Challenges to Comprehension Implied by the Logo
of Laetus in Praesens
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Threshold of Comprehensibility: a fourfold minimal system?

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Part 4 of Development through Alternation. Augmented version of a paper originally prepared for Integrative Working Group B of the Goals, Processes and Indicators of Development (GPID) project of the Human and Social Development Programme of the United Nations University (UNU). This document was originally distributed as a separate monograph in 1983. The paper provides a structure linking reviews of alternation as it emerges in studies from a wide range of sources. The paper is in 9 separate parts [searchable PDF version]

0. Introduction / Abstract

1. Monopolarization
1.1. Questionable answers
1.2. Forms of truth
1.3. Accumulative answers
1.4. Developing a new "meta-answer"
1.5. Decodification of analyses of capital accumulation
1.6. "New International Conceptual Order"
1.7. Accumulation and development
1.8. Development of accumulation
1.9. Domains of significance

2. Antagonistic dualities: polarization and paradox
2.1. Oppositional logic
2.2. Polarity
2.3. Paradoxes and antinomies

3. A third perspective
3.1. Beyond method
3.2. Constraints on a meta-answer
3.3. Meta-answer patterning
3.4. Containing discontinuity through aesthetics
3.5. Observer entrapment and micro-macro complementarity
3.6. Order through fluctuation: dissipative structures
3.7. Opening and closing: alternation for discontinuous learning
3.8. Third-perspective "containers": patterns of alternation
3.9. Revolutionary cycles of alternation
3.10. Trialectics: a logic of the whole

4. Threshold of comprehenisibility: a fourfold minimal container?
4.1. Omnitriangulation: interlocking cycles
4.2. Number and time
4.3. Logos and lemma for interparadigmatic dialogue
4.4. Epistemological mindscapes
4.5. Complementary languages
4.6. Nonlinear cybernetics
4.7. Modes of managing

5. Further constraints on conceptual container design
5.1. Cyclic self-organization requirements
5.2. Encompassing system dynamics
5.3. Encompassing varieties of form

6. Comprehension and learning
6.1. Non-comprehension "holes"
6.2. Discontinuity: comprehension and internalization
6.3. Pattern accumulation in a learning society

7. Complexification of integration
7.1. General systems and holonomy
7.2. Cognitive systematization
7.3. Wholeness and the implicate order
7.4. Health and space-time
7.5. Dissonant harmony and holistic resonance

8. Development of comprehension and compehension of development
8.1. Interwoven alternatives: organizational tensegrity and resonance hybrids
8.2. Non-comprehension as a structuring characteristic of a learning society
8.3. Learning cycles
8.4. Patterns of alternation: a musical key from a political philosopher
8.5. Patterns of alternation: an agricultural key from crop rotation
8.6. The entropic crisis and the learning response
8.7. Alternation between energetic expansion and mentalistic reduction
8.8. Uncertainty: the source of meaning
8.9. Morphic resonance
8.10. Toward an enantiomorphic policy
8.11. Game comprehension and identity transformation
8.12. Ecodynamics and societal evolution
8.13. Language of probabilistic vision of the world

9. Implications
9.1. Implications for agreement and consensus
9.2. Implications for action formulation
9.3. Implications for values and norms
9.4. Implications for organizations
9.5. Implications for unemployment
9.6. Implications for the developmental responsibility of answer domains
9.7. Implications for forms of presentation
9.8. Implications for information processing
9.9. Implications for the human self-image

10. Conclusions


It has been sufficient to present the argument in terms of learning "cycles". But such cycles are rather abstract concepts. They may constitute good descriptive "geometry", but the challenge is to find additional features whereby the abstract geometry is geared or anchored into the complexities of perceived reality. Additional design constraints are required to relate any such cycle to its environment and prevent it spinning out of control or losing its integrity. This question can be examined in very different ways, each of which, as a "language", throws a different light on the relationships and significance of the dimension required to structure a minimally comprehensible system of adequate complexity. For this reason the arguments of the following authors are presented at some length.

4.1 Omnitriangulation: interlocking cycles

The interrelationships of circles has been extrensively studied by Buckminster Fuller (46), an architect, as the basis for a model of the non-transient existence of energy and material systems. He makes the point that:

"Not until we have three noncommonly polarized, great-circle bands providing omnitrangulation as in a spherical octahedron, do we have the great circles acting structurally to self-interstabilize their respective spherical positionings by finitely intertriangulating fixed points less than ISO degrees apart..." (46, I, 706.20)

Furthermore, the more minutely the "sphere" so delineated is subtriangulated by other great circles, the lesser the local structural-energy requirements and the greater the effectiveness of the integrity resulting from such mutual interpositioning. This interlocking is then spontaneously self-stabilizing (42, I, 706.22).

Assuming the circular representation of cycles, Fuller is in effect saying that it takes at least three interweaving cycles before there is interaction (entrainment?) of a type to stabilize the abstract processes within a minimal non-abstract form which their interlocking brings about, in this case a sphere (#2). With less than three, the form can exist only as a transient phenomenon, if at all. In his terms, three cycles is the condition for a minimal system (#3).

But whilst three such cycles can interlock to engender a system, the system can only become comprehensible if a fourth cycle (corresponding to the processes of the observer's involvement in a comprehended system) is added. With less than four, the system may be identified with, opposed, proposed, or participated in, but it can only be partially contained within any communication. Its totality is only apparent as a succession of experiences in time. The unity of a minimal system as a whole only emerges in terms of a minimum of four event foci (46, I, 400.08). In Fuller's terms "Systems are aggregates of four or more critically contiguous relevant events..." (46, I, 400.26). All conceptually thinkable experiencings are fourfoldedly characterized (46, II, 1072.22). This is the basis for the "the minimal thinkable set that would subdivide Universe and have interconnectedness where it comes back upon itself" (46, I, 620.03) and is differentiated from its environment (46, I, 400.05).

