Neurodynamic system theory: Scope and limits - Springer Link

NEURODYNAMIC SYSTEM THEORY: SCOPE AND LIMITS

PÉTER ÉRDI Biophysics Group, KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, H-1525 Budapest, P.O. Box 49, Hungary

ABSTRACT. This paper proposes that neurodynamic system theory may be used to connect stmctural and functional aspects of neural organization. The paper claims that generalized causal dynamic models are proper tools for describing the self-organizing mechanism of the nervous system. In particular, it is pointed out that ontogeny, development, normal performance, learning, and plasticity, can be treated by coherent concepts and formalism. Taking into account the self-referential character of the brain, autopoiesis, endophysics and hermeneutics are offered as elements of a poststructuralist brain (-min& computer) theory. Key words: brain, causality, chaos, dynamic structuralism, hermeneutics, hierarchical structures, neural oscillation, self-organization, self-referential systems

1. INTRODUCTtON The term 'brain' is orten associated with the notions of 'mind' and of 'computer'. The brain-mind-computer problem has been treated within the framework of three separate dichotomies. First, the brain-mind problem is related to the age-old philosophical debate among monists and dualists. Second, the problem of the brain-computer analogy/disanalogy has been the product of early cybernetics, recenfly revived by the neurocomputer boom. Third, according to the suggestion of the computational theory of mind the computational metaphor is considered as the final explanation of the mental processes. A rather ambifious approach would be to treat the brain-mind-computer trichotomy by coherent concepts. 'Connectionism' [1] might be qualified not only as a new scientific paradigm, but also as an ambitious movernent. Based on the principles of 'brain-style computation' (or 'parallel distributed processing') it offers a conceptual framework for a would-be general brain-mind-computer theory. The connectionist movement posed the question: What can neurobiology suggest to engineers of near-future generation computer systems and to cognitive psychologists? Furthermore, it had a feedback effect on brain theory itself, offering a conceptual and mathematical framework to describe the dynämics of neural organizaüon.

Theoretical Medicine 14: 137-152, 1993. © 1993KluwerAcademicPublishers. Printedin the Netherlands.

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The intention of this paper is to contribute to the methodological aspects of the brain-mind problem. It will be shown that dynamic system theory, originated in physics, but generalized to more complex causal systems, can be a proper conceptual and mathematical framework of a non-reductionist brain- (and more ambitiously, mind- and computer-) theory. Though the paper does not (explicitly) address philosophical problems, it has some (implicit) message. What I believe, is that neither the naive eliminative materialistic monism [2] nor the open interactionist dualist hypothesis [3] are sufficiently satisfactory for being acceptable as a basis of reasoning. Out starting point is the belief that 'downward causation' [4] from 'mental to neural' does exist, but does not make the dividing line between eliminative reductionistic materialism and dualistic interacüonism. When the structure and function of the brain are studied by theoretical methods, two concepts have to be emphasized: hierarchy and dynamics. The brain is considered as a prototype of hierarchical structures. ("What does create problems ... for brain research, more than for most other sciences, is its multilevel structure" ([5], p. ix)). Obviously, neural systems can be studied at different levels, such as the molecular, membrane, cellular, synapfic, network and system level. Mathematical models of dynamic systems can be classified into two groups: single level and multilevel (hierarchical) models. The concept of the state space, derived from the theory of mechanics and thermodynamics and generalized by mathematical system theory, is particularly useful in describing single level phenomena. While a class of neurodynamic problems can be studied by single-level models (e.g. the temporal change of neural activities), the majority of the network models uses two-level models describing single neuron activity and synaptic modifiability. Historically, the McCulloch-Pitts model [6] is in the former category, while models adopting modifiable learning rule (e.g. Rosenblatt's Perceptron [7]) are in the latter one, The brain, at least partially, is a physical device, so it is rather natural to ask what physical theories, such as quantum theory [8, 9] and thermodynamics [10, 11], can offer to the understanding of the brain. As for the quantum-theoretical approach to the brain, such nonclassical concepts, as nonlocality and quantum reality [12] might perhaps lead to a new interpretation of neural (as weil as mental) interactions [13]. I believe, however, that such a macroscopic structure as the nervous system, can properly be treated by macroscopic tools. Thermodynamics, as a theory of macroscopic marter, might be useful for the analysis of energetic aspects of brain processes. Earlier, energetic aspects have been qualifled as not too characteristic; it has been pointed out tbat ingenious and confused ideas do not show any difference from the point of view of glucose consumption. (Biochemical energy production is strongly related to glucose consumption). The improvement of (dynamic) brain mapping techniques [14,

