Medical Hypotheses I h&d Maw (1992) 39,67-72 ~LlmgmmlormpuKud1992
Deterministic Nonlinear Chaos in Brain Function and Borderline Psychopathological Phenomena N. PEDIADITAKIS 3123 Essex Circle, Raleigh, North Carolina 27608, USA
Abstract-There exists a fundamental overall property of the brain which monitors, modulates, and ensures a smoothness of function and which further determines elegance and grace in functioning. This property also imparts a quality of, or a sense of proportion among all other faculties of the brain. It is postulated in this paper that such a property/function, up to now almost taken for granted, is maintained/exercised by a nonlinear deterministic chaotic mode of brain function. If this is the case, borderline psychopathological phenomena, when they flare up, can be explained as resulting from sudden reduction of such a deterministic chaotic mode and the emergence of a pathological order, as the system becomes an oscillating one.
A poignant example of the absence of such a quality can be seen in a patient suffering from Parkinson’s disease, where the elegance and smoothness of movement is replaced by awkward, painful to observe, jerky, zombie-like motions of the sufferer (9). There is now suggestive evidence to support the proposition that this ubiquitous quality is mediated through a deterministic nonlinear chaotic mode of brain function (l-5, 7, 8, 9).
Introduction The brain normally exercises all of its functions with smoothness, subtlety, elegance and grace, as well as a sense of proportion. It accomplishes all of this while keeping the expression of higher functions more or less in balance along the median. A dancer, a diplomat, a person in courtship, an athlete in action, a fiddler, a person alone in contemplation of himself, a citizen discharging his duties, and a person at work all have something very important in common: as they exercise their individual skills, strive to fulfill needs, express their altruism, interact socially, contemplate and perceive themselves, foreplan, yield or restrain, negotiate desires or terms of endearment; all have a smoothness, a grace, an evenness-in-function, a sense of proportion and a restraint which prevents extreme oscillations to either side of the spectrum of what is considered appropriate, socially acceptable and personally comfortable. Date received 8 August 1991 Dale accepted 23 December 1991
Deterministic nonlinear chaotic dynamic systems and their properties
The concepts of the study of deterministic nonlinear chaos phenomena are only now becoming familiar in the behavioural sciences, so let us begin by defining and outlining our interpretation of such a concept and its ramifications. The term, nonlinear deterministic chaos, does not refer to the phenomena of total ran-
67
68 domness (entropy) treated by the Second Thermodynamic Law, but to an exciting new mathematical held of study of certain (constrained) random processes in dynamic systems. For the last decade it is becoming increasingly evident that such processes are abundant in nature and have recently been found involved in the physics of weather (from which the first perception of deterministic chaos was finally firmly established by Ed Lorenz in 1972, though previously suspected by A. Poincare (14) and others), fluid dynamics and, in increasing number, in biological system dynamics (5, 7, 10, 11). In this new science, deterministic nonlinear chaos can be defined as a stochastic behavior (Stohos = Gr. for ‘aim’) in a deterministic system (12). Stochastic behavior of a dynamic system is a behavior whose rules are loosely outlined or defined in a ‘more-orless aiming at’ fashion, as opposed to precisely laid rules having an ‘either-or’ nature. Traditional classical modeling of physical systems sought the latter kind of specificity, as well as relied on the view, based on the traditional scientific rationalism of the West, that ‘a system can always be understood by breaking it down and studying each piece’ (3). Such thinking and method actually obscured and hindered, rather than illuminated the understanding of the function of large and complex dynamic systems. Furthermore the existence of deterministic chaos affects the scientific method itself, since long predictions are intrinsically impossible, verifying a theory becomes a more delicate operation, relying on statistical and geometric properties rather than on detailed prediction (4). The uncertainty, not always the results of the coarse graining of measurements performed (Heisenberg Uncertainty Principle) although it often is, can result as well from the nonlinear properties of the system itself (1). Since deterministic chaotic systems generate randomness on their own, without the need of any external random input (4), it is impossible to predict ‘reality’ of their own, though the latter derives from the past. The deterministic chaotic mode, treated by the mathematics of nonlinear chaos, implies a consuained kind of randomness. Chaotic dynamic systems manifest, within limits and finite boundaries, properties that can be described by such adjectives, as insured flexibility, robustness, adaptability (2, 3, 4), stability (3,4)-since the system is able to absorb disturbances and randomness-novelty (4), variability of action, resilience and avoidance of entrainment (4). Since such characteristics are the very essence of the expression of human behavior, it is reasonable to suggest that deterministic chaotic mechanisms are of fundamental importance in global brain functions. In ad-
MEDICAL
HYFDTHESES
dition, there is actual evidence that such systems are indeed involved in brain function (4-7). Furthermore, the actual architecture of the brain with its dendrites is a fractal arrangement, There is another critically important phenomenon associated with deterministic nonlinear chaotic systems, that becomes of particular importance, in this context: such systems can be bimodal. If a critical threshold of loading is reached, or conversely, if the system becomes excessively ordered by exact rules or ‘either-omess’, then it can rapidly transition from a contrained chaotic mode with all its remarkable properties previously mentioned to that of a simple oscillating one or vice versa. This threshold can originate from within or be introduced from without, in the form of new information (increased randomness) or increased dimensionality (3) (how many factors make up the system, i.e. the reaches of the fractral dendritic neuronal arrangement of the brain). Fractrals, a term often mentioned in the study of deterministic nonlinear chaotic systems, can be defined as geometric constructs with self-similarity in any scale, as in clouds, mountains, coastlines, the bronchial tree of the lungs and, of course, the dendritic arrangement in the brain. Fractrals can also be considered as the footprints of the deterministic nonlinear chaotic system, as its functioning, then such fractral tracings are called strange attractors (2, 3). A purposely chosen illustrative example, quite removed from our field, which nevertheless gives insight and understanding of elegance and beauty of a chaotically regulated albeit constrained dynamic system will perhaps help to clarify our argument: we travel by car to work. We ease ourselves into the traffic and continue to drive together with other car drivers stochastically, i.e. with loose rules aiming at the direction of our job location, while all along we are allowed to move as others do, from lane to lane, behind or in front of other drivers, a little faster or slower, within the speed limit, as the occasion dictates, i.e. in constrained randomness. The boundaries of the road, direction of the traffic, and speed limit provide the deterministic setting. Thus the whole traffic is operating in a dynamic constrained chaotic mode. The traffic governed by deterministic chaos, even though it may not be the most efficient possible, is the most effective method of moving great numbers of cars, each having different destinations and timetables. The system has robustness and resilience, but if we tried to substitute with orderly controlled algorithm with its rules for maximum efficiency, the new system will soon bring the entire traffic to a standstill (gridlock) after wild, jerky swings/oscillations, i.e. pathological order.