As is clarified below, this suggests that not even a conceptual process involving the three classic processes of the dialectic can render any kind of meta-answer comprehensible (#4). It is no wonder that unitary or dualistic answers are insufficient, even though they may be necessary as part of a larger scheme.

These considerations cause Fuller to distinguish four interwoven processes which relate to the learning perspective. "Life consists of alternate observing and articulating interspersed with variable-recall rates of "retrieved observations" and variable rates of their reconsideration to the degrees of understandability." These four are therefore: observation (or recall), (re)consideration, understanding, and articulation. (46, I, 513.06-07)

4.2 Number and time

The concern with alternation cycles arises because of a collective need to obtain a more conscious awareness of integration in a developing world system. It is therefore appropriate to take account of the insights of psychoanalysis. Marie-Louise von Franz, in pursuing the work of C G Jung and linking it to modern physics, makes points which bear a strong relationship to the distinctions made by Fuller. She presents material indicating the fundamental role which number plays in ordering both the psyche and matter.

"Taken as rhythm or dynamism, three thus introduces a directional element into the oscillatory rhythm of two, whereby spatial and temporal parameters can be formed. This step involves the interference of an observing consciousness, which inserts a symmetrical axis into the two-rhythm, or else "counts" the latter's temporal and spatial succession. In terms of content the number three therefore serves as the symbol of a dynamic process....three signifies a unity which dynamically engenders self-expanding linear irreversible processes in matter and in our consciousness (e.g. discursive thought)" (47, pp. 103-106)

Her remarks, citing Jung, clarify further the limitations of single-answer or dualistic thinking:

" the level of one, man still naively participates in his surroundings in a state of uncritical consciousness, submitting to things as they are. At the levewl of two, on the other hand, a dualistic world....image gives rise to tension, doubt, and criticism, nature, and oneself. The condition of three comparison denotes insight, the rise of consciousness, and the rediscovery of unity at a higher level...But no final goal is reached, for "trinitarian" thinking lacks a further dimension; it is flat, intellectual, and consequently encourages intolerant and absolute declarations." (47, p.l24-125)

This suggests again that, despite the necessity of answers formulated in such modes, they are not sufficient at this time. The difficult step across the "incommensurability" between three-fold and four-fold thinking is effectively a progression from the infinitely conceivable to finite rezlity "based on the inclusion (no longer avoidable) of the observer in his wholeness within the framework of his processes of understanding" (47, p. 122). Citing both myths and sets of physical constants von Franz notes: "The fact that mankind's repeated attempts to establish an orientation toward wholeness possess a quaternary structure appears to correspond to an archetypal psychic structural predisposition in man" (47, p. 115).

For von Franz, a fourfold approach appears "to constitute the fundamental minimum means for subdividing and thus classifying the circle or wholeness" (47, p. 121). "Two pairs of opposites, a quaternion, are required to set up a bodily unity" (47, pp. 1 27). Below four the perception of wholeness is partly unconscious. As soon as the unconscious content enters the sphere of consciousness it has already split into four basic modes of awareness. "It is perceived as something that exists (sensation); it is recognized as this and distinguished from that (thinking); it is evaluated as pleasant or unpleasent (feeling); and, finally, intuition tells us where it came from and where it is going" (47, pp. 1 21). As a minimum condition, if they are not incorporated into an "integrated" approach, they must necessarily be projected onto competing approaches in the environment, with all the intellectual and institutional consequences for any harmonious integration. Such a fourfold approach is a necessary requirement for comprehending any "meta-answer".

The significance of a quaternary attitude is evident, whether for any human and social development programme or arising from it:

"Instead of proclaiming absolute dogmas, a "quaternary" attitude of mind then develops which, more modestly, seeks to describe reality in a manner that will - if it is based on archetypal concepts - be understandable to others. One remains simultaneously aware of the fact that assumptions of the unconscious do indeed reflect outer or inner reality, but also that they are transformed, through their passage into consciousness, into constricted, time-bound language." (47, p.26)

The step to a fourfold approach to the world problematique was beyond the impotence of mental processes revolving about "intellectual theorizations" into those which partake of the creative adventure of "realizations in the act of becoming" (47, p. 131). Von Franz cites Ferdinand Gonseth's advocacy of a quaternary outlook which would no longer involve "the summary and brutal coercion of one variant over another, but the play of identifications and differentiation, agreements and complements, limitations and expansions, a game which can lead to dialectical synthesis, built up in four rhythms." (48, p. 583)

4.3 Logos and lemma for interparadigmatic dialogue

In discussing the conditions for inter-paradigmatic dialogue, especially in the social sciences, Kinhide Mushakoji, Vice-Rector of the United Nations University, argues for the need to move beyond the accepted limits of formal logic:

"Inter-paradigmatic dialogue - not only in natural but also in social sciences - should be concerned not with the determination of who is right or wrong in defining a concept one way or the other. It should rather concern itself with the question of what part of the natural or social realities are best approached by one or the other position.

Two formally contradictory definitions of the (natural or social) realities may be both relevant and complementary in shedding light on different aspects of the same social realities. This is why the logic of inter-paradigmatic dialogue cannot be bound by the laws of Aristotelian formal logic: identity, contradiction, and excluded middle." (49, p. 19)

He also draws attention to the problem of "binary" approaches and the need for a "third pole":

"By the very nature of scientific logic which is binary, intellecturals tend to form bi-polar structures with two opposed camps rallied under two paradigmatic banners. The polarization often takes place even within each of the two poles which then divide themselves into two sub-poles, and so on...An inter-paradignatic process should be able to break the bi-polarity of the intellectual community by introducing a third pole in the dialogical process....The role of such a pole is to introduce extra paradigmatic considerations (into the discussion) and to break the dichotomic argumentation bringing into the discussion innovative ideas." (49, pp. 15-16)

Mushakoji sees such a pole as "a basic condition of a successful scientific revolution". Without it the "opposed schools of thought send their best champions for a cholastic exercise...leading to nothing else but a reaffirmation of one's paradigmatic superiority over the others" (49, p. 18).