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15] might help to get more direct information about the relationship between mental activity change and energetic processes, e.g. oxidative metabolism. Thermodynamics is not only a narrow discipline for studying energetic interactions, but also the general system theory of the physical world, and its notions can be extended to 'higher than molecule' levels. This will be discussed in Section 2. Some problems of causality and dynamics, related to emergence, will be pointed out in Section 3. Formal aspects of neurodynamic models will be sketched in Section 4. Examples of self-organizing phenomena, occurring at different hierarchical levels of the nervous system, are given in Section 5. In Section 6 the limits of dynamic structuralism will be explained, and it will be suggested that hermeneutics, as a possible paradigm, may serve as a framework for a brain theory to be formulated. The paper ends with some concluding remarks and gives some indications towards mental and computational aspects of a brain theory, Section 7.

2. HIERARCHICAL THERMODYNAMIC APPROACH TO THE BRAIN Based on the notions of dissipative structures and cooperafive phenomena appearing in physicochemical systems, Katchalsky and his coworkers [16] tried to give a coherent explanation of dynamic patterns emerging during the operation of neural networks. Physicochemical dissipative structures are products of the cooperation arnong the elements of molecule populations. The notion of entropy - one of the vaguest concepts of modern science - has been defined within the framework of (phenomenological and/or statistical) physics [17, 18]. A question can be raised [19], whether entropy preserves its fundamental role if the investigated system (e.g. the brain) is considered as a thermodynamic system only at a relatively low level of the description, and as a Thermodynamic Based Non-Thermodynamic (TBNT) system at a higher hierarchical level. Entropy, as a thermodynamic concept reflects the molecular complexity of the system. Though other kinds of complexity might have similar significance, attempts for finding a 'unique measure of complexity' have not been successful. At least three different notions of complexity might be relevant to neural systems. First, structural complexity can be associated to the graph structure of neural networks. Second, functional complexity can be identified with different attractors of dynamic processes, such as point attractors, closed curves and strange attractors. Third, algorithmic complexity can be measured as the minimal time needed to compute the solution of a problem. The question whether the information-theoretical (i.e. mathematical) entropy may be identified with the thermodynamic (i.e. physical) entropy in some sense,

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or whether they have similar formal structures only, has been much discussed. Brillouin's 'Negentropy Principle' [20], that suggests the almost interconvertibility of all kinds of (syntactic) information to thermodynamic entropy, has been questioned [21]. A specific relationship between thermodynamic and information-theoretical entropies has been demonstrated [19] expressing the connection between the actual state and all possible states of a system. A properly formulated hierarchical thermodynamic theory should not only take into account the material-energetic flow, but might also be able to incorporate the informational aspects, as well. Syntactical information, however, has a rather limited role in neurobiology. Semantic information can be stored, and processed in, and even generated by the nervous system [22]. The main difficulty with the concept of biological information comes from the selfreferential character of biological systems. Self-reference was earlier analyzed mostly in logic and linguistics. (The most famous example is the 'liar paradox': "This statement is false".) In more general terms self-reference means, that something refers not only to an object but sirnultaneously to itself. The popularity of this notion, rather neglected earlier, has increased tremendously [23, 24].

