    
|
|
15 February 2005 | Draft
Cardioid Attractor Fundamental to Sustainability8 transactional games forming the heart of sustainable relationship- / - Introduction IntroductionAs explored in an associated paper (Being Positive Avoiding Negativity: Management challenge -- positive vs negative, 2004), exhortations and injunctions to "be positive" are a common feature of some religious groups, in the development of selling techniques, in self-help therapies, in work group development, and in living with potentially fatal illnesses. These are seen as a means of avoiding or defeating negativity in those different contexts [more]. Here the focus is on highlighting the existence of a set of games, rather than a single game, that potentially are all aspects of a sustainable cyclic system that merits further attention. The paper explores, in the light of a general systems perspective, the possibility that this sustaining cycle can be understood in terms of the Carnot heat engine cycle and the Coaction Cardioid cycle of Edward Haskell (1972), further developed by Timothy Wilken (2002). It also explores whether any such generic cycle, relating "positive" and "negative" conditions, can also be related to the conditions identified by the Taoist Ba Gua mirror, and notably as a reflection of the cycle of processes described in Taoist spiritual disciplines. Interrelating positive-negative hybridsIt is very likely that it will prove fruitful to distinguish between several forms of "positive" and "negative" -- to recognize valid concerns but to avoid collapsing valid distinctions. A helpful pointer is provided by Edward Haskell (Generalization of the structure of Mendeleev's periodic table, 1972) in his work on the coaction cardioid (see below), as introduced by Harold Cassidy. Cassidy points out that:
Haskell applies this insight to a range of systems, notably in the natural environment (in Figure 1) but also in the social environment. In the case of the different kinds of relations between animals in an ecosystem, the following patterns then emerge -- of which 8 of the 9 are non-neutral. Note that there are variations in the teminology of biological interaction, notably differing from Haskell's usage [more | more]. The dynamics of each of the 8 relationships might be described as a "game", however asymmetrical or predictable the outcome (as with the "cat-and-mouse" game of predation).
Figure1 allows distinctions to be made between a form of "being positive" such as "symbiosis" in which there is indeed mutual enhancement. This contrasts with one such as "predation" in which one party (the controlling one) in a transaction prides itself on achieving a "positive" outcome at the expense of the other -- namely "feeding off" the other. This is distinct from the situation of "parasitism" where it is the latter party (the subordinated one) which successfully feeds off the former. The point about such a table is its merit in avoiding confusion between different forms of "being positive", some of which may be quite problematic because their "negative" aspects are camouflaged by appearing to borrow some of the desirable qualities of the mutuality of "symbiosis". Parasitism and predation are not relationships of mutually beneficial mutuality. One party effectively benefits at the expense of the other. Similarly what is might be considered most problematic is a form of (double) "negativity", typical of "synnecrosis" in the table, in which both parties lose energy through the interaction to the point of mutual destruction. But again this should not be confused with other hybrid conditions in which one or other may benefit unequally from the interaction. The table is an indication of the possible range of interactions between positive and negative as a form of psycho-social cybernetic system. The table is particularly significant in that, as with environmental systems, it is not the case that all "parasitism" or "predation" should be eliminated from the pattern of psycho-social interactions -- however much there is an expectation that the "Lion will lie down with the Lamb" in a form of symbiosis. There are in fact conditions under which even synnecrosis would appear to be appropriate -- as in decay processes necessary as precursors to regeneration. The real challenge is to ensure an appropriate systemic balance between the various forms of interaction - and, metaphorically, to avoid."throwing the baby out with the bathwater". Ordering classes of interpersonal relationshipEdward Haskell's insights have been very usefully (and extensively) adapted by Timothy Wilken (The Relationship Continuum, 2002) to an ordering of the spectrum of personal relationships: adversity -- neutrality -- synergy. Wilken equates "synergy" with "positive" and "adversity" with "negative" therefore pointing to the relevance of his adaptation to the preoccupation of this paper. Wilken's study reframes Haskell's above ordering in the following table, where "win" equates with "positive" and "lose" with "negative"
This raises the question whether a psycho-social system, any more than a biological one, can be based on expectation of a win-win outcome for all parties under all circumstances. How would life survive on the planet if there were not both "winners" and "losers" in the feed chain. The emphasis on "win-win" is an exemplification of the focus on the positive (cf Hazel Henderson. Building a Win-Win World: life beyond global economic warfare, 1996). There are all sorts of reasons why this is a useful notion, and why there is useful mileage in it. The Judgement Day of religions might even best be understood as the day when every profoundly held belief system gets to say "I told you so" -- the only twist being that we cannot understand how each needs to understand how they were wrong in order to accommodate the rightness of others. It is at this level (which in biblical terms "passeth all understanding") that win-win does indeed hold in reality. It also holds as a useful slogan. But it is not clear that it is with this notion that we can build a sustainable bridge between the ideal and the practical levels for the following reasons:
The point is that there are several understandings of "winning". People respond readily to the "gain without pain" interpretation. There is a danger that Henderson's book will be used as justification for this perspective. Although there may indeed be value in this, such appreciation will tend however to obscure other levels of interpretation which may well be where the real breakthroughs lie. Corresponding Taoist perspective: Ba Gua diagramThere is a striking similarity between Haskell's cybernetically-inspired presentation and a widely-known classical Taoist presentation of the 8 basic trigrams of the I Ching -- ordered into what is termed the Ba Gua (or Pa Kua) diagram. This diagram of 8 "houses", also known as the Ba Gua Mirror, is the basic tool for Feng Shui analysis, providing a practitioner with keys concepts with which to analyze a situation [more | more]. There are a very large number of (often highly ornate) circular representations of the diagram available as images over the web. The following is a purely schematic tabular version of that binary coding system. The full and broken lines signify positive and negative respectively, each trigram (in the cells of the table) therefore constituting the codification of a particular positive-negative (win-lose) hybrid.