But Mushakoji then draws attention to the "logico-real" problem of the relationship between the logical and the reality levels. He suggests that catastrophe theory (19) can help to shed light on the different logical positions in the morphogenetical space by relating the continuous reality (i.e. "signifie") to the discrete set of concepts (i.e. "signifiant"). This leads him to advocate a fourfold non formal logic model to provide a logical basis for inter-paradigmatic dialogues. Such a logic emerges from the work of Tokuryn Yamauchi (50) who interrelates oriental thinking based on "lemma" with occidential thinking based on "logos". Lemma concerns itself with the modalities according to which the human mind grasps reality, rather than how human intellect reasons about it. Mushakoji sees the lemmic approach as offering a breakthrough in response to the static ontology of the West.

"The tetralemmic model which has been developed in oriental logic stipulates the existence of four lemmas: (a) affirmation (b) negation (c) non-affirmation and non-negation (d) affirmation and negation (49, p. 21)

Here (a) and (b) both belong to formal logic, whereas (c) and (d) are unacceptable to it, although they are acceptable in theoretical physics. "Only an acceptance of the third and fourth lemmas can allow a full representation of the contemporary world problematique in its totality since contemporary world reality is full of cases where a mere affirmation or negation does not make sense." (49, pp. 21-22)

It is unfortunate that Mushakoji has limited his concern here to representing or grasping reality for the purposes of revolution in thinking. This does not respond to the problem of how to intervene in that reality on the basis of any such revolution - a vital preoccupation in furthering human and social development. And yet the four lemmas lend themselves to such an action-oreinted interpretation as the basis for a more general "action logic".

(a) affirmative action, including support, commitment, initiative, proposition, cooperation, consensus formation, empowering, "opening" (b) negative action, including sanction, withdrawal (of support), denial, disassociation, delimitation, criticism, opposition, promotion of dissent, disempowering, "closing" (c) non-affirmative and non-negative action, including indifference, indecision, non-action (in the oriental sense), "neither confirm nor deny", "opening and closing" (d) affirmative and negative action, including ambiguous action, non-violent resistance, "dumb insolence", "giving with one hand and taking with the other", "double dealing", "stick and carrot tactics", the "yes but no" response of the frustrated cross-examinee.

The conventional western-based logic of international actions uses modes (a) and (b) consciously, although some groups promote strategies based on one or the other only. For example, those in favour of "positive thinking" claim not to use (b), despite the positive value of closure as discussed earlier. Whereas those who fear "contamination" by a system gone wrong claim not to use (a).

The strength of the tetralemmic perspective is that it draws attention to the complementary role of the two other modes (c) and (d), which are outside the framework of action explicitly (consciously) accepted by the international community, although they are evident in its interstices. The (a) and (b) modes are embodied in formal agreements and procedures and are the focus of academic study of international action. The existence of other modes can only be publicly "recognized" as scandalous illegality meriting no serious attention, except as the spice of information discussion. The (c) and (d) modes are the tools of wily, world-wise actors, as well as of those they are trying to maneuver, both being aware that there are degrees of freedom of action which the (a) and (b) modes are unable to reveal. In contrast to the "cut and dried", overt (a) and (b) modes, in the essentially covert (c) and (d) modes what is not done is as significant as what is.

Most of the examples given suggest the questionable value of the (c) and (d) modes because until recently they have been largely embedded in the collective unconscious at least for the Western mind. These are the kafkaesque worlds of double dealing ("crime"), influence ("old boy networkds"), double standards ("hypocritical leadership"), and collective resistance ("bureaucratic stonewelling"). Other possibilities are however suggested by the oriental approach to action, by their extensive literature on non-action, and by the recent innovative use of "non-violent" strategies. All the modes are significant for development, as well as being vulnerable to misuse.

4.4 Epistemological mindscapes

In a remarkable series of articles, Magoroh Maruyama has studied patterns of cognition, perception, conceptualization, design, planning and decisions processes (51, 52, 53, 54). His central concern is the role of epistemological types, especially as they affect cross-disciplinary, cross-professional, cross-paradigm and cross-cultural communications (5). In contrasting his own work with that of previous research in this area, he distinguishes two traditional approaches: the psychological and psychoanalytical bases of individual differences in patterns of cognition, and the cultural and social differences as determined by sociologists and anthropologists.

Marauyama notes the various terms that have been used to describe such patterns, none of which has proved satisfactory: models, logics, paradigms, epistemologies. To these might be added Kenneth Bouldings "image" (55). In Maruyarna's latest work he favours "mindscapes". This is a more attractive term than "answer (domain)" as used here, although it lacks the active connotation of responding to a need. He provides a very valuable summary of these different exercises in "paradigmatology" and their relation to social organization (3).

Although he no longer favours the term, he defined paradigmatology as the "science of structures of reasoning" whether between disciplines, professions, cultures or individuals (53). He notes that the "problem of communication between different structures of reasoning had not been raised until recently", since scholars tended either to advocate their own approach or describe that of others. Contributing to this neglect is the fact that the choice between logics is based on factors which are beyond and independent of any logic.

Although he carefully emphasizes that there are many possible mindscapes or paradigms, Maruyama argues that "for practical purposes" it is useful to distinguish four main types (53, p.6). He stresses that these are not meant to be either mutually exclusive nor exhaustive and warns that any attempt at separating them into non-overlapping categories "is itself a victim of a paradigm which assumes that the universe consists of non-overlapping categories" (53, p. 142). What is intriguing is that over the years he has continued to struggle with the same attributes, grouping them first into three types (51), extended to four (52), then to five (53) and now seemingly stabilized at four again (54).

