Emergent potential of the "next zero"

Reintegration of a Remaindered World (Part #12)

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Transcending definition: The nature of the uncertainty necessarily precludes "definition", as suggested by theological reflection on apophasis or "unsaying, separately discussed with respect to individual identity (Being What You Want: problematic kataphatic identity vs. potential of apophatic identity? 2008). The image above invites imaginative exploration of  cognitive associations to:

• the vortical dynamics of a smoke ring (Enabling Governance through the Dynamics of Nature: exemplified by cognitive implication of vortices and helicoidal flow, 2010)
• the geometry of a torus (Implication of Toroidal Transformation of the Crown of Thorns: design challenge to enable integrative comprehension of global dynamics, 2011)
• a strange attractor, namely a set towards which a dynamical system evolves over time (Human Values as Strange Attractors, 1993; Cardioid Attractor Fundamental to Sustainability: 8 transactional games forming the heart of sustainable relationship, 2008).
• a challenging form of mirror, as implied by both the mirror test of self-awareness (Self-reflective Embodiment of Transdisciplinary Integration (SETI): the universal criteria of species maturity? 2008) and the "magical" possibility of "stepping through" it (Stepping into, or through, the Mirror: embodying alternative scenario patterns, 2008)
• a "stargate", variously imagined and depicted in science fiction (People as Stargates: an alternative perspective on human relations in space-time, 1996)

Co-relating one and zero dynamically: The apparent simplicity of the Möbius strip facilitates consideration of the paradoxical cognitive implications of "zero", as remarkably explored by Douglas Hofstadter (I Am a Strange Loop, 2007) following his widely appreciated study of self-reflexivity (Gödel, Escher, Bach: an Eternal Golden Braid, 1979).  As a circular loop, it is a surface with only one side due to an inbuilt half-twist -- resulting in right-handed and left-handed variants.

Figure 2: Möbius strip

This simple form can therefore be understood as embodying both one and zero -- although with a requisite degree of uncertainty. Appreciation of its nature requires that it be "traversed" -- implying the necessary cognitive dynamic indicated above. It is suggestive of the nature of the "next zero" through the challenge it poses to conventional thinking, as variously discussed (Psychosocial Work Cycle: beyond the plane of Mobius, 2007; Sustaining a Community of Strange Loops: comprehension and engagement through aesthetic ring transformation, 2010).

Much of the challenge lies in the "twist" -- as traditionally essential to any good story plot (Engaging with Questions of Higher Order: cognitive vigilance required for higher degrees of twistedness, 2004). As with the argument of Deacon (2011), it appears necessary to recognize the manner in which, as an attractor, the form does not "exist" in any conventional sense.

"Next wheel"?: It is worth considering whether the cognitive transformation associated with "re-cognition" of "nothing" -- the "next zero" -- will engender an innovation in technology. What are the cognitive analogues to zero-point energy and the associated technological explorations? If discovery of "zero" is to be understood as associated with invention of the wheel, what might be the "next wheel"? And, citing Lao Tzu again, what is the corresponding "re-cognition" with respect to the "hub" of that  next "wheel", as a progression beyond:

Thirty spokes share the wheel's hub.
It is the centre hole that makes it useful...
Therefore profit comes from what is there;
Usefulness from what is not there.

Imagining the "next wheel" necessarily calls for a degree of playfullness in the quest for clues, as separately argued (Enacting Transformative Integral Thinking through Playful Elegance, 2010; In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics, 2007). In that spirit it could prove fruitful to "confront" the cognitive implications of:

