The authors begin by drawing attention to the problem of the transition from the biological to the psychic, noting that Freud himself, with his background in the neuroscience, grappled with it throughout his career. Certain recent paradigms more commonly applied to the natural sciences, such as in particular chaos and complexity theory, can in their view prove fruitful in psychoanalysis too, and it is shown how these notions are inherent in some of Freud’s conceptions. The unconscious is stated to operate like a neural network, performing the kind of parallel processing used in the computing of highly complex situations, whereas the conscious mind is sequential. Dreams, in the authors’ opinion, are organisers of the mind, imparting order to the turbulence of the underlying wishes and unconscious fantasies and structuring them through the dream work. Through dreams, the structured linearity of conscious thought can emerge out of the non-linear chaos of the drives. The dream’s navel can be seen as the chaotic link, or interface, between the unconscious wish, which constitutes an attractor, and the conscious thought. The attractor may be visualised as having an hourglass or clepsydra shape, the narrow section being the dream’s navel, and, being the same at any scale of observation, has the property of fractality.

Anyone who hopes to learn the noble game of chess from books will soon discover that only the openings and end-games admit of an exhaustive systematic presentation and that the infinite variety of moves which develop after the opening defy any such description (Freud, 1913, p. 123).

INTRODUCTION

One problem common to the natural sciences and to those of the mind remains unsolved to this day: the form of the transition from the biological to the psychic. Despite all our efforts, the 'mysterious leap’ continues to confront us, but we must try to narrow the gap by seeking to extend our knowledge of 'everything that lies between’.
Freud, too, faced this problem: 'No attempt, of course, can be made to explain how it is that excitatory processes in the * neurones bring consciousness along with them. It is only a question of establishing a coincidence between the characteristics of consciousness that are known to us and processes in the * neurones which vary in parallel with them. And this is quite possible in some detail’ (Freud, 1950, p. 311).

Many years later he was more specific:

Psycho-analysis makes a basic assumption, the discussion of which is reserved to philosophical thought but the justification of which lies in its results. We know two kinds of things about what we call our psyche (or mental life): firstly, its bodily organ and scene of action, the brain (or nervous system) and, on the other hand, our acts of consciousness, which are immediate data and cannot be further explained by any sort of description. Everything that lies between is unknown to us, and the data do not include any direct relation between these two terminal points of our knowledge. If it existed, it would at the most afford an exact localization of the processes of consciousness and would give us no help towards understanding them (Freud, 1940, p. 144f.; our italics).

This quotation might suggest that Freud considered it not to be the task of psychoanalysis to investigate the relationship between brain and psyche, yet we know that he attempted many times to solve this puzzle, from On Aphasia (1891) and the 'Project for a scientific psychology’ (1950) on, and that he never gave up. This paper presupposes that the study of this relationship is a matter not only for the neuroscience but also for psychoanalytic research, and we shall use Freud’s metaphor of the dream’s navel to exemplify the possible use of supradisciplinary scientific paradigms applicable both to psychoanalysis and to the neuroscience - in this case, the paradigm of (deterministic) chaos and complexity.
In the 'improbable’ event of some meta-paradigm unifying all fields of knowledge, or at least the various dialects of one and the same field, we have at our disposal a number of scientific paradigms that constitute a conceptual cement capable of linking seemingly very distant scientific domains.
The Freudian theory of the functioning of the mental apparatus in fact already contained conceptions that can now be found precisely in our new models and global paradigms. The latter, although stemming from different spheres, possess a high degree of abstraction, so that they can be extrapolated from their original context to a wide variety of heterogeneous scientific fields. Examples include von Bertalanffy’s general systems theory, Thom’s catastrophe theory, Shannon’s information theory, Rumelhart and McClelland’s parallel distributed processing (PDP), computer science, Kauffman’s random grammars and landscapes, and - most relevant for our purposes - the science of chaos and complexity. The above paradigms have already been applied to biology, business organisation, market fluctuations in economics, meteorology, the neuroscience, etc., and also have valuable potential applications in the domain of psychoanalysis or some of its aspects.
Of course, a full description of all these disciplines is beyond the scope of this paper, as each would require a study in itself, but it is worth mentioning two which are most relevant to our subject: parallel distributed processing and complex systems, with particular reference to chaos and complexity theory.
In the last few years renewed interest has focused, for example, on a different branch of artificial intelligence (AI), namely parallel distributed processing (see Scalzone, 1994). Here, the computer software does not use sequential instructions and rules to process data but instead simulates a neural network, performing its calculations by parallel distributed processing (PDP) in a very similar way to the functioning of the brain. True parallel-architecture machines containing a large number of processors1 working in parallel may also be used and substantially increase the processing rate. In PDP, computation and processing are performed by the interaction of a large number of appropriately connected simple units. The power and strength of these machines may be said to lie, as with the brain, in their architecture and connections.
Most digital computers, on the other hand, use the classical von Neumann architecture, whose theorist was Turing (cf. the Turing machine2), in which memory and the central processing unit (CPU) are separate and processing is sequential.
It is interesting to consider the following quotation from Freud in which consciousness is seen as a sequential process:

For there is some justification for speaking of the 'defile’ of consciousness. The term gains meaning and liveliness for a physician who carries out an analysis like this. Only a single memory at a time can enter ego-consciousness. A patient who is occupied in working through such a memory sees nothing of what is pushing after it and forgets what has already pushed its way through. If there are difficulties in the way of mastering this single pathogenic memory - as, for instance, if the patient does not relax his resistance against it, if he tries to repress or mutilate it - then the defile is, so to speak, blocked. The work is at a standstill, nothing more can appear, and the single memory which is in the process of breaking through remains in front of the patient until he has taken it up into the breadth of his ego. The whole spatially-extended mass of psychogenic material is in this way drawn through a narrow cleft and thus arrives in consciousness cut up, as it were, into pieces or strips. It is the psychotherapist’s business to put these together once more into the organization which he presumes to have existed. Anyone who has a craving for further similes may think at this point of a Chinese puzzle (Freud, 1895, p. 291).