3. CAUSALITY, NETWORKS, EMERGENT NOVELTY According to the mechanistic world view, Science, Technics and Metaphysics seemed to be unified by the Newtonian principles. The motion of mechanical machines as well as celestial bodies were thought to be determined by the (same) Laws of Nature. The clockwork world view of Kepler and Newton, characterized by causality, determinism, continuity and reversibility, promised to reduce all kinds of dynamic phenomena to mechanical motions. At the end of the 18th century chemistry and medicine started to challenge the view that material nature is nothing but inert mass and motion. The invention of the steam engine contributed to the disorganization of the cyclic, reversible mechanistic world concept, and to the birth of the theory of irreversibility. (For notes of history of science in this respect, see Brush [25].) One of the supporting-pillar of the Newtonian world view - paradigm, if you like - is the strict principle of causality, which can be stated as follows: "Every event is caused by some other event" ([26], pp. XXII). The concept of the linear causality, which separates 'cause' and 'effect' by a simple temporal sequence, has been found to be appropriate for describing simple systems, and could not be considered as a universal concept. Circular causality relies on the suggestion that in a feedback loop there is no meaning in separating cause and effect, since they are mixed together [27]. As Sattler points out, "Circular causality is not just

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a subcategory of causality, but a concept that supersedes the traditional notions of cause and effect. Hence, these traditional notions no Ionger apply" ([28], p~ 129). The term 'network causality' has been coined ([28], p. 129) to describe interactions among circles. The models of linear causal systems are proper subsets of single level dynamic systems. As Rosen [29] has pointed out, three of the four Aristotelian causal categories can be expressed with the terminology of dynamic systems. Initial conditions, parameters and forcing functions may be associated with material, formal and efficient causes. We assume hefe that models of the generalized causal phenomena can be given within the framework of dynamic system theory. Since material causation has to be acknowledged as a creative agent [30], dynamic system theory can try to tackle the emergent complex structures and creative processes. We can not stare, however, that the dynamic approach does not have methodological alternatives. We shall return to this point in Section 6. We will not go further into the metaphysical issues of causality and dynamics; we will examine the mathematical structure of models of neural networks in a pragmatic way. A part of the emerging complexity (e.g. rhythmic and chaotic neural activity, normal ontogenetic development, plastic rearrangement, as well as evolution) can be explained within the framework of dynamic system theory. I will cautiously suggest, however, that generalized causal systems might leave the land of simple systems.

4. NEURODYNAMIC MODELS

4.1. Conceptual and Mathematical Skeleton Neural tissues are considered now as networks of intricately connected neurons. A rather large subset of brain models is formulated within the framework of neural network models. Real neural network models can at a certain level of description, be considered as three level dynamic systems:

ai(t+At) = ai(t) +fi(a(t), O(t), S(t))A(t) + Ii(t) A(t) O(t+At) = (9(0 + e(a(t))At Sü(t+At) = Sij(t) + gij(a(t), S(t))uAt + Rij(t)At

(1)

Here a is the activity vector, 0 is the threshold, S is the matrix of synaptic efficacies, I is the sensory input, R(O is an additive noise term to simulate environmental noise, u scales the time, the functions e, f and g will be discussed soon.

There area couple of underlying assumptions behind this model. The state of a neuron is characterized by a scalar variable at a fixed time; anatomical,

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biophysical and neurochemical details, such as compartments of the cells, ion channel kinetics and almost the whole body of knowledge on transmitters are neglected. One of the main difficulties of establishing a well-founded theory of neurodynamics, in contrast to dynamic theories of physics, is the lack of 'first principles' for deriving dynamic equations. As we see now, nothing similar to the fundamental geometrical properties of the space and time can be postulated for the brain, therefore we have more than necessary freedom to specify the functions e, f a n d g. The function e describes the modification of the threshold due to 'adaptation', but it is offen neglected. Activity dynamics is many times identified with the membrane potential equation, and the potential change (i.e. the form of ä+) is determined by the spontaneous activity decay: dai(t) _ _

dt

-

~ i ( t ) + ¢~(ZSij(t)aj(t) +

Ii(t)

(2)

