Relationships

With reference to Table 1

Table 1 offers a particular pattern characterized by four-fold and eight-fold relationships. Other patterns of course merit investigation, as noted above and elsewhere (Representation, Comprehension and Communication of Sets: the Role of Number, International Classification, 1978; Distinguishing Levels of Declarations of Principles, 1980; Patterns of Conceptual Integration, 1984).

The eight relationships in Table 1 are here considered as four continuous feedback loops "driving" (or "driven by") the four epistemological domains. The circles could be visualized as cross-sections of cylinders over which each loop runs as a band or belt. This raises distinct issues:

Möbius strip: The question is whether there are insights from technical innovation that can usefully integrate the four disparate domains in a manner of relevance to sustainability. Of particular interest in this respect is the power transmission achieved by belt drives -- specially designed belts and pulleys introduced with the industrial revolution and common to many factories. In practice flat belts over wheels were often given a half-twist before joining the ends -- thus taking the intriguing mathematical form of a Möbius strip [more]. This twist ensures that the belt has only a single side, a single boundary and of being non-orientable [more]. Clifford Pickover (The Mobius Strip: Dr. August Möbius's marvelous band in mathematics, games, literature, art, technology, and cosmology, 2006) describes the Möbius strip as the ultimate metaphor for something simple, yet profound -- a metaphor for magic and mystery, and "a perpetual icon stimulating the search for depths even in seemingly shallow waters". It exemplifies the transformation of an appearance of "us and them" into recognition of an underlying reality of "them is us".

Möbius strips have been used in "twist belt conveyors" (lasting longer because the entire surface area of the belt gets the same amount of wear), as continuous-loop recording tapes (to double the playing time), and in other manufacturing applications. Mobius-wrap coils are also common in electrical transformers. The artist M. C. Escher, with his strong interest in topology, was skilled at depicting Möbius strips (cf his woodcuts Möbius Strip I and Möbius Strip II, 1963).

An experiment with any such belt (a strip of paper) further suggests that, at least with a mechanical system, the cylindrical surfaces over which it runs are best oriented so that their axes of rotation are at right angles to one another. This enhances the difference they are called upon to carry as distinct epistemological domains.

In Table 1 the twist ensures that one side of the belt is associated with a positive charge and the other with a negative charge -- each side appropriately in contact with the circular domain (as clarified below in the discussion of the Van der Graaf generator as a metaphor).
Wilber's "conveyor belt": Ironically Ken Wilber (Integral Spirituality: a startling new role for religion in the modern and postmodern world, Shambhala, 2006) has a widely referenced key chapter on "The Conveyor Belt". It focuses on the role of the traditional religions as a sacred "conveyor belt" to move people through all the stages of psychospiritual development -- a developmental conveyor belt. Wilber sees it as "quite possibly, the single greatest problem facing the world... fixing this problem, if there is a fix, would provide a startling new role for religion in the modern and postmodern world" (12 June 2006).

There is however no mention of the "twist" that has been so vital to industrial conveyor belts. In fact there is seemingly no recognition that a conveyor belt has to move in both directions if it is to sustain its ability to "convey" in one direction -- with the return (unconscious?) movement typically invisible from the "active" (conscious?) side. A "one-sided" developmental conveyor belt? Those on a people conveyor may well be unaware of the necessarily hidden reverse motion. Such "unconsciousness" is the subject of a study by John Ralston Saul (The Unconscious Civilization, 1997). This suggests that the use of the metaphor typically exemplifies such unconsciousness, as illustrated by other issues:
- in the drug trade the focus is on the problematic movement of the drugs but not on whether the demand for them is problematic (Kevin Nelson, 'It's Like a Conveyor Belt', AlterNet. 11 August 2003).
- the expression "global conveyor belt" has been applied to the movement of qualified health personnel from developing countries [more].
- the expression "conveyor belt artists" has been applied where too many graduates want to be famous artists without first learning their trade [more].
Cognitive "twist": The twist in the feedback loop between epistemological domains in Table 1 highlights their fundamental distinction through an apparent discontinuity. The challenge of any such a twist is discussed elsewhere (Engaging with Questions of Higher Order: cognitive vigilance required for higher degrees of twistedness, 2004; Twistedness in Psycho-social Systems: challenge to logic, morality, leadership and personal development, 2004).

The operation of such a twist, and the challenge to comprehension, has been remarkably well depicted in the work of the artist M C Escher, specifically with respect to the Möbius strip, but more generally as discussed below (in relation to enantiodromia).

The problem of interpretation/translation between languages is well-recognized. Curiously, it is readily assumed that such translation is not required between the conceptual "languages" that characterize different domains -- and that that challenge is insignificant to communication (rather than potentially of much greater difficulty). There is notably no recognized profession for interpretation/translation between conceptual languages. For example, the EU annually spends some €1.1 billion on translation and interpretation, namely 1 percent of the EU budget (for 3,000 staff to interpret some 11,000 meetings and to translate over 1.3 million pages of text). EU meetings are not known for their use of "facilitators".