Conscious processes, then, even according to early Freud, take place sequentially, so that consciousness evidently operates in accordance with a 'von Neumann’ type of architecture. The unconscious, by contrast, works in a parallel mode, rather like the kind of data processing undertaken by neural networks. Note that 'parallel’ here means not the simultaneous operation of mutually independent processes, but the development of a complex algorithm, which, precisely for that reason, cannot, when active, be localised at any specific point in the brain, but is instead distributed, in the same way as mental processes. Freud, it will be recalled, borrowed the distributed, hierarchical conception of brain structure - which is thus 'non-localisational’ - from the holistic doctrine of Hughlings Jackson, on which he drew for the model of the linguistic apparatus (cf. Freud, 1891) that for him underlay the organisation of memory and indeed of the mental apparatus as a whole, as subsequently presented in Chapter VII of The Interpretation of Dreams (1900).
Towards the end of the above quotation, Freud tells us that the mass of psychic material, if it is to be usable by consciousness, must be communicated in words and worked through as, for example, in the conscious work of an analysis. It must also be drawn through a narrow cleft, so that it arrives in consciousness as if cut into pieces or strips. These strips can obviously be likened to the 'tape’ of a Turing machine. For Freud, the difference between Ucs. and Pcs. was that preconscious representations were bound up with language - that is, unconscious thing presentations plus word presentations. He considered that an unconscious content or thing presentation, to attain consciousness, had to become bound to a word presentation; by virtue of the connection with language, consciousness was thus a typically sequential process.
Classical artificial intelligence works by simulating a kind of top-down knowledge, using instructions originating from high symbolic levels, whereas neural networks operate the other way round, in bottom-up fashion, commencing on the level of subsymbolic or presymbolic configurations and involving experience-based self-learning (by the network) through the random assignment of weights (which are simply numerical values such as, for example, 0 and 1 or +1 and -1); as the Freud of the 'Project’ would say, they proceed from quantities to qualities.
The PDP notion that 'the quantity of the weight can be seen as a measure of the conductivity of the relevant connection’ is reminiscent of the notion of facilitation in Freud’s 'Project’, described in the context of the functioning of the neuronal apparatus: a nerve impulse, he tells us, may encounter such facilitations in its passage through the contact barriers of the * neurones, which are closely connected with memory. As we know, when the passage of excitation from one neurone to another through the contact barriers gives rise to a permanent reduction in resistances, the result is a facilitation, in consequence of which future excitations will preferentially choose the facilitated path. Freud, after all, saw memory traces merely as particular configurations of facilitations. In both the PDP and the psychoanalytic models, a memory is therefore deemed to be constructed by the organisation of neuronal configurations in which certain circuits and neuronal groups, whose stability is greater because they are more facilitated, are preferred to others in future encounters with similar types of signals. Long-term changes in synaptic forces thus constitute the basis of learning and memory. The inhibitory synapses are also important, because they substantially increase a network’s computing power.
PDP thus sees both mind and brain as particular cases of a wider class of systems characterised by a large number of simple elements that mutually intersect in complex, non-linear relationships (see Scalzone, 1994). In other words, the individual elements of the system are so interconnected that a linear proportionality does not exist between input and output.
Let us now briefly examine complex systems, which are structures and processes whose characteristic property is non-linearity. They include sets made up of a very large number of objects interacting in non-linear fashion, often organised in a hierarchy of levels. In addition, they exhibit overall behaviour that cannot be predicted from a knowledge of the individual elements and their interactions, and they respond in their own unique ways to external perturbations. Complex systems have certain characteristics in common - for instance, exponential dependence on initial conditions, invariance of scale, recursiveness, self-similarity, attractors, and phase space. The field of complexity includes a wide variety of phenomena that have become important fields of research in recent years, such as spin glasses, artificial life, cellular automata, fractal geometry, genetic algorithms, neural networks, parallel distributed computing, and chaos and complexity theory.
Here are some brief notes on some of these entities. Spin glasses are a generalisation of the Ising model for studying the transition from disorder to order in magnetic systems. Artificial life involves the construction of computer models of the fundamental mechanisms underlying evolution or life itself, which are very similar to genetic algorithms and classification systems. Holland’s cellular automata are algorithms that follow programmer-specified rules and can generate dynamical and complex systems, yielding images of configurations that can be displayed on a computer screen and navigate between successive 'evolutionary’ calculation strategies. Neural networks have, of course, already been discussed.
The chaos paradigm, which appeared as such in the nineteen seventies, is due principally to the French theorist D. Ruelle and to B. Mandelbrot, a stateless Pole also working in France. It is concerned with the evolution in time of unstable systems that are sensitive to initial conditions and therefore highly unpredictable. The non-linear evolution of the system in time can be represented by graphs of a phase space criss-crossed by lines indicating the trajectories of the system’s states. Attractors are the graphical - and conceptual - representation of the overall system within which a point indicating the state of a deterministic dynamical system at a certain time moves. In chaotic phenomena, furthermore, we can observe how deterministic order can create the disorder of chance.
Note that the chaos paradigm is also applicable to the functioning of the central nervous system (CNS) at any plane of organisation and complexity of its functional hierarchy, from the lowest neural-network levels to the highest levels of psychic organisation; this does not imply any confusion between these levels. The brain, too, is a complex in which a series of agents operate in parallel, at different organisational levels, in accordance with a hierarchic and heterarchic order, in correlated and distributed fashion, although they are assigned to different locations; the relevant processes are top-down, bottom-up and horizontal in the spatial dimension and synchronic and diachronic in the temporal dimension. It is a dissipative system open to the outside world for exchanges of energy but closed operationally, informationally and cognitively, as postulated by some modern theories of autopoiesis3. It can evolve by the process of synaptogenesis and possesses an ongoing capacity to strengthen or weaken the connections between neurones. However:

One might criticize this paper for an apparent use of mind-body isomorphism: locating cause at one conceptual level and consequence at another, or mixing the languages of psychological and non-psychological disciplines. But I am not reducing mental events to brain events, and I am not suggesting an identity of cause for these two different kinds of phenomena. In this paper I make a comparison between mental phenomena and fluid systems on a formal level in the hopes of expanding our understanding of complex mental processes. Using non-psychological models to enrich and enhance the accuracy of psychological models is not the same thing as mixing levels of causality, such as attributing a physiological cause to a specific mental event. Chaos may indeed accurately describe brain functioning, and some aspects of nonlinear brain functioning may impinge on mental phenomena. But I leave the exploration of that interface for another time. The phenomena I have sought to explore through nonlinear dynamic principles are mental phenomena (Moran, 1991, p. 218).

This essay seeks (1) to show that certain conceptions observable in other fields of science today already existed in nuce in Freud and that the use of such models in psychoanalysis can contribute to the development of our discipline; (2) for this purpose, to exemplify one of the many possibilities by linking the metaphor - or, if you will, the boundary concept - of the 'dream’s navel’ to the area of chaos and complexity theories with a view to postulating a model of a limited field of mental activity bordering on the somatic, and its possible psychoanalytic developments (the diagnostic function of dreams, exploration of the sphere of the systemic unconscious, etc.); and (3), finally, to demonstrate how - precisely by the use of supradisciplinary paradigms - psychoanalysis can be re-united with the neuroscience, given that this union was present in Freud’s early works and certainly in his thought. All these points are included in our more general project, namely the study of the development of and interconnections between aspects of Freudian thought and its constructions - a project of which this paper constitutes but a part.

DREAMS AND THOUGHT

As Freud notes in The Interpretation of Dreams:

Thought is after all nothing but a substitute for a hallucinatory wish; and it is self-evident that dreams must be wish-fulfilments, since nothing but a wish can set our mental apparatus at work. Dreams, which fulfil their wishes along the short path of regression, have merely preserved for us in that respect a sample of the psychical apparatus’s primary method of working, a method which was abandoned as being inefficient (Freud, 1900, p. 567; our italics).

