Challenges to Comprehension Implied by the Logo
of Laetus in Praesens
Laetus in Praesens Alternative view of segmented documents via Kairos

6th January 1983

Further Constraints on Conceptual Container Design

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Part 5 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


In an earlier paper (22) the nature of sets of further design constraints was explored (as detailed above). Three such sets are illustrated here.

5.1 Cyclic self-organization requirements

The previous section has demonstrated the need for at least four distinct approaches to be able to "contain" the complexity with which we are faced. These are the minimum number of complementary languages through which a "rounded" understanding of human and social development may be achieved.

Whilst four distinct approaches are sufficient to contain a general conceptual understanding, Buckminster Fuller argues that specific, concrete instances require a fifth: "all recallably thinkable experiencings, physical and metaphysical, are fivefoldedly characterized...All conceptually thinkable, exclusively metaphysical experiencings are fourfoldedly characterized" (46, II, 1072.21-23). For Fuller the fourfold is the basis for a minimal conceptual system, whereas fivefoldness "constitutes a self-exciting, pulsating propagating system" (46, I, 981.03). He demonstrates this in many structural systems.

The difficulty with the four languages, as Fuller implies, is the additional ordering required to get to grips with particular cases. As such they together only offer an unanchored potential for grasping the particular. The question is how distinct approaches interrelate, or "resonate" together (since linear or "mechanical" interlinkage is unlikely) to underpin and stabilize any new order, whether conceptual, social, or physical. This is clearly of central importance to any practical approach to human and social development.

In Jantsch's investigation of cyclic self-organization of social systems (21), he draws attention to the work of Manfred Eigen in molecular genetics. Eigen explores the question of how new information originates (66). This is a general problem of evolution, which 3antsch relates to development and to learning. The question is how the new information emerges to provide the basis for any new patterns of ordering. Any given language, or "answer domain", effectively functions like a self-replicating ecosystem. Margalef (67) has described the evolution of such ecosystems as a process of information eccumulation. Each such system seeks information from the environment, but only to use it to prevent the assimilation of more new information. Novelty is continuously transformed into confirmation. The question is how any new order can emerge under such circumstances.

Eigen uses the term "hypercycle" to denote any such new order. A hypercycle is a closed circle of distinct transformatory or catalytic processes in which one or more participants act as autocatalysts. For Jantsch: "Hypercycles-play an important role in many natural phenomena of self-organization, spanning a wide spectrum from chemical and biological evolution to ecological and economic systems and systems of population growth." (21, p.15) Eigen, in reporting on his detailed analysis with Peter Schuster of the emergence of such new order (68), states: "The self-replicative components significant for the integration of information reproduce themselves only in a coexistent form when they are connected to one another through cyclic coupling. The mutual stabilization of the components of hypercycles succeeds for more than four partners in the form of nonlinear oscillations..." (67, p. 252)

Such a hypercycle is illustrated by Fig. 1 which can be seen as a linking process between the participating (sub)systems, themselves cyclically ordered. The formation and maintenance of such a cycle which runs irreversibly in one direction and reconstitutes its participants and thereby itself, is possible only far from equilibrium. Its rhythm is controlled by the cycle of the slowest acting participant, thereby liberating transformative energy steadily rather than explosively (67, p. 90).

Hypercycle model
Hypercycle of live self- replicating RNA-cycles

Scheme of a hypercycle of live self- replicating RNA-cycles (I0to I4) and their translation products (E0 to E4). which mediate the couplings. The proteins E0 to E4 at the same time provide for the replicase and synthetase functions. Reproduced from Eigen (66, p. 254)

From this one could conclude that whilst an adequate new (world) order can be envisaged with the aid of four internally consistent, self-replicating languages, it could not be rendered practicable without a fifth language of some kind.

For Eigen "the hypercyclic order is a theoretically justifiable, essential requirement for the integration of subsystems capable of replication into a unit of greater informational content" (67, p. 255). It alone is capable of integrating and stabilizing such otherwise competing (sub)systems. Simple connections "would not be sufficient for cooperative stabilization of the components" (67, p. 255). From a multitude of such replicative units, the hypercycle can discover those appropriate to one another and, if the combination offers some advantage, amplify them selectively. In this manner a totally novel order comes into being through "sympathetic" interaction which does not change the nature of the participating (sub)systems, although it may optimize their characteristics (67, p. 256).

Eigen, through his hypercyclic ordering principle, addresses directly the question of the nature of the non-Darwinian constraining mechanism in an environment in which each "species" would otherwise expand exponentially. This is a problem with any individual answer domain, whether discipline, ideology or religion. "Coexistence of competitors requires some sort of stabilization, which confirms the exponential growth law, or the formation of niches that uncouple the competition." (67, p. 247) Eigen's "decisive question" is also of interest for the emergence of any new world order: "The decisive question for the evolutionary ability of an information-integrating system is that of the stability of the respective coupled reaction systems, whose components must be coexistent, at the same time behaving in toto selectively with respect to other competitors." (67, p. 251) The latter would then presumably be those hypercyclic features characterizing the old order.

