A wide variety of fractal images, including the Mandelbrot set, Lorenz attractor and others mentioned in this article, may be found in Sprott’s online fractal gallery, http://sprott.physics.wisc.edu/fractals.htm
The Universe is built on a plan the profound symmetry of which is
somehow present in the inner structure of our intellect.
-- Paul Valery
-- Homer Smith, Computer Engineer, Art Matrix
The rise of cybernetics, the science of
information, following World War II, brought a new metaphor to psychology – the
notion of mind as mechanism. This metaphor inspired the cognitivist
revolumartion, in which psychological activity was likened to information
processing in machines. In the decades to follow, a wellspring of new knowledge
and empirical methods followed and even continues today.
While invaluable for its early insights, I
believe the notion of mind as mechanism has run its course. In this paper, I
introduce a different guiding metaphor in order to conceptualize the psyche,
one with particular significance to clinicians immersed in the complexity of
human affairs. This new metaphor represents the pendulum swung full circle,
from machine back to nature, where psychology started when it first diverged
from philosophy during Renaissance times. Ironically a return to organic models
occurs just as the computer plus related technology ascends takes an ever more
central role in most our lives.
More than ever, the computer affords us rich
tools for simulating nature’s complexity. Among the most powerful of these is
fractal geometry. Because fractals provide a lexicon for nature’s outer
complexity, it makes sense that this new geometry is equally as effective for
describing the complex terrain characteristic of inner processes.
This paper introduces the significance of
fractal geometry to the psyche. In the first section, I describe this new
branch of mathematics plus how to render a fractal by computer. I then articulate
the significance of fractals to the development of psychological identity.
Next, I claim that self-similarity, the hallmark of fractals, is a useful lens
for viewing personality organization and especially repetitive patterns of
behavior. I also argue that related concepts of dimensionality and scaling help
lend breadth to intraspychic analysis. I use the notion of fractal boundaries
to illuminate paradoxes of subjectivity and interpersonal relationships.
Finally, I assert that fractal boundaries are not just a source of endless
confusion and deep psychopathology, but also a fount of novelty, creativity and
endless mystery in us all.
Technical fractals are rendered, often quite artistically, on the palette of the computer. They consist of very simple formulas, such as the classic Mandelbrot set, X ← X2 + c, iterated on the complex number plane. To render a mathematical fractal, the same equation is computed over and over for every point on the complex plane, as endless cycles of reentry. Each time, the final result of the equation is fed back in again as the new starting point. In theory, this continues indefinitely, as the calculation of fractal dimensionality presumes the presence of infinite feedback loops. In practice, iteration continues until either there is a stable endpoint or an artificial cut-off that gives clear indication of where the equation is headed.
When gazing at a mathematical fractal, the
territory outside the fractal is out of control. It gallops unpredictably
towards infinity at one speed or another, indicated by gradations of color. By
contrast, the territory inside the fractal is ordered. It is relatively stable
and settles down to one or more fixed points. The edge between these two realms is what constitutes the actual
fractal. Here, in the delicate interface between unbounded and bounded areas,
the fractal neither flies out of control nor comes to rest. Instead it
self-organizes into an infinitely deep border zone that moves dynamically along
with the perspective of the observer.
When the computer is used like a microscope
to zoom closer and closer in on this edge, ultimately there is no resolution to
be found. Instead there is paradox of the nonlinear kind. That is, the tinier
the area under investigation, the more appears to be seen. This may sound like
Merlin’s bag of magical tricks, but doesn’t it also sound just like the psyche,
where the more we gaze inward, the more there is to see? In both fractal
inspection and the act of self-reflection, observed and observer merge
seamlessly, as the very act of looking helps to articulate the details to be
found.
Fractals are highly complex, dynamic shapes.
In fact, the Mandelbrot set is the most complex mathematical object known to
humankind. Mathematical fractals contain an ordinary, Euclidean dimension plus
a fractional or fractal dimension that indicates its complexity. For example,
the fractal dimension of a squiggly one-dimensional line, such as a child’s
scribble, might range from 1.256 to 1.894, depending upon how little or much of
a two-dimensional plane of paper it occupies. The fractal dimension of a
scrunched up sheet of paper tossed away might range from 2.364 to 2.943,
depending upon how loosely or tightly we wad it up into a space-filling ball.
In general, fractals carve out system
dynamics in one of two ways. Either, they are lower dimensional objects that
strive towards higher dimensions by recursively adding structure. An example of
this is the Koch snowflake, where each side of a triangle is replaced by tinier
triangles.
