Paradoxical cycling between inside-outside and outside-inside

World Introversion through Paracycling (Part #8)

World introversion: Missing from the argument above, notably as illustrated by the admirable articulation of Edward de Bono (Six Thinking Hats, 1985), is the paradoxical process of "world introversion". It is one thing to "change hats" according to his metaphor -- a process difficult in its own right -- but it is another matter to shift the cognitive centre of identity from "inside-outside" to "outside-inside". Thus whilst a particular "hat" can indeed offer a distinct "objective" window on external reality -- if one can successfully "put it on" -- introverting the worldview of that framing implies a fundamental paradox and a distinct challenge to the imagination. Some, such as radical constructivists, would of course usefully argue that it is the "external" reality that is imagined, rather than the "internal" one (Paul Watzlawick, The Invented Reality: how do we know what we believe we know?, 1984)

Mobius strip: It is here that the apparent simplicity of the Mobius strip is helpful -- so readily made with simple twist in a paper strip, before joining the ends. The conventional "objective" sense of "inside-outside" can be associated with one side of the strip. The often-deprecated "subjective" sense of "outside-inside" can be associated with the other. The twist in the strip then offers the paradox of one side being continuous with the other, whilst offering the "illusion" that this is not the case at any particular point.

The illusory distinction can only be "managed" by effectively travelling the circuit of the strip -- riding the paradoxical cycle -- if not "paracycling" (as discussed below). The transcendent reality is associated with that dynamic cognitive skill -- much as in the distinct perspective acquired through the art of balance required in riding a bicycle. Curiously it is easier to recognize and to acquire that skill than that of the more complex art of riding a monocycle.

Klein bottle: The process of imaginatively exploring the dynamics of the relationship between "inside-outside" and "outside-inside" can be extended through consideration of the Klein bottle (see below) as a paradoxical form of higher dimensionality than the Mobius strip -- although combining two such strips is one means of forming a Klein bottle (which cannot "exist" in three dimensions). Considerable attention has been given to the cognitive implications of the Klein bottle by Steven M. Rosen further to his earlier consideration of the Mobius strip (Science, Paradox and the Moebius Principle: the evolution of a "transcultural" approach to wholeness, 1994). There he notes that the philosopher Oliver Leslie Reiser (Cosmic Humanism: a theory of the eight-dimensional cosmos based on integrative principles from science, religion, and art, 1966):

...speculated that "the atom is a galaxy turned inside out, rotated through a higher dimension" (1966, p. 412). But while Reiser emphasized the general importance of "circumversion" (the action of turning inside out [Reiser, 1966, p. 495]) and stated that it is only possible by a hyperdimensional movement, he was uncertain as to just how the performance of such an operation might be conceived. The topology of the Moebius surface offers a clue in this regard: it provides a basis for the occurrence of circumversion through a natural, internal transformation. (p. 14).

Earlier Rosen proposed a dialectical, double-aspect model of general interaction as a means of visualizing existence (A Plea for the Possibility of Visualizing Existence, Scientia: International Review of Scientific Synthesis, 1973). This was constructed from observation of the transformational properties of the Moebius surface, with hyperdimensional extrapolation to the Klein bottle. The interaction of systems is viewed there as a process of circumversion whereby systems exchange relations, become mutually negated, then exchange identities.

Cognitive locus: The emphasis here is however on the cognitive locus of the "rider" of the "paracycle" -- as implied by the transcendent cognitive locus of the rider of a bicycle. The question is how, as "rider", to hold the capacity to transition between "inside-outside" and "outside-inside" in the paradoxical cycle. In particular how does this apply to "wrestling" with realities widely acclaimed to be "external" -- and disempoweringly so -- far beyond the individual capacity of "mortals". Through "world introversion", transforming those "realities" into features of one's psychic space, one is empowered to "wrestle" with them otherwise. Such wrestling can be helpfully reframed in terms of Eastern martial arts and the philosophy associated with them (Ensuring Strategic Resilience through Haiku Patterns: reframing the scope of the "martial arts" in response to strategic threats, 2006).

The argument in terms of representation can be taken further by combining traditional philosophical consideration of Plato's cave with current explorations of how technically to enhance visual presence in wrap-around virtual reality -- and the cognitive implications this embedding then imaginatively implies. Also helpful is the work of Erik Davis (TechGnosis: Myth, Magic, and Mysticism in the Age of Information, 1998). Exploiting the Mobius representation, the locus of the "rider" can be assumed to be at the illusory nexus of the twist between the appearances of "inside-outside" and "outside-inside" -- with the distinct curves suggesting contrasting screens in the sense of Plato's cave (but two rather than one).