Here ~ is some sigmoid function. Obviously, the term corresponding to the sensory input is only non-zero for afferent neurons. The function g specifies the learning rule. Current theories generally assume that memory traces are somehow stored in the synaptic efficacies. The celebrated Hebb rule has been given as a simple tocal rule based on the correlation between pre- and postsynaptic activity for explaining synaptic modifiability. Qualms regarding the neurophysiological plausibility and some obvious mathematically unpleasant properties (as unlimited growth, the lack of decreasing term) led to the introduction of a whole family of learning rules. (For a set collected, see e.g. [31].) 4.2. N e u r o d y n a m i c

Problems

Most neurodynamic problems can be categorized into two groups. First, we may assume fixed wiring, i.e. the matrix S is assumed to be constant over time. Either the dynamics of activity spreading through the nodes of the network, or the temporal change of specific activities a i can be studied. In the latter case the occurrence of 'regular' (i.e. convergence to stable equilibrium point) or of 'exotic' (oscillatory and chaotic) behaviour is analysed. The qualitafive dynamic behaviour of a network is strongly determined by the excitatory-inhibitory activity patterns in the network. In order to have an alternative formulation and better understanding of the old 'structure-function' problem of real networks (and to have more efficient methods for designing artificial neural networks with given properties), the connections between (static) network architectures and (dynamic) functional behaviour have to be

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investigated. In the cybernetic and biomathematical literature there is a well-known, but many times misinterpreted, theorem on the connectivity-stability dilemma [32-34]. This theorem suggests that at least for a class of - randomly interconnected but deterministic - networks, the degree of connectivity works against stability. Recent developments in the theory of differential equations [35, 36] illuminated better the assumptions leading to regular dynamics. Still, the important general question, whether what kinds of network architectures lead to stable equilibrium, and which are the structural conditions for a network to be a candidate of rhythmicity or chaos generator, will be the subject of further research. Second, the existence of modifiable synapses can be taken into consideration. Models based on the modification of synaptic efficacies are associated both to pattern formation, as normal ontogenetic development and plastic rearrangement, and to pattern recognition. It is more or less accepted thai embryonic and postnatal development is the result of the interaction between a built-in 'patterngenerator' and the environment. The full genetic coding of the brain structure is highly unlikely since the complexity of the anatomical structure increases much faster than that of the genome [37]. Biological pattern-generating mechanisms, in general, have quite similar structure, since they are frequentIy based on the notion of selection. Selectionist brain theories [37, 38] and the adaptive resonance theory [39] are not based on, but at least partially (explicitly or implicitly) apply, the concept of self-organization.

5. SELF-ORGANIZATION IN THE NERVOUS SYSTEM The convergence between empirical data coming from neurobiology and approaches of dynamic system theory suggest that neura! phenomena occurring at different hierarchical levels can be interpreted in terms of self-organization. Although vague in many respects, the idea of 'self-organization' is nevertheless a powerful concept of theoretical sciences. The term has at least two different meanings, as it was explored in a classical paper of Ashby [40]. First, "a system is 'self-organizing' in the sense that it changes from 'part separated' to 'parts joined': an example is the embryo nervous systems, which starts with cells having little or no effect on one another, and changes, by the growth of dendrites and the formation of synapses to one in which each part' s behaviour is very much affected by other parts". Second, it may be interpreted as 'changing from a bad organization to a good one ~. But then, of course, we need to specify the meaning of the terms 'good' and 'bad'. Self-organization phenomena have been demonstrated in cell culture experi-

