Mapping the cognitive dynamics of the begging moment

Confusion in Exchanging Something for Nothing (Part #10)

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In the absence any more systematic study focused on the begging process, the following schematics endeavour to hold within the same framework many of the threads as identified, mentioned or discussed above.

Preliminary mapping in terms of the implications of a Venn diagram

The complexification of the aboce schematic, as presented below, endeavours to:

• give central focus to the subjectivity of the begging moment and its confusion, especially in evoking intangible values
• highlight the ambiguity associated with the different threads in terms of the contrasting manner in which they are experienced from an internal perspective and portrayed externally from a collective (objective) perspective -- using a set of Möbius strips to hold both that ambiguity and the paradoxical limitations on conventional definitions
• offer both an apparent internal locus within each Möbius strip and an apparent external locus -- labelled to indicate contrasting preoccupations (however illusory)
• tentatively present an 8-fold configuration of "dimensions" (recognizing those other distinctions might be made to amend and enrich the mapping) which could arguably be collapsed/conflated to a:
  • 6-fold configuration: combining conscience-alleviation/alms-giving and public relatioms/image & identity cultivation
  • 5-fold configuration: combining marketing and negotiation
  • 4-fold confiuration: combining game-playing within marketing/negotiation

Tentative mapping of the cognitive nexus of the begging moment (external / internal ****)

The associated dynamics recall the following presentation by Kenneth Boulding of patterns of threat and exchange, especially relevant to the begging process.

Threat and exchange patterns (reproduced from Kenneth Boulding, Ecodynamics: a new theory of societal evolution, 1978, p. 186)

The conflation to a more limited number of dimensions could be fruitfully associated with the arguments regarding hgher orders of cyberetics of Maurice Yolles and Gerald Fink (A general theory of generic modelling and paradigm shifts: cybernetic orders, Kybernetes, 2015). With respect to the reference above to 3D negotiation, from a cybernetic perspective (as argued by Yolles), these three dimensions would appear to represent a recursion of the living system agency model at the cognitive level. In other words it would appear as though it is possible to postulate that during processes of negotiation, levels of consciousness are created in a temporary generic system hierarchy that operates as a living system in its own right. It suggests that perhaps the creation of a new level of consciousness might perhaps always involve the living system agency model, i.e. with 3 domains connected by figurative and operative intelligence.

Experimental 3D configurations of Möbius strips around the "begging moment": In the case of conflation of the above schematic to 6 dimensions, the following alternative visualization possibilities are interesting to explore. [3D Images prepared with the aid of Stella Polyhedron Navigator and X3D-Edit].

Views of three mutually orthogonal Möbius strips framing the begging moment in a sphere at the centre of a cube Central animation can be interpreted as rotation of cube into 6 positions. Access interactive virtual reality version

Views of six Möbius strips (in pairs) framing the begging moment in a sphere at the centre of a cube Access interactive virtual reality version of which the images below are screen shots

Views of six Möbius strips (in pairs) tangential to the begging moment in a sphere at the centre of a cube Access interactive virtual reality version of which the images below are screen shots

Further insights could be suggested by combining the three configurations into a single virtual reality file. Solid spheres of contrasting colours could move from the "outermost" positions to fuse into the central sphere. The Möbius strips could be rotated on their longer axes. Also of potential interest is to revert to a configuration of 8 Möbius strips passing through the vertices of the cube along the diagonals through the centre. Switching any virtual reality rendering into wireframe mode is also insightful, as shown below.

Screen shots of wireframe renderings of above images in virtual reality

Framing the decision-making nexus: The "begging moment" recalls the decision-making focus of the I Ching as the Book of Changes, as can be variously interpreted and adapted (Transformation Metaphors derived experimentally from the Chinese Book of Changes (I Ching) for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997). The 64 conditions it indicates, and the transformations between them, are traditional described by a 6-line hexagram, each line being either broken or unbroken. The images above can be understood as offering a 6-fold framework through the 6 sides of the cube. The Möbius strip associated with each side can be recognized as offering the illusory ambiguity between broken/unbroken (negative/positive) which enable it to be used in constructing a hexagram framing the decision-making moment of the sphere.