Of greater relevance to the relationship between positive and negative (as fundamental to Taoist insight) is the use of this Pa Kua framework as one of the Chinese internal personal development systems intrinsic to qi gong breathing exercises, meditation and a particular martial art: Pa Kua. The martial art variant of Pa Kua is known for its evasive footwork, including the characteristic circle walking and the spiraling, coiling, drilling, twisting, and spinning movements, combined with powerful palm heel strikes. Pa Kua is as much a martial arts combat style as it is a martial art taught for its health benefits. There is every possibility that the dynamic relationship between expressions of "positive" and "negative" in an interpersonal transaction can be usefully understood as a martial art. Metaphorically, "evasive footwork" is not something that is totally foreign to dialogue situations! The suggestion above that "being positive" might be understood as one form of form of game, from a transactional analysis perspective, can now be reviewed from a Chinese perspective where it is both game and martial art. It may well be that the discipline of Pa Kua facilitates the emergence of skills in dialogue, or in responding to all complex combinations of positive and negative, winning and losing. In the Pa-Kua approach to Feng Shui, the compass is divided into eight directions, each of which is depicted by a trigram (as above). Each of these directions has a different significance, depending on the individual. Four of those directions have a "positive" implication for the person, while the other four have "negative" implications. The eight directions can be briefly summarized as follows:
There is a vast body of Chinese literature exploring the philosophical and practical implications of this and related schemas -- and their extension to reflect finer distinctions in the pattern of psycho-social change through 64 hexagrams (Transformation Metaphors derived experimentally from the Chinese Book of Changes (I Ching) for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997). Its merit is that it reframes the simplistic polarization of "positive" vs "negative", extending it to include a complex set of hybrid variants that are inadequately recognized by injunctions to "be positive" or "avoid negativity" (cf Discovering Richer Patterns of Comprehension to Reframe Polarization, 1998). Given the theme of this paper, and the rich Taoist perspective, there is a certain irony to the widely cited point that the Chinese symbol for "crisis" is a compound of "danger" and "opportunity" -- "negative" and "positive". This can readily be used to exploit a crisis inappropriately (cf Victor H. Mair. How a misunderstanding about Chinese characters has led many astray, 2005). Perhaps the most dramatic example of such exploitation was the UK government communications specialist who advocated releasing controversial government policies on the occasion of the 9/11 crisis -- creatively taking the opportunity to ensure that the public would be otherwise distracted [more]. Transcending dualismImplicitly recognizing the function of different systemic conditions identified in such tabular presentations, Bob Rusbasan (In Praise of Negativity, 26 September 1999) argues:
In envisaging ways of transcending positive-negative duality, it is worth noting that negativity tends also to be associated with "dualism" and adversarial "polarization", whereas it is then argued that "non-duality" is associated with being positive. Many disciplines of spiritual experience (whether Eastern or Western) distinguish between:
From the Eastern educational perspective of the Ananda Marga Gurukul Network, Ac Shambhushivananda Avt (Cardinal Human Values, 2002) argues that core values are primarily of two types: vidya-related (those which lead to knowledge of divinity), avidya-related (those which keep people tied to a material perspective, ignorant of divinity):
It might be usefully asked whether both a via affirmativa and a via negativa are necessary to comprehension and response to any complex and challenging relationship -- not just to that of "God". What indeed is the "healthy balance" between the countervailing forces basic to any form of sustainability? The poet John Keats (Negative Capability, 21 December 1817) is renowned for recognition of the essence of maturity in terms of "negative capability". This is the capacity of "being in uncertainties, mysteries, doubts, without any irritable reaching after fact and reason". Dynamics of a sustainable cycleIf it is indeed the case, as demonstrated by Haskell in the case of ecosystems of animal species, that sustainability is achieved by an appropriate mix of of positive-negative (win-lose) conditions, the question is how this mix "works" -- and why the most appropriate system is not entirely based on a "win-win" condition. One insight is that the win-win condition is merely one particular dynamic, a game, that is sustained within a set of games that are mutually dependent for the viability of the system as a whole. Elsewhere (Comprehension of Appropriateness, 1986) it was suggested that the interdependence of these "game" dynamics was expressed through a cycle linking them together. Understanding how such cycles of contrasting phases accomplish effective transformative work in society may be facilitated by a thermodynamic metaphor. The Carnot reversible cycle of heat and work, basic to the operation of any heat engine. A heat engine is a thermodynamic system that can undergo a sequence of transformations which ultimately return it to its original state. The Carnot cycle involves four successive and contrasting operations:
The notion of a work cycle is introduced here because it is relatively clear that a living system cannot exist in a condition of stasis. Living is synonymous with one or more active work cycles through which energy is moved through feedback loops to ensure integrity in the moment. The most obvious in mammals may be the respiratory cycle. This energy may take the form of attention -- even vigilance. The heat engine is driven by a particular difference between two conditions -- to produce mechanical work by carrying a working substance through a cyclic process. In the conventional heat engine this difference is temperature. Heat is transferred to the sink from the source, and in this process some of the heat is converted into work. The suggestion here is that from a general systems perspective this may be generalized to apply to other forms of difference and other forms of work -- making it potentially relevant to new insights into socio-economic cycles necessary for sustainability (notably in the light of theory regarding the maximum efficiency of a Carnot cycle engine). The perceived difference between "positive" and "negative" may also drive such a cycle, possibly at an axiological level. Psycho-social heat cyclesA variety of heat engines have been constructed. The question to be asked is whether an analogous variety of "heat engines" could be usefully recognized in psycho-social systems. For example, might the variety of such cycles correspond to the variety of metaphorical uses of "heat" currently recognized:
Of relevance to such explorations would be Marshall McLuhan (Understanding Media, 1964), given the distinction he explored between "hot" and "cool" media (cf Gordon Gow. Thawing out Media: Hot and Cool, 1995; G E Stearn, McLuhan: Hot and Cool, 1967). A hot medium is one that extends one single sense in high definition. Hot media are, therefore, low in participation, and cool media are high in participation -- requiring completion by the audience. Also of relevance is the work of Orrin Klapp (Opening and closing: Strategies of information adaptation in society, 1978). The concept of a work cycle is basic to thermodynamics -- and is exemplified by the Carnot cycle. Elsewhere (Composing and Engendering the Future, 2001), it was used to explore whether this provides insights into a necessary dynamic relationship between past, present and future in terms of the nature and focus of attention. This would be the challenge in a cyclic shift between various positive-negative combinations. Is there a sense in which living embodies some such cycle -- of which the the heat engine is merely a limited material analogue? The heat engine cycle does indeed have to relate past, present and future in order to sustain its activity. The insights of such circulation may also be evident in the psycho-social attraction of certain pattern dances -- presumably providing some kind of time-binding resonance transcending past, present and future for participants. Disrupting the cycleAny attempt to isolate and prolong unduly the most effective work phase simply jeopardizes the ability of the engine to continue operating -- as is illustrated by the value of fallow phases in crop rotation. This may also be true of the "win-win" condition. It is then quite inappropriate to view the non-work phases as "inefficient". The operation of a task force (or meeting) of individuals with distinct functions may also be interpreted as involving a cycle of phases in which each function enters and leaves the limelight in turn. This is best illustrated by the results of research by R Meredith Belbin into the roles required for good teamwork. These have been labelled as: chairman, company worker, completer-finisher, monitor-evaluator, plant, resource investigator, shaper and team worker. A preponderance of any one role type, especially the "most productive", jeopardizes both the appropriateness of the group's work and its ability to renew itself and continue functioning. The different levels of attention required in discussing the relationship of distinct policies to policy cycles may be illustrated by the metaphors of walking and dancing. In walking the right and left foot are moved forward alternately, shifting the weight of the body from one to the other. Although in places of difficulty attention may be focussed on one foot to the exclusion of the other, the body can be more satisfactorily moved forward by focussing on the process of walking, namely on the alternation between the two contrasting positions. In a 2-party political process however, there is a necessary struggle between the "right" and the "left", with no institutionalized awareness of what is achieved by the process of alternation between them. There is little recognition of when it is appropriate to relinquish a policy (increasingly framed as "negative") in favour of an alternative (increasingly framed as "positive") and then renew it to fulfil a new role. This may perhaps be more accurately compared to the preoccupation of a drunkard, or a spastic, with the forward movement of one leg (temporarily forgetting the need for the other). Appropriateness of the 1st order may be compared to movement of a foot, whereas 2nd order appropriateness may be compared to the process of walking. Higher