Or, fractals are higher dimensional objects that retreat into lower
dimensions by recursively removing structure. An example of this is Cantor
dust, where the middle third of a line is successively removed, over and over,
until only a sprinkling of points remain.
In psychology, the distinction between
progressing towards higher versus regressing towards lower dimensionality may
help us model whether a person’s psyche is better characterized by structure building
evolution of consciousness or structure eroding involution. Note that high or
low levels of complexity are equally as likely at any dimension. When it comes
to consciousness, this could help clinicians make important distinctions
between issues of complexity versus those of dimensionality.
For example, a person with borderline
personality disorder often displays high levels of complexity at low levels of
involuted consciousness. A description of borderline complexity, which results
in self and other getting sucked into irresolvable boundary confusion, follows
in a later section. By contrast, a spiritually enlightened person
characteristically displays low levels of complexity at high levels of
consciousness. Many religious leaders utter simple, yet profound statements,
like “God is love.” While a Marxist might argue that such simplicity appeals to
the lowest common intellectual denominator, a mystic might counter that such
simplicity reflects deep truth that flows from the invisible interconnectedness
of all things. In support of the mystic, fractal geometry actually provides
evidence for such hidden, invisible connection, especially beneath the surface
of chaos in nature, despite all its surface uncertainty and unpredictability.
Some natural fractals are detectable only via
mathematical abstraction, one reason why computers are sometimes necessary for
their detection. Computer modeling reveals hidden, fractal order beneath
apparently random, surface behavior typical of many chaotic systems.
An example of this is the Lorenz attractor, which models the
unpredictable flow of weather patterns. A slice of this strange attractor,
known as a Poincaré section, reveals fractal form not unlike Cantor dust.
One profound insight to be derived from
contemporary nonlinear science stems from the fact that human nature is
embedded within nature at large, whose essence is chaotic and fundamentally
unpredictable. Fundamental unpredictability means that the local, or
minute-to-minute details of specific instances can never be precisely
anticipated. Yet, beneath the surface of even the most turbulent chaos, usually
lurks invisible, exquisite order in the form of fractal attractors. While
self-similar patterns can be reliably detected at the global level, their local
details remain uncertain and fundamentally unpredictable.
I believe the presence of nonlinearity
accounts for the abysmal performance of predictive experiments historically in
psychology. Because statistics capture global attractors of highly nonlinear,
complex phenomena, this means that even in theory, we can never hope to predict
specific behavior in specific individuals. Yet with this new perspective, there
is a wealth of new information to be found in old experiments, when statistics
are re-examined as evidence for global attractor patterns.
Brownian motion of particles, the ups and
downs of the stock market, the spread of epidemics as well as the destructive
paths of forest fires are all examples of chaos in nature, with invisible,
fractal order lurking underneath. When time series data is plotted for each, a
strange attractor is revealed, such as the well-known Lorenz attractor. Lower dimensional cross-sections of these
attractors usually display order in the form of fractal structure, including
self-similarity at multiple scales of observation.
In highly nonlinear systems, which are
characterized by output extremely disproportionate to their input, fractal
structure becomes significant in that it serves as the mechanism for sensitive
dependence on initial conditions. Sensitive dependence, the hallmark of chaos,
means that tiny changes in any starting condition can send a chaotic system
careening off into new, entirely unpredictable directions. Underlying fractal
structure aids rapid escalation of change by facilitating propagation of
pattern from tiny to large scales.
Within the human psyche, chaos is ubiquitous
in the brain, where it forms a background for more ordered, perceptual states
(Freeman, 1991). Because of high sensitivity and easy mobility, a background of
chaos enables us to mobilize attention and change perceptual states rapidly in
response to unpredictable environmental shifts. Chaos also appears to form the
background of our ordinary mood shifts. Perhaps this sheds light on the use of
weather-related metaphors to express human nature, e.g., “feel in a fog,” or
“have a brainstorm.” The ups and downs of normal emotion usually display more
chaos than the excessive periodicity of certain psychopathological states, like
manic-depressive disorder (see Hannah, 1990).
Motor development involves the presence of technical
chaos in the unpredictable, jerky movements of the infant, which become
constrained and channeled over time (e.g., Thelen & Smith, 1994). Finally, impulsive behavior in adults may
represent the immature condition of original chaos improperly constrained
(Marks-Tarlow, 1993). With the psyche as with other parts of nature, where
chaos is present, fractal structure tends to lurk invisibly beneath in fractal
form.