Animation of alternating views of 6 Möbius strips cycling through 64 I Ching hexagrams
	Position 6	Illusory perception of the 6 paradoxical Möbius strips in the 3D schematics above suggests their use as indication of the 6 yang or yin symbols of which each of the 64 I Ching hexagrams is composed. The illusion derives from the lack of any distinction in fact between the apparently contrasting colours in a single strip, as the above images make clear
	Position 5
	Position 4
	Position 3
	Position 2
	Position 1

The 3 schematic animations relating Möbius strips with the cube suggest a further imaginative consideration in relation to the traditional encoding offered by the trigram pattern of the 8-fold BaGua "mirror" fundamental to the structure of the I Ching. Rather than treating the alternative schematics above as distinct, the axial 3-foldness they share in relation to the cube could be understood as indicative of the 3 symbolic lines in a trigram -- with their commonality denoted by the colours in the alternative representations. On any given axis the Möbius strip then alternates between a singular form (the first schematic) and its separation into two -- which move apart to different degrees along that axis (the second and third schematics), only to move together again, fusing into one. In its singular form, this would be indicative of the unbroken yang form -- with the separation then indicative of the broken yin form.

With respect to such reflection, the 12 edges of the cube offer a means of mapping patterns of 12-foldness considered so significant to many collective decision-making contexts, as separately summarized (Implication of the 12 Knights in any Strategic Round Table, 2014). More complex insights could be associated with the drilled truncated cube, a toroidal polyhedron with whose 64 edges the 64 "changes" of the I Ching could be associated (Proof of concept: use of drilled truncated cube as a mapping framework for 64 elements, 2015).

Dynamics of strange attractors implied by Möbius strip: Missing from the above schematic is the sense in which each seemingly static Möbius strip is in fact indicative of a cognitive dynamic in the confusion of the begging moment -- namely a further challenge to comprehension. Of particular interest is the manner in which the form of the Möbius strip is evident in various attractors associated with system dynamics. [The writer is indebted for this insight to the presentation by Vasileios Basios, on What Emerges from Complexity Science? to a gathering of the Scientific and Medical Network, 2015].

The point is simply made in the following image and animation of the Lorenz system attractor. It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight -- recalling that of the Möbius strip. Each of the eight such strips in the above schematic could then be suggestively understood in those terms. Curiously, as a feature of chaos theory, the attractor is also associated with the so-called butterfly effect, namely the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.

Lorenz attractor
30 second animation	screen shot
Licensed under CC BY 2.5 via Wikimedia Commons.

Other significant strange attractors are the multiscroll attractor (double-scroll attractor, or Chua's attractor) and the Rössler attractor. The Wikipedia entry on the Lorenz attractor offers other images and animations. [See also Visions Of Chaos 2D Strange Attractor Tutorial] Interaction, using "butterflies", has been enabled by Malin Christersson (Interactive Lorenz Attractor, 2015)

The half-twist that occurs in the Rössler attractor only affects a part of the attractor. Rössler showed that the attractor was in fact the combination of a "normal band" and a Möbius strip (Otto E. Rössler, Chaotic behavior in simple reaction system, Zeitschrift für Naturfoschung A, 1976). The banding evident in the Rössler attractor is similar to a Cantor set rotated about its midpoint.

Double scroll attractor	Rössler attractor
Licensed under CC BY-SA 3.0 via Wikimedia Commons (by www.chuacircuits.com)	Licensed under CC BY-SA 2.5 via Wikimedia Commons.

As noted in one description of the Rössler attractor:

The original Rössler paper states the Rössler attractor was intended to behave similarly to the Lorenz attractor, but also be easier to analyze qualitatively. An orbit within the attractor follows an outward spiral close to the x, y plane around an unstable fixed point. Once the graph spirals out enough, a second fixed point influences the graph, causing a rise and twist in the z-dimension. In the time domain, it becomes apparent that although each variable is oscillating within a fixed range of values, the oscillations are chaotic. This attractor has some similarities to the Lorenz attractor, but is simpler and has only one manifold.

As described by C. Henry Edwards and David E. Penney (Elementary Differential Equations, 1996) with respect to the Rössler attractor, thr associated system of differential equations originated in studies of oscillations in chemical reactions:

In its motion along its trajectory the point may appear to spiral repeatedly around a set -- the so-called Rossler band -- that somewhat resembles a (twisted) Mobius strip in space.... As the point travels around and around the band, it may be observed to drift radially back and forth across the band in an apparently unpredictable fashion. Two points that start from nearby initial positions may loop around and around the band somewhat in synchrony, while moving radially in quite different ways, so that their trajectories diverge appreciably with the passage of time. This illustrates the phenomenon of chaos, in which tiny differences in initial conditions can result in great differences in the resulting situations some time later.

In considering a visual representation, especially in three or more dimensions, there is a case for exploring how the above schematic might be configured "around" experience of the begging moment for one or both participants. Especially intriguing is how both the form of any visualization and the implied experiences of the begging moment -- notably questions relating to identity -- could be related to the 7 elementary catastrophes of catastrophe theory (Conformality of 7 WH-questions to 7 Elementary Catastrophes: an exploration of potential psychosocial implications, 2006).

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