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The entire system is boxed into its severe degree of orderliness of function. Conversely, if the number of cars on the road greatly increases or there is no longer a speed limit or greatly different types of vehicles, such as trucks, bicycles, tractors, even pedestrians are mixed in (i.e. increase in dimensionality), again the entire system will become increasingly vulnerable to an additional small perturbation (the so-called sensitivity to the initial conditions) and like the straw that broke the camel’s back, will soon push the system back into an oscillating jerky-mode with final gridlock. The traffic in Istanbul, Turkey, with essentially no traffic lights to control it, provides the amazed visitor with a convincing demonstration of an effective deterministic chaotic mode traffic process. Compare this with the frequently occurring gridlock of Western cities at rush hour, when exact, rigid rules are imposed at intersections by traffic signals.
Deterministic nonlinear chaotic system and brain function
So we propose that the presence of chaotic stochastic mode of mental functions, with its proposed constrained built-in randomness, provides smoothness of function, grace, subtlety, flexibility, effectiveness, even novelty, but above all, in this paper’s context, precludes (prevents) entrainment (1, 4). This deterministic chaos may underline everything that is most admirable in humans. From this point of view, we must now postulate that when borderline phenomena flare up, the condition can be explained as a mental disturbance, in which the chaotic stochastic mode of all the high mental faculties is temporarily and precipitously diminished or absent (entrainment). This phenomenon is hinted by M. Conrad in his statement: ‘It is conceivable that in the absence of chaos either a dull pacemaker activity will develop or highly explosive global neural firing would emerge’ (4). Thus, the system becomes orderly, rigid, ‘either/or’ and ‘boxed in’ and the faculties now tend to express themselves in violent perturbational/oscillating extremes of their functions and expressions which are slow to correct (pathological order). Thus, ironically, the word disorder’ in borderline conditions may be misapplied, since it is precisely the occurrence of ‘order’, which heralds the emergence of extreme oscillations of whatever high mental faculties are involved. This view runs counter to our training as clinicians and to conventional wisdom in medicine ‘which hold that diseases arise from stresses and pressure on an otherwise orderly system’ (11) and that ‘disease is traditionally defined as a disorder of failure of homeostasis
in a linear system’. By now ‘it is becoming apparent in several areas of medicine that an increase in “regular” behavior sometimes accompanies disease’ (11) with some types of heart attacks, epilepsy, muscular stress, cocaine intoxication, Parkinson, as Goldberger et al further stresses. This counterintuitive discovery may have broad and exciting ramifications and can be applicable in the understanding of borderline phenomena. The borderline psychopathological syndrome
The definition of Borderline Psychopathological Syndrome (BPS) by DSM=II- (15) is given as ‘a pervasive instability of...‘, implying an extreme oscillation from the median, even though not explicitly stated. In the literature, the description of BPS is accompanied often by terms such as ‘polarization’ (good/bad, all-or-nothing, now/never, within BPS) (17) or ‘oscillations of attachment’ (16) or ‘splitting’ (18). It is even proposed that such conditions ‘evoke polarized responses from the environment...‘. Patients are being seen as either deprived waifs or entitled bullies (17). Furthermore, as the phenomenon of pathological order is implicitly recognized ‘as a hierarchy from the healthiest to sickest, the number of distinct options becomes more circumscribed, and the subtlety and complexity of the personality becomes simplified’ (17). Actually to an experienced clinical observer the so-called Borderline Personality Disorder, as defined by the DSM-III-R Axis II, invariably co-exists with other personality disorders, especially of the B Cluster. Furthermore it occurs as a periodic ‘flare-up syndrome raising the very possibility’ that borderline personality disorder could only be a syndrome occurring periodically on a matrix of other personality disorders in accord with the view and the logic of this paper. A recent study (20) in its conclusions raises such a possibility. To even the seasoned clinician, dealing with BPS patients it is always startling and even amazing to witness the phenomenon of abrupt change of behavior, mood, attitude or stated reasoning of such a patient, under even mild pressure of the therapeutic interaction+onducted with delicacy and tact This is strongly manifested in the display of unbridled rage, only to be replaced by profuse apologies and pmstration. ‘Short fuse’ is the expression often used by many clinicians. Such rapid, abrupt, precipitous and catastrophic change, corresponds exactly with the properties of the proposed existence of a dynamic system, which previously operated in constrained nonlinear chaos (with all its already stated qualities contributing to the patients’ skills of humanity and grace), now