It is only with the cultural organization of societies, according to the composer Dane Rudhyar, that isolated tones are "organized into specific series, enclosed within what is then made to sound as repetitive tones (usually octave-sounds) (69, p.23). Such tone organization is cyclic, operating within definite limits, in a cyclic, repetitive series.

In European music the structure of the entire tonality scale, its unifying principle, rests upon five types of relationship or intervals which are in Rudhyar's words:

"the octave, which defines the wholeness of the whole; the fifth, which is the organic factor of centrifugal expansion inherent in all living wholes; the fourth, which seeks to reintegrate the centrifugal elements within the organic whole; the whole tone, which is the building block of the organism; and the semitone, which refers to the circulation of sonic energy, the fluidity of life as well of psychic feelings..." (69, p. 95)

Self-reproducing hypercycle of second degree

as it may have played a decisive role in precellular evolution. Each information carrier Ii (a nucleic acid molecule) carries the information for its own self-reproduction-indicated by the arrow in a closed circle-as well asforto be production ofan enzyme Ei (a protein molecule). The latter acts as catalyst for the formation of the next information carrier Ii+1. A closed hypercycle of this type is capable of a high degree of error correction in its self- reproduction and therefore of the preservation and transfer of complex information. After M. Eigen and P. Schuster (68) Reproduced from Jantsch (21, p. 181)

Self-reproducing hypercycle of second degree,


Model of mature ecosystem organized as a hypercycle of transformatory reactions in which all matter is recycled.

The dotted arrows within the cycle indicate that also the metabolic end products, as well as the decay products after death, are recycled by the plants. Viewed as a whole, the cycle catalyzes the transformation of energy-rich photons in the region of visible light (yv) into energy- deficient photons in the infrared or heat radiation region (yir)- P, plants; H, herbivores; C, carnivores. Reproduced from Jantsch (21, p.189)

Ecosystem as a hypercycle of transformatory reactions

These types can be defined and used in different ways: monodic, heterophonic, melodic, polyphonic, and harmono-melodic. "Each type represents a specific approach to the problem of psychomusical integration..." (69, p. 95)

5.2. Encompassing system dynamics

It is not to be expected that a fivefold grasp of a developing reality is sufficient. It is a minimal requirement for a certain degree of comprehension of that reality. For example, Jantsch notes:

"If, in the development of the organism, two types of non-linear processes play the main role, namely genetic and metabolic processes, the number rises to at least six in ecosystems (competition for niches, predator-prey, symbiosis, and optico-acoustical communication)....All these processes bring their proper rhythms into play..." (21, p. 247)

As he remarks, similar coupling of oscillations occurs to an even higher degree for sociocultural systems resulting in structures of "autopoietic and temporarily harmonious nature which are capable of carrying a great deal of creativity" (21, p. 248). In material systems Fuller also distinguishes six basic ways in which a system can "move" in relation to its environment, namely spin, orbit, inversion (inside-out), expansion-contraction, torque, and precession.

"The six basic motions are complex consequences of the six degrees of freedom. If you want to have an instrument held in position in respect to any cosmic body such as Earth, it will take exactly six restraints...Shape requires six restraints. Exactly six interrestraints produce structure. Six restraints are essential to structure and to pattern stability." (46, H, 400.664)

Fuller also notes that it takes a minimum of six interweaving trajectories to establish a boundary (insideness-outsideness) between any system and its environment (46, I, 240.32). It is thus a pre-condition of individuality (46, I, 458.05-11), and consequently of characteristic patterns of interference resultants: tangential avoidance, modulation, reflection, refraction, explosion, and critical proximity (46, I, 517.05, 101-12).

As an interesting confirmation of Fuller's statements, six muscles outside the eye govern its four basic movements in tracking any object - "restraining" it in order to be able to bring it into focus. The movements towards and away from the nose are each controlled by one muscle; the upward and downward movements are each controlled by two. Other movements involve a combination of muscles. Focusing is achieved by a muscular ring, the ciliary body, within the eye. This suggests that the distinct languages required to restrain a phenomenon conceptually could usefully be thought of as "counteracting together in a manner somewhat analogous to such muscles.

The learning dimension is introduced by Arthur Young in attempting to formalize how a free agent "interferes" with any system. The resulting freedom or unpredictability is then part of the system. He points out that a minimum of six observations are then required to determine the behavior of the free agent:

  1. To know the position of a body in space, we need one instantaneous observation (for instance, the photo finish of a race).
  2. To know its velocity, which is computed from the difference in position of the body and the difference in time between the two observations, we need two such observations.
  3. To know its acceleration, we need three observations.
  4. To know that a body, for example, a vehicle, is under control, and thus distinguish it from one in which the controls are stuck, we need at least four observations. That is, we need three to know acceleration and one more to know that acceleration has been changed. (This still does not tell us the body's destination or goal.)
  5. To know the destination, provided the operator does not change his mind or try to fool us, we need five observations.
  6. To know the operator has changed his mind or is trying to fool us, we need six observations. (70, p. 18)

Young notes that observation "categories five and six repeat the cycle", the fith falling into a position category (like the first), and the sixth falling into a velocity category (like the second). This shows the relationship between the minimum of four categories required for any analytical grasp and the six observational elements to encompass the behavioural complexity.