The unaddressed challenge is evident in many efforts at interdisciplinary communication and might be considered fundamental in the case of any "clash of civilizations" (witness the minimum number of Arabic interpreters/translators in the initial period of the "war on terrorism"). In a supposedly democratic world, who interprets between the "languages" of "right" and "left", "north" and "south", "east" and "west" -- and between any "clashing civilizations"? (cf Review of Frameworks for the Representation of Alternative Conceptual Orderings as Determined by Cultural and Linguistic Contexts, 1986)
Labelling of relationships: The "movement" of a Möbius belt "around" any pair of epistemological domains requires that one domain move in a "clockwise direction" and the other in an "anti-clockwise" direction. The former may be understood as being charged positively by this process (thereby gaining energy), whether or not it is in effect "driven" by that which is consequently charged negatively (thereby loosing energy). The "charging" is discussed below with respect to the Van der Graaf generator. This process may be understood to make apparent two distinct parts of the continuous belt:
- one moving from the domain charged positively to the domain charged negatively
- one moving from the domain charged negatively to the domain charged positively
Two indicative labels have been tentatively attached to each such portion of the continuous loop:
- that close to the arrow indicative of the kind of effect it is bringing into the domain
- that distant from the arrow indicative of the understanding of the domain engendering it
It should be understood that each such label could carry other more positive or more negative connotations through alternative terms. The pattern of indicative labels, as currently in Table 1, could indeed be usefully understood as poorly "tuned". The labels constitute an array that calls for "conceptual tuning" -- with all the challenges which the musical metaphor implies with regard to choice of tuning system.

Eight-fold relationships: It is appropriate to note that the thousands of bidirectional systemic relationships linking entities in databases developed by UIA² for the Encyclopedia of World Problems and Human Potential, were only given generic names (such as aggravates, aggravated by, alleviates, alleviated by, etc). These could have been more specifically described.

Value memes of Spiral Dynamics: mastering values, leadership, and change (by Don Beck and Christopher Cowan, 1996): This system is frequently cited as complementary to use of the AQAL quadrant system. It distinguishes a spiral sequence of eight progressively more complex (colour coded) conceptual models of the world through which humans (and cultures) adapt to handle new problems. Potentially reflecting higher order cybernetics, each new model includes and transcends all previous models understood to be organized around core values or collective intelligences (termed vMemes). These are:
- Beige: Instinctual
- Purple: Magical-animistic, tribal
- Red: Egocentric, power, feudalistic
- Blue: Mythic-membership, conformist, fundamentalist, ethnocentric, traditional
- Orange: Excellence, achievement, progress, modern
- Green: Postmodern, multicultural, sensitive, pluralistic
- Yellow: Systemic, flexible, flowing
- Turquoise: Cosmic unity, integrative, nested hierarchies of interrelationships, holism
BaGua and I Ching "houses": The traditional I Ching (The Book of Changes) offers a quite different way of encoding and portraying the eight-fold (paired) relationships of Table 1. It offers the additional advantage of allowing the complexity to be scalable. The 64 hexagram-encoded conditions are traditionally clustered into 8 houses. No explicit relationship to the colour coding of spiral dynamics appears to have been made, but an interesting step in that direction is that of Jeff Mishlove ( The Rainbow YinYang, 2006) -- a rainbow coloured representation of the Tao symbol.

Within the Chinese culture, an 8-fold pattern of relationship is a fundamental philosophical concept known as the BaGua (or Pa Qua). It is an octagonal diagram, widely reproduced as a symbol, with one trigram on each side. Its implications are associated not only with Taoist thought and the I Ching, but also other domains of Chinese culture (such as fengshui, martial arts, navigation, etc). Numerous images are available on the web -- oriented and coloured in a variety of ways. Of interest is the manner in which the eight conditions are generated from "positive" and "negative" -- generically understood as yang and yin respectively. Of particular interest is the fact that the dynamic relationships between the 8 conditions are typically not explicit in any representation. They are implicit -- although an indication of their explicit nature is offered below.

The further significance of the Ba Gua is discussed more extensively below in relationship to the cycle of the combustion engine.

Transactional games: Elsewhere (Cardioid Attractor Fundamental to Sustainability: 8 transactional games forming the heart of sustainable relationship, 2005) an eightfold pattern of relationships was described in terms of a generalized understanding of transactional games understood as constituting a cycle. The "relationship games", in the light of the work of Edward Haskell (Generalization of the structure of Mendeleev's periodic table, 1972) and its development by Timothy Wilken (The Relationship Continuum, 2002), are there defined in terms of a "control component" and a "work component" as follows:

Table 3: Possible 8-fold Positive-Negative Hybrid Conditions
.	.	X = "Work component"
.	.	Negative	Neutral	Positive
Y = "Control component"	Positive	*predation* (positive negativity)	allotrophy (positive neutrality)	*symbiosis* (positive positivity)
	Neutral	amensalism (neutral negativity)	O (neutral neutrality)	commensalism (neutral positivity)
	Negative	synnecrosis (negative negativity)	allopathy (negative neutrality)	parasitism (negative positivity)