70 moves into that of an (rapidly) oscillating, ‘orderly’ system of ‘either/or-tress’. We can recall that with dynamic systems operating on deterministic chaotic mode, the former occurrences take place under the following conditions: 1) the system is too rich in randomness or dimensionally or the constrains are weakening or absent; 2) if conversely, the system is constricted with excessive orderliness (reduction of randomness) and rigidity. Bordertine psychopathological syndrome as an expression of an oscillating mode of deterministic nonlinear chaotic system
We now propose that borderline phenomena are the expressions of systems operating on an oscillating mode, i.e. in such conditions all mental functions to various degrees tend to express themselves in symptoms of oscillating extremes. Thus, in the patient suffering from BPS syndrome with regard to the ‘brain faculty’ of perceiving danger from within or without, the oscillating phenomenon shows up as uneasiness, tension, and insecurity on one side, versus fearlessness, unreasonable freedom, freedom in risk-taking, daring, and even recklessness on the other-within the time frame of minutes, hours or days. In the ‘faculty’ of dealing with foreplanning, scheduling, and sequencing, BPS manifests itself as ‘scatterbrainess’, slovenliness, neglect of personal appearance and personal hygiene on one side and then fastidiousness, over-orderliness, punctuality, and obsessive preoccupation with one’s own health on the other. In the faculty of thinking (aside from their inability to think in more-or-less fashion, perceiving everything in terms of ‘either/or-ness’), BPS patients exhibit psychotic-like distortions in perceiving, elaborating and interpreting reality at one extreme, versus overclarity, often remarkably creative thinking about novel alternatives at the other extreme. With regards to the ‘faculty’ of mood modulation (emotional tone), an often strong component of BPS (19) is cyclothymic (i.e. oscillating) expression of, on one side, black moods to be replaced by an unwarranted emotional effervescence. This cyclothymia is often present in addition to the chronic unhappiness, sadness, and low self-esteem, often expressed by borderline patients-understandably, since the patient is being buffeted by these oscillations, ‘akin to the buffeting of winds on an abode in a Kansas prairie’, as a bright borderline patient stated. In the ‘faculty’ of internalized ‘dos’ and ‘don’ts’ (perhaps corresponding to the Superego of Freudians) the BPS becomes manifested in disregarding morals, conventions and law (i.e. shoplifting) versus, often,
MEDICAL HYFOTHJSES
the presence of demoralizing guilt and shame. In the ‘faculty’ of coordinating needs in the context of social expectations and decorum (perhaps corresponding to the Ego functions of Freudians) the BPS patient exhibits extremes of impulsivity, rage, sexual promiscuity, opportunism and harshness on one side versus overdecorum, solicitousness, often abstinence and celibacy on the other. In the ‘faculty’ of forming intimacy and bonding/mutuality-in-affection, the normally subtle, finely turned interplay of approach in intimacy and equally imperceptible, subtle distancing are now replaced by extreme, crude, conspicuous oscillations between energetically and intensely shown closeness on one side and abrupt recoiling and distancing on the other (16). In the area of mental representation and attitude towards important people in the patient’s life, the phenomena show up as extreme idealization and admiration on one side, versus debasement, devaluing, and disdain on the other (splitting) (18). In social contexts, borderline psychopathological oscillating behavior is often misinterpreted as intentional manipulativeness, e.g. consider a person who exhibits unbridled and unwarranted rage for a few minutes and then returns a few minutes later, prostrating himself with self-deprecation and apologizes, only to go into another possible rage a few hours or days later. The normal person will interpret this behavior as intentional manipulativeness, instead of being the other leg of the oscillation. This interpretation will also be common among clinicians. Conversely, socially, appropriate, but extreme, behavior may be overlooked, being in fact the other leg of oscillation, or may even be considered as an ‘improvement’. The above partitioning of such ‘faculties’ is somewhat artificially drawn with much overlap, but the list is useful in helping us to discern the baffling intricacies of the borderline phenomena. Proposed causes triggering pathological or&r and oscillating phenomena
The BPS patient clinically appears to lack, in various degrees and combinations in their temperament, the components which constitute the so-called psychobiological attributes/constrains, such as relatedness, emotional connectedness. capacity for intimacy, empathy, and altruistic concerns. The deficits may be shared by the other disorders of Cluster B of the DSM-III-R, such as narcissistic and histrionic disorders (often patients in fact have multiple diagnosis for these disorders). The deficits may originate from birth or they occur developmentally by separate events or more likely are an interplay of both.
