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2 December 2019 | Draft

Envisaging a Comprehensible Global Brain -- as a Playful Organ

Patterns connecting the dots between hemispheres, epicycles and quavers

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Introduction
Patterning and framing a global brain?
Systemic feedback cycles of global brain interrelationships in 2D
Various representations of cyclic dynamics with implications for a global brain
Implication of 3D representation of a global brain
Dynamic patterns of play engendered by Homo ludens and Homo undulans?
Requisite helical cognitive engagement within a global brain
Brainwaves and feedback loops in a global brain?
Pathology of the global brain?
Global brain as an organ: playable, playful or neither?
References


Introduction

Collectively distributed cognition: This exploration is partly inspired by the work of Stafford Beer, as a management cybernetician, into the design of an appropriate collective brain (Brain of the Firm: the managerial cybernetics of organization, 1981), especially given the requisite complexity for a "viable system" (Giuliana Galli Carminati, The Planetary Brain: From the Web to the Grid and Beyond, 2011). Use of the metaphor followed from the influential study by an earlier cybernetician, W. Ross Ashby (Design for a Brain: the origin of adaptive behavior, 1952). The design preoccupation was the primary feature of a presentation by Shann Turnbull (Design Criteria for a Global Brain, 2001) as presented to the First Global Brain Workshop (Brussels, 2001).

The argument follows from the controversial assertion recently made by President Macron of France with respect to the "brain death" of NATO and the potential implications for any "global brain" (Are the UN and the International Community both Brain Dead -- given criteria recognizing that NATO is brain dead? 2019).

The question that is obviously raised with respect to the brain metaphor is the nature of the "brain waves" which might be detectable as indicative of life and intelligence in any global collective such as the United Nations or in any "think tank" (originally termed a "brain box"). Such waves are otherwise recognized in terms of neural oscillation -- a metaphor in itself valued with respect to any future global dependence on artificial intelligence in terms of neural learning networks. How are collective intelligence and distributed cognition to be comprehended?

Logical organization of memory: The argument follows from recognition of the similarity of 8-fold patterns in computer memory design and in the Chinese encoding which originally inspired the work of Gottfied Leibnitz on binary logic, as presented separately (Framing Cognitive Space for Higher Order Coherence: toroidal interweaving from I Ching to supercomputers and back? 2019). As noted below, the latter stressed the necessary difference between the elements in any such 8-fold pattern -- the requisite variety.

The discussion which follows offers a visual articulation of the traditional Chinese circular configuration of 8x8 elements -- the Shao Yung circle -- which featured in the image originally communicated to Leibniz. The pattern of transformations between these conditions denoted by these elements had been the subject of earlier experimental animations using scalar vector graphics.

The brain metaphor has been further exploited with respect to recognition of the division of the world into "hemispheres" -- recalling the lateralization of brain function. Such hemispheric distinction can also be seen as characteristic of politics, whether democratic or otherwise, the division into right and left wings, into government and opposition, and into science-versus-religion. Whatever form it takes, this division is currently highly problematic and "toxic", even in the countries which claim to be exemplars of democracy -- whatever optimistic claims to the contrary are made.

The quest for any "corpus callosum" offering global integration of such hemispheres is suggestively emergent from the extended visualization of the Shao Yung circle as articulated in what follows.

Patterns of connectivity: The subtitle highlights the challenge of the "pattern that connects", as so notably highlighted by Gregory Bateson and discussed by Helene Finidori (Patterns that Connect: exploring the potential of patterns and pattern languages in systemic interventions towards realizing sustainable futures, ISSS, 2016; Configuring Patterns and Pattern Languages for Systemic Inquiry and Design, Proceedings of the 25th Conference on Pattern Languages of Programs (PLoP), 2018). For Bateson:

The pattern which connects is a meta-pattern. It is a pattern of patterns. It is that meta-pattern which defines the vast generalization that, indeed, it is patterns which connect (Mind and Nature: a necessary unity, 1979). To which he added in a much-cited phrase: Break the pattern which connects the items of learning and you necessarily destroy all quality.

This connectivity is further stressed by use of the phrase "connecting the dots", now considered a characteristic of the desirable integration of "joined-up thinking". The reference to epicycles recalls the problematic comprehension of the solar system prior to recognition of the heliocentric pattern. The argument which follows emphasizes the toroidal dynamics in any such pattern, as presented and illustrated previously (Imagining Toroidal Life as a Sustainable Alternative: from globalization to toroidization or back to flatland? 2019).