The four types are:

(a) H-mindscape (homogenistic, hierarchical, classificational): Parts are subordinated to the whole, with subcategories neatly grouped into supercategories. The strongest, or the majority, dominate at the expense of the weak or of any minorities. Belief in existence of the one truth applicable to all (e.g. whether values, policies, problems, priorities, etc.). Logic is deductive and axiomatic demanding sequential reasoning. Cause-effect relation may be deterministic or probabilistic.

(b) I-mindscape (heterogenistic, individualistic, random): Only individuals are real, even when aggregated into society. Emphasis on self-sufficiency, independence and individual values. Design favours the random, the capricious and the unexpected. Scheduling and planning are to be avoided. Non-random events are improbable. Each question has its own answer; there are no universal principles.

(c) S-mindscape (heterogenistic, interactive, homeostatic): Society consists of heterogeneous individuals who interact non-hierarchically to mutual advantage. Mutual dependency. Differences are desirable and contribute to the harmony of the whole. Maintenance of the natural equilibrium. Values are interrelated and cannot be rank-ordered. Avoidance of repetition. Causal loops. Categories not mutually exclusive. Objectivity is less useful than "cross-subjectivity" or multiple viewpoints. Meaning is context dependent.

(d) G-mindscape (heterogenistic, interactive, morphogenetic): Heterogeneous individuals interact non-hierarchically for mutual benefit, generating new patterns and harmony. Nature is continually changing requiring allowance for change. Values interact to generate new values and meanings. Value of deliberate (anticipatory) incompleteness. Causal loops. Multiple evolving meanings.

The above descriptions are brief summaries of extensive listings of characteristics in relation to overall social philosophy, ethics, decision-making, design, social activity, perception of environment, human values, choice of alternatives, religion, causality, logic, knowledge, and cosmology (52, 53, 54). Of special interest, in the light of Attali's "seductive" concern, are the implications for aesthetic principles favoured (54). Maruyama considers that the influence of such "pure" types predominates in certain cultures, although in practice the types are quite mixed. Thus the H-type predominates in European, Hindu and Islamic cultures. The I-type develops in certain individuals, such as those of existentialist philosophy. The S-type is characteristic of Chinese, Hopi, and Balinese cultures. The G-type predominates in the African Mandenka culture, for example. H, S. and G characteristics can be distinguished in different streams of Japanese cultures.

Maruyama has recently (54) compared his four types with an extensive survey of epistemological data grouped by O J Harvey into four "systems" (56).

System I: high absolutism, closedness of beliefs, high evaluativeness, high positive dependence on representatives of institutional authority, high identification with social roles and status position, high conventionality, high ethnocentrism.

System II: deep feelings of uncertainty, distrust of authority, rejection of socially approved guidelines to action accompanied by lack of alternative referents, psychological vacuum, rebellion against social prescriptions, avoidance of dependency on God and tradition.

System III: manipulation of people through dependency upon them, fairly high skills in effecting desired outcomes in his world through the techniques of having others do it for him, some autonomous internal standards especially in social sphere, some positive ties to the prevailing social norms.

System IV; high perceived self-worth despite momentary frustrations and deviation from the normative, highly differentiated and integrated cognitive structure, flexible, creative and relative in thought and action, internal standards that are independent of external criteria, in some cases coinciding with social definitions and in other cases not.

The two authors find that they agree on three types and differ on the nature of the fourth (which Jungian's would presumably consider as corresponding to a partially "repressed function" they have in common). It is much to be regretted that such surveys have not explored the epistemologies in "developing" countries to a greater degree, nor the extent towhich different epistemologies are co-present in the same culture, group, individual or life-cycle.

Maruyama uses his approach to clarify the essential weaknesses of the interdisciplinary, holistic programmes associated with generalists and their education.

"The concept "interdisciplinary" presupposes that there are first disciplines which have to be put together later....Such "interdisciplinary" programs, "holistic" views and production of "generalists" are all patchwork which perpetuates and aggravates the inadequacies of the classificational thinking. What we need, instead, is non-disciplinary programs, de-categorization of science and trans-specialization. Trans-specialization consists in maintaining a contextual view while focusing on specifics and details." (53, p.243)

But in analyzing such inadequacies of classificational thinking, Maruyama seemingly fails to recognize that they necessarily arise from over-reactions to inadequacies in non-classificational thinking (to which he does not accord any attention). Any pre-logical tabulation of this kind must however necessarily reveal the sympathies/antipathies of the formulator for particular types therein. Is it then useful to ask, for example, how "valid" is Maruyama's seeming over-reaction to the (excessive) dominance in world society which is engendered by the dominant (homogenistic) mode?

To clarify the need for "trans-specialization", Maruyama (53) distinguishes between:

(1) The study of paradigms engendered by different types of logic which are chosen in terms of extra-logical factors. Such work has been done in anthropology, history, psychology and psychiatry, physics and biology. (2) The study of cross-paradigmatic communication. Work on this has focused either on inter-cultural communication or on the problem of researching other cultures. More recently this has been related to communication in community development situations. (3) The study of the trans-paradigmatic process, namely of the process whereby new paradigms are created. Little work has been done on this.

Of this last process Maruyama says: "Perhaps there cannot be such a methodology: a methodology, once established, would limit the type of paradigms that it can generate." (53, p.278) This is the essential dilemma in this paper. His approach to this "methodology" is given in a subsequent paper on ways of increasing heterogeneity and symbiotization as a basis for epistemological restructuring (54). In contrast to causal (homogenistic) or random (heterogenistic) paradigms, he notes that no adequate mathematical formulation has been provided for mutual causal heterogeneity (54, p.l53) (#20) In a later paper he concludes that although "mindscapes are learned rather than innate", they are mostly formed in childhood and it seems extremely difficult to change them later in life (52, p.23).

Perhaps the widespread disaffection with existing models is evidence to the contrary, especially where it results in "alternatives" being adopted. And, as argued here, maybe it is not so much a question of "changing" existing modes as of being able to "alternate" into and out of them whenever appropriate. The problem is how to "formulate" the nature of alternation in order to make this trans-paradigmatic process credible in practice.