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If this is the case, one may venture to speculate that the deficits may deprive the patient of an important built-in behavioral guide/constraints for genuine social participation. The patient is now puzzled, at a loss, after resorting to a sham, bluffing behavior dictated by his intellect. Furthermore, the patient is now left without the emotional benefits, which derive from genuine social participation, and feels lonely, cut-off, ‘empty’, ‘numb’, bored, meaningless, with a chronic sense of ‘absence’-terms actually used by BPS patients themselves. They often rely on an enormous need of external reassurance of being ‘loved’ for their self worth and emotional ‘succor’. On the other hand, such sufferers may hold striking advantages in other areas of their life. As these patients are relatively not bound by the above mentioned constrains, they have now the freedom (i.e. an enlarged randomness and with relatively few constrains) to act creatively, able to see new patterns, be original, and deal in novelty. These ‘pathfinder’ qualities are often very much present in BPS patients and are shared by gifted and talented people. Lastly, deprived of the mentioned social emotional constrains, they feel uneasy, tense, and unbalanced. These intensities may very well act as the straw that breaks the camel’s back, heralding a shift of their phenomena and pathological order. From the sufferer’s point of view, once behavior is initiated, the patient ‘feels it’ as a cascading tidal wave and he is unable to restrain or modify it towards a reasonable middle ground. Thus, he finds himself in paraphora (Gr. for being carried away in extremes). One BPS sufferer described it as ‘a sense of going for broke, but unable to help it’, a kind of disorganizing hyperintensity aptly added. To the observing clinician, BPS manifests itself in many substitutions; impulsivity instead of appropriate restrained exuberance or circumspect; quick, mindless rage instead of reasonable expressions of displeasures; explosivity, instead of candor mixed with tact; harshness instead of civil remonstration; vituperativeness instead of polite explicitness; feelings of emptiness in place of clarity in perceiving one self in place and time; intense yearnings of total fusion with object of affection or total recoil, instead of elegance of approach and subtle courtship; obsequiousness instead of reasonable civility; overcompliante instead of respectful consideration of the rules; display of arrogance instead of self-assurance, etc.
Nature. In complex dynamic biological systems, especially relating to brain function, deterministic chaotic mode may have enormous significance with its intrinsic qualities. Its ability, within certain limits, to absorb randomness as well as generate randomness of its own and to promote stability, flexibility, robusmess, diversity, novelty, and by precluding entrainment, to create elegance, smoothness, and more-or-lessness of functions, finally allows it to maintain a sense of proportion. Disturbances in the brain may explain BPS and even other so-called ‘functional disorders’. Research in its intricacies and properties of such a mode is urgently needed, as well as finding ways to influence the components of such a system for the preventive and therapeutic benefits of the patients. Conclusion This paper proposes several new insights. Specifically it proposes the existence of an overall quality of the brain function responsible for smoothness of function, elegance, and delicacy, shared by all the faculties of the brain, not fully acknowledged previously. Furthermore, we have proposed a logical underlying mechanism based upon deterministic chaos in explaining such an overall quality. We have made a case that BPS has an underlying vulnerability due to the possible existence of an enlarged randomness of the deterministic chaotic mode and the diminishing or absence of certain important constrains relating to social aspects of humans, a situation that is most likely shared in part by gifted and talented people. We further propose that borderline phenomena, when the conditions flare up, are due to the sudden reduction of deterministic chaotic mode and the emergence of pathological order, thus the entire system becomes oscillating. The proposed view provides us with a new perspective and openings in understanding the development and mechanism of expression of borderline phenomena and perhaps even more importantly, of other so-called ‘functional disorders’, whose exact origin, cause and mechanism have stubbornly eluded us thus far. Acknowledgements I wantto express my warm appreciation and gratitude to Dr John Rather of Livemtore National Laboratoty for his help in advising me, editing the paper and offering me suggestions in how best to express the concepts outlined.
Discussion The discovery of the nonlinear, deterministic chaotic mode operating on complex dynamic systems is an exciting and important one. Such a mode has been found to have important application in many areas in
References 1. West J. An Essay on the Importance of Being Nanlinear. Springer-Verlag. ~~138. 140. 191-193. 1980. 2. Schuster H. Deterministic Chaos. Physik Verlag Weinheim,
72 ppl-3. 1984. 3. Crutchfield J et al. Chaos. Scientific American. oo3ti9.57. _. December. 1980. 4. Holdm V. Chaos. Princeton University Press, 1986. 5. Holdm A V, MuhanedM A. Chaotic activity in neural systans. Cybernetics and System Research 2 Elsevier. Amsterdam, pp245-50. 1984. 6. Laos in a three-variable model of an excitable cell. Physics 16-D. pp233-242. 1985. 7. The identification of deterministic chaos in the activity of single neunns. Journal of Electrophysiological Techniques Il. ~~133-142, 1984. 8. Conrad M. Adaptabiiig Plenum Press, New York, hdon. 1983. 9. Goldberger A L. Rigney D, West B J. Chaos and fractrals in human physiology. Scientific American, February, 1990. 10. West B J. Goldbenzer A L. Phvsioloav in fractral dimensions. Americ& Scies&75. pP35c365, ky-August 1987. 11. Goldberger A L. Rignery D, West B J. Chaos and fractrals in human physiology. Scientific American, February. 1990.
MEDKALHY-Es 12. Stewart I. Does God pisy dice? ‘lhc mathematics of chaos. Basil Blackwell. 1989. 13. Psaltis D. Brady D, Xiang-Guang Gu L S. Hdography in artificial neural networks. Nature 343, January, 1990. 14. Poincare. ‘Les problems de troid corps’ 15. Diagnostic Criteria. DSM-III-R. The American Psychiatric Association Press, 1987. 16. Melges F, Swartx M. Oscillations of attschment in borderline personality disorder. American Journal of Psychiatry. 146:9, September, 1989. 17. Gunderson J G. Borderline Personality Disorder. American Psychiatric Press, 1984. 18. Kernberg 0. Borderline personality organization. Journal of American Psychiatric Association. 15: 641-685, 1987. 19. Gunderson J G et al. The interface between borderline personality disorder. Joumal of American Medical Ascrociaticn, 20.
March 1985. Numberg H G et al. The comorbidity of Borderline Perscmality Disorder and other DSM-III-R Axis II Personality Disorders. American Journal of Psychiatry. 148: 10, 1991.