Why is [Euclidean] geometry often described as
‘cold’ and ‘dry’? One reason lies in its inability to describe the shape of a
cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains
are not cones, coastlines are not circles, and bark is not smooth, nor does
lightning travel in a straight line (Mandelbrot, 1977, p. 1).
To date, many scientists have dismissed
fractals as mere pretty pictures. Perhaps this is because most scientific
papers primarily involve fractal identification and classification. I foresee a
new era in which fractals can be understood more deeply. I believe this is
inevitable, because I perceive fractal form to relate intimately to its
function – as record keepers of history as well as boundary keepers between
various strata of existence.
Fractals are a means by which time, or system
dynamics, gets etched into form
via self-similar, recursive loops that exist on multiple size scales. Fractals
exist in the paradoxical space between dimensions, levels and forces of
existence. They arise at the interface between processes, at boundary zones
where they serve both to connect and separate multiple levels.
Before turning in greater depth to the
psychological level, here I’ll sketch fractal boundaries and recursive,
self-similar dynamics that exist at multiple levels within the human body. My
list is not meant to be exhaustive, only indicative. At each level, we can see
how fractals are involved with the communication, transportation or
transformation of energy, matter and information in and out of the mind/body or
between its various subsystems. This is the hallmark of open, complex, self-organizing
systems existing in far-from-equilibrium conditions (Prigogine & Stengers,
1984).
At the biological level, our skin is pocked
with fractal pores that negotiate the transportation of oxygen inside and of
water and toxins outside. Wrinkles, physical evidence of our unique histories
becoming etched into our faces, are fractal as well. So too are the pattern of
animal markings, such as spots and stripes on leopards and zebras, lending each
animal a unique fractal signature.
Many of our internal organs display fractal structure. These include the lungs, which bring air into the body; branching patterns of our arteries and veins, which circulate blood and nutrients throughout the body; the intestines, which transport waste outside; and the brain, our executive center for communication, transportation, navigation and broadly modulating relations between internal and external worlds.
In the field of perception, many of our
sensory systems, such as sight and hearing, follow psychophysical power laws.
Power laws involve nonlinear, exponential relationships between variables, in
this case between how energy is transduced from the material level of signals
outside the body to the spiritual level of conscious perception. For example,
the formula that relates the internal quality of subjective loudness ( L
) to the external quantity of physical sound intensity
( I ) is L ~ I 0.3. The fractional exponent means that in
order to double the loudness of a string quintet, we must increase the number
of players tenfold – to fifty, with all musicians maintaining equal power
output.
Power laws are self-similar, because the same
relationship holds between their variables no matter how they are scaled or
rescaled. Newton’s universal law of gravitational attraction, F~ r -2,
is another example of a power law. The same relationship holds between
mass and gravitational attraction in Newton’s formula, whether manifest at the
tiny scale of the wavelength of light or the cosmic scale of light-years.
Due to their nonlinear, exponential increases, power law dynamics in psychophysics ensure that at the lower end of the signal spectrum, tiny amounts of a signal can be detected, as little as a single photon for the eye or single decibel for the ear. Meanwhile at higher ends, because distinctions are made with far less precision, we become capable of perceiving the widest possible range of signals. There is a paradoxical element to power laws – that the same relationship holds between variables at every scale means that they possess no characteristic scale. This hallmark of fractal dynamics is critical not just to psychophysics, where we enjoy the widest range possible of perception, but also to the psyche in general.
We take for granted that our minds generate
patterns across broad categories of space, time and person – large and small,
short and long, personal and universal – wandering freely within various
scales, without being restricted to any characteristic one. Yet this fact is
actually quite remarkable. I believe the issue of scale will prove highly
fruitful for harvesting regarding how fractal dynamics affect psychotherapy.
For example, as a clinician, if I persist in paying attention to tiny,
microlevel, process details that seem trivial or irrelevant to my patients,
because they are busy with macrolevel, survival level concerns, this can be
conceptualized as a misattunement of scale. The degree to which scale matching
is critical to feeling understood is an empirical issue in need of further
investigation.
