1. Introduction

[E]ach of us is a source of meaning, a wellspring for the flow of fresh constructions within our brains and bodies. These constructions are by the exuberant growth of patterns of neural activity from the chaotic dynamics of populations containing myriads of neurons. Our intentional actions continually flow into the world, changing the world and the relations of our bodies to it. This dynamic system is the Self in each of us.

(Freeman 1999, p. 190)

Over the last two decades, in the context of the ‘integrative’physiology (Silverthorn, 2003), various measures of complexity¹ (Van Emden, 1971) have been applied to describe and distinguish different patterns of parameters, like the brain activity. The intuition and the science say that our brain is “complicated”: it is an epistemic system that interacts with itself and its environment (Fingelkurts, 2004). The history of the search for chaos in the nervous system, with its successes and errors, is truly fascinating. For example, several branches of studies were searching for chaos in the electroencephalogram (EEG) of epileptic patients (for a detailed review see Litt, 2003; Bruzzo et al., 2006); in particular, Babloyantz et al. (1985) were the first to study the human EEG with the tools of non-linear dynamics that they applied to recordings obtained during sleep. In such way, it has been reinforced the belief in ‘dynamical diseases’and in the nonlinear methods for diagnostic purposes. In spite of some hasty conclusions and naive enthusiasm that relied on ill-adapted measures of multidimensional and noisy systems, these stream of research led to amazingly sharp insights, confirmed more recently, with the arise of a new discipline, called neurodynamics. In a few words, what we must keep in mind is that chaos is inherent to brain activity and crucial for its normal functioning. Loss of chaos can actually be dangerous. The seizure in epilepsy, for example, may appear as an attack of chaos, but it is in fact due to loss of chaos: it is the result of an abnormally periodic order in the brain. Epilepsies involve the synchronization of large areas of the brain cortex, and so an epileptic EEG appears much more ordered than a normal one (Solé & Goodwin, 2000). Now, let me go behind these considerations in matter of neurophysiology, in order to speculate about the possible isomorphism between brain and mind, taking the point of view of a functionalistic reductionism: if chaos is present in the brain as I have briefly marked out, what does it mean for the question of who we are? Far away from substituting our structural Self² simply with our brain, it may at least be legitimate to claim, that our brain “enables” us to pose the question of who we are. Only recently a new multidisciplinary perspective on the Self has begun to emerge (Proust; Prinz; Newen & Vogeley; Metzinger & Gallese, 2003), claiming that essential questions about our Self can not be explained without studying the physical, measurable world of phenomena. However, I think that when we discuss about the Self, we have two possibilities: either treating it from a phenomenological perspective, completely as an interior experience, or emphasizing its social components, including cultural determinants along with their physiological underpinnings. Here, I don’t tend to define the essence of Self but only its “physiology”.