Deterministic Nonlinear Chaos in Brain Function and Borderline Psychopathological Phenomena N. PEDIADITAKIS 3123 Essex Circle, Raleigh, North Carolina 27608, USA
Abstract-There exists a fundamental overall property of the brain which monitors, modulates, and ensures a smoothness of function and which further determines elegance and grace in functioning. This property also imparts a quality of, or a sense of proportion among all other faculties of the brain. It is postulated in this paper that such a property/function, up to now almost taken for granted, is maintained/exercised by a nonlinear deterministic chaotic mode of brain function. If this is the case, borderline psychopathological phenomena, when they flare up, can be explained as resulting from sudden reduction of such a deterministic chaotic mode and the emergence of a pathological order, as the system becomes an oscillating one.
A poignant example of the absence of such a quality can be seen in a patient suffering from Parkinson’s disease, where the elegance and smoothness of movement is replaced by awkward, painful to observe, jerky, zombie-like motions of the sufferer (9). There is now suggestive evidence to support the proposition that this ubiquitous quality is mediated through a deterministic nonlinear chaotic mode of brain function (l-5, 7, 8, 9).
Introduction The brain normally exercises all of its functions with smoothness, subtlety, elegance and grace, as well as a sense of proportion. It accomplishes all of this while keeping the expression of higher functions more or less in balance along the median. A dancer, a diplomat, a person in courtship, an athlete in action, a fiddler, a person alone in contemplation of himself, a citizen discharging his duties, and a person at work all have something very important in common: as they exercise their individual skills, strive to fulfill needs, express their altruism, interact socially, contemplate and perceive themselves, foreplan, yield or restrain, negotiate desires or terms of endearment; all have a smoothness, a grace, an evenness-in-function, a sense of proportion and a restraint which prevents extreme oscillations to either side of the spectrum of what is considered appropriate, socially acceptable and personally comfortable. Date received 8 August 1991 Dale accepted 23 December 1991
Deterministic nonlinear chaotic dynamic systems and their properties
The concepts of the study of deterministic nonlinear chaos phenomena are only now becoming familiar in the behavioural sciences, so let us begin by defining and outlining our interpretation of such a concept and its ramifications. The term, nonlinear deterministic chaos, does not refer to the phenomena of total ran-
67
68 domness (entropy) treated by the Second Thermodynamic Law, but to an exciting new mathematical held of study of certain (constrained) random processes in dynamic systems. For the last decade it is becoming increasingly evident that such processes are abundant in nature and have recently been found involved in the physics of weather (from which the first perception of deterministic chaos was finally firmly established by Ed Lorenz in 1972, though previously suspected by A. Poincare (14) and others), fluid dynamics and, in increasing number, in biological system dynamics (5, 7, 10, 11). In this new science, deterministic nonlinear chaos can be defined as a stochastic behavior (Stohos = Gr. for ‘aim’) in a deterministic system (12). Stochastic behavior of a dynamic system is a behavior whose rules are loosely outlined or defined in a ‘more-orless aiming at’ fashion, as opposed to precisely laid rules having an ‘either-or’ nature. Traditional classical modeling of physical systems sought the latter kind of specificity, as well as relied on the view, based on the traditional scientific rationalism of the West, that ‘a system can always be understood by breaking it down and studying each piece’ (3). Such thinking and method actually obscured and hindered, rather than illuminated the understanding of the function of large and complex dynamic systems. Furthermore the existence of deterministic chaos affects the scientific method itself, since long predictions are intrinsically impossible, verifying a theory becomes a more delicate operation, relying on statistical and geometric properties rather than on detailed prediction (4). The uncertainty, not always the results of the coarse graining of measurements performed (Heisenberg Uncertainty Principle) although it often is, can result as well from the nonlinear properties of the system itself (1). Since deterministic chaotic systems generate randomness on their own, without the need of any external random input (4), it is impossible to predict ‘reality’ of their own, though the latter derives from the past. The deterministic chaotic mode, treated by the mathematics of nonlinear chaos, implies a consuained kind of randomness. Chaotic dynamic systems manifest, within limits and finite boundaries, properties that can be described by such adjectives, as insured flexibility, robustness, adaptability (2, 3, 4), stability (3,4)-since the system is able to absorb disturbances and randomness-novelty (4), variability of action, resilience and avoidance of entrainment (4). Since such characteristics are the very essence of the expression of human behavior, it is reasonable to suggest that deterministic chaotic mechanisms are of fundamental importance in global brain functions. In ad-
MEDICAL
HYFDTHESES
dition, there is actual evidence that such systems are indeed involved in brain function (4-7). Furthermore, the actual architecture of the brain with its dendrites is a fractal arrangement, There is another critically important phenomenon associated with deterministic nonlinear chaotic systems, that becomes of particular importance, in this context: such systems can be bimodal. If a critical threshold of loading is reached, or conversely, if the system becomes excessively ordered by exact rules or ‘either-omess’, then it can rapidly transition from a contrained chaotic mode with all its remarkable properties previously mentioned to that of a simple oscillating one or vice versa. This threshold can originate from within or be introduced from without, in the form of new information (increased randomness) or increased dimensionality (3) (how many factors make up the system, i.e. the reaches of the fractral dendritic neuronal arrangement of the brain). Fractrals, a term often mentioned in the study of deterministic nonlinear chaotic systems, can be defined as geometric constructs with self-similarity in any scale, as in clouds, mountains, coastlines, the bronchial tree of the lungs and, of course, the dendritic arrangement in the brain. Fractrals can also be considered as the footprints of the deterministic nonlinear chaotic system, as its functioning, then such fractral tracings are called strange attractors (2, 3). A purposely chosen illustrative example, quite removed from our field, which nevertheless gives insight and understanding of elegance and beauty of a chaotically regulated albeit constrained dynamic system will perhaps help to clarify our argument: we travel by car to work. We ease ourselves into the traffic and continue to drive together with other car drivers stochastically, i.e. with loose rules aiming at the direction of our job location, while all along we are allowed to move as others do, from lane to lane, behind or in front of other drivers, a little faster or slower, within the speed limit, as the occasion dictates, i.e. in constrained randomness. The boundaries of the road, direction of the traffic, and speed limit provide the deterministic setting. Thus the whole traffic is operating in a dynamic constrained chaotic mode. The traffic governed by deterministic chaos, even though it may not be the most efficient possible, is the most effective method of moving great numbers of cars, each having different destinations and timetables. The system has robustness and resilience, but if we tried to substitute with orderly controlled algorithm with its rules for maximum efficiency, the new system will soon bring the entire traffic to a standstill (gridlock) after wild, jerky swings/oscillations, i.e. pathological order.