In arguing for a heterogeneity of expestemologies, Maruyama offers a beautiful metaphor in response to the (homogenistic) question "but which one is correct?" He suggests that in binocular vision it is irrelevant to raise the question as to which eye is correct and which wrong. "Binocular vision work, not because two eyes see different sides of the same object, but because the differential between the two images enables the brain to compute the invisible dimension" (52, p.84). The brain computes a third dimension which cannot be directly perceived. And if we live in a multidimensional space even more epistemological "eyes" are required (53, p.269-272). Reducing such vision to the parts in common provides much less than monocular vision. The difficulty with Maruyama's presentation however, is that he often appears to associate such "poly-ocular" vision with the heterogeneity characteristic of Japanese culture, although this may not be his intention. This would then preclude the use of a homogenistic epistemological "eye" in any such poly-ocular configuration. Each "eye" has its inherent limitations and strengths, and the homogenistic "eye" presumably has its own vital contribution to make to the process of encompassing (or responding to) the complexity of our collective condition. In terms of his metaphor, this paper is about the design of such poly-ocular configurations and how they may be comprehended through any given "eye". His work, with Harvey's, demonstrates that a minimum of four such "eyes" are required to describe the variety of perceptions of our collective reality.

4.5 Complementary languages

A philosopher of language, Antonio de Nicolas, has studied the limitations of single languages as a vehicle for complex, action-oriented, human-centred meaning. His use of "language" corresponds to "answer" as used here. For him one of the most widespread misleading misconceptions is the implied existence or possibility of one universally adequate language. The problem becomes more crucial when within a culture everything that is said is necessarily reduced to what can be said by only certain criterion of one particular language (30, p.190).

Given this point of departure de Nicolas explores the problem of the variety, interrelation and mutual exclusivity of rational thought systems, particularly of Western origin. To obtain perspective on the problem, he analyzes the philosophical languages embodied in the Rig Vedic hymns to which much oriental philosophy can trace its origins. These clarify the problem of responding to a multiplicity of perspectives which, even when understood, each on their terms, do not themselves offer any reconciliation of the multiplicity of "answers" which they constitute. Any synthesis of them is unable to "provide the antithetical perspectives essential to freedom" (30, p.66).

De Nicolas points out that reconciliation is not a question of compromise between opposing views, since each such compromise is an "amputation" of a portion of "one's own flesh". What is then significant in the prevalence of Western-style compromise "is not that a questionable compromise is being carried out; but rather...that a new human orientation has been demanded, or been imposed through power, on all humans; in fact, a single perspective has been imposed or demanded on all humans." (30, p.68)

Any form of reconciliation between answers has to contend, not only with saving the multiplicity of perspectives, but with the fact that these perspectives have become embodied in psycho-social structures (30, p.67). The "songs" characteristically sung in the expression of each answer engender the "bodies" through which we function in society and determine our images of ourselves. But "if thought is the ground of man, then it follows that thought is radically man's body. The limits of his body being again the same limits of the thought that grounds it." (30, p.82) In this sense, as explored by Geoffrey Vickers (57), the proponents of any answer are trapped by the bodily image they engender (#21). Getting out of such traps calls for continuing attention to the decision process, whereby they are engendered:

"If the plight of man is grounded neither in language nor in the mirror (thought) but, rather, in man's decision to reduce himself to a universalized form of thought by grounding himself on it, then the_emancipation of man will be in radicalizing himself on his decisions rather than on his images. But in order to do so man needs other men and the ability to discover them at their origin - at the radical level of their decisions and not just their images or ours, for this is man's own origin and, ultimately, his own flesh, though this might demand of every man a constant sacrifice of images - the ability to liberate himself from the prison of his mirrors - and to acknowledge a human reality which, though the source of multiple images, can neither be reduced nor identified with any of them. The other is my own possibilities and, in realizing these possibilities, I actualize my right to innovation and continuity." (30, p.3)

The distinguishing "linguistic" and epistemological feature of the hymns is the manner in which they are grounded in sound and demand a selection amongst alternative musical patterns. Since the number of tonal systems is infinite, the selection of a finite number of them by the singer/musician at the moment of execution, not only closes him within a certain limitation or determination (e.g. just tuning, equal temperament) but, more radically, it forces him to constantly face the internal incompatibility of any such selection. In order to be able to accept "a democracy" or "a plurality" of such systems, the tones of every conceivable system must constantly face and submit to a radical sacrifice to permit others to emerge (30, p.12).

"Therefore, from a linguistic and cultural perspective, we have to be aware that we are dealing with a language where tonal and arithmetical relations establish the epistemological invariances. Language grounded in music is grounded thereby on context dependency; any tone can have any possible relation to other tones, and the shift from one tone to another, which alone makes melody possible, is a shift in perspective which the singer himself embodies. Any perspective (tone) must be "sacrificed" for a new one to come into being; the song is a radical activity which requires innovation while maintaining continuity, and the "world" is the creation of the singer, who shares its dimensions with the song." (30, p.57)

Recalling Klapp's (41) concern with alernation between opening and closing, each necessary choice is a closure to alternatives, but each such choice can be sacrificed through the movement which must open to other possibilities if development is to continue.

"Rg Vedic man, like his Greek counterparts, knew himself to be the organizer of the scale, and he cherished the multitude of possibilities open to him too much to freeze himself into one dogmatic posture. His language keeps alive the "open-ness" to alternatives, yet it avoids entrapment in anarchy. It also resolves the fixity of theory by setting the body of man historically moving through the freedom of musical spaces, viewpoint transpositions, reciprocities, pluralism, and finally, an absolute radical sacrifice of all theory as a fixed invariant." (30, p.57)

Of great interest is the manner in which the sets of categories, necessary to order the perceptual world, are developed and related, highlighting both the potential dynamics for harmony and discord between them. This possibility is entirely lacking in the present fashion for "pragmatically objective" elaboration of sets of categories (#22). Thje consequences of basing work on sets of 2, 3 or more categories has not been recognized, despite obvious conflictual implications of a 2-element set (whatever the content) when reflected in a 2-division organization, for example (58). And yet, the process whereby such sets are defined, determines how whole psycho-social systems are fragmented for analysis, comprehension, and communication.

