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1980
Liberation of Integration, Universality and Concordthrough pattern, oscillation, harmony and embodiment- / - Originally prepared for the 5th Network Meeting (Montreal) of the United Nations University's project on Goals, Processes and Indicators of Development (GPID) as a contribution to the discussion on integration of the findings of the project.
IntroductionThis paper is an exploration of the range of ways in which "things can be put together" or conceived as being interrelated. In undertaking this it is hoped that widely advocated approaches to integration may be shown as simple options in a context of subtler, more complex possibilities, many of which are essentially more "elegant", if only in the mathematical or topological sense. It is possible, however, that this elegance is also an indicator of vital properties of symmetry, harmony and balance, which are desirable in any domain in which integration is sought and even necessary for that integration to be brought about. The domains in which integration is of considerable concern may be indicated by reference to the sub-projects of the UN University's project on Goals, Processes and Indicators of Development of its Human and Social Development Programme. For example, how are the different "models" implicit within the following sub-projects to be integrated in each case, especially when there is some degree of incompatibility between them:
In each case alternatives can be formulated in the light of different patterns of priorities. The question is how such alternatives are to be reconciled in practice in a real world. Integrative minimalismAlthough integrative skills may be successfully applied to a situation, their elusive nature can be partially defined by the ways in which such skills may fail or be used to conceal abuse. The following approaches to integration or synthesis stress the manner in which an impression of integration can be created even if little is achieved. It is partly base on material assembled in a section on "Integrative Concepts" in the Encyclopedia of World Problems and Human Potential (2) which identifies some 620 such concepts. The bibliography therein has recently been complemented by a bibliography of 1600 items on "the relationship between and the structure of science, philosophy, and social/political organization" (3).
Approaches to integration1. Integrative skillsAlthough during meetings there is much discussion of "integration" and there are many attempts at producing a "synthesis", the skills called upon seem to be poorly understood, hard to communicate, and very difficult to put into practice. It is therefore useful to note very different domains where integrative skills are practice successfully, even if it is not immediately clear what can be learnt from them for use in a meeting environment.
2. Conventional integrationThe most systematic approach to interdisciplinary integration is probably that of Erich Jantsch (4), as outlined in Annex 1. There are two extremes in the conventional approach to "integration":
The first approach tends to be unsatisfactory in an increasingly complex society in which undesirable conflict does result from incompatibilities between the models. The second tends to be unsatisfactory, either because of conflict arising from what is excluded, or because such fusion is quickly perceived as a constraint on further development if the model is successfully implemented. The more successful it is, the more its proponents will resist any further reconceptualization. Such models do not acknowledge their limitations, the need for their limitations, and the need for their eventual demise. They are conceived as a "final solution" detached from the processes which brought them (temporarily) into being. 3. Ecological integrationAs a first step in the search for subtler patterns of integration we may consider a situation exemplified in ecological systems although typical of more complex organized systems. Consider two species in an ecosystem as being analogues of two conceptual models in a psycho-social system. The processes that characterize species X may, in the interaction with Y, be accelerated or in some way enhanced (+), or may be unaffected (0), or may be decreased (-). The same is true for species Y. When such possibilities are cross-tabulated, it becomes evident that there are nine qualitatively different coactions. Ignoring the (0,0) coaction, the remaining eight are as follows: + + symbiosis - - synnecrosis
+ o commensalism - o amensalism
+ - parasitism - + predation
o - allopathy o + allotrophy
This scheme was elaborated by E Haskell (5) who made it into the basis for a periodic coaction coordinate system. It provides a rich method for exploring species interaction. Under certain conditions it may be desirable to view the relationship between models in this light. Note that in an ecosystem an interaction with a "negative" component (e.g. parasitism) is not necessarily "bad". It may be part of a complex interspecies web or merely the corrective mechanism for a temporary imbalance between species. For the relationship between species is of course not rigidly determined. Species rise and fall numerically in relation to each other. Homeostasis is achieved by compensating patterns of oscillation around a condition of dynamic equilibrium. 