion of the unconscious mind and the idea of psychological conflict. We do not explicitly model the unconscious mind. However, we propose that just as a minimum level of arousal of an interest is required to trigger an activity, there is a level of arousal so low that it fails to trigger awareness. We do not see this threshold as being sharp or sudden, but imagine that interests at a certain low level of arousal exist at the corner of our mind much as we may just see something at the corner of our eye.

Levels of Un-conscious, Conscious and Activating Arousal

Amongst sub-aroused interests are those at the vitally important interface with motor and other low level functions. This interface requires interests at minimal emotional arousal, certainly below the threshold of consciousness. Indeed, its functioning is often impaired by continuous awareness, as the sportsman or the artist will attest. In our model, competition between interests is not a symptom of mental disease, but the fundamental condition of a functioning system. Behaviours are vectors whose components are conflicting interests. Psychological conflict does not arise unless attractive and aversive interests are simultaneously aroused.

II vii

The final area of correspondence that I will mention in this brief overview is biochemical. There is a parameter, N, in the model that controls the amount of attention available. Attention is the primary resource of the model. Increasing the value of this parameter N increases activity, without affecting the state of the model in any other way. This may be an idealised representation of an increase in the quantity of available excitary neurotransmitters.

III. Born to Forage – a Model of Autism

We have outlined some of the areas in which our model resembles everyday mind to make it easier to understand what we mean by the model having an Autistic calibration. We believe that the attention tunnel or Monotropic Condition is a central feature of behaviours in the Autistic spectrum [11,12,13,14]. In our model, the degree to which a mind exhibits the Monotropic Condition is controlled by a single parameter, Ro, which governs the strength of the feedback between interests. If the parameter Ro is set to a low value then many interests are aroused to a moderate degree. If Ro is set high then a few interests are very highly aroused. When many interests are aroused, multiple, complex, behaviours emerge. When few interests are aroused then a few, intensely motivated, behaviours are engendered.

Broad Arousal

Everyday Parameterisation Ro=1


Deep Arousal

Monotropic Parameterisation Ro=30


Our understanding of the mechanisms which underlie the attention tunnel have informed our intervention in cases of diagnosed Autism. Our work with the animator Ferenc Virag, which many of you have seen, emerged from our attempts to, start where the child is, to enter his attention tunnel, to share with him a set of mutually aroused, common interests. Our choice of the personal computer as the environment in which to set up the attention tunnel also sprang from our understanding of these mechanisms [15].

However, in addition to providing a theory which can be tested by experiments, certain general features of the situation have recently become apparent. We observe that, in the model, the Monotropic calibration is a particular region in a continuum of types of mind which includes everyday mind. We observe that the Monotropic Condition is merely a possible calibration of the model. It is not associated with the content, or arrangement of the contents of the model.

A Theory of Autism

It seems to us that the Autistic spectrum of behaviours is evidence of one extreme of the normal distribution of types of mind that we would expect to find, given the environment in which the human race has evolved [16]. It is a mind optimised for searching for sustenance in a dangerous environment in which resources are scarce. The attention tunnel which links the unarmed hunter to the prey must be optimised for the immediate high gain high risk opportunity. It must have a propensity to accept what is seen, even when this contradicts what was formerly thought to be known. It must be sensitive to immediate data rather than to pre-existent or received information, sensitive to clues to where future food resources might be concealed, rather than to knowledge of where food is presently known to be available. Such a mind must have a propensity for actual rather than literal information.

Such a mind seems to have the will to error, but is in fact the only sort of mind capable of discoveries that go beyond the known and transform situations. Only error making leads to metamorphic discovery.

In the light of this understanding several paradoxes of the condition become less puzzling. The capacity for a high degree of sensory acuity is essential in the hunter. Spatial abilities are an obvious requirement. The ability to endure pain, to ignore the agony of the long distance chase and to go without sleep have also emerged in the selection process.

The skills required in food foraging are similar to those required in war. The stories of Enkido, Achilles, CuChoran, Hercules, Perseval, boy Cornwall on the burning deck and many other military heroes provide a lexicon of aspects of the syndrome. The stories of heroes also provide examples of exploitation of the weaknesses inherent in the conditions . We believe that where there is the capacity for extreme depth of arousal there is often less capacity for breadth of arousal. The advantages of adaptation for depth, not breadth, of awareness are apparent in the field not in the camp, at the edge not in the centre, in crisis not in stability. People with the ability to concentrate very hard typically lack the capacity to sustain large numbers of simultaneously aroused interests.

People with the capacity for great depth of interest, adapted for pathfinding at the edge of the known, are poor at elaborate low risk/low gain social activity. This is because language and self are the most dense and complex areas of the interest system, requiring maximum breadth of modelling. We postulate that self and language tasks as they are habitually performed may require more breadth of arousal than is available in some interest systems. Many of the problems in relating to society experienced by people described as autistic are the result of different modalities of language use and of the modelling of the self, other and the words between.

The other extreme of this normal distribution of types of mind consists of people with very broad but not very deep minds. This category includes those most highly rewarded by society, chat show hosts and politicians. Such people do not posses outstanding specific talents, but have great ability to model other people, giving them power to manipulate social, rather than actual, situations.

We cannot think of Autism as an illness for which a cure can be discovered [17]. We do however observe in people described as Autistic a cast of mind that renders them unsuitable for conventional forms of employment. However, we see this economic frame of reference as holding the key to a happy outcome. In benign circumstances, people with the capacity for deep concentration have a great capacity to learn skills which are beyond the broad mind. Mass production culture may have deprived the deep minded of occasion to contribute to society as the pathfinders to physical resources, but it has opened a vast spectrum of new opportunities. It is the deep mind that has the capacity to read, understand and apply the technical manual, to enter into the intricate labyrinth of the logic of the integrated circuit and the computer program. It is the forager mind, insensitive to the way everybody knows things should be done, which creates the paradigm transforming technologies. Appropriate education would enable many ingenious and creative people to be part of things, who are now totally excluded from the mainstream of society. Education based on understanding could transform this apparent problem into an opportunity.

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