In a musically grounded language, the basic whole is the octave. That tones recur cyclically at every doubling or halving of frequency is the basic miracle of music. But the octave refuses to be subdivided into subordinate cycles by integer ratios. "It is a blunt arithmetical fact that the higher powers of 3 and 5 which define such subordinate intervals in music never agree with higher powers of 2 which define octave cycles. It is man's yearning for this impossible agreement which introduced a hierarchy of values into the number field." (30, p.56)

This dilemma with all that it signifies for music, philosophy and social organization has been explored by Ernest McClain (30, 31, 127). The present day equivalent is the problem of how different sets of concepts, with differing numbers of categories, can nest together to encompass the societal whole without creating a degree qualitatively unacceptable discord in use - namely a "gap" or "error" between reality as envisaged (or desired) and as perceived through the chosen pattern of categories. This gap provokes demands for an alternative in which the gap is at least diminished. (The process of reducing the gap is itself encoded in Rg Veda according to McClain's analysis (127).

It is not the case that numbers or ratios control movement, but it is the case that movement may be ordered according to certain ratios. Conceptual movement, and development in general, takes place through the elaboration of constellations of categories in which each category is context and structure dependent (#23). Opposite or reciprocal possibilities can be perceived as equally relevant, whether co-present or succeeding each other. "Any perspective remains just one out of a group of equally valid perspectives...but no song has so universal an appeal that it terminates the invention of new ones...the function of any language is to make clear its own dependence on, and reference to, other linguistic systems." (30, p.63.4)

"In a language ruled by the criteria of sound, perspectives, the change of perspectives and vision, stand for what musicologists call "modulation". Modulation in music is the ability to change keys within a composition. To focus within this language, and by its criteria, is primarily the activity of being able to run the scale backwards and forwards, up and down, with these sudden shifts in perspectives. Through this ability, the singer, the body, the song and the perspectives become an inseparable whole. In this language, transcendence is precisely the ability to perform the song, without any theoretical construct impeding its movement a priori, or determining the result of following such movement a priori. Nor can any theoretical compromise substitute for the discovery of the movement of "modulation" itself in history. The human body would then be asked to lose the memory of its origins; a task the human body refuses to do by its constant return to crisis." (30, p.192)

Given this context, it is not surprising that the Rg Veda requires four languages, rather than one, in order to convey the contrasting natures of its meaning. De Nicolas, following Husserl, describes such languages as intentionality-structures. "The intentionality-structure of a particular question, then, determines or prefigures the kind of answer it will receive." (30, p.79) The four languages, with their multiple perspectives, function as four spaces of discourse within which human action takes place, and from which any given statement in the text gains meaning. The languages show the human situation within disparate linguistic contexts embodying different ways of viewing the world. (30, p.9and 73). The four languages may be described as follows:

(a) Language of non-existence: Provides the modality of being in a world, either of possibilities to be discovered, or of stagnant dogmatic attitudes. It is the field condition out of which all differentiation in human experience emerges. It is the continuing context for choice. In this world there is always the tendency to lift one explanatory set to the level of an internal image as a guide for action. It then functions as a suppressed premise or fundamental myth, and is hardly ever made explicit (30, p.92-4). When the originating potential of this world is not recognized, man is deprived of the possibility of returning existentially to his origins and those of others by the dogmatic reduction of multiplicity to the "song" of one theoretical voice. In de Nicolas words the tragedy of human and social development in this world is that "We have cried for and praised many Saviours, but have lost our own act of creation and the power to revive it." (30, p.73 and 107)

(b) Language of existence: Provides the modality of acting in a world of truth to be built, formed or established, as the discontinuous results of innovation. This world is one of continuity and discontinuity, multiplication and division, with a pluralism of perspectives generated from a common field admitting many alternative structures and autonomous images. In this world man is challanged by the possibility of embodying any perspective, of being bodily "at home" within any structure or autonomous space (with which his body then shares its dimensions). This world is characterized by forces experienced either as constraining, enclosing and destructive, or as liberating and growth-enhancing. The root of contemporary man's crisis in terms of this world lies in the reduction of these multiple aspects of man to the names of objects with which he is confronted and to which he then has no effective originating relationship.

(c) Language of images and sacrifice: Provides the modality of acting in a world through regathering the images of the dismembered sensorium (the multiplicity of worlds of existence) by sacrificing their multiple and exclusive ontologies. In contrast to the centrifugal language of existence, the images are grouped and regrouped, creating and erasing boundaries, in a centripetal process converging on a unique configuration of forces in a final "efficient-moment" of sacrifice which reveals the underlying "common body of the norm", the efficient centre of creative action, or "embodied-vision". The image of sacrifice stands therefore for an activity of eternal return to the radical originating power through which the multiplicity of perspectives is engendered. It is the efficient centre of the discontinuities of space of perception and time, or the link between efficient acts and discontinuous acts. It is not a renunciation of action, but rather a renunciation of the limits of perspectives which interpretations attach to the structured subject-object sensorium. (30, pp.139-154)

Sacrifice is the necessary response to the ills of polycentricity with their many consequences for the fragmentation of the body of man. No idea of the body, whether monocentric or polycentric (validly chosen as styles of expression), is prior to man and therefore prior to this embodiment. (30, p.141) Fundamental to the problem of human development is that "any identification of man with a theory of "man" obscures the fact that any and all theories of man about "man" are made of the radical dismemberment of man himself, and distract him from engaging in his only original and primal activity: the sacrificing of all theories about himself so that he may recreate himself as man." (30, p. 70) It is for this reason that Rg Vedic man does not accept any way of understanding man's role other than as an original and continuous sacrifice (an activity rather than a theory)." (30 p.70)