Music as universal key to comprehension: The emphasis on the comprehension of globality is further stressed in what follows through the association with meaningful musical patterns, most obviously the pattern of octaves -- and hence the reference to the pattern of quavers in the subtitle. This is notable for its 16-fold subdivisions into semiquavers, its 32-fold division into demisemiquavers, and its 64-fold division into hemidemisemiquavers. These are especially valuable in framing recognition that any integration may be a matter of one or more time signatures. rather than lending itself to static framing. Instead of being a framed as a static singularity, comprehension of the globality of any brain may relate in as yet unexplored ways to its dynamic nature (Engaging with Elusive Connectivity and Coherence: global comprehension as a mistaken quest for closure, 2018). Music perhaps offers the most sophisticated articulation that is readily and widely comprehensible --- especially given its grounding in the theory of harmony and the variety of tuning systems, and most obviously the 12-note scale

Use of a musical metaphor in relation to any global understanding of a brain, also recalls the suggestive development in such terms by Mary Catherine Bateson (Composing a Life, 1991; Composing a Further Life, 2010). Whilst emphasis could be placed on the organization of the global brain, the engagement with any viable design suggests that it could well be more fruitfully an ambiguously understood as an "organ" in the sense of a musical instrument -- inviting, if not requiring, a process of creative play as a primary characteristic of life rather than of the "brain dead" (Humour and Play-Fullness: essential integrative processes in governance, religion and transdisciplinarity, 2005).

Global wave functions: However "brain waves" are best to be understood and experienced in a global collective, the wave metaphor readily associated with music and dance also merits recognition in terms of the relevance of quantum insights, as extensively developed and clarified with respect to international relations by Alexander Wendt (Quantum Mind and Social Science: unifying physical and social ontology, 2015; The mind-body problem and social science: motivating a quantum social theory, Journal for the Theory of Social Behaviour, 48, 2018, 2). Other than as "waves of change" and "waves of globalization", it is however curiously significant that preoccupation with the "global brain" has not as yet extended to the nature of any "brain waves" which might be essential to its viability -- as they are in the case of human intelligence.

If the future evolution of human society is to be explored in relation to the interplay between understandings of a "global brain" and the hypothetical collapse framed as an ultimate singularity, then how might any collapse of associated "global wave functions" be recognized (Emerging Memetic Singularity in the Global Knowledge Society, 2009)? Presumably this is implied by the preoccupations of the Global Brain Institute (Cadell Last, Global Brain Singularity: universal history, future evolution and humanity's dialectical horizon. Vrije Universiteit Brussel, 2018).

Or is the reverse to be understood, as originally implied by Peter Russell (The Global Brain Awakens: our next evolutionary leap, Global Brain Inc, 1995)? In either case, is the failure to represent the global brain and human evolution in dynamic terms an indication that the constraints of publishing industry reproduction (as chosen for the dissemination of emerging insights) are themselves curiously symbolic of a cognitive "black hole" -- the ultimate exemplification of a restrictive singularity of global proportions?

Quavering? In a period in which many have every justification for "quavering" at the future prospects for global civilization and the planet, there would therefore seem to be a strong case for a degree of recognition of the musical connotations of "quaver", as understood in the quest for harmony of some kind. A contrast might well be made between the brutal existential realities of Slavoj Zizek (Living in the End Times, 2010) and the poignant aesthetic connotations of the Songs of the Dying Earth (2009) -- a compilation of insights by George Martin and Gardner Dozois. Is this representational failure itself a characteristic of institutional "brain death" -- even pathological in times of global crisis, given the associated copyright constraints?

Of further relevance is Wendt's argument that individuals merit recognition as "walking wave functions", as discussed separately (On being "walking wave functions" in terms of quantum consciousness? 2017). However, although making extensive reference to quantum brain theory in sustaining quantum coherence -- a wave function -- "at the macro, whole-organism level", no reference is made to a global "macro-organism" or to any "brainwaves" which might sustain its coherence. Might this imply that the "global brain" is assumed to be a standing wave, to the extent it is recognized at all?

Quest for visual clues: What follows could be understood as a quest for clues to ways of thinking about the nature, dynamics and dimensions of the global brain, as suggested in earlier arguments (Time for Provocative Mnemonic Aids to Systemic Connectivity? 2018; In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics, 2007). The argument is primarily designed to evoke impressions from visual patterns and animations -- concluding with their potential implications for comprehension of the coherence associated with "brainwaves" and feedback loops through musical aesthetics. The patterns presented could be understood as an exercise in storyboarding a narrative, as used in movie design.

From that perspective, to what extent is the global brain narratives, with trending toward singularity-collapse, to be understood as a dramatic pretence? Is the high drama comparable with the mutual entanglement of the classic tales (Entangled Tales of Memetic Disaster: mutual implication of the Emperor and the Little Boy, 2009; "Big Brother" Crying "Wolf"? But them "wolves" are a-changin' -- them's becomin' "werewolves"! 2013)

Patterning and framing a global brain?

The global brain is a conceptualization of the worldwide network formed by all the people on this planet together with the information and communication technologies that connect them into an intelligent, self-organizing system. The term was coined by Peter Russell (The Global Brain: speculations on the evolutionary leap to planetary consciousness, 1982).

The original metaphor was first presented as a model by Francis Heylighen and Johan Bollen (The World-Wide Web as a Super-Brain: from metaphor to model, 1996). Heylighen reviewed the history of the underlying ideas in terms of