2. The functional nature of Self

Even if both functionalism and reductionism are the two positions that I admit to conceptualize the Self, these alone are not enough I need to keep in mind the non linear concept of fractal³ because the difficulty in defining the Self could to stem primarily from the lack of this chaotic feature, where identity is conceptualized multivalently, in terms of self-similar processes repeating on multiple size and event scales. Let me accept that the Self alternates periodic states of integration and disruption (Zinkin, 1986). With this assumption, it is clear that Jung’s arguments concerning the operational definition of Self as psychosomatic entity are denied. Therefore, I agree with Fordham (1985), acclaiming that the experience of wholeness is not a reliable basis on which to construct a definition of the Self. From the intra-psychic to the universal, I believe each level of analysis to be equally as valid and useful to tell about Self. Each folds into the next, displaying recursively embedded dynamics that recur on multiple levels of observation. Using these fractal lenses, I conceptualize the Self as an open, multileveled system coupled to other dynamical systems of different scales, from biological, physiological levels through intrapsychic, social, cultural, and even transpersonal ones. A personal Self exists in the interior phenomenological space of our heads; a family Self supplies the uniqueness of each person’s relational dynamics; a regional Self refers to the local garb of particular geographical areas; a national identity forms the butt of international jokes and stereotypes. A global Self may even struggle to emerge and bring geographical differences into harmony. In general, such multivalent existence is highly suggestive of fractal dynamics. Fractals also come into play within the internal attractor structure of Self, which organizes self-similar patterns of behavior at various scales of observations. I assume a perspective of Self as open, dynamical system and fractally constellated, sympathetically with Francisco Varela’s framework of autonomy in biological systems (e. g., Varela, 1979). In a few words, Varela’s model involves endless feedback loops, which allow biological systems to re-enter themselves continuously. This results in paradoxical dynamics when biological systems are characterized in opposite terms, as being functionally closed yet structurally open. I claim that Self follows the same pattern. All sub-aspects of Self too are «closed» in that, when we are healthy, we retain a cohesive, coherent, ongoing sense of identity. Yet, Self is clearly unlock via interaction with the others. Likewise, Marks-Tarlow, Robertson & Combs (1999) have modeled the emergence of “identity” through endless cycles of reentry, in which, consciousness arcs away the Self, in order to enter into the perspective of another, and then circles back round again. This model conforms nicely to social mirror theory (e. g., Baldwin, 1902; Cooley, 1968; Mead, 1934; Whitehead, 2001), which posits the development of Self and the perception of others to arise hand in hand. Contrary to popular lore, which maintains that it takes huge, traumatic events to shape basic Self, it is increasingly evident to most clinicians that the tiny falls, tweaks and mishaps are equally, if not more, significant in the formation of basic personality. Like endless waves on a shoreline, ever-similar yet ever-changing at a minute-to-minute level, day in and day out, mommy or other caretakers plus their children are embedded in paradoxical, feedback cycles of subtle nuance. Tiny events, like the toddler’s stumble, form endless feedback loops in both directions, from self other, other to Self. Over time, these cycles shape both people by building a repertoire of memory and experience. Out of this foundation, at the next level of complexity, self-image emerges to form self-referential loops in consciousness. By requiring the ongoing presence of others to become present to our selves, this model of development emphasizes the paradoxical dimensions by which Self and other, observer and observed are inseparable. Self retains a paradoxical quality because the truth of a fixed identity, i. e., its functional closeness, rests precisely on its underlying falsity, i. e., its structural openness.