(d) Language of embodied-vision: Provides the modality of having gone through, and being in, a world which remains continuously because it comprehends the totality of the cultural movement on which it is grounded (30, p.74). It is the embodiment of choosers in movement. Rationality is not then based on "the narrow logic of appeal to permises and conclusion, but rather, on an appeal to a community of listeners capable of understanding and changing, or re-directing the movement of their song". (30, p.154) The vision becomes an objective norm, not as the result of a dogmatically imposed constraint on action, but rather as the embodiment of the norm as discovered in a community of plural activities, decisions and descriptions. (30, p.154) Within such a context "we find ourselves facing moving webs, moving structures; each structure a rhythm through which a body-world appears, revealing a background of living beings together with the glory and terrors of their life". (30, p.122)

In contrast to the Western emphasis on a visually-based "linear kind of movement, which disclosed a perspectival, three-dimensional space and linear time...the audial space-time structure opened by sound...was articulated not only by rhythm and cyclically recurring movements, but movement itself became the base of all contexts (structures), and the sources of meaning within each and every field of experience." (30, p.84-5) There is no substitute for the historical discovery of the criteria by which music became one form of music as opposed to another; for it was by these criteria of music, that the body of man became now one flesh, now another. Furthermore, "without the historical mediation of the criteria of sound, by which man both imagined and lived his worlds, there is no eternal return, and therefore, no emancipation for man's memory and imagination." (30, p.175) "Man's emancipation lies precisely in his ability to break the barriers imposed on his memory and imagination by any abstractions which serve to reduce the human body to only the movements of a theory, and deprive man from the whole historical movement of which his historical body is the visible path." (30, p.170)

Of striking significance to the inertia characteristic of human and social development initiatives is the advocation of a movement which points "straight at the heart of the stillness we never dared to move: the human body...we come face to face with our most radical problem...we have never dared to set into motion our own beliefs about the human body." (30, p.155) Using the perusal of his own work as an example, de Nicolas states "It would indeed be a radical failure of the way of these meditations if, at the end of the journey, the human body...remained still, unchanged, undivided, and as silent with its memories and imaginations as when we started this journey." (30, p.l56) "Every man must actively constitute himself by creating a certain order with the things around him (structure) within a general orientation he already has (or has received) about the whole of life; it is in relation to this activity that the body of man appears as flesh, and that the flesh of man makes present for us a context and a structure with which it shares its dimensions. For this reason, our path or method must focus on the silent and fleshy unity which underlies and is the root of any human reflective thinking." (30, p.53)

The body can then be brought to share the dimensions of every perspective or song it encounters, "thus turning theory into human flesh". (30, p. 176) "Theory must turn into song; it must be performed" to guarantee man's and society's continuity and innovation. (30, p.l67) This can only be adequately done by placing theory "within a different historical context: the context of sound." (30, p. 174) Every vision "carries concomittantly an act of creation which can only be effective if that vision coincides with the original viewpoint" whereby that world was created. "By creating structures of knowledge to see the world in such a manner, the doer of this activity becomes the efficient vision and its concomittant creation." (30, p.l59) It is this identification with the active power of the word making the world that joins efficient action with efficient vision (30, p.61). Opening and closing are involved for the "structure of the embodied subject has the double-barrel effect of opening a horizon of inquiry and restricting what may appear within that horizon." (30, p.l56)

This calls for a three-fold acceptance: the possibility of viewpoint shifting through the activity of dialogue-ing, the integration of the formal aspects of experience by the rationality of practical life, the (re)achievement through practical life and action of a unity which unrelated formal models render otherwise impossible (30, p.166). Such activity, which "keeps the community moving" is of course "not formalizable, but the spaces of discourse within which it appears may be formalized." (30, p.168)

In calling philosophers "to discover the language ruled by the criteria of sound" de Nicolas contrasts the atomicity of classical physics and Western philosophy with that of modern physics in its correspondence to Eastern views of reality.

"It is only secondarily that classification of individual entities is made possible, and for this we revert to ordinary (Boolen) symbolic manipulation. In other words, to perceive anything apart from the total field is to perceive it as a subsystem, an artificially created aspect of a field of stresses, i.e. pattern. In fact, according to the law of complementarity, what can truly be said in one context-language, the same cannot be truly said in the other context-language." (30, p.33)

The implications of this point have been explored in different wasy by a number of authors including Bohrn (8), Capra (59), Zukav (60), Heelan (32), Hooker (33). But a special merit of de Nicolas presentation is that he draws attention to a response to the radical misunderstandings which arise from the

"detached objective aloofness with which we in the West are accustomed to view whatever is presented to our speculative reason. This is the precise error of knowledge which the Rg Veda is trying to correct....As a result (of the error), philosophical activity became (in the West), not liberating knowledge, but an alienation of man from man, since he was bent on equating himself with the objects of his knowledge." (30, p.186-7)

As a systems theorist, Francisco Varela, in developing the insights of Spencer Brown (61), clarifies this problem in a manner which is a warning to formulators of models of human and social development:

"In finding the world as we do, we forget all we did to find it as such, and when we are reminded of it in retracing our steps back to indication, we find little more than a mirror-to-mirror image of ourselves and the world. In contrast with what is commonly assumed, a description, when carefully inspected, reveals the properties of the observer. We observers, distinguish ourselves precisely by distinguishing what we apparently are not, the world." (62, p.22)

These considerations enable de Nicolas to turn to the ordering of complementary frameworks in the logic of quantum mechanics as a way to formalize the spaces of discourse through which action (dialogue) in the world may take place. It appears that such complementarity or contextual logic offers "a very suggestive 'model' for positive dialogue between rival philosophies, and even more important, within human experience itself." (30, p.10) As a partial ordering (lattice) of complementary descriptive languages, such frameworks involve changes in the embodied subjectivity of the knower, changes that make possible mutually exclusive objectivities or horizons. The "sacrifice" called for "involves a partial ordering of languages in a non-Boolean logic, the non-Boolean character of which is the mediation for growth and liberation." (30, p.l X7)