Hence, the entity that is capable of setting in train the 'functioning’ of the (psychic) machine once the brain tissue has reached a 'critical mass’ - i.e. of bootstrapping the system - is for Freud the unconscious wish, which tends towards fulfilment (in accordance with the laws of the pleasure principle, and thus of the primary process). This unconscious wish merely represents a drive demand - what some call a (biological) need. However, the (psycho-physical) drive, the internal tension that gives rise to unpleasure, must be accompanied by a (psychic) wish in order to trigger mental activity and induce it to perform a specific action directed towards finding the object in reality, with a view to thereby fulfilling the wish through the motive power of the drive.
Jones set particular store by Freud’s conceptions of neuronal disorder due to 'unpleasure’, of order restored by pleasure, of the significance of electrical variations at synaptic level, of the nature of memory traces, of his ideas on associative areas, etc., and maintained that Freud’s basis had been what he regarded as the sole engine of the entire apparatus, namely the wish (including the wish to know), defined as a current circulating in the apparatus, starting from unpleasure (Unlust) and proceeding towards pleasure (Lust) (cf. Jones, 1953).
The wish is therefore the primum mobile of psychic development. In addition, the unpleasure and tension resulting from drive needs destabilise the system and introduce disorder into the neuronal apparatus of the 'Project’ (later the psychical apparatus). Order is restored by the achievement of pleasure, the goal towards which the system tends - that is, by the fulfilment of the wish. The subsequent spontaneous self-organising activity (in the 'Project’, accruing, for example, from discharge) initiated under the synthesising aegis of the ego may lead the system towards more appropriate equilibrium states. This demonstrates the twofold role of the drive, which, on the one hand, produces disorder by eliciting the need and, on the other, re-establishes the system’s homoeostasis by discharge; it is for this second reason that Freud held the drives to be conservative. A fundamental part in the entire process is played by memory and its functioning - in effect the linchpin of all mental activity. The importance of the mnemic systems and the function of memory for the working of the self-organising systems is obvious; indeed, some take the view that memory operates simply as a mapping machine and that even a 'high-level’ function like intelligence may be nothing other than a form of good management of 'crude memory’.
Note that in therapeutic practice the analyst may perform two basic functions. (1) By interpreting defences, he destabilises the patient’s psychic system and disturbs the existing pathogenic equilibria. (2) By making sense out of non-sense and supplying analytic constructions, he tends, through the same interpretation’s attempt at narrative historicisation of the merely economic and hence unrepresentable 'pure trauma’, to restabilise the system, organising new mental attitudes, promoting the process of psychic re-elaboration and the formation of new meanings. However, the ordering narrative function that constructs meaning through symbolisation can never dispense with the event (e.g. the real trauma); nor can it ignore the biological4 determinants of the human psyche (for instance, the prolonged period of gestation, the helplessness due to the extended period of physical and psychosexual immaturity in man, paedomorphism, substantial brain development and consequent cerebralisation, or bisexuality); it can only transform the relevant representation by subsequent secondary elaboration. Freud thus constantly confronts us with complexity, showing that in psychoanalysis one is always dealing with 'different levels of reality’. (It may be recalled in passing that the analyst’s functions also include reverie, whereby a new order can be imparted to the patient’s mental chaos by giving meaning to the formless, holding, etc.)

THE DREAM’S NAVEL AND THOUGHT

Let us now try to describe the birth of thought from dreams by a model5 that uses concepts derived from the new global paradigms established in the fields of non-linear dynamics and deterministic chaos. As stated, even if these paradigms arose in non-psychoanalytic contexts, they possess a high degree of abstraction, which renders them supradisciplinary and hence suitable for extrapolation from their original context to even very remote and heterogeneous scientific domains.
Consider the following quotation:

[...] now that analysts at least have become reconciled to replacing the manifest dream by the meaning revealed by its interpretation, many of them have become guilty of falling into another confusion which they cling to with equal obstinacy. They seek to find the essence of dreams in their latent content and in so doing they overlook the distinction between the latent dream-thoughts and the dream-work. At bottom, dreams are nothing other than a particular form of thinking, made possible by the conditions of the state of sleep. It is the dream-work which creates that form, and it alone is the essence of dreaming - the explanation of its peculiar nature (Freud, 1900, p. 506f., n. 2).

As we know, the dream work transforms the latent content (dream thoughts) - that is, the expression of the dreamer’s wish - into the dream images (the manifest content), which conceal organisations of thoughts and meanings. Interpretation, by contrast, proceeds from the manifest content to the unconscious wish, laying bare precisely these meanings.
Freud also writes:

When the whole mass of these dream-thoughts is brought under the pressure of the dream-work, and its elements are turned about, broken into fragments and jammed together - almost like pack-ice - the question arises of what happens to the logical connections which have hitherto formed its framework. What representation do dreams provide for 'if’, 'because’, 'just as’, 'although’, 'either - or’, and all the other conjunctions without which we cannot understand sentences or speeches? In the first resort our answer must be that dreams have no means at their disposal for representing these logical relations between the dream-thoughts. For the most part dreams disregard all these conjunctions, and it is only the substantive content of the dream-thoughts that they take over and manipulate. The restoration of the connections which the dream-work has destroyed is a task which has to be performed by the interpretative process. The incapacity of dreams to express these things must lie in the nature of the psychical material out of which dreams are made (p. 312).

The point we wish to emphasise in this quotation is that the dream work applies destabilising pressure to a (critical) mass of thoughts and, acting as an agent of change, shifts the organisation towards a far-from-equilibrium (FFE) condition, thereby permitting the subsequent initiation of a spontaneous process of self-organisation.
In Freud’s view, 'the dream-work is doing nothing original’ (p. 345f.). In our terms, the dream work performs a transformation that may also destroy meaning; interpretation may subsequently reveal the dream thoughts and restore meaning to them.
This is the realm of the censorship, which, through the dream work, underlies the processes of condensation, as well as those of the other mechanisms and of the various energy cathexes, producing overdetermined representations; we therefore consider that information is not only transmitted but also generated here. For this reason, information generated and accumulating on the edge of chaos is then transmitted by the manifest dream and its graphic metaphors: here is the locus of the area of thinkability (see Scalzone, 1987). The dream work also uses other mechanisms, namely displacement, symbolisation and, finally, secondary revision, which is much closer to consciousness.
All this involves dynamic transformations of psychic contents, which break and reforge bonds and establish new relations between distant phenomena and representations of new realities. Here we have an indication of the complexity of the psychic system, which is in a process of continuous autopoietic development.
As to condensation in particular, Ella Sharpe, for example, sees unconscious dynamic interest as a magnet that attracts past and present experiences - a kind of attractor (see below) - with the implication that the ego is expanding its boundaries. It follows that the unconscious mechanism of condensation can act on a wider range of experiences, that our intellectual experiences are less susceptible to subjective data selection, and that we are not obliged to make hurried formulations dictated by unconscious wishes and fears (cf. Sharpe, 1937). In other words, the freedom of the system is thereby increased.
Let us now show how meaning, in mental functioning, arises from the formless as thought, and how the process of transduction from a somatic to an affective code, and from the latter to a symbolic code that creates meaning, allows thinkability and subsequent communicability. Bion intended his Grid precisely to demonstrate how thoughts develop from the basic level of dreams.
We may begin with two quotations from The Interpretation of Dreams in which Freud describes the obscure point in a dream, which he calls its navel. As we know, this metaphor appears for the first time in a note on the analysis of the dream of Irma’s injection; it then recurs in the section on the forgetting of dreams.
The first quotation reads:

I had a feeling that the interpretation of this part of the dream was not carried far enough to make it possible to follow the whole of its concealed meaning. [...] There is at least one spot in every dream at which it is unplumbable - a navel - as it were, that is its point of contact with the unknown’ (Freud, 1900, p. 111, n. 1).