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The entire system is boxed into its severe degree of orderliness of function. Conversely, if the number of cars on the road greatly increases or there is no longer a speed limit or greatly different types of vehicles, such as trucks, bicycles, tractors, even pedestrians are mixed in (i.e. increase in dimensionality), again the entire system will become increasingly vulnerable to an additional small perturbation (the so-called sensitivity to the initial conditions) and like the straw that broke the camel’s back, will soon push the system back into an oscillating jerky-mode with final gridlock. The traffic in Istanbul, Turkey, with essentially no traffic lights to control it, provides the amazed visitor with a convincing demonstration of an effective deterministic chaotic mode traffic process. Compare this with the frequently occurring gridlock of Western cities at rush hour, when exact, rigid rules are imposed at intersections by traffic signals.
Deterministic nonlinear chaotic system and brain function
So we propose that the presence of chaotic stochastic mode of mental functions, with its proposed constrained built-in randomness, provides smoothness of function, grace, subtlety, flexibility, effectiveness, even novelty, but above all, in this paper’s context, precludes (prevents) entrainment (1, 4). This deterministic chaos may underline everything that is most admirable in humans. From this point of view, we must now postulate that when borderline phenomena flare up, the condition can be explained as a mental disturbance, in which the chaotic stochastic mode of all the high mental faculties is temporarily and precipitously diminished or absent (entrainment). This phenomenon is hinted by M. Conrad in his statement: ‘It is conceivable that in the absence of chaos either a dull pacemaker activity will develop or highly explosive global neural firing would emerge’ (4). Thus, the system becomes orderly, rigid, ‘either/or’ and ‘boxed in’ and the faculties now tend to express themselves in violent perturbational/oscillating extremes of their functions and expressions which are slow to correct (pathological order). Thus, ironically, the word disorder’ in borderline conditions may be misapplied, since it is precisely the occurrence of ‘order’, which heralds the emergence of extreme oscillations of whatever high mental faculties are involved. This view runs counter to our training as clinicians and to conventional wisdom in medicine ‘which hold that diseases arise from stresses and pressure on an otherwise orderly system’ (11) and that ‘disease is traditionally defined as a disorder of failure of homeostasis
in a linear system’. By now ‘it is becoming apparent in several areas of medicine that an increase in “regular” behavior sometimes accompanies disease’ (11) with some types of heart attacks, epilepsy, muscular stress, cocaine intoxication, Parkinson, as Goldberger et al further stresses. This counterintuitive discovery may have broad and exciting ramifications and can be applicable in the understanding of borderline phenomena. The borderline psychopathological syndrome
The definition of Borderline Psychopathological Syndrome (BPS) by DSM=II- (15) is given as ‘a pervasive instability of...‘, implying an extreme oscillation from the median, even though not explicitly stated. In the literature, the description of BPS is accompanied often by terms such as ‘polarization’ (good/bad, all-or-nothing, now/never, within BPS) (17) or ‘oscillations of attachment’ (16) or ‘splitting’ (18). It is even proposed that such conditions ‘evoke polarized responses from the environment...‘. Patients are being seen as either deprived waifs or entitled bullies (17). Furthermore, as the phenomenon of pathological order is implicitly recognized ‘as a hierarchy from the healthiest to sickest, the number of distinct options becomes more circumscribed, and the subtlety and complexity of the personality becomes simplified’ (17). Actually to an experienced clinical observer the so-called Borderline Personality Disorder, as defined by the DSM-III-R Axis II, invariably co-exists with other personality disorders, especially of the B Cluster. Furthermore it occurs as a periodic ‘flare-up syndrome raising the very possibility’ that borderline personality disorder could only be a syndrome occurring periodically on a matrix of other personality disorders in accord with the view and the logic of this paper. A recent study (20) in its conclusions raises such a possibility. To even the seasoned clinician, dealing with BPS patients it is always startling and even amazing to witness the phenomenon of abrupt change of behavior, mood, attitude or stated reasoning of such a patient, under even mild pressure of the therapeutic interaction+onducted with delicacy and tact This is strongly manifested in the display of unbridled rage, only to be replaced by profuse apologies and pmstration. ‘Short fuse’ is the expression often used by many clinicians. Such rapid, abrupt, precipitous and catastrophic change, corresponds exactly with the properties of the proposed existence of a dynamic system, which previously operated in constrained nonlinear chaos (with all its already stated qualities contributing to the patients’ skills of humanity and grace), now