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ments [41], showing that randomly interconnected neurons, even without sensory input, might produce 'biologically significant' behaviour. The spontaneous activity of single neurons has a random character; so the coherent, organized activity is the result of some self-organizing mechanism, (see also [42]. Molecular self-organizing mechanisms are responsible, e.g., for the development of ion channels [43], the oscillatory activity of single neurons [44], and for the regulation of the synaptic efficacy based on 'receptor desensitization' [45]. A central pattern generator (CPG) is a network of neurons that produce rhythmic behaviour in the absence of sensory input. Relatively simple invertebrate systems, such as the crustacean somatogastric ganglion, are capable of generating temporal patterns independently of peripherial reflex loops. The network structure [46] and the transmitterology [47] of this system has already been quite thoroughly uncovered. The fundamental temporal patterns can be explained by coupled oscillator models. At a higher phylogenetic level, the locomotion of lower vertebrates, such as lampreys and tadpole, has been studied. Motor patterns underlying locomotions are produced by the spinal circuit. Not only the neural circuitry, but also the transmitters and the membrane properties are largely known [48]. It is assumed that the ulümate source of neocortical rhythmicity is the thalamus. The underlying thalamic oscillation is not generated by single 'pacemaker' cells but seems to be a 'network property' [49]. The hippocampus, which is involved in the memory trace formation, exhibits different kinds of temporal patterns. It shows rhythmic slow (or theta) activity during exploratory behaviour and irregular sharp waves during slow wave sleep and awake mobility (see e.g. [50]). The machinery of the hippocampus is based on the unidirectional neocortical-hippocampal-neocortex loop, a complete cycle requires about 20-25 ms. Though the discovery of subcortical afferents causing feed-forward inhibition [51] and disinhibition [52], and the demonstration of anatomical divergence of intrahippocampal projections [53] might significantly modify the scenario about the information flow, it still seems rather likely that the neuronal information is preserved during the cyclic operation. Oscillation seems to play an important role in both the olfactory bulb [54] and the olfactory cortex [55]. The occurrence of bulbar oscillation is the consequence of the interactions among excitatory mitral and inhibitory granule cells populations. The (slow) modification of some synaptic strengths due to the learning process might result in switching the system from one dynamic regime to another (e.g. from limit cycle to chaos or vice versa). Oscillations in the olfactory bulb tend to be synchronized with bulbar oscillation. The study of global brain activity dynamics by electroencephalography (EEG) gave the evidence that spatiotemporal patterns of cortical neural activity are

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internally generated representations of expected sensory input and not merely responses to such input. Following this line [54] the assumption can be made that the macroscopic cooperative activity of weakly but widely interconnected neurons emerges from the operation of individual neurons coupled by conventional synaptic transmission. Additionally, the construction of a perceptual representation from sensory input can be described in terms of self-organization. Recent findings of synchronized oscillation of the multiunit activity in the visual cortex [56, 57] generated excitement. It seems remarkable, from a functional point of view, that rather remote columns oscillate in phase. It was suggested [58] that phase- and frequency-locked oscillations are strongly connected to the neurobiological basis of visual awareness. Experimental facts resulting from anatomy, physiology, embryology, and psychophysics give evidence of highly ordered structures composed of 'building blocks' of repetitive structures in the vertebrate nervous system. The building block or modular architectonic principle is rather common in the nervous system. The modular architecture of the spinn cord, the brain stem reticubx formation, the hypõthalamus, the subcortical relay nuclei, the cerebellar and mostly the cerebral cortex [59] has been reviewed [60, 61]. After the anatomical demonstration of the so-called cortico-cortical columns it was suggested [59] that the cerebral cortex might be considered on large scale as a mosaic of vertical columns interconnected according to a pattern strictly specific to the species. Having been motivated by the pioneering work of Katchalsky [16] on the dynamic patterns of neural assemblies, Szentägothai [60] offered to interpret the cortical order in terms of 'dynamic structures' instead of applying some static, 'crystaMike' approach. The more precisely a system is specified, the greater the danger of mistakes. Spatially ordered neural su-actures are the product of some self-organizing mechanisms. Even 'the essence of the neural' may be its self-organizing character [62].

6. FROM DYNAMIC STRUCTURALISM TO HERMENEUTICS Natural structures can be categorized into two classes: static and dynamic. The two appear as distinct forms of the macroscopic world. Static structures are maintained by the large interacting forces among their constituents. The perturbation of the environment causes very slight effects only, at least in the range of the (stmcturally stable) structures. More intensive perturbation leads to the complete breaking down of the structure. The new, 'structureless' structure is also static, more precisely "the final situation may be topologically very complicated, but generally it behaves as a static tbrm" ([63], p. 101). The solid bodies may be considered as typical examples of the static

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structures. Dynarnic structures are maintained by the interaction between the system and its environment. The system itself, is in permanent material, energetic and informational interaction with the external wofld. The borderline between static and dynamic structures is, however, rather arbitrary: the static structures of the morphologists may be considered as dynamic ones from thermodynamic point of view. More precisely, they might be interpreted as the final states ('attractors') of real processes. The 'simplest' attractor is the equilibrium point. Very loosely speaking, linear systems tend towards equilibrium points. The closed curves are more complex attractors, nonlinear systems leading to limit cycle behaviour might be identified with such attractors. Strange attractors are associated with chaotic processes. Chaotic processes are often labeled as 'causal, but unpredictable', and they are considered as 'complex' behaviour generators. It is an acceptable view, that "chaos is complex only because it is complexity preserving, and not for instance, complexity producing" ([30], p. 313). (According to this interpretation, the input, not the transformation is complex. The complexity of initial conditions, however, cannot be evaluated without knowing the transformation. The transformation and the initial conditions, together, are - potentially - complex.) Chaotic phenomena have already been found at almost all hierarchical levels of the nervous system, from the membrane through the network to the system level. The problem of the possible mechanisms of the emergence of chaos at a certain level has recently been discussed [64]. It can be argued, partially based on [64], that three different mechanisms might occur. Chaos (i) might be the direct consequence of a lower level chaos ('spatial cascade'), (ii) can be independent of lower levels, and might be the product of coupling of oscillators, and (iii) might be the result of self-organized lower activities. The technique of recording electroencephalogram (EEG) has opened a window for measuring and understanding brain activity. Though the underlying biophysical mechanisms of EEG signal generation is not completely clear, still the processing of EEG curves provides information about the structure-function relationship of the brain [65]. According to the nowadays already classical approach, the records as time series are considered as stationary stochastic processes, and their characteristic frequencies are determined by spectral analysis. Nonlinear dynamic system theory offers a different conceptual approach to EEG signal processing (see e.g. [66]). Time series, even irregular ones, are considered as deterministic phenomena generated by nonlinear differential equations. First, the phase space of the dynamic system is reconstructed, then its (embedding and correlation) dimensions are calculated [67]. Low (but larger than two) and fractal dimensions are associated with deterministic chaos, while

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it is not easy (if at all possible) to discriminate between high-dimensional chaos and random process. Lyapunov exponents measure the exponential divergence of nearby trajectories. (For a new and efficient algorithm, see [68].) The presence of at least one positive Lyapunov exponent is the signature of chaotic dynamics. The criteria of chaos was reported to be fulfilled for the sleep cycle [69], epileptic petit-mal seizure [70], alpha rhythm [71], and the CreutzfeldJacob disease [72]. Such kinds of concepts as circular and network causality, chaos, unpredictibility, information, emergence, complexity, etc., lead to the limits of 'dynamic structuralism'. The hegemony of the Newtonian paradigm, has willy-nilly probably the latter - been weakened by physics and chemistry motivated neostructuralist theories such as the theory of dissipative structures [73], and of synergetics [74]. In spite of their ambitious endeavours, and undeniable succes, no theory of brain and theory of evolution can be given within a pure structuralist framework. Brain theory and evolutionary theory ought to be 'poststructuraIist' . One important aspect of the brain, which cannot be incorporated within an (even dynamic) structuralist theory, is its self-referential character. Of course, problems associated with Gödel's theorem have been formulated even earlier. Is the brain a formal system? If the answer is yes, can we interpret this as a limit to the brain understanding itself? Even if the answer is no, self-reference is still very important, and will be discussed in the following. A poststructuralist brain theory might include three ingredients, autopoiesis, endophysics and hermeneutics. A theory of self-referential systems, namely autopoiesis [75, 76] is based on the concepts of feedback and network causatity as well as on organizational closure. It is not unreasonable to consider the brain as a system of closed networks. It could be true, that internal structures, shape, and relative position of neurons determine the connectivity of the network (and, as we know, the connectivity determines the possible dynamic behaviours). The plausibility of the autopoietic approach is supported by the fact that about 80-90% of all connections of the cerebral cortex are cortico-cortical. The existence of reentrant loops is an important organizational principle in the cerebral cortex. The mathematical formalism of the autopoiesis is partially based on SpencerBrown's indicational calculus [77] which was suggested to be appropriate to treat the object-subject relationship by coherent logicaI concepts. The present author does not know whether there is any attempt to use this 'modeling technique' for interpreting neural phenomena. Debates around the quantum-mechanical reality [12] and more generally about relativity [78], the 'postmodern attitude', substantially weakened the position of the belief of the 'one, objective reality' and enforced the philosophi-

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cal view according to which reality is a mental construct [79]. In fact, the Universe can be described in two different ways [80], from the outside ('exophysics') and from within ('endophysics'). Rössler [80] pointed out some limits of the classical cognition of the Universe, and demonstrated the power of the endophysical approach even for some classical physical phenomena. (For quantum endophysics, see e.g. [81].) What can a brain theoretician do after realizing the crisis of the notion of universal rationality? He or she can attempt to accept that modern (- reductionist) science lacks self-reflexivity, and therefore perhaps turn to hermeneutics and emphasize the cyclic nature of perception and learning. The concept of 'preunderstanding' and the hermeneutic processes of the brain were associated with chaotic information processing [82]. More generally hermeneutics was offered as an indispensable building block of the theory of self-modifying systems in biology and cognitive science [30].

7. CONCLUDING REMARKS In this paper some concepts and methods of neurodynamic system theory have been presented. We restricted ourselves here to the study the dynamic aspects of the brain, while the brain-mind problem and the brain-computer analogy/disanalogy were neglected. Dynamic system theory, however, offers a reconciliation between alternative approaches. One possibility was to consider the brain, as a pure symbol-manipulating, computational device (see e.g. [83]). Another possibility would be to adopt a connectionist approach, since the nervous system obviously consists of networks of neurons connected by synapses. I agree with Pattee [84], who suggested a complementary application of the 'symbolic' and 'dynamic' approach. Neurodynamic system theory, as it stands now, does not give any mechanism for the embodiment of the mind, but suggests some pragmatic methods for understanding mental structures. As an illustration, earlier we suggested to use the concept of 'double architecture' to speak about neural and mental architecture of the semantic memory [85]. Network representation and dynamic analysis proved to be useful in understanding mental level memory organization (see e.g. [86]). The conclusions of the paper are: 1. The brain, as a physical device, may be interpreted in terrns of dynamic system theory. It might be considered as hierarchically organized self-organizing structures. 2. Not only the material-energetic, but also informational aspects of the biological structure organization have to be taken into account. The nervous system is open to various kinds of information, and the resulting dynamic

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structures can be modified by information flow. 3. Brain models can be set up within the framework of system theory by applying the concepts of circular and network causality. 4. Self-organization is considered as a mechanism for generating emergent neural structures. Neurodynamic phenomena, such as ontogeny, development, normal performance, learning, and plasticity, can be treated by coherent concepts and with the formalism of neurodynamic system theory. 5. We might adopt the view that the brain is a self-referential system. The study of self-referential systems leads out from the land of 'conventional analysis'. It is cautiously suggestecl that a poststructuralist brain (-computermind) theory could benefit from such theories as autopoiesis, endophysics and hermeneutics. Acknowledgements - I would like to thank Dr. Peter Arhem for his kind invitation to this special issue. This work is an emerging product of many discussions with Professor Jfinos Szentägothai. Dr. György Kampis motivated me very rauch to think on biological hermeneutics.

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