It is to be expected that the degrees of freedom of sociocultural systems call for a "corresponding array of conceptual "restrainers" in order to grasp their nature or contain them. This would also be true of any new order based on a hypercycle. Jantsch points out that the cyclical organization of any such new order may itself evolve if the participating (sub)systems mutate or new processes become introduced -- namely the hypercycles exploitation of its degrees of freedom. "The co-evolution of participants in a hypercycle leads to the notion of an ultracycle which generally underlies every learning process" (21, p. 15)

The term "ultracycle" was originally proposed by Thomas Balmer and Ernst von Weizaecker (71) to clarify the co-evolution of subsystems of an ecosystem. In such an ultracycle, according to Jantsch, the evolution of higher complexity does not result from competition, as in the hypercycle, but from interdependence within a larger system (21, p. 106). Each self-replicating "answer domain" in a hypercycle would then represent a niche within a sociocultural ecosystem, each such niche constituting a smaller ecosystem. Each "mutation" in a niche then catalyzes changes in other niches with which it is in contact - an increase in the complexity of one tending to increase in the complexity of others. The result of the co-evolution within the domains is then the evolution of the overall system. Jantsch sees this as applying to national economic systems, for example, but he does not focus on the inequalities in such development (21, p. 195-6)

"The ultracycle is a model for the learning process in general. Learning is not the importation of strange knowledge into a system, but the mobilization of processes which are inherent to the learning system itself and belong to its proper cognitive domain....Learning may generally be described as the co-evolution of systems which accumulate experience - a capability already characteristic of simple chemical dissipative structures. In the ultracycle information is not only transferred but also produced." (21, p. 196)

5.3 Encompassing varieties of form

In the light of the arguments above concerning fourfoldness as providing the basis for the minimal conceivable system through which distinct domains could be related, it is possible, as Mushakoji noted (see above), that recent work on catastrophe theory can clarify the kinds of discontinuity which might then become apparent. Clearly knowledge of the forms such discontinuities take is necessary if the dynamics of such a developing system are to be encompassed conceptually.

If the behaviour of the minimal conceivable system interrelating the domains is determined by four control factors only, Rene Thorn demonstrated that, irrespective of their nature, there are only seven qualitatively different types of discontinuity then possible (19). In other words, while there are an infinite number of ways for such a system to change continuously (around an equilibrium position), there are only seven structurally stable ways for it to change discontinuously (through non-equilibrium states). "To put it very simply, in a wide range of situations - physical, biological, even psychological - where experience tells us that 'something's got to give'...there are only seven fundamentally different ways it could happen".

Recalling the importance of fivefoldness for implementability, it is appropriate to note that subsequent work on catastrophy theory has demonstrated that in systems with five control factors, a further four types of characteristic catastrophy emerge, making a total of eleven. Above five there are no unique patterns.

The question is then what are these possible "catastrophes" or discontinuities as they emerge in human and social development? What are these processes with which people are presumably intimately acquainted, but which are seemingly difficult to "objectify" despite their importance? In a sense the discontinuities are "irrationalities" to which man is subject in the development process. Thus the "cusp catastrophy", for example, has been used to explore the flight/fight and love/hate transitions.

The nature of such developmental discontinuities does not seem to have been determined. A related problem in cultural anthropology has however been explored by a philosopher, W T Jones (162). He is concerned, like Maruyana, with discontinuities in communication which prevent people, supposedly concerned with the same subject, from achieving any effective dialogue. To clarify this situation, he demonstrates that the discontinuities can be described in terms of the different positions of the participants (or schools of thought) on seven pre-rational axes of bias. These differences are reflected in aesthetical, theoretical, value, life-style, policy, and action preferences, as well as in the preferred style of discussion. Any transition "along" an axis gives rise to discontinuity which it is difficult to handle within a rational frame of reference. The axes identified by Jones are:

It is worth noting that in Fuller's analysis of systems, conceptual and otherwise, he identifies a total of seven axes of symmetry necessary for the descriptions of the variety formes (46, I, 1040-1042.05). He shows that if each axes passes through two distant planes, then the fourteen resultant planes together encompass all possible asymmetries in relationships, as typified by arrays of biological cells or bubbles (46, II, 1041.12-1041.13). If each extreme mode (or "domain") on Dones axes (above) is represented by a plane, then the variety they represent together could be "contained" by a "space" of fourteen facets. Much of Fuller's work is concerned with the fundamental significance of the regenerative transformations possible with systems represented by such a fourteen-faced figure.

Jantsch attributes a seven level structure to the autopoiesis and evolution of man. He notes that such "a concept of multilevel life presents considerable difficulties to Western thinking" (21, p. 240). But he draws attention to the reality of such a sevenfold system in Hindu thinking concerning human development.

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