orders of appropriateness may be compared to dancing and to a cycle of dances. It is the movement between the steps, and the manner in which they are ordered, which renders the dance meaningful. Focusing attention exclusively on any individual step prevents the rhythm from emerging and thus obscures the meaning of the dance. It is the rhythm which guides the self-organization of a dance, based on the execution of the individual steps, whose importance can in no way be neglected. The test of the appropriateness of any new mode is whether it embodies a more "seductive" pattern in the sense of Jacques Attali (Noise: The Political Economy of Music, 1985). In terms of 2nd order appropriateness current policy initiatives -- and narrowly focused exhortations to "be positive" -- may be compared to a drunkard's walk, a monotonous dance or, more dangerously, a lock-step march. The past century has provided widespread familiarity with engines, notably combustion engines in motorbikes and other vehicles. The operation of the piston cycle has entered collective consciousness in many ways -- as well as the distinction between 2-stroke engines, 4-stroke engines, irrespective of the number of cylinders. This suggests a line of inquiry as to whether thinking itself can be understood as operating in cyles that might be usefully modelled by such engines for many people. In this sense a basic cycle would alternate between the extremes of any form of polarized thinking -- with each extreme providing a turning point. One might be associated with the charge that drives the cycle. Clearly this might be understood as a cruder pattern than that associated with multiple cylinders -- if their operation could be integrated to reinforce a common rotation. Of special interest in this respect are rotary engines (cf the Wankel rotary engine). Related to such understanding of an engine is that of gearing whereby rapid rotation is translated into slower and more powerful rotation that can perform certain kinds of work. Many forms of thinking might be associated with rapid cycles. These need to be geared down to speeds that can mesh with operations in the material world (see Conceptual Birdcages and Functional Basket-weaving. 1980). This challenge might be seen in relation to that of gearing down principle to practice. Coaction cardioid: interrelating the "games"As noted earlier with regard to Figure 1, Haskell's particular synthesis also highlighted the interrelationship of the different conditions through a cycle -- described as a coaction cardioid. This work has been extensively elaborated by Timothy Wilken (UnCommon Science, 2002). In terms of Haskell's generalization of the periodical table pf checmical elements, the cycle is the generally heart-shaped path of the radius vector in his Periodic Coordinate System. This system provides a symbolic representation of the nine possibilities whenever "parts" relate with other "parts" to form "wholes" or unities, and whenever choices are made by the "parts" within the "whole" or unity. As admirably explained by Wilken (UnCommon Science, 2002, pp 141-145):
The initial conditions of X and Y can in each case also be represented by the area of circles.
The cardioid cycle is then defined in relation (as seen in the figure below) to a circle of unchanging order (or entropy). The coaction cardioid turns into the zero-zero or scalar zero circle in the region of predominantly negative coactions (inturning, in Greek, is entropy) -- toward Alpha (in Teilhard de Chardin's terms). It turns out of the circle in the region of predominantly positive coactions (turning out, in Greek, is ectropy) -- toward Omega (again in Teilhard de Chardin's terms). The interactions, or "games", which reduce the degree of order (increasing entropy) are then within the circle, whereas those that increase the degree of order (decreasing entropy) lie outside the circle. The cardioid describes the "path" between these different conditions that is effectively associated with the sustainability of the system.
With respect to this geometric representation of Haskell's earlier tabular version (Figure 1), Harold Cassidy notes:
Mathematical functions of the cardioidAs noted by Wilken (UnCommon Science, 2002, pp 159):
Mathematically, as a curve, the cardioid has properties that distinguish it in terms of membership of an exceptional variety of remarkable curves:
With respect to its generation:
(see also cardioid enveloped by circles, cardioid as envelope of tangents, cardioid sliding inside nephroid, cardioid-evolute and involute) [more | more | more] It notably figures at the centre of a Mandelbrot set . In the following argument, for the sake of simplicity, the cyclic nature of the cardioid is emphasized. A more interesting and relevant agument would need to be made in terms of the role of a cardiod as a strange attractor -- notably in the light of its emergence in relation to the Mandelbrot set [more]. In such a set the main cardioid part contains orbits with an attractor of period 1. However there are buds on the buds ad infinitum, all following that same structure. Then the ends of all these double and re-double, eventually ending in a spike. Every spike is composed of tiny Mandelbrots, similar to the first -- but each has all of its parts with periods multiplied by m, the period in its own cardioid body [more | more]. The role of the cardioid in the Mandelbrot set is explored separately ( | ||||||||||||||||||||||||||||||||||||||||||||
