Engendering holistic integration: Borromean knots and Klein bottles?

Engendering Invagination and Gastrulation of Globalization (Part #8)

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The above arguments merit reconsideration within the context of long-standing challenges. As described separately (Annex C), these are highlighted by the improbable collaboration between psychoanalyst Carl Jung and physicist Wolfgang Pauli in co-authoring (The Interpretation of Nature and the Psyche, 1955 -- including Synchronicity: an acausal connecting principle by Carl Jung, and The influence of archetypal ideas on the scientific ideas of Kepler by Wolfgang Pauli). As noted above, this preoccupation is consonant with the later arguments of biologist Gregory Bateson (Mind and Nature: a necessary unity, 1979).

However, as noted in Annex C, particularly symptomatic is the failure of communication between scientists -- even of the same discipline and with related preoccupations. This is recognized as having been especially disturbing to the physicist David Bohm, for whom the fundamental breakdown in communication between Albert Einstein and Niels Bohr was especially significant. He recognized it as a failure pervasive in modern society, engendering dangerous fragmentation (Naomi Gryn, David Bohm and Group Dialogue -- or the interconnectedness of everything, The Jewish Quarterly, Autumn 2003, pp. 93-97).

In an account of the collaboration between Jing and Pauli, physicist Arthur I. Miller (137: Jung, Pauli, and the Pursuit of a Scientific Obsession, 2009, and Deciphering the Cosmic Number: the strange friendship of Wolfgang Pauli and Carl Jung, 2009) notes Pauli's extraordinary conclusion, as one of the most eminent physicists of the century, that:

• "even the most modern physics lends itself to the symbolic representation of psychic processes"
• that there are "deeper spiritual layers that cannot be adequately defined by the conceptual concept of time" (Miller, p. 162)

Whether mathematics, physics or numerology, the problematic temptation is to generate complex "logical" correspondences inaccessible to cognitive experiential significance (Dynamics of Symmetry Group Theorizing, 2008).

It is in this sense that Pauli's own statement ("even the most modern physics lends itself to the symbolic representation of psychic processes") calls for a cautionary reservation. Any potentially sterile capacity of "representation of symbolic processes" does not by that token correspond to meeting the need for psychoactive engagement with those processes -- as discussed above in relation to enactivating "gastrulation" of "globalization". There is a corresponding reservation with respect to tendencies to imbue physics, numbers or geometry with experiential significance rendered inaccessible to others by questionable mystification. It is in this respect that, as noted above, Alan Sokal has challenged the obscurantism of deconstructionists.

Borromean knot: On the other hand, individuals and collectives are necessarily obliged to work with what they have and with what offers a meaningful, memorable degree of coherence -- however incomplete -- namely with explanations that "work", at least apparently to them. Of particular interest in this respect is enactivism -- what is known is brought forth, in contraposition to the more classical views of either cognitivism or connectionism -- as articulated by Francisco Varela (The Tree of Knowledge: the biological toots of human understanding, 1998; Laying Down a Path in Walking: essays on enactive cognition, 1997).

Varela's associated interest in neurophenomenology has focused on giving an explicitly naturalized account of the present nowness (in which people live) based on two complementary approaches: phenomenological analysis and cognitive neuroscience (The Specious Present: a neurophenomenology of time consciousness, 1997). Recognition of a "specious present" is of course consistent with Spivak's recognition of a "vanishing present" in a context of globalization (as noted in Annex B).

Varela's work has resulted in further research by neuroscientists and philosophers. As previously discussed, this involves an articulation of a phenomenological epoché  using a Borromean knot (Present Moment Research: exploration of nowness, 2001). Whether as used by Lacan in relation to chiasm (as noted above), by Varela, or otherwise, it is tempting to see the Borromean knot as related to the challenges of contemporary governance as traditionally represented by the Gordian knot -- a metaphor for an intractable problem, only to be resolved by action whose radical nature is yet to be understood. Such a knot may be understood as corresponding to the "incompatible knot" described by psychiatrist R. D. Laing (Knots, 1970) -- expanding on the "double bind" hypothesis put forth by Bateson and other anthropologists. It can be readily argued that globalization has brought civilization into a double bind situation.

As discussed separately with regard to variants of the Borromean knot (Cognitive Cycles Vital to Sustainable Self-Governance, 2009), Varela provides a valuable review of Edmund Husserl's extensive philosophical studies of "intimate temporarility", noting Merleau-Ponty's concern that "Time is not a line but a network of intentionalities" (1945, p. 479). Varela presents a four-fold model of nowness based on flows and dynamical trends.

With respect to the argument above, Varela's representation of the phenomenological epoché may be fruitfully compared compared to two other representations as in the following table (from Present Moment Research: exploration of nowness, 2001).

Comparison of 3-fold articulations
Borromean rings (notable for their topological implications, in Lacanian psychoanalysis and as an early depiction of the Christian Trinity)	Phenomenological epoché (explored by Francisco Varela)	Traditional Celtic knot pattern (and its associations to the mythopoeic of the megalithic period)

The relationship between the three cognitive "sensibilities" to which Robert Romanyshyn refers -- those of the poet, the philosopher, and the scientist -- are then usefully understood as intertwined or entangled as suggested by these representations (Psychology is Useless; Or, It Should Be, Janus Head, Fall 2000). Especially interesting is the sense in which any sense of a "ring" is then better understood as a dynamic or process "cycle" (see also discussions in Psychosocial Energy from Polarization within a Cyclic Pattern of Enantiodromia, 2007; Conditions of Objective, Subjective and Embodied Cognition: mnemonic systems for memetic coding of complexity, 2007).