Power laws appear not just in psychophysics and Newton’s law, but also all over nature (see Schroeder, 1991). At times their appearance takes on a magical feel, because they connect seemingly unrelated things. For example, over a hundred years ago, the Italian economist Vilfredo Pareto recognized that a simple power law models the number of people whose personal incomes exceed particular values. More recently George Zipf recognized that a power law connects word rank and word frequency for many natural languages. Suppose we take any ordinary book and count all the words it contains. If we list the words first by rank order of word popularity and next by the actual number of many times each word appears, we find a power law relationship connecting the two. Power laws seem magical when they relate the apparently unconnected, e.g., qualities like rank order, to quantities like frequency.
Continuing with this survey of fractal
dynamics related to human boundaries, along with Zipf’s law, self-similar
dynamics are evident in language even more broadly, whose symbolic arena is one
of the cornerstones of our humanness. Fractal dynamics afford language its
remarkable flexibility – the ability for a limited number of words and
grammatical rules to enjoy unlimited combinations. At a purely formal level,
language clearly consists of self-similar structures: words are embedded within
words, phrases within phrases, thoughts within thoughts, etc. That our number
system is fractal is so obvious as to seem almost trite. Yet, interestingly,
only at the point when it became so, did the concept of infinity arise. That
is, only when numbers served as place-holders, could they be recycled
infinitely. This made way for continued novelty in the form of calculus and
other mathematical advances.
Cyberneticist Ron Eglash (1999; Eglash &
Broadwell, 1989) examines fractal processes cross-culturally, observing both
physical and symbolic fractals as they appear in art and architecture. Eglash
and Broadwell make the interesting suggestion that the two levels of concrete
versus symbolic fractals correspond to analog versus digital information
processing. They illustrate this by examaming the Dogon culture of Mali, where
the human body is the primary organizer of meaning.
Reoccurring on multiple size scales among the
Dogon, self-similarity manifests partly concretely on smaller size scales and
partly symbolically on larger ones. At a small scale, the human form is carved
into doorposts, pots and other parts of houses. At a larger scale, the Dogon
house is arranged in the form of a human, with various spaces and rooms serving
as head, arms and torso. At a larger scale still, the village is laid out in
the form of a person, with the smithy symbolizing the head, etc. Finally at the
cosmic level, heaven is conceptualized yet again in the shape of a human being.
But here the realm is entirely symbolic. In this example, as is typical of
fractals broadly, each level is recursively embedded within the next. Meanwhile
self-similar structure progresses from concrete to abstract levels, as if from
analog to digital processing.
In previous papers (Marks-Tarlow, 1995; 1999), I examine fractal processes related to the purely abstract level of identity formation in the psyche. Perhaps partly because it is so highly symbolic, the self is a vague concept that has never been precisely defined. Some treat the self from a phenomenological perspective, completely as an interior experience. Others emphasize social and interactional components of the self. Still others broaden the lens to include cultural determinants along with their physiological underpinnings. From the widest perspective of all, the self has been viewed in universal, transpersonal terms. Here, pan-cultural themes are woven into tapestries of local, personal and cultural variation.
Historically these perspectives have vied for legitimacy. They compete for the prize of univalent, objective truth. They fight to the death, as if only one correct definition of the self exists. The difficulty in precisely defining the self may stem primarily from the lack of a fractal vantage point where identity is conceptualized multivalently, in terms of self-similar processes repeating on multiple size and event scales.
From the intrapsychic to the universal, I believe each level of analysis to be equally as valid and useful. Each folds into the next, displaying recursively embedded dynamics that recur on multiple levels of observation. Using fractal lenses, I conceptualize the self as an open, multileveled system coupled to other dynamical systems of broadening scope, from biological, physiological levels through intrapsychic, social, cultural, and even transpersonal ones.
A personal identity exists in the interior phenomenological space of our heads; a family identity supplies the uniqueness of each person’s relational dynamics; a regional identity dons the local garb of particular geographical areas; a national identity forms the butt of international jokes and stereotypes. A global identity 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 personality, which organizes self-similar patterns of behavior at various scales of observations. A timid middle-aged housewife tries to enter the professional world once her children have grown and her nest is empty. One day, early in therapy, she forgets to turn on the red light in the waiting room. By so doing, she keeps her presence invisible. Coincidentally, similar themes of disconnection and invisibility have also appeared in a dream from the night before. In it, the woman frantically tries but fails to get the attention of her boss in order to alert him to a critical flaw she has found in his business machinery. The flaw is miniscule, but so serious it could shut down the whole enterprise.