70 moves into that of an (rapidly) oscillating, ‘orderly’ system of ‘either/or-tress’. We can recall that with dynamic systems operating on deterministic chaotic mode, the former occurrences take place under the following conditions: 1) the system is too rich in randomness or dimensionally or the constrains are weakening or absent; 2) if conversely, the system is constricted with excessive orderliness (reduction of randomness) and rigidity. Bordertine psychopathological syndrome as an expression of an oscillating mode of deterministic nonlinear chaotic system
We now propose that borderline phenomena are the expressions of systems operating on an oscillating mode, i.e. in such conditions all mental functions to various degrees tend to express themselves in symptoms of oscillating extremes. Thus, in the patient suffering from BPS syndrome with regard to the ‘brain faculty’ of perceiving danger from within or without, the oscillating phenomenon shows up as uneasiness, tension, and insecurity on one side, versus fearlessness, unreasonable freedom, freedom in risk-taking, daring, and even recklessness on the other-within the time frame of minutes, hours or days. In the ‘faculty’ of dealing with foreplanning, scheduling, and sequencing, BPS manifests itself as ‘scatterbrainess’, slovenliness, neglect of personal appearance and personal hygiene on one side and then fastidiousness, over-orderliness, punctuality, and obsessive preoccupation with one’s own health on the other. In the faculty of thinking (aside from their inability to think in more-or-less fashion, perceiving everything in terms of ‘either/or-ness’), BPS patients exhibit psychotic-like distortions in perceiving, elaborating and interpreting reality at one extreme, versus overclarity, often remarkably creative thinking about novel alternatives at the other extreme. With regards to the ‘faculty’ of mood modulation (emotional tone), an often strong component of BPS (19) is cyclothymic (i.e. oscillating) expression of, on one side, black moods to be replaced by an unwarranted emotional effervescence. This cyclothymia is often present in addition to the chronic unhappiness, sadness, and low self-esteem, often expressed by borderline patients-understandably, since the patient is being buffeted by these oscillations, ‘akin to the buffeting of winds on an abode in a Kansas prairie’, as a bright borderline patient stated. In the ‘faculty’ of internalized ‘dos’ and ‘don’ts’ (perhaps corresponding to the Superego of Freudians) the BPS becomes manifested in disregarding morals, conventions and law (i.e. shoplifting) versus, often,
MEDICAL HYFOTHJSES
the presence of demoralizing guilt and shame. In the ‘faculty’ of coordinating needs in the context of social expectations and decorum (perhaps corresponding to the Ego functions of Freudians) the BPS patient exhibits extremes of impulsivity, rage, sexual promiscuity, opportunism and harshness on one side versus overdecorum, solicitousness, often abstinence and celibacy on the other. In the ‘faculty’ of forming intimacy and bonding/mutuality-in-affection, the normally subtle, finely turned interplay of approach in intimacy and equally imperceptible, subtle distancing are now replaced by extreme, crude, conspicuous oscillations between energetically and intensely shown closeness on one side and abrupt recoiling and distancing on the other (16). In the area of mental representation and attitude towards important people in the patient’s life, the phenomena show up as extreme idealization and admiration on one side, versus debasement, devaluing, and disdain on the other (splitting) (18). In social contexts, borderline psychopathological oscillating behavior is often misinterpreted as intentional manipulativeness, e.g. consider a person who exhibits unbridled and unwarranted rage for a few minutes and then returns a few minutes later, prostrating himself with self-deprecation and apologizes, only to go into another possible rage a few hours or days later. The normal person will interpret this behavior as intentional manipulativeness, instead of being the other leg of the oscillation. This interpretation will also be common among clinicians. Conversely, socially, appropriate, but extreme, behavior may be overlooked, being in fact the other leg of oscillation, or may even be considered as an ‘improvement’. The above partitioning of such ‘faculties’ is somewhat artificially drawn with much overlap, but the list is useful in helping us to discern the baffling intricacies of the borderline phenomena. Proposed causes triggering pathological or&r and oscillating phenomena
The BPS patient clinically appears to lack, in various degrees and combinations in their temperament, the components which constitute the so-called psychobiological attributes/constrains, such as relatedness, emotional connectedness. capacity for intimacy, empathy, and altruistic concerns. The deficits may be shared by the other disorders of Cluster B of the DSM-III-R, such as narcissistic and histrionic disorders (often patients in fact have multiple diagnosis for these disorders). The deficits may originate from birth or they occur developmentally by separate events or more likely are an interplay of both.
