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Threshold of Comprehensibility: a fourfold minimal system?


Threshold of Comprehensibility: a fourfold minimal system?
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

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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)

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