4. Meta-modelsIt is interesting that few "meta-models" even attempt to handle the relationship between models. Each of the latter tends of course to claim some form of exclusive validity viewing any alternatives as heretical, sub-optimal, or distortions of the most realistic. It could be said that, in comparison with the ecosystem case, models are defined at the "species level" and that few, if any, have been successfully defined at the "ecosystem level". The "species level" provides a distinct reproducible pattern of organization, whether in the case of species or of conceptual models. The presence of other "species" necessarily gives rise to an inter-species dynamic which is associated with a logical hiatus, since there is a distinct logical discontinuity between any such species-level perspectives. As will be discussed further below, it would appear that the ecosystem level logic cannot be adequately contained or expressed through a separate logic, it must necessarily be modelled by the a-logical pattern of inter-species dynamics. Integrating incompatibles1. Use of incompatible modes in practiceBefore going on to a more systematic exploration of integration patterns, it is useful to note down some examples in which practical results are achieved by "oscillation" between essentially incompatible or mutually unacceptable modes:
Note that in each case the transition from one mode to the other is through a decision governed by qualitative judgemental factors combining art and science beyond the realm of simple models and logics. Within some oriental cultures the ability to move smoothly between two such essentially conflicting modes is modelled by the circular process of inhalation and expiration. For this reason much emphasis is placed on eliminating defects in this process through breathing exercises for the individual. (But, strangely, never for a group). 2. Model mixes in space/timeIt is important to recognize that integration can be achieved in space and/or time. For example:
Note that it is unlikely that these two limiting cases are independent of one another. It is more probable that they engender each other in space- time as do rotation and revolution in any solar system model, for example. In fact such spin and orbital motions are part of a set of six basic motions which also includes: expansion-contraction, torque, involuting- evoluting, and precession (6, point II, 400.654 and II, 986.857); These may suggest other forms of integration in space-time, as well as introducing the less-evident (spiral) evolutionary movements. As a complete set, each of these "motions" is necessary to the existence of the others. Further possibilities for integration are indicated by the following:
Patterns and rhythmsThe question now is whether we can identify the nature of the series of patterns or rhythms in the light of the first few members of which we are more or less aware.
The simpler possibilities for N elements are clarified in Annex 2. Note that the "relationship" indicated there by a line could, in binary terms, be considered either as one of "compatibility" (space) or "consonance" (time), indicated by "-", or as one of "incompatibility" or "dissonance", indicated by " - ". Integration indicated by the degree of symmetry which in the time case is related to recurrence. Annex 2 only focuses on patterns which are significant in 2 dimensions. These patterns are in fact those which have been the focus of attention in the classic communication net experiments (7). A valuable approach to more complex patterns, particularly in relation to time, are the Chladni figures visualized by vibrating powders on a metal sheet (8). Another source is the range of progressively more complex patterns from graph theory (9). Reference should also be made to Johan Galtung's suggestions regarding the use of graph theory (10). In previous papers (11, 12) the limitations of the 2-dimensional approach have been criticized as a preliminary to considering the significance of the simple 3-dimensional patterns, especially in relation to tensegrity. The latter achieve stability as patterns of oscillation around a dynamic equilibrium condition. The concept of oscillation will now be considered in more detail. Oscillation1. Conventional exampleThe simplest example of oscillation occurs with 2 states (models) between which the system moves. A number of examples were given above, of which the most typical is perhaps the classic 2-party political system. Oscillation as a phenomenon has been extensively studied in physical and electromagnetic systems where it is an aspect of vibration and wave motion. Such studies should suggest interesting questions for oscillating in psycho-social systems. For example:
2. Psycho-social interpretationA useful way of describing the periodic behaviour of simple harmonic oscillation is to employ the sine curve whose complete cycle thus represents the complete oscillatory cycle. This may also be viewed as a projection of motion in a circle. (Diagram) a, c, and e = points of maximum kinetic energy b and d = points of maximum potential enrgy (max. displacement) In the psycho-social case, it is at point (a) that maximum momentum has been acquired towards the realization of Model A. At point (b) the "maximum distortion" of the system in this direction has been achieved and a restoring force enters into play which progressively phases out Model A, such that at point (c) the maximum momentum towards the realization of Model B has been acquired. This in turn achieves maximum "distortion" at point (d) when a reverse restoring force enters into play. It is most important to note that within the Model A perspective, for example, there is no way in which the reversal at point (b) can be logically acknowledged or accepted (except possibly as a temporary set back). Model A necessarily strives to extrapolate along the curve (a) - (b), presumably to some static "plateau" curve of "A-perfection". The increasing momentum from points (b) through (c) must necessarily be viewed by the proponents of Model A as the proliferation of unresolved problems and "irrational" tendencies, which are seen to achieve their maximum deployment at point (d). Obviously the proponents of Model B see this sequence in exactly the opposite light and would strive to extrapolate along the curve (c) - (d), presumably to some static "plateau" of "B-perfection". The cycle therefore involves two "inversions" of logic (comprehension discontinuities) between the two models which are incompatible and as such mutually incomprehensible (except that what is partially "comprehended" is used to fuel the antagonism between them). This "irrationality", as related to the circular projection above, recalls the manner in which mathematicians have succeeded in interrelating positive and negative "irrational" quantities by use of the Argand circular diagram. It is this inability to handle curvature which traps the proponents of each model in the linearity of whatever portion of the curve they are associated with. It appears linear, just as the earth appears flat to a rational observer insensitive to longer range phenomena. Nevertheless, despite the mutual incompatibility, of the models, in the real-world dynamic situation each is effectively defined in terms of change to or from the other. 3. "Multiphase" oscillationsThe argument above has focused on two extreme states (models) between which oscillation occurs. As indicated in the discussion of Annex 2, combinations of states may be envisaged between which oscillation can take place. Some of these are "damped" as discussed in a subsequent section. In a three phase oscillation, for example, Model A would be replaced by Model B, to be replaced by Model C, replaced in turn by Model A. Namely a triangular configuration. Many such configurations are possible and can be represented by 2- dimensional configurations. Note however that the longer the chain of models in a circular sequence, the more difficult it is to comprehend the sequence as a whole. An interesting example of a 64-phase sequence is that of the the sequences of changes associated with the Chinese I Ching (or Book of the Changes). It is unusual in that a justification for switching from one model to the next is given, thus implying a holistic perspective "meta" to that which is explicit. 4. Coupled and damped oscillatorsWhereas the previous section focuses on a succession of models, it is also possible to envisage, for example, the simultaneous presence of 3 oscillating systems A/B, C/D, and E/F. If the oscillations of one affect another then the two are coupled. Such coupling may have amplifying or dampening effects. A system set into oscillation by some initial displacement will not continue to remain so indefinitely unless energy is supplied from some external source. An oscillation cannot create energy. The oscillation gradually dies away and is said to be damped. The decay will be slow if the mass of the oscillator is large, and slow if the initial frequency is high. An oscillator absorbs energy from a source at maximum average rate at the resonance frequency, namely the frequency at which it prefers to oscillate. At this frequency it loads the energy source to maximum extent. Dampening effects may be counteracted by coupling with other oscillators as note above. Three-dimensional configurationsIn Annex 2 the focus is on 2-dimensional configurations. But even in the simplest 2-phase case, the existence of that oscillating system is only possible by virtue of an appropriate contextual system within which it is embedded. (e.g. attachment of spring and gravitation governing movement of a mass). If the oscillation is described in the form of motion in a circle, the question to ask is how that circle is "balanced" when considered as a rotating wheel. For either the wheel is unrelated to anything else (or includes everything), or it must be joined to its environment in some way, especially if energy is received to maintain the oscillation. But, just as the models associated with each phase of the oscillation are insensitive to the cycle as a whole, any cyclic perspective is equally insensitive to the forces required to maintain the cycle in stable relationship to its environment -- namely to compensate for the instabilities associated with and generated by its existence. If the configuration of such contextual forces is rendered explicit, and integrated with the 2-dimensional cyclic configuration, one probable result would take the form of a tensegrity (12, 13). This may be considered as a spherical pattern of coupled oscillations (usually three or more interwoven cycles). In string-and-stick models of tensegrities, for example, when a stick is displaced by application of stress, the whole system undergoes symmetrical modification to accommodate the local movement. The system's symmetry is not deformed; the system expands as a whole or contracts as a whole. Ability to respond as a system means that local stresses are being uniformly transmitted throughout the structure, and uniformly absorbed by every part of it. We have here a classic case of synergy; behaviour of whole systems, unpredicted by knowledge of the parts or of any subset of parts. A complex tensegrity is never quite still, however lightly the tendons are stretched. There will always be minute oscillations, tiny stick displacements at the order of magnitude where elasticity multiplication is truly enormous and compensating forces have enormous advantage. The equilibrium point "is that ideal condition of rest which nothing real ever attains, and about which a tensegrity in particular dances an eternal jig of pre-Socratic derision" (14, pp. 12-19). Organization of time1. Time-bindingThe previous sections have considered progressively more complex ways in which oscillations can be interrelated into some "macro-pattern". The progression has been guided by what is known about the organization of space, given the argument of Annex 2 that these indicate equivalents for organization over time. Note that this progression has in effect moved from:
The question is now whether more clarification can be obtained from the manner in which time is organized. The above argument has not focused on the possible distinctions between oscillations, and yet oscillations organize time in different ways depending on their characteristics. Some of these ways may be more significant and may thus indicate opportunities opportunities for more viable temporal configurations of models -- possibly with corresponding simplifications for configurations in space. The point of departure is the recognition that oscillation "organizes" time by determining a characteristic complete cycle. This is composed of both the "incompatible" half cycles of the simple example discussed earlier. It encompasses the incompatibilities typified by polarized perspectives only capable of recognizing/accepting the swing of a pendulum in one direction (or the other). It is the periodic complete cycle which characterizes the organization in time. In developing the argument, oscillation in psycho-social contexts may be considered:
Since the micro-historical cycles are more easily perceptible and appear less abstract than the macro-historical, the remaining argument will focus on them. In fact of course, "macro" cycles with periods of decades or centuries could also be subject to the same approach (cf the work of Pitrim Sorokim). Relationships between micro and macro cycles will be explored in a later paper. Since the human perceptual apparatus organizes ("integrates") oscillations with considerable sophistication in the process of hearing, this argument will focus on indications suggested by musical sound. Analogous arguments could be developed on the basis of the organization of oscillations in the process of seeing colours, but since sound can be discussed with less ambiguity, and with more precise exploration of possibilities of integration, this is to be preferred. (On colour, see: Johannes Itten. Art de la Couleur. Paris, Dessain et Toira, 1974) 2. Oscillation and musical soundThe perceptual apparatus distinguishes sounds as noise or tone. Noise is usually identified not by its character but by its source. Tones are recognized as being more independent of their source, are more organized, and as such are more amenable to integration into musical compositions. The choice of sounds for music making has been severely limited in all places and periods by a diversity of physical, aesthetic, and cultural considerations. Tones are generated as oscillations. Within this context it is now possible to consider how a series of events involving the interactions of Model A and Model B -- a characteristic defence-attack, challenge-response sequence in any diplomatic incident, for example -- might be usefully perceived as a particular "tone". The suggestion is that there are characteristics which enable events to be recognized as part of a familiar pattern. When such characteristics cannot be recognized, a succession of events is considered as incidental/accidental "noise". When the events do fall into a recognizable pattern, this "tone" can then be used as a higher unit of analysis through which the development of the stream of events can be integrated for comprehension. The individual events generated by incompatible models responding to each other are thus encompassed by a pattern usefully characterized by a tone. The tone is independent of the particular event sequence which functions as an "instrument" to render it perceptible. Clearly the conventional approach in society is to recognize events generated by an opposing model and to respond with a counter-event governed by one's own model. The "tone" is not perceptible at this level. The question is how to create "instruments" (meta-models?) which could generate tones, in order to move beyond the present subjection to the essentially uncontrollable reactive dynamics of event-level interaction. If society could discover when particular tones are an appropriate response to circumstances, it would no longer need to be torn by the dualities of event-level interaction. Note however that event patterns are still required, since it is through them that society functions. It is their status which is dramatically changed. In this sense "planning" becomes "composition", which works not by using a set of events to achieve something but by using tones (namely event/counter-event patterns). 3. Music"Music is time made audible" (Susanne K Langer). Perception of music depends largely on the ability to associate what is happening in the present with what has happened in the past and with what one expects to happen in the future -- whatever the probability that the expectation will be fulfilled. The previous section clarified the integration to the tonal level. It is useful to consider three dimensions of time as structured by music for comprehension (noting that recent thinking contests Einstein's one- dimension concept of time). Within this context it is again possible to consider how models in a psycho-social system might be integrated.