Personal "globalization": One possibility, consistent with the above arguments, is to frame the challenge of engendering holistic integration as a "personal" initiative (Personal Globalization, 2001), as explored under the following headings:

Conceptual prosthetics and surrogates
Conceptual traps and Ponzi schemes
Globalization of experience
Conceptual de-regulation
Conceptual dimensions of globalization
Reflecting the environment
Recognizing the 'cultural rainforests' of the globalized person
Universe, solar system, cell and atom
Technology as metaphor
Planetary thinking and human experience
Globalized experience as nonlocal consciousness
Patterns that connect
Clues to the pattern that connects

This is then consistent with the understanding of the nested embedding of integrative initiatives, as described in Annex B. This might be understood as a morphogenetic catalyst of "globalization" on a larger scale (Future Generation through Global Conversation, 1997)

Klein bottle: The cognitive twists and mirrored complexity, as highlighted by the preoccupations of deconstructionists, suggest the need to go further than any such personal appropriation of "globalization", the question is then how to enactivate and engage with "invagination" and "gastrulation".

The Klein bottle is recognized as offering a means of giving visual expression to the paradoxical cognitive challenges of self-reflexivity and to the psychodynamics of "knowing thyself". It has been held to be the most unifying topological structure by various authors, including David Bohm and Steven Rosen (What is Radical Recursion?) -- as clarified by Melanie Claire Purcell (2006). Its role in this respect is consistent with arguments originally made by the psychoanalyst Jacques Lacan. Purcell, for example, sees it as integrating the characteristics of wholeness, formative causation, and an ontological bridge for comprehending consciousness through an epistemology that invokes pantheism as the most universal spiritual; construct.

From a topological perspective, the paradoxical nature of the Klein bottle offers interesting guidance to a more fruitfully complex process. It is characterized as having no identifiable "inner" and "outer" sides (as with the related Möbius strip). A representation of bottle, a 4-dimensional structure, highlights its resemblance to the invaginated embryo in which some "outside" cells have migrated to become the "inside" during gastrulation -- with a degree of continuity between inside and outside. However in the case of the Klein bottle a self-intersection is apparent in 3-dimensions which disappears in 4-D.

It is in this respect that the Klein bottle is capable of appropriately holding a degree of self-reflexivity which is not otherwise possible -- effectively a fourth "cognitive dimension". It is in this sense that "invagination", and "gastrulation" are complexified in the emergence of self-aware "globalization". This is discussed further with respect to the traditional injunction to "know thyself" (Knowing Thyself: embodying engagement with otherness, 2009; Intercourse with Globality through Enacting a Klein bottle: cognitive implication in a polysensorial "lens", 2009). The following figures are reproduced from the latter paper.

Fig. 5: Klein bottle Konrad Polthier (Imaging Maths: inside the Klein bottle, +Plus Magazine, September 2003) View Polthier's animated version (997K) or explore his java applet

Fig. 6: Klein bottle video developed by University of Hannover (available on YouTube)

As noted there the discussion is taken further by Melanie Claire Purcell (Towards a New E.R.A: epistemological resolution analysis in, from and through Klein bottle wholeness and transdisciplinary education. 2006; Imperatives for Unbiased Holistic Education: the Klein bottle, a universal structure: an archetypal image, 1999).

Ironically the comprehension challenge of self-reflexive globalization, represented visually by the Klein bottle, is potentially rendered far more intimately and accessibly through use of snoring as a metaphor (Snoring of The Other: a politically relevant psycho-spiritual metaphor? 2006).

In terms of both the Indian tradition of Advaitic philosophy and of European phenomenology, Peter Wilberg (The Nature and Shapes of the Awareness Body, 2006) offers interesting schematic visualizations based on "invagination", commenting as follows:

The human form of the awareness body can be best visualised by imagining a spherical balloon whose surface has been pushed in by a finger or hand to create an inner protrusion or 'invagination' of its surface - one that remains when the finger is withdrawn. It is only this inwardly protruding part of the spherical capsule - our Awareness Body as a whole - that can take the shape and form of the human body as we know it. Yet its inner awareness field is not a space fully contained and encapsulated by our physical form.... it is inwardly unbounded - leading into an unbounded field of awareness... which actually surrounds the entire circle, or spherical capsule of awareness as a whole.

It is of course in that tradition of Hindu practice that a degree of recognition is given to a toroidal-helicoidal-vortical emergence of kundalini (meaning coiled) -- an unconscious, instinctive or libidinal force that may, through meditation, be "raised" through various chakras, each mapping a particular vortex pattern of energy as a from of mandala.

It is also curious the degree to which symbolic logos -- notably of international institutions -- echo visually configurations that might be associated with the blastosphere and its invagination, as highlighted separately with respect to dialogue arenas (Transformation of Global Governance through Bullfighting: visual symbols and geometric metaphors, 2009). To the extent that these are representative of "global" value systems, such associations raise interesting questions about the implied attractors for any "raising" of human awareness, and the requisite of morphogenesis of such systems (Human Values as Strange Attractors: coevolution of classes of governance principles, 1993; Topology of Valuing: dynamics of collective engagement with polyhedral value configurations, 2008).

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