• the 30 spokes of the Tao Te Ching (cited above)
• the 30 edges of the icosahedron fundamental to the argument for syntegrity of Stafford Beer (1994)
• the 30 pieces of silver  for which Judas Iscariot is alleged to have betrayed Jesus on the occasion of the Last Supper (Gospel of Matthew 26:15)
• the 30 birds described in the Iranian Sufi Conference of the Birds, a quest for the Simorgh - exploiting a word play referring to both the mysterious bird in Iranian mythology (similar to the phoenix bird)  and to "si morgh" - meaning "thirty birds" in Persian.
• the 30 parts (juz') of roughly equal length into which the Qur'an is divided to facilitate nighly recitation during the month of Ramadan
• the 30 transcendent virtues ascribed to a Buddha
• the 30 degrees of perfection through the acquisition of ascetic virtues according to the Christian perspective of Saint John Climacus. He uses the analogy of Jacob's Ladder as the framework for his spiritual teaching.
• the Gregorian Thirty, namely the the Benedictine practice of a continuous series of 30 masses on 30 consecutive days (as instigated by Pope Gregory the Great) through which it has traditionally been believed that the soul of a deceased person would be released from the punishments of Purgatory and enter Heaven.
• the 30 facets of the NEO Personality Inventory, composed of five factors (extraversion, agreeableness, conscientiousness, neuroticism, and openness to experience) each with six subordinate divisions.

To these might be added the efforts of various cultures to embody and encode their fundamental insights into the segments of a "wheel" in the form of circlets of prayer beads (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000). The resultant pattern might then be compared with the checklists of bullet points -- so assiduously articulated in the presentation of global strategies. As is more evident in the case of the spokes of a wheel, each effectively functions as a kind of "footprint" through which insight engages with reality in order to "transport".

Curiously, if not predictably, it is such a "to-do checklist list" of issues which the Occupy movement has been challenged by its critics to produce. There is only scorn for the possibility that its supporters might think otherwise -- in quest of a mindset more adequate than that engendering the current crises.

Circular "quest" of one: The overriding ambition to be "number one" can be fruitfully reframed by the metaphors of circularity above. The question fundamental to that quest is where "one" is going. The challenge is highlighted by the recognized tendency to travel in a circle -- when walking with deliberation towards a goal in a featureless wasteland. In this sense, the succession of steps in traversing the desert then goes "nowhere", except back to the starting point. Whereas the development of calculus (as noted above) provided a means of solving Zeno's paradox through enabling treatment of values which were virtually zero, this suggests an analogue in the one-pointed steps of the ambition to be "number one" -- appropriately reminiscent of the Ourobouros and the much-cited verse of T. S. Eliot.

We shall not cease from exploration And the end of all our exploring Will be to arrive where we started And know it for the first time.
T. S. Eliot, Little Gidding (1942)	Depiction of Ouroboros (from Wikipedia)

In a world of "spin" and "smoke and mirrors", the argument has been fruitfully anticipated by the classic remark of Chuang-tzu (The Pivot):

Tao is obscured when men understand only one of a pair of opposites, or concentrate only on a partial aspect of being. Then clear expression also becomes muddled by mere wordplay, affirming this one aspect and denying the rest. Hence the wrangling... each denies what the other affirms, and affirms what the other denies. What use is this struggle to set up "No" against "Yes", and "Yes" against "No"?.... When the wise man grasps this pivot, he is in the center of the circle, and there he stands while "Yes" and "No" pursue each other around the circumference.

This is given particular focus when the "yes" and "no" are understood in terms of "belief" and "unbelief" (perhaps understood as nihilism). Whilst the two modes can play off against each other, the interrelation may take additional forms through "belief in unbelief" (the paradox of nihilism) or "unbelief in belief" (as in traumatic personal loss of faith). Such complexification  merits extension of "theology" to encompass "belief" in general, as discussed separately (Mathematical Theology: Future Science of Confidence in Belief, 2011). Such considerations are especially significant in a world charcterized by faith-based governance, in which particular forms of "belief" may be required, with "unbelief"  severely sanctioned or criminalized as apostasy (C. H. Spurgeon, The Sin of Unbelief, 1855). In an analogous manner, absolute forms of "belief" may be condemned in the form of fundamentalism or integralism -- notably framed as "extremism" supportive of terrorism (Norms in the Global Struggle against Extremism, 2005).

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