Freud realises that his interpretation of the dream in question did not suffice to reveal 'the whole of its concealed meaning’. Although this fact is not to his liking because he sees it as a limit to analytic activity, he justifies himself by acknowledging that every dream intrinsically includes 'at least one spot [...] at which it is unplumbable’. That spot might coincide with the conceptual 'virtual location’ of the object representation (Objektvorstellung in On Aphasia) or thing presentation (Dingvorstellung in The Interpretation of Dreams and 'A note upon the “mystic writing-pad”’). This would lie at the transition between the somatic and the psychic, and between the neurophysiological functioning of the brain and the symbolic and metaphorical functioning of the mind.
It is important to note that the dream’s navel is a virtual and not an imaginary point: 'virtual’ means that it is situated between systems that, as Freud says, are 'not in any way psychical’6 but organic entities, because they are formed by the brain’s neural network.
Let us now examine the second quotation, which more clearly exemplifies the concept:

There is often a passage in even the most thoroughly interpreted dream which has to be left obscure; this is because we become aware during the work of interpretation that at that point there is a tangle of dream-thoughts which cannot be unravelled and which moreover adds nothing to our knowledge of the content of the dream. This is the dream’s navel, the spot where it reaches down into the unknown. The dream-thoughts to which we are led by interpretation cannot, from the nature of things, have any definite endings; they are bound to branch out in every direction in the intricate network of our world of thought. It is at some point where this meshwork is particularly close that the dream-wish grows up, like a mushroom out of its mycelium (p. 525; our italics).

This evidently alludes to a non-linear dynamic.
There are at least four points of interest in the two Freud quotations presented above:
(1) The dream’s navel as its obscure, unplumbable centre, the defile through which two worlds (unconscious and conscious) communicate - the omphalos, as the area to which the idea of particular importance and secrecy is connected, and which is made up of the tangle of the dream thoughts.
(2) The specific state of the relevant psychic system, namely the dream state.
(3) The importance of the interpretative activity of the analyst, who tries to introduce order (into the tangle of dream thoughts) by identifying the dream wish.
(4) Finally, the dream’s navel, as a boundary concept between the areas of the unthinkable and the thinkable - between chaos and order.
A brief digression on the fundamental difference between the unthinkable and the unthought is appropriate here. The former concerns a merely economic pure trauma and foreclosure, as the Lacanians would say, and hence the repetition compulsion, whereas the latter has to do with the repressed. Whereas the former can never attain thinkability, the latter is much more accessible to memory and working through, for example by way of dreams and analytic therapy.
Out of the chaos of the intricate network of our world of thought, therefore, there grows up the dream wish, which can at this point be represented and conceived in thought through union with verbal symbols; acquire a meaning that is the result of the self-organisation of the psychic system, and hence a coherence specific to the subject that takes account of his history and intersubjectivity; and, finally, be communicated and interpreted.
As Laplanche & Pontalis (1967, p. 294) point out, this wish constitutes the final term that is not amenable to further over-interpretation. In this way the circle is completed: starting from the wish that sets mental activity in train, once this activity has expanded in its manifold transformations, we return through interpretation to the wish, which is revealed as the significant nucleus that cannot be further reduced. Again:

[...] dream-interpretation traces the course taken by the dream-work, follows the paths which lead from the latent thoughts to the dream-elements, reveals the way in which verbal ambiguities have been exploited, and points out the verbal bridges between different groups of material [...] (Freud, 1916-17, p. 229).

The dream’s navel - that is, the centre of a turbulent vortex connecting the dream to the unconscious matrix that fuels it - metaphorically puts us in mind of the point that connects the foetus to the mother via the interface of the placenta. Even though the navel is a scar left by a physical relationship that no longer exists in reality - an absence - it continues to represent a virtual point of transition within the psyche, as is clear from Freud’s phrase 'a navel, as it were, that is its point of contact with the unknown’ (our italics). This matrix, 'the unknown’, could be identified with the future id, because that structure is less organised than the topographical unconscious and because it affords a better representation of the realm of drive chaos situated in a timeless dimension. The subsequent passage into consciousness will reveal the role of time, which, in open systems with decreasing entropy, has a constructive and creative function rather than a destructive one.
In the images of the 'dream of Irma’s injection’, the navel may be represented by the patient’s mouth. When invited to open it to allow the doctor to look down her throat, she 'showed some recalcitrance’: this is the beginning of the unthinkable, of mystery.
Through the metaphor of the dream’s navel, Freud seems to be telling us of a particular organisational point in the topography and functioning of the psychical apparatus - of a functional interface between two contiguous areas. It is a boundary area between the unconscious and the preconscious that comes to be the locus of energy transformations (where free energy becomes bound, thus marking the transition from the primary to the secondary process) and of representational transformations (from unconscious - i.e. thing - presentations) to conscious representations (made up of thing presentations plus word presentations). This is the place of the transition from the disorder of the freely rising and falling energy of the unconscious to the bound energy and (representational) order of the preconscious and of consciousness, as well as of that from the parallel processing of the unconscious to the sequential processing of consciousness. Here information also arises out of the noise resulting from the emotions and affects ('order from noise’). Chief among these is anxiety, so that this is also the place where thought comes into being, as the psychic function responsible for the ongoing re-ordering, re-organisation and re-categorisation of the available data.
The work of elaboration is thus possible if we assume the existence of frontier zones, as elaborative spaces separating territories in which psychic work is performed in accordance with different rules. Three types of frontier may be considered:
(1) The somato-psychic frontier between the soma and unconscious mental activity. This is the frontier that must be crossed by endosomatic excitations if they are to be manifested psychically (in the drives).
(2) The frontiers of the preconscious, separating unconscious from conscious mental activity.
(3) The 'protective shield against stimuli’ (Reizschutz), which constitutes the frontier between outside and inside, between me and not-me, between the individual and external reality (cf. Green, 1995).
The above quotations thus reveal Freud’s awareness of the spontaneous emergence of a structure from an area of chaotic tangle - that is, the appearance of a qualitatively different phenomenon when a particular level of complexity of the process of self-organisation of the system under examination is attained; in our case, this is the emergence of the (dream) wish from the network of latent thoughts in the dynamic process of dream activity. The boundary region is the site of the transition from the disorder of the drive to the order of consciousness, and vice versa, by the sequence disorder-complexity-order; this demonstrates the formation of order from chaos. Expressed graphically, the dream’s navel might constitute the virtual location on the boundary of the chaos of the drives, where the complexity of the transformations effected by the dream work arises out of the uncertainty cloud (Bion), and where, for this reason, an attractor is situated. This is an (unconscious) wish from early infancy that represents the entity towards which the system’s behaviour is attracted or towards which the system tends to stabilise as the wish seeks fulfilment. More precisely, we would identify the unconscious fantasy (or phantasy), the mental representative of the instincts and a psychological phenomenon closer to the biological, as the psycho-somatic attractor belonging to the primal unconscious, while placing the infantile wish, a more genuinely psychic phenomenon, in the repressed unconscious. For Freud, after all, thought is interposed between impulse and action, interrupting the simple peremptory functioning of the stimulus-response reflex arc. At the end of the process, we would find another attractor: thoughts thought by means of the function of thought, which, unlike action, uses small quantities of energy, which this function therefore saves. This process, which leads to the creation of meaning, can also be observed in the interpretative activity of analytic therapy.
Before ending this section and proceeding further, however, we must ask the reader to be patient while we quote some further passages from Freud as the starting point for some considerations on the complexity of his thought. He writes:

It says “six or seven” in the dream. Six is the number of children that were eaten; the seventh escaped into the clock-case. It is always a strict law of dream-interpretation that an explanation must be found for every detail (1918, p. 42, n. 1; our italics).

This quotation seems in some respects to conflict with the two reproduced above, on the dream’s navel. In other words, Freud first told us that an obscure point had to be left in the interpretation of a dream, or that this was necessarily the case, but now he stipulates that every detail of the dream must be explained. We have, of course, long been accustomed to such 'contradictions’ in Freud, which are inevitable given the nature of the complex material he is seeking to understand - namely, mental life. It is as if he were leaving it to us to resolve the contradiction, compelling us to think. Perhaps Freud means that the conscious representation of the dream attempts to pull together various contents on different levels of multidimensional unconscious psychic reality by means of sensors suitable only for perceiving a three-dimensional reality. From the unceasing flow of the unconscious, a dream acts like a probe, picking out fragments which it then attempts to transduce and translate in accordance with a conscious code.
Again, the fact 'that an explanation must be found for every detail’ does not perhaps conflict absolutely with the idea that a dream, as an expression of the unconscious, is by its nature not fully susceptible to interpretation, and that there will always remain an 'obscure passage’ - an unrepresentable, or at least uninterpretable, residue. The foregoing shows that statements that are only seemingly irreconcilable are not necessarily mutually contradictory.
In our view, the interminability of analysis results from the fact that investigation of the unconscious in general, and therefore also of dreams, generates its object at the same time as it explores it. This process activates a multiplier of meanings, so that the reservoir of meanings does not shrink with the progress of interpretative activity. Instead, the boundary between the analysed and the analysable 'shifts constantly forward’, resulting in a Zuider Zee that can never be completely drained. Moreover, every interpretation throws light on a new part of the dream to be interpreted - but, to make the work of interpretation inexhaustible, it is not necessary for this part of the dream to be uninterpretable, but only for it to be interpreted in such a way as to generate new parts to be interpreted in turn, and so on in an interminable process.
Freud himself says something similar:

I have already had occasion to point out that it is in fact never possible to be sure that a dream has been completely interpreted. Even if the solution seems satisfactory and without gaps, the possibility always remains that the dream may have yet another meaning. Strictly speaking, then, it is impossible to determine the amount of condensation (1900, p. 279; our italics).

Yet even this last observation is, in a sense, untrue, because he writes elsewhere:

Dreams frequently seem to have more than one meaning. Not only, as our examples have shown, may they include several wish-fulfilments one alongside the other; but a succession of meanings or wish-fulfilments may be superimposed on one another, the bottom one being the fulfilment of a wish dating from earliest childhood (p. 219).

As so often, the richness of Freud’s thought lies precisely in his continuous oscillation between complementary points of view.
Finally, it is important not to underestimate the fact that Freud first mentioned the dream’s navel in connection with a dream of his own and, moreover, in a footnote (Van der Berg, quoted by Mahony, 1996, p. 38, note 11). This bears out Anzieu’s (1975) hypothesis, based partly on observations of Eva Rosenblum, that we here have a token of his internal resistance, bound up with the prohibition of incest and associated fantasies, and that the obscurity of the navel might, therefore, be due solely to deficiencies in his theoretical and clinical equipment. This is perhaps why Freud writes: 'I had a feeling that the interpretation of this part of the dream was not carried far enough to make it possible to follow the whole of its concealed meaning’ - that is, not as far as the wish to defend himself or Fliess from the charge of having damaged a woman patient, or, we may add, 'not as far as the unconscious infantile incestuous wish’. This tends to bear out the impossibility of self-analysis, because, as Freud himself says in his letter to Fliess of 14 November 1897, (mental) illness would not exist if it were possible. Hence the meanings concealed within the dream’s navel can be confronted, but only in a relationship between two people in analytic therapy. Again, if Irma is also seen as an aspect of Freud himself, the dreamer, then the dream’s navel might allude to the still active residue of the obscure and indissoluble link between his own female part and the primal mother.
As stated, the dream’s navel is one of the boundary areas between order and chaos. As an area of complexity, it reminds us of the interface discussed by Bion - the alpha function as the place of the transformation of beta elements from perceptions and emotions into alpha elements that can be used for thought activity. Bion considered that sensory data from the outside world and the data of internal emotional experience were manifested in the form of beta elements - i.e. meaningless elements in the crude state. In his view, the function of thought transforms emotional experience, conferring on it a meaning and a symbolic form that renders it capable of being thought. Let us recall, in this connection, that on the boundary between neurophysiological and psychic functioning, he placed the protomental apparatus, whose task was the evacuation of undigested experiences through group action or psychosomatic phenomena. All this takes place because the mental apparatus is constantly 'bombarded’ with data from emotional experience, so that an apparatus for thinking thoughts is necessary in order to process this crude data and impart meaning to it, to prevent it from producing nothing but chaos and thereby potentially destabilising the psychical apparatus excessively. As Meltzer (1982) points out, the term soma-psychotic indicates, precisely, the failure of the mental functions, which in this way have pathological effects on the body.