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If this is the case, one may venture to speculate that the deficits may deprive the patient of an important built-in behavioral guide/constraints for genuine social participation. The patient is now puzzled, at a loss, after resorting to a sham, bluffing behavior dictated by his intellect. Furthermore, the patient is now left without the emotional benefits, which derive from genuine social participation, and feels lonely, cut-off, ‘empty’, ‘numb’, bored, meaningless, with a chronic sense of ‘absence’-terms actually used by BPS patients themselves. They often rely on an enormous need of external reassurance of being ‘loved’ for their self worth and emotional ‘succor’. On the other hand, such sufferers may hold striking advantages in other areas of their life. As these patients are relatively not bound by the above mentioned constrains, they have now the freedom (i.e. an enlarged randomness and with relatively few constrains) to act creatively, able to see new patterns, be original, and deal in novelty. These ‘pathfinder’ qualities are often very much present in BPS patients and are shared by gifted and talented people. Lastly, deprived of the mentioned social emotional constrains, they feel uneasy, tense, and unbalanced. These intensities may very well act as the straw that breaks the camel’s back, heralding a shift of their phenomena and pathological order. From the sufferer’s point of view, once behavior is initiated, the patient ‘feels it’ as a cascading tidal wave and he is unable to restrain or modify it towards a reasonable middle ground. Thus, he finds himself in paraphora (Gr. for being carried away in extremes). One BPS sufferer described it as ‘a sense of going for broke, but unable to help it’, a kind of disorganizing hyperintensity aptly added. To the observing clinician, BPS manifests itself in many substitutions; impulsivity instead of appropriate restrained exuberance or circumspect; quick, mindless rage instead of reasonable expressions of displeasures; explosivity, instead of candor mixed with tact; harshness instead of civil remonstration; vituperativeness instead of polite explicitness; feelings of emptiness in place of clarity in perceiving one self in place and time; intense yearnings of total fusion with object of affection or total recoil, instead of elegance of approach and subtle courtship; obsequiousness instead of reasonable civility; overcompliante instead of respectful consideration of the rules; display of arrogance instead of self-assurance, etc.
Nature. In complex dynamic biological systems, especially relating to brain function, deterministic chaotic mode may have enormous significance with its intrinsic qualities. Its ability, within certain limits, to absorb randomness as well as generate randomness of its own and to promote stability, flexibility, robusmess, diversity, novelty, and by precluding entrainment, to create elegance, smoothness, and more-or-lessness of functions, finally allows it to maintain a sense of proportion. Disturbances in the brain may explain BPS and even other so-called ‘functional disorders’. Research in its intricacies and properties of such a mode is urgently needed, as well as finding ways to influence the components of such a system for the preventive and therapeutic benefits of the patients. Conclusion This paper proposes several new insights. Specifically it proposes the existence of an overall quality of the brain function responsible for smoothness of function, elegance, and delicacy, shared by all the faculties of the brain, not fully acknowledged previously. Furthermore, we have proposed a logical underlying mechanism based upon deterministic chaos in explaining such an overall quality. We have made a case that BPS has an underlying vulnerability due to the possible existence of an enlarged randomness of the deterministic chaotic mode and the diminishing or absence of certain important constrains relating to social aspects of humans, a situation that is most likely shared in part by gifted and talented people. We further propose that borderline phenomena, when the conditions flare up, are due to the sudden reduction of deterministic chaotic mode and the emergence of pathological order, thus the entire system becomes oscillating. The proposed view provides us with a new perspective and openings in understanding the development and mechanism of expression of borderline phenomena and perhaps even more importantly, of other so-called ‘functional disorders’, whose exact origin, cause and mechanism have stubbornly eluded us thus far. Acknowledgements I wantto express my warm appreciation and gratitude to Dr John Rather of Livemtore National Laboratoty for his help in advising me, editing the paper and offering me suggestions in how best to express the concepts outlined.
Discussion The discovery of the nonlinear, deterministic chaotic mode operating on complex dynamic systems is an exciting and important one. Such a mode has been found to have important application in many areas in
References 1. West J. An Essay on the Importance of Being Nanlinear. Springer-Verlag. ~~138. 140. 191-193. 1980. 2. Schuster H. Deterministic Chaos. Physik Verlag Weinheim,
72 ppl-3. 1984. 3. Crutchfield J et al. Chaos. Scientific American. oo3ti9.57. _. December. 1980. 4. Holdm V. Chaos. Princeton University Press, 1986. 5. Holdm A V, MuhanedM A. Chaotic activity in neural systans. Cybernetics and System Research 2 Elsevier. Amsterdam, pp245-50. 1984. 6. Laos in a three-variable model of an excitable cell. Physics 16-D. pp233-242. 1985. 7. The identification of deterministic chaos in the activity of single neunns. Journal of Electrophysiological Techniques Il. ~~133-142, 1984. 8. Conrad M. Adaptabiiig Plenum Press, New York, hdon. 1983. 9. Goldberger A L. Rigney D, West B J. Chaos and fractrals in human physiology. Scientific American, February, 1990. 10. West B J. Goldbenzer A L. Phvsioloav in fractral dimensions. Americ& Scies&75. pP35c365, ky-August 1987. 11. Goldberger A L. Rignery D, West B J. Chaos and fractrals in human physiology. Scientific American, February. 1990.
MEDKALHY-Es 12. Stewart I. Does God pisy dice? ‘lhc mathematics of chaos. Basil Blackwell. 1989. 13. Psaltis D. Brady D, Xiang-Guang Gu L S. Hdography in artificial neural networks. Nature 343, January, 1990. 14. Poincare. ‘Les problems de troid corps’ 15. Diagnostic Criteria. DSM-III-R. The American Psychiatric Association Press, 1987. 16. Melges F, Swartx M. Oscillations of attschment in borderline personality disorder. American Journal of Psychiatry. 146:9, September, 1989. 17. Gunderson J G. Borderline Personality Disorder. American Psychiatric Press, 1984. 18. Kernberg 0. Borderline personality organization. Journal of American Psychiatric Association. 15: 641-685, 1987. 19. Gunderson J G et al. The interface between borderline personality disorder. Joumal of American Medical Ascrociaticn, 20.
March 1985. Numberg H G et al. The comorbidity of Borderline Perscmality Disorder and other DSM-III-R Axis II Personality Disorders. American Journal of Psychiatry. 148: 10, 1991.