3. The space between Self and Other

The idea of Self arising in the paradoxical space between people was articulated elegantly by British object relations psychoanalyst, D. W. Winnicott (1971). Winnicott’s most important contribution was the notion of the transitional object. This consists of baby’s first possession, such as a blanket or teddy bear, which occupies the fertile space between mother and baby. The transitional object is the first symbolic object that serves both to connect and separate baby and mother. This object is partly discovered and partly created, neither wholly of the one nor of the other, yet it partakes of both. Out of the nebulous space of the transitional object, Winnicott envisions the creative emergence not only of symbol and play, but also most broadly of culture at large. Winnicott came to his idea of transitional objects after returning again and again to a Tagore poem, “On the seashore of endless worlds, children play. ” Like a barnacle, this fragment lodged in his psyche upon first encounter. Over the years, wave after wave of meaning washed over him. At first the poem represented endless intercourse between man and woman, with the child emerging from their union. Then the sea represented the mother’s body and the land her ego, with the baby spewed upon the land like Jonah from the whale. Finally out of a long, chaotic state of not-knowing, the notion of “transitional object” crystallized in Winnicott’s mind. Both psychoanalyst Stuart Pizer (1998), a pioneer who conceptualizes psychotherapy in nonlinear dynamical terms, and myself believe it no coincidence that Winnicott’s creativity emerged through contemplation of a fractal image. Because fractals inhabit the nebulous territory of the «space between,» their borders provide endlessly fertile, endlessly deep frontiers. I suggest that the Self arises in the paradoxical space between people and events as an ongoing, co-creative, interactive and iterative process. Just as with any fractal, internal structure gets added or removed through the ongoing negotiation of boundaries. This complex border area, where inner and outer, self and other are melded, can be conceptualized in terms of fractal separatrices. The ordinary conception of a boundary is literally a bounded, or fixed area whose resolution is easily detectable, e. g., the door of our houses or edge of our desks. By contrast, fractal separatrices can never be resolved. Instead they form endless, infinitely complex zones of articulation and negotiation. Here, between any two points, e. g., of self and other, inside and outside, exist infinitely many other points. The image of fractal separatrices can be viewed in terms of intrapsychic dynamics, such as the dilemma of a person with obsessive-compulsive personality disorder in an ice-cream store. Each color, or basin of attraction, represents a different flavor, and the complex fractal boundary between the four choices illustrates the obsessive nightmare of attempting to use intellect or logic to figure out the «right» choice, when rightness isn’t the issue at all. In order to understand the complex, nether zone of a fractal separatrix interpersonally, it is useful to examine the psychopathology of the borderline personality. People with this character disorder display chaotically organized psyches, which includes intense, shifting affect and highly unstable relationships. These individuals tend to oscillate between subjective poles of engulfment and abandonment, often harboring central issues of rage and shame. They repeatedly express confusion between Self and other. At times, interpersonal confusion reaches a crescendo, to the point denying psychological existence altogether. That is, the borderline is wont to claim that she has no Self, to assert in essence, «I don’t exist.» This is the ontological equivalent of the Liar’s paradox, «This statement is false.» In both cases, if it’s true, then it’s false; and if it’s false, then it’s true. Because of such intense confusion, extreme defensiveness and rigidly closed boundaries, interaction with a borderline personality frequently results in what anthropologist and scientist Gregory Bateson identified as the double-bind. The double-bind, which Bateson postulated as the cause for schizophrenia (e. g., 1972/1956), consists of seemingly impossible, paradoxical demands made on relationships, that involve contradiction at multiple levels of communication. When it comes to borderline personality disorder, paradoxical demands often center upon the issue of blame. For example, «You’re to blame for my hurt. If you don’t think so, you’re wrong, because I know you better than you know yourself. But even if you’re right, you’re still to blame, because you’re always trying to be right at my expense.» In this closed feedback loop that serves to keep contradiction in place, which is what Ben Goertzel (1994) calls «chaotic logic,» we see that engagement with a borderline easily becomes a paradoxical morass, including the potential for endless recursion. Attempts to ignore multiple realities and ambiguity by always being right while making others wrong results in failure to recognize the fractal quality of boundaries, along with their irresolvable openness. People with borderline personality disorder have often been so hurt or abused by letting others in emotionally, they now feel entirely threatened. Yet the more they fight the open, contradictory nature of psychological boundaries, ironically the more everyone gets sucked into the endless vortex in the space between. Fractal separtrices between inside and outside mean we all carry the potential for confusion between Self and world, projections, delusions, hallucinations or self and other, e. g., introjections, projective identification, delusions and borderline double-binds. Yet, except under extreme conditions of stress, most of us resist these vulnerabilities. We can usually let this seam alone, because in ordinary daily functioning, it proves irrelevant. By contrast, psychopathology is characterized either by excessive rigidity or too much chaos that causes us to deny, fight, reject, ignore or repress this potentially scary, disheartening condition. The major difference between psychological health and psychopathology is not so much the possession of clearer or cleaner boundaries. Rather it is more that in health we possess the wherewithal and flexibility to recognize, tolerate, and if we’re lucky even welcome, the vagueness, uncertainty and ambiguity inevitable with fractal separatrices. We don’t need to lose ourselves in infinitely complex, irresolvable boundaries as long as we understand them. Along with a source of psychopathology, open boundaries are a fount of aliveness, creativity, and even higher consciousness. They preserve the mystery and wonder of life. We grow through our ability to tolerate ambiguity, to hold opposites without succumbing to the tension of reducing one side to the other, and to understand ambivalence. All these emotional skills relate to embracing rather than rejecting underlying fractal dynamics, along with their paradoxical elements.

4. General conclusions

In synthesis, my paper claims that the Self is not a substance but a function.

Thus, I have not absolutely described it as a substratum of psychological and/or physical properties, spatially located and causally active.

In so doing, I have demonstrated that using fractals and the nonlinear attribute of self-similarity is possible providing a parsimonious account on the function of Self.

Principally, I have rejected the Self as an object among others in the world, compatibly with some interpretations of the Buddhist ‘no-soul’theory, as well as with Kant’s claim. Finally, I have explained the potentialities of fractal bound for a prior differentiation between oneself and the other, without taking into account other specific systems of self-attribution (e. g. “Who” system into the brain (cfr. F. de Vignemont and P. Fourneret, 2004). Punctually, three principles have been applied to discuss the Self:

1. the presence of the phenomenon Self on different scales of observation;
2. its fractal growth both in phylo- and ontogenesis;
3. its appearance and disappearance (elusiveness) on different structure levels by contrast its constancy as function.

In a few words, the role (function) of the Self-as complex system, likely the brain, is determined by its interaction with what states itself creates. It is clear that, on one hand, it can to open the possibility of re-stabilizing itself at another level or, on the other hand, the Self can to fall victim of regression.

Like psychologist, I could provide to the readers several anecdotes confirming that the danger, anxiety, and stress produced during a confrontation with “the Other” can create chaos, usually leading to what is called a bifurcation or splitting of the energy in two different directions.

We know in this regard that the experience may be shattering. But sometimes regression serves the process of evolution of Self and leads to creative transformation and its renewal. Therefore, the potential benefit makes the risks worthwhile.

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