Together, patient and therapist interpret the dream. Deeply rooted fears are uncovered of tiny flaws under the surface, which endanger the very continuation of this woman’s enterprise, both personal and professional. With her children gone and caretaker role all but eliminated, her primary identity is threatened. This woman feels invisible and disconnected at multiple, recursively embedded levels. She wonders if she will be seen as vital to anyone, including her boss, therapist, and most importantly herself.
When the dream is examined self-referentially, as all dreams can be, this patient’s concerns about visibility and vitality recursively implicate her relationship to her own inner world. In self-fulfilling, self-similar fashion, as this housewife struggles to transform and broaden her role in society, she unconsciously enacts the very conflict she fears most. Ironically, by “forgetting” to turn on the light, she isolates herself at the very moment that consciously she is most eager to discuss and share her predicament.
Because of the capacity for the tiniest fragment of a dream to reflect the whole of the psyche, it is easy to see how beneath the surface, every dream carries fractal structure. Every dream carries full potential for an infinitely deep and wide nexus of interpreted meaning.
The fractal display of personality at multiple scales in everyday life is something most of us pick up intuitively. It comes as no surprise that someone who interrupts us frequently during conversation might simultaneously brag about road rage. This person, who seems to take pleasure in running over us verbally, also enjoys trying to run a fellow traveler off the road. Meanwhile we hear rumor of this man backstabbing a colleague or undercutting his business competition unfairly.
From the micro level of speech patterns, through a medium-scale event of a chance encounter on the highway, to the large-scale level of ongoing business relations, people generally demonstrate self-similar behavior across multiple scales of observation. When this gets rigidly stereotyped, we might think in terms of Freud’s notion of repetition compulsion. But a certain degree of self-similar repetition of behavior is natural, perhaps representing the characteristic “signature” of personality by which others recognize us and we recognize ourselves. When it comes to behavior emitting from the depths of personality, the same fractal dynamics crosscut every scale. This is because when it comes to the psyche, there is no characteristic scale of operation.
Selves
in the Paradoxical Space Between
The perspective of the self I offer is of an open, dynamical system that is fractally constellated. My view dovetails with Francisco Varela’s framework of autonomy in biological systems(e.g., Varela, 1979). 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. Selves follow the same pattern. They too are “closed” in that, when we are healthy, we retain a cohesive, coherent, ongoing sense of identity. Yet, selves are clearly open via interaction with the others, which constitutes the social mechanics of their negotiation.
My colleagues and I (Marks-Tarlow, Robertson & Combs, under review) have modeled the emergence of identity through endless cycles of reentry. Here, consciousness arcs away from the self, in order to enter into the perspective of another, and then circles back round again. (I see you seeing me; as a result, I see myself ever more clearly.) 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.
We can readily perceive such feedback cycles through observing young children. A two-year runs carefree, yet inevitably falls down. Not terribly hurt and mostly startled, she immediately looks towards mommy for a reaction. If her mother becomes scared or concerned and protectively rushes over to her child, this toddler will probably become upset, start to cry and take refuge in the very comfort being offered. Alternatively, if mommy smiles and nods approvingly, treating the fall as a necessary part of living and learning, chances are good this toddler will comply with mother’s call for independence by getting up, brushing herself off and taking the event literally into stride.
Of course, such feedback loops work in both directions. If the toddler really is hurt and mother merely nods and smiles, this parent is failing to take any cues from her own child. Mother is in danger of missing the emotional mark. If similar events, however minor, occur frequently over time, the toddler may become confused by mother’s misattunement. The child might begin to mistrust either her own internal signals or mommy herself, who increasingly appears as disconnected and invalidating.
Contrary to popular lore, which maintains that it takes huge, traumatic events to shape basic personality, 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. Selves retain a paradoxical quality because the truth of a fixed identity, i.e., its functional closedness, rests precisely on its underlying falsity, i.e., its structural openness.
The idea of selves arising in the paradoxical space between people was articulated elegantly by British object relations psychoanalyst, D. W. Winnicott (e.g.,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.
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.
Based on this example alone, we may be tempted to conclude that fractal separatrices characterize only severely pathological states, such as borderline or paranoid personality disorders or psychotic states. Whereas in paranoid states, confusion between inside and outside leads to delusions of trailing FBI Agents or invisible alien attack, in psychosis, such confusion takes on even more profound proportions to invade perception itself, in the form of visual or auditory hallucinations.
Here and previously (Marks-Tarlow, 1999) I propose that fractal separatrices are not just evidence of pychopathology, but characterize all psychological boundaries. 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.