THE DREAM’S NAVEL AND COMPLEXITY

What follows is speculation, often far-fetched speculation, which the reader will consider or dismiss according to his individual predilection. It is further an attempt to follow out an idea consistently, out of curiosity to see where it will lead (Freud, 1920, p. 24).
We have postulated that dreams might be organisers of mental functioning. The function of dreaming, which leads to the construction of the manifest dream, organises the unconscious wish (and/or the unconscious fantasy) in such a way that it can pass to another state of the mind, namely the conscious state.
In other words, our hypothesis is that the unconscious and consciousness are two states, two modes, or two phases of the functioning of one and the same system, the psyche. The psychical apparatus can be represented as an N-dimensional space in which there is a succession of states, represented by points in a hyperspace, phase space, which varies along a trajectory that passes through various phases - Ucs., Pcs. and Cs. - and leads, at least temporarily, to a stable state in which an attractor - a kind of (morphological) organiser - is situated. A number of attractors may exist in the Freudian model. One may be a wish from early infancy; the corresponding stable state is represented by its fulfilment. In a dream, what Freud calls the dream’s navel - a virtual point and not an imaginary one, as stated, located close to drive chaos - constitutes the site of formation of the complexity of the transformations wrought by the dream work: the eye of the turbulence that remains as an irremediably unknowable point, the point of access to the unthinkable: Bion’s O.
The transition from one type of mental functioning to another may be assumed to be non-linear. A 'product’ of the mind, in other words, is not transformed from an unconscious to a conscious one by linear rules of transformation obeying predetermined and generalisable laws, but instead conforms to the laws of deterministic chaos and complex systems. Within this hypothesis, therefore, we have supposed that the dream itself (the dream process) might be an organiser, something that gives form to unconscious fantasies and/or repressed wishes, allowing them to appear in consciousness after passing through the censorship at the interface between systems and after undergoing a series of transformations.
If the mental apparatus is regarded as a complex system, the infantile wish may be deemed to function as an attractor. An attractor can be defined as the trajectory of a system upon which all the other trajectories of that system converge (cf. Gleick, 1987). This is the first level of knowledge of the system, necessary for characterisation of its properties. Strange attractors, so-called because of their complexity, combine order and disorder; they give rise to order from disorder in accordance with the laws of deterministic chaos, thereby generating information about the system. The strange attractor is located in phase space - that is, in the space contained between the various phases of the dynamical system under examination - which defines it at every instant and represents its history, by virtue of the form assumed by the attractor itself.
In considering the possible geometrical and mathematical nature of a strange attractor, Ruelle and Takens were confronted by a complex situation that seemed extremely difficult to define in mathematical and geometrical terms. A strange attractor had to be an orbit, a trajectory in phase space, with few degrees of freedom and no periodicity - i.e. it could never repeat itself identically and never fall into constant rhythms. Such an orbit must be an infinitely long line in a finite space, something that was possible only if these trajectories were assigned a dimension of 'folding back’ on themselves - a fractal (or fractional) dimension.
Mandelbrot was the first to study objects with a fractional dimension. His fractals are famous not only for the beauty of their graphical representations, but also for their essential quality of self-similarity. On whatever scale they are observed, they are always similar to themselves. This implies recursiveness - a structure within a structure identical to the former structure.
Considering these concepts in metaphorical terms, we have postulated that the dream wish, and by extension the dream as a process formed from a number of mental elements (memories, thoughts, affects, etc.), might have the character of a chaotic attractor. On the assumption that the mind is a dynamical system that can be described by a number of states - chief among which are the Ucs., the Pcs. and the Pcpt. - dreams can be seen as attractors that describe the transition from one phase to another. In this way the wish and/or unconscious fantasy may, under the pressure of its own drive energy on the one hand and that of the censorship on the other, assume a turbulent regime and thus become reorganised in the form of the manifest dream by the work of condensation, displacement, symbolisation and secondary revision. This phase change, which gives rise to the displacement and reorganisation of the drive energy from the reservoir of the Ucs. to that of the Pcpt.-Cs., is mediated by preconscious thought (day’s residues).
The dream process, therefore, as a strange attractor, can be represented graphically by the image of the clepsydra (water clock), which constitutes both a theoretical model for undertaking certain mental experiments (Gedankenexperimente) and an analogue-type, dynamical model. Many of Freud’s diagrams possess these two qualities - for example, the sexuality diagram of Draft G or the representations of the psychical apparatus in The Interpretation of Dreams. One side of the clepsydra is immersed in the unconscious with its wishes and unconscious fantasies, while the other is connected to the system Pcpt.-Cs. with its store of preconscious images, perceptions, thoughts and symbolic-abstractive elements. The central defile, or bottleneck, of the clepsydra could be represented by the virtual point that Freud calls the dream’s navel.
Considering the fractal dimension of strange attractors, we can now take our analogy a little further.
For example, the mother-foetus relationship may be regarded as one of the organisers of foetal synaptogenesis, a biological indicator of which is REM sleep. In this observational dimension, dreams would lie between the two phases of the dynamical mother-foetus system - a gate linking two worlds. Their organising role on this scale might therefore include the phylogenetic transmission mentioned by Freud in Totem and Taboo (1912-13), which provides for the intergenerational communication of psychic contents.
On another dimensional level, the same dynamic would be repeated in self-identical form, but on a different scale, acting as an organiser between more and less primitive levels of functioning of the individual’s CNS, integrating highly archaic and undifferentiated processes in which the biological and the psychic are at first merged and out of which various different functions can subsequently develop and evolve (for instance, the formation of a mental self as distinct from a neurophysiological self). Brain plasticity is also due to synaptogenic activity during epigenesis (for example, during the newborn’s active sleep7, under the stimulation of external agents, including traumatic ones). Attention is drawn to the importance, during the course of this process, of the affects, and thereafter of affective memory, as well as their later role, for example in the transference in therapy. The foetus’s active sleep may be deemed a biological situation ideal for the transmission of the parental genetic code, in the form of bio-psychological elements organised by the dream experience itself. This primitive organisation of the protomental is seen to contain not only psychological but also biological elements, as already mentioned by Freud in the 'Project for a scientific psychology’ and Beyond the Pleasure Principle - elements that punctuated his writings as the undecidable boundary of psychic experience itself.
On a subsequent, more specifically psychological level, dreams are located between the subject’s primary and repressed unconscious, and then between the unconscious and the preconscious, and, finally, between the preconscious and the system Pcpt.-Cs., performing the organising functions discussed above and eventually becoming part of the process out of which thought is born.
The fractal dimension of the dream attractor is thus revealed by its structural repetition in identical form on the various scales of observation (self-similarity).
As stated, we can imagine the dream’s navel as the central neck (defile) of the clepsydra; this is the point of maximum turbulence and hence of maximum unknowability and undecidability of the system, where all forms resemble each other, the point at which 'everything is possible’ and upon which the initial conditions of the system itself, its history and its context converge in order to determine a progression and a final outcome specific to that particular system. However, representational activity, which begins here, is capable of calming the turbulence - in other words, dreams play a central part in the process of catastrophic resolution of metastability. Hence the existence of the dream’s navel allows the individuality of the system to be preserved, even if the functioning of the mind, as a complex semantic system, is compatible with the existence of laws susceptible of extension (but not of generalisation, like those of deterministic systems) and with a degree of predictability in the dynamical evolution of the system itself, strictly dependent on its initial conditions.
Starting from the dream’s navel, then, a mechanism of transduction results in the generation at psychological level of a new state of the system - a new phase, a different complexity (for example, in the transition from the latent to the manifest dream).
Interpretation (of a dream and/or symptom) seeks to pass through the defile in the opposite direction and, starting from the known state of the system, to reach the possible initial state that generated it. In fact, dreams also accomplish two bidirectional movements: on the one hand, they allow repressed wishes to emerge, while, on the other, they permit repression of the latent thoughts. Again, in assessing the scope of words in Freud, we should not confine ourselves to the signifiers and the signified, neglecting the bodily and affective components of an utterance. Much research on the immense psychic power of words remains to be done - specifically, on the transformative and therapeutic power of the words exchanged in the analytic situation. As Pally (1997, p. 593) writes, since 'it is known that consciously attending to and verbalising something can enhance cortical activation, it could theoretically be argued that treatments such as analysis enhance cortical functioning, and take advantage of cortical plasticity, to modulate deeply engrained emotional responses’. Modell (1997), on the other hand, expects the eventual construction of a new biology of meaning to reaffirm the importance of the therapeutic action of words. Although always intuited and used empirically by Freud in the 'talking cure’, this power has not yet been comprehensively explained, so that its full potential cannot be utilised. If psychoanalysis can relieve psychic suffering, it is because of its incomparable capacity to facilitate the emergence of the potential of human language, which is placed at the service both of the internal affective discourse and of affectively meaningful interpersonal discourse (cf. Rizzuto, 1995).