Another helpful image is the widely cited tale of the butterfly dream of Chuang Tzu -- considered to be the most celebrated dream ever to be recorded in the history of Chinese Philosophy:

Once Zhuangzi dreamt he was a butterfly, a butterfly flitting and fluttering around, happy with himself and doing as he pleased. He didn't know he was Zhuangzi. Suddenly he woke up and there he was, solid and unmistakable Zhuangzi. But he didn't know if he was Zhuangzi who had dreamt he was a butterfly, or a butterfly dreaming he was Zhuangzi. Between Zhuangzi and a butterfly there must be some distinction! This is called the Transformation of Things.

Positive vs. Negative: Any contrasting colouring of the "two sides" of the Mobius strip, for purposes of illustration -- using black and white, for example -- is also of value in addressing the preoccupation with emphasizing the "positive" and deprecating the "negative" (Barbara Ehrenreich, Smile Or Die: how positive thinking fooled America and the world., 2010). Both to enable the "rider" to be effective and in the light of the cybernetics of human cognition, the paradoxical relationship between the two needs to be internalized and transcended. This suggests the possibility of integrating the relationship between doom-mongering and hope-mongering worldviews and the questionable efforts to see matters one way to the exclusion of the other. The argument takes on dramatic dimensions in the experiential reality of those with bipolar disorder. Whilst the cybernetics of human cognition does indeed point to possibilities, its current disadvantage lies in the nature of its abstractions -- especially with respect to self-reference. These are difficult to internalize and render widely meaningful.

Recognitions of a paradoxical cycle: Understandings of "paradoxical cycle" have been articulated in contrasting ways, for example:

Cindy Lindsay (Paradoxes of Organizational Diversity: living within the paradoxes, Academy of Management Proceedings, 1990) proposes three paradoxical cycles of incorporating diverse members in organizations: paradox of values: paradox of fit; and paradox of categories. Disclosure is suggested and explained as a method for living within these paradoxes. The work is based on the paradoxical perspective expounded by Smith and Berg (1987).
Tjeerd B. Jongeling, Teun Koetsier and Evert Wattel (Self-Reference in Finite and Infinite Paradoxes Logique and Analyse, 2002) present a mathematical proof that for a certain class of paradoxes the following result holds: if the paradox is finite (consists of a finite number of sentences), self-reference is necessarily involved, while if the paradox is infinite, no self-reference need be involved. This result suggests how the viewpoints of those who see self-reference as essential and those who see it as inessential can be combined.
Willis F. Overton (Metaphor, recursive systems, and paradox in science and developmental theory. Advances in Child Development and Behavior, 1991) argues that:

The contradictions found at any level of abstraction among concepts such as subject-object, whole-part, synthesis-analysis, metaphor-observation, organicism-mechanism, and interpretationism-realism cannot be eliminated or resolved at that level. They can, however, be reconciled into productive paradoxes by recognizing them as components of recursive systems. The resolution of the paradox occurs only at the next higher level of abstraction where a synthesis can be established. However, this synthesis at the next higher level entails its own contradictions. These can again be reconciled into productive paradoxes through the recognition of broader recursive systems. This progressive solution continues at each iteration, or level or recursion,... the innermost cycle represents the knowing organism, knowing in the paradoxical cycle of metaphor-assumptions-concepts-observations. This knowing organism is explained and hence understood, and the paradoxes reconciled, only by moving to the next level of recursive cycle.

In more recent work, Overton's focus on "dual system" competence may prove especially relevant to the above argument (Robert B. Ricco and Willis F. Overton, Dual systems Competence -- Procedural Processing: a relational developmental systems approach to reasoning, Developmental Review, 2011).

Cyclic identity embodied in paradoxical cycles: There is no lack of commentary on the extent to which "being human" and "human nature" is characterized by paradox, contradiction and inconsistency -- typically acknowledged with a degree of humour imply a higher order of integrity (Humour and Play-Fullness: essential integrative processes in governance, religion and transdisciplinarity, 2005). Rather than the simplistic understanding of identity framed by external authorities, the challenging question is then threefold:

how an "individual" is embodied by one or more cycles, as is well-recognized at the metabolic level (Emergence of Cyclical Psycho-social Identity: sustainability as "psyclically" defined, 2007)
how those cycles "interlock" to frame an identity which transcends them, as explored with respect to externality (Spherical Configuration of Interlocking Roundtables: internet enhancement of global self-organization through patterns of dialogue, 1998; Transcending One-eyed Global Modelling Perspectives Incorporating under-currents into global circulation of value, 2010)
how to engage with the associated paradoxes, as variously explored (Embodying the Paradoxes and Contradictions of the Pursuit of Happiness: en-joying the world through en-joying oneself, 2011; Intercourse with Globality through Enacting a Klein bottle: cognitive implication in a polysensorial "lens", 2009)

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