Four basic types of musical form are distinguished in ethnomusicology: iterative, the same phrase repeated over and over (as in some chants); reverting, with the restatement of a phrase after a contrasting one (as in sonata-allegro, aria, and rondo refrains); strophic, a larger melodic entity repeated over and to different strophes of a poetry text (as in hymns, traditional ballads, and instrumental variations); and progressive, in which new melodic material in continuously presented). But what is the significance of tone? 4. Significance of toneAll sound is composed of a complex of oscillations of a certain frequency (which determines the wavelength). Tones are characterized by four attributes revealed in their oscillatory wave form:
Most musical tones differ from an ideal single oscillatory wave form. Any material undergoing oscillation imposes its own characteristic oscillations on the fundamental oscillation. The material would probably oscillate in parts as well as a whole. These partial wave forms bear harmonic relationships to the foundational motion that are expressible as simple integer frequency ratios of 1:2, 3:4, etc. One way of expressing this is to say that half the body (e.g. a stretched string) is oscillating at a frequency twice as great as the whole; a third of it is oscillating at a frequency three times greater, etc. Tones are in practice composites of such "overtones" which are ignored by the untrained car. It is however the presence or absence of overtones and their relative intensities that determine the timbre of any tone. Tone is primarily characterized by pitch, or frequency of oscillation. Man's aural perception of pitch is confined within a span of roughly 15 to 18,000 cycles per second, with 440 cycles per second having been adopted as the middle point on the keyboard. It is now useful to ask the question what is the frequency range of psycho-social event-pair patterns to which man is sensible? What are the "tones" he can detect? Clearly there are some event cycles whose frequency is so low that man cannot be directly sensitive to their cyclic nature. Detecting the cyclicity of such phenomena is anal;ogous to detecting the curvature of the earth's surface. The cycle of a human "generation" is barely perceptible as such, and even a year or a month are long cycles to many. At the other extreme, one indicator is the period of seconds associated with fast conversational repartee. Even more rapid would be the mind "experiments" of protagonists in any game or fight in which each runs through the action options open to him and the probable responses of the adversary (e.g. chess, fencing, business negotiation, etc). Cellular processes in man are however beyond the range of his sensitivity. In this light is it possible that psycho-social functions are each associated with a characteristic event cycle frequency? And, when such functions are activated in a particular case, is this frequency accompanied by the presence of harmonic frequencies, namely associated functions? Before clarifying these possibilities, it is necessary to consider the whole question of harmony as it has been elaborated for music. 5. HarmonyMusical sound is usefully regarded as having horizontal and vertical dimensions. The horizontal aspects are those considered so far, namely those that proceed in time. The vertical aspect is the sum total of what is happening at any given moment. This includes the result of notes that sound against each other in counterpoint. In the case of melody and accompaniment, it includes the underpinning of chords that the composer gives to the principal notes of the melody. In music, harmony can be broadly defined as the sound of two or more notes heard simultaneously. In practice this can include notes sounded one after the other in cases when the ear creates its own simultaneity and perceives the harmony that would h |