Man may then "re-create himself and his society through the appropriate sacrifice, eternally, exercising thus his right to innovation and continuity. This sacrifice is the constant watch man must keep over himself for re-directing his own radical interpretive activity." (30, p.187) The present inability of individuals and societies to "sacrifice" their cherished beliefs is instrumental in "freezing" society and increasing its alienation, aside from the material consequences for development. Re-thought sacrifice could constitute the sort of fundamental myth which can give "philosophical meaning to the facts of ordinary life." (30, p.l48) For de Nicolas, "it would be unphilosophical and inhuman not to open up man's possibilities by grounding him on that movement which will set him free." (30, p.46)

His emphasis on "critical" philosophy recalls the preoccupations of the Frankfurt School (63) which would presumably also give a central role to some equivalent of "sacrifice". Indeed de Nicolas approaches their language in identifying the presuppositions of his formalization:

"the construction of the structures of experience both affirms and denies experience; the negation of experience has to be again denied through the activity of experiencing through other constructed experiences (i.e., other frameworks); this negation of the negated constructed experience produces the real affirmation of experience in insight, or a series of insights, which such activity generates; these discontinuous insights should eventually produce a continuous (eternal or a perspectival) viewpoint which would be effective in the sense that no separations could be established between seeing and action, vision and action." (63, p.87)

As a way of perceiving the de Nicolas formalization raises critical questions of how it is to be perceived in its own terms. Such questions include:

It is perhaps a paradoxical necessity that the very openness and fluidity of its philosophy should be based on a set of hymns which has remained unchanged (although each interpretation is conceived as a renewal). But it would seem that, like it or not, his perception/presentation of it is paradoxically a temporary product in the process he so usefully clarifies. His perception is necessarily impermanent and incomplete and does not encounter the dynamics of those who would disagree with it.

4.6 Nonlinear cybernetics

Edgar Taschdjian has recently suggested that if cybernetics is to move byond its current preoccupation with the "simplified world of abstract models", it appears to be necessary to develop a "nonlinear cybernetics able to handle regulations which are time-dependent and dialectic rather than mechanistic". (64) Many world modelling exercises are based on such simplified models.

Tashdjan argues that human behaviour is not constant and that "too much of a good thing can become a bad thing". Furthermore, the "bipolarity of human motivations permits switches from positive to negative, from attraction to repulsion", whether in the case of an individual or of a group. The classic concepts of negative and positive feedback fail to encompass this reality since the results of such interaction in a system are purely linear, in the sense that regulators either add or subtract output from the unit governed. Regulation maintains an "equilibrium". The negative feedback concept, based on nullifying deviations, is "not sufficient to explain the real behaviour of the steersman of a sailing vessel buffeted by changing winds, who has to "tack" first in one direction, then in another." 3ust as in the case of (development) policy-making, there is a need to "change the course abruptly and repeatedly in order to reach his objective", especially if he has to steer around an obstacle. On the other hand, the positive feedback concept, based on amplifying deviations, is only able to explain exponential growth, whereas "real growth processes are not exponential but sigmoid", namely a function of time. All growth is constrained by counteracting processes.

Now in a situation where there are effectively two interacting regulators governing the same working unit, for example two alternative policies (political parties) by which a society is (successively) governed, this "three-body problem", even in mechanical systems, is not susceptible to deterministic analysis. The synergisms and antagonisms which emerge are essentially nonlinear interactions. Such double regulation is of great importance in natural systems and society.

The overall effect of such interactions is a continual disequilibrium. In the case of physiological systems, "Once the organism reaches equilibrium, it is dead." In attempting to regulate any such oscillating systems, timing of intervention is vital, as is evident in attempting to control a child's swing. The timing of any therapeutic treatment is as important as its nature and direction.

From these considerations Taschdjan concludes that "when we want to analyze and model systems existing in nature and society, the dialectic process of successive antagonistic actions requires the model to be quadripolar rather than bipolar". He points out that there is no difficulty in representing this mathematically since the totality of positive and negative real numbers constitute a bipolar system, representable on one axis. It is accepted mathematical practice to add another axis perpendicular to this to indicate the bipolar system of imaginary numbers, which then, as discussed by C Muses (65), represent the temporal dimension necessary to describe nonlinear processes. For Taschdjan, therefore, "to say that a system of dialectic interactions is quadripolar, is merely another way of saying that the system is nonlinear". Analysis then requires the use of vectors and tensors rather than scalars, and these are multiplicative rather than additive.

4.7 Modes of managing

In discussing the dilemmas of the organized society, Charles Handy, a management scientist, distinguishes three types of management problem: (a) steady-state, programmable, predictable problems that can be handled by systems; (b) development problems designed to deal with new situations; and (c) exceptional problems or emergencies where speed and instinct are essential (125, p. 45)

Handy identifies four styles of organization and management which respond to these problems. He points out that any organization will tend to make use of all these styles, although the larger the organization the more evident will be their role in the blend of styles used. The manager therefore has to embrace within himself all four of the styles, using each in appropriate circumstances, since none is sufficient to contain all combinations of problems (even though style-bound managers may believe it possible). Each has a place under certain circumstances.

For convenience, Handy labels each of the four philosophies of management (and the corresponding organizational culture) with the name of a Greed god (11):

Handy points out that the ways of each style are anathema to the others. Linkage between these modes is however essential. He distinguishes three elements of effective linkage: cultural tolerance, allowing each mode to develop its own methods of control: bridging mechanisms, including exchanges of correspondence, liaison groups and task forces; and a common language. He argues that the organization of the future will be a membership organization, multi-purpose and dispersed, combining the search for community, the economics of quality, and the revolution in communications.

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