CONCLUSIONS

We may take comfort, too, for the slow advances of our scientific knowledge in the words of the poet: 'What we cannot reach flying we must reach limping .... The Book tells us it is no sin to limp’
(Freud, 1920, p. 64).

My grandfather used to say: 'Life is surprisingly short. It is now so compacted in my memory that I can hardly understand how, say, a young man can decide to ride to the next village without fearing that - quite apart from chance mishaps - the time of an ordinary, happy life is too short by far for such a ride
(Kafka, The Next Village, 1916-17, p. 143, translated).
We have used the phrase the dream’s navel in constantly shifting senses because this metaphor appeared to us multivalent and polysemic. It inherently possesses a number of meanings, because it is situated in the multidimensional reality of the human psyche, so that it can be either used in a purely metaphorical sense or incorporated in concepts analogous to those shared with other sciences. In other words, it offers itself as an instrument for thinking.
Psychoanalysis cannot predict how a person will develop during the course of his or her life, but can rather reconstruct the past and assign meaning to it. The behaviour of extremely complex systems defined by a large number of variables is known to be almost impossible to forecast; this is particularly true of a complex system like the human psyche. Chaos theory could be applied in psychoanalysis, for example, to investigate certain sequences, not only in dreams but also during therapy, and might help us to discover the presence of regularities, patterns and structures hidden from the simple observation of phenomena; we should then have an opportunity of hazarding evidence-based forecasts as to the course of certain processes, at least in the short to medium term. An example might be the analysis of sequences of repetitive behaviour in a series of sessions over the period of a year, or the appearance of particular elements repeated more or less regularly in the dream production of an individual patient over a given period - specifically, before weekend breaks or other types of interruptions implying separation.
On the basis of the foregoing, dreams may be postulated as performing a diagnostic function for the mind, for example by analysing its chaotic-regime transformations. Dreams may be seen as a cognitive process arising out of the self-generated internal activity of the nervous system.
Freud had already drawn attention to the diagnostic activity of dreams, as follows:

The 'diagnostic’ capacity of dreams - a phenomenon which is generally acknowledged, but regarded as puzzling - becomes equally comprehensible, too. In dreams, incipient physical disease is often detected earlier and more clearly than in waking life, and all the current bodily sensations assume gigantic proportions. This magnification is hypochondriacal in character; it is conditional upon the withdrawal of all psychic cathexes from the external world back on to the ego, and it makes possible early recognition of bodily changes which in waking life would still for a time have remained unobserved (1916-17, p. 223).

The reference here is mainly to somatic rather than psychic diagnosis.
Freud’s proposition that the dream is the 'guardian of sleep’ is also well known. It is based on his concept of a 'threshold’, whereby a stimulus of internal or external origin liable to interrupt sleep may, if it exceeds a certain intensity, up to a point be incorporated in a dream, with the aim of contradicting the message of the stimulus and deferring its potential waking effect on the dreamer. All this applies to stimuli whose intensity is not excessive; in the case of more powerful stimuli, the sleeper awakes, as he also does from the anxiety dreams of traumatic neurosis.
Let us now extend the scope of this concept and deem the dream process to be the guardian not only of sleep but also of the mental apparatus itself. From this point of view, one function of this process might be the maintenance, or indeed the management, of the system and its internal trim in order to preserve its stability; this it would do by 'discharging’ excess (drive) energy through the hallucinatory fulfilment of wishes in a dream or, where this is impossible, by accommodating the stimuli in a particular memory connected with what Bion calls the protomental apparatus or somapsychotic apparatus, after which they are discharged in the form of beta elements through group action or psychosomatic phenomena.
Note that, for the dream process to work properly, it is not necessary for its representational contents to reach consciousness, or rather conscious memory, or for them to be interpreted.
As stated, analytic therapy, as a perturbing element from the outside world, may of course modify the psychic trim of the individuals concerned, because words (i.e. those of the analyst) can bring about changes in the brain, while dreams constantly monitor this process within the transference. In other words, our mental apparatus produces dreams as a diagnosis of itself in self-referential mode. Diagnostic activity is the complementary and unconscious active phase of dream activity. The members of the analytic couple, moreover, can interpret a dream as a diagnosis of the relationship between them, which has in turn participated in the dream’s production: the whole is in the part that is in the whole. It is a unique kind of cognitive process that produces elaborations and elaborations of elaborations of mental states and representations of psychic reality, which have the potential for subsequent narration through the use of language. This constitutes a cognitive process based neither directly on sensory data nor on logical reasoning, but which originates from a 'third state’. The wish triggers the dream, which activates the wish. The process is obviously one of infinite recursiveness (self-reference), so that, from the vertex of the dream processes, life may - to paraphrase Calderón de la Barca - be regarded not as a dream but as the 'dream of a dream’ (see Scalzone & Zontini, 1998).
These characteristics might account for the fact that, if it is to work, an interpretation must come from outside the 'patient’, as the recursive properties of a system can be assessed and validated only from outside the system itself; it is never possible to depart from the system comprised by the analytic couple. The same characteristics also account for the length of an analysis and make it possible to understand the recursiveness of certain recurring themes in a patient’s psychic system, and hence the 'form’ of his attractor.
This kind of introspection, performed by the activity of dreaming and the manifest dream, does not explicitly determine the functioning of the psychic system but constantly takes account of it. Reflection may therefore be seen as the system’s capacity to act on the internal process itself on the basis of the introspective activity of the dream, so that, in addition, the mind that describes the world is thereby describing itself. At operational level, we here encounter the significant concepts of self-referential metalanguage and the self-organising system, which in our case is represented by the brain itself on the biological level and by the mind on that of psychology.
In analysis, furthermore, we continue to have dreams of dreams in an interminable process that constitutes a representation of the flux of mental life and the analytic process; this often turbulent dream flux always remains closely connected, through procedural and semantic memory, with the emotional history of both the subject and the analytic couple, which proceeds in parallel with the history of their interrelationship.
A final point is that analytic interpretation treats dreams as if they were signs. If this diagnostic process serves to furnish knowledge through signs, it becomes a form of gaining knowledge through dreams. As signs, dreams may therefore also serve the purpose of communication, and diagnostic activity may be undertaken either to place the various parts of the psychic apparatus in communication with each other (intrasubjective communication) or, for example, to perform the same function between the members of the analytic couple (intersubjective communication), thereby conferring a meaning which, as stated, is the result of the self-organisation of the psychic system, its history and intersubjectivity. Account must therefore be taken of the elements of the dream, its text and their context. The interpretation will thus seek also to identify the order of the dream - something the patient has already done through his own narration - as well as to give coherence to the dream and thereby to identify its meaning.
Let us end by noting that our present culture is favourable to the re-establishment of the ancient alliance between psychoanalysis and the neuroscience. We believe that there are signs of considerable interest, among the psychoanalytic community, in accomplishing this re-union; it is, after all, surely inherent in Freud’s thought and hence in psychoanalytic theory, and emerges precisely from the works of the last years of the nineteenth century - in particular, On Aphasia and the 'Project for a scientific psychology’, as well as the papers on the motor paralyses, hysteria, etc. As Solms & Saling (1990, p. xvii) point out in their preface, 'Between 1877 and 1900 Freud published over one hundred neuroscientific works’. The historical extent of his work in these fields alone indicates that the 'neurobiological’ determinants of mental life were anything but alien to him (see Scalzone, 1997). Again, the fact of being a psychoanalyst surely does not preclude one from delving into other disciplines, such as the neuroscience; such an attitude would be antiscientific and hence unacceptable. In our view, a solid foundation for future research might be afforded by the re-establishment of the ancient alliance between psychoanalysis and the neuroscience, as well as by the use of new supradisciplinary global scientific paradigms such as chaos and complexity, with their substantial heuristic strengths.
To conclude these brief notes, we should like to point out that our model of dreams, which we see as containers for thoughts, should be seen predominantly as an analogue, as a heuristic instrument for speculative exploration of certain mental areas and phenomena. It is not for the time being mathematisable, or, at least, it was not our ambition to construct a mathematical model of the dream process, partly because complex systems are in particular susceptible to simulation. However, it would be wrong to minimise the importance of drawing analogies between different sciences, because an analogy indicates a similarity of structure between two complex entities, a resemblance of relations within two configurations. Analogy is therefore par excellence the function whereby structures of completely different kinds can be connected, while also facilitating the transition from myth to science and from one scientific model to another; it is therefore a function of communication (cf. also Moran, 1991; Galatzer-Levy, 1995; Quinodoz, 1999; and Palombo, 1999). We have also done our best to heed the warning of Sokal & Bricmont (1997) about the danger of misusing scientific concepts and terminology from the exact sciences out of context, and to avoid arbitrary extrapolations and - worse still - impostures intellectuelles. We cannot be certain of having totally avoided this risk, but have at any rate borne it in mind.
Research is not always conducted solely with a view to obtaining concrete results; one often begins to explore a field which may find a practical application only later, as investigation proceeds. All attempts to utilise conceptualisations from other scientific domains in psychoanalysis and elsewhere fall within this logic; while they should not be rejected out of hand, a watchful period of waiting is advisable. That is why we decided to produce this limited model of psychic functioning even though it may lack immediate utility, in the conviction that its heuristic potential is capable of development. We therefore agree with the following statement: 'At this time, psychoanalysis can only use deterministic chaos and fractals metaphorically, but in the future, especially if psychoanalysis is seen in terms of process or organismic theory, it is likely that such models can be produced’ (Spruiell, 1993, p. 3).
In conclusion, the shortest of short stories by Kafka that introduces the last section of this paper may be seen as a poetic representation of the appreciable dependence of the 'system of life’ on initial conditions and random perturbations, as well as of its temporo-spatial fractality. The metaphor can be extended to analysis, its unforeseeable course and its potential interminability.

NOTES

1. This is the silicon processor or chip (electronic circuit) that constitutes the 'brain’ or 'engine’ of an entire computer. It executes the 'instructions’ (runs the programs) we give the computer. The processors used in personal computers are called microprocessors.

2. The term Turing machine usually refers to one that, while abstract, could be built. This ideal machine, with finite states, consists of a read head and an infinitely extensible tape. It can perform a limited number of operations (read, delete, write, move, stop), which, however, suffice for it to perform any task expressible in computational terms. A universal Turing machine can simulate all particular Turing machines.

3. The theory of autopoietic systems is due to two Chilean neurophysiologists, Humberto R. Maturana and Francisco J. Varela, working with, among others, McCulloch and Pitts, who in turn devised the PDP (parallel distributed processing) model together with D.E. Rumelhart. Autopoietic systems are a class of homoeostatic systems capable of self-organisation and self-transformation, which thus keep their organisation constant by means of the network of relations that define them.

4. Biology plays a twofold part in psychoanalysis: on the one hand, it is one of the determinants of the organisation of living matter from which mental life will emerge, and, on the other, it is a rich source of models of functioning parallel to mental activity, on which mental activity draws.

5. We use the term model in the sense of a representation limited to certain aspects of a complex reality; it facilitates understanding of the requirements of a system.

6. 'We can avoid any possible abuse of this method of representation by recollecting that ideas, thoughts and psychical structures in general must never be regarded as localized in organic elements of the nervous system but rather, as one might say, between them, where resistances and facilitations [Bahnungen] provide the corresponding correlates. Everything that can be an object of our internal perception is virtual, like the image produced in a telescope by the passage of light-rays. But we are justified in assuming the existence of the systems (which are not in any way psychical entities themselves and can never be accessible to our psychical perception) like the lenses of the telescope, which cast the image. And, if we pursue this analogy, we may compare the censorship between two systems to the refraction which takes place when a ray of light passes into a new medium’ (Freud, 1900, p. 611).

7. Active sleep is characterised by slow or fast movements of the eyeballs with the eyelids closed, half-closed or open, the presence of coarse and fine body movements and mimetico-expressive facial activity, irregular, frequent respiration alternating with brief periods of apnoea, loss of antigravity muscular tone, raised, irregular pulse rate, raised systolic pressure with wide variations, and basic variability of heart rate. Proprioceptive reflexes are reduced or absent, and the volume of urine increases, as do intracranial pressure, cerebral circulation and cerebral temperature.

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Author’s addresses:

Franco Scalzone Gemma Zontini
Via S. Pasquale a Chiaia, 79 Vicolo Delle Nocelle, 79 bis
81021 Naples 80136 Naples
Italy Italy
e-mail address: MC5347@mclink.it

Translated by Philip Slotkin MA Cantab. MITI

* This paper has already published on International Journal of Psychoanalysis, 2001, volume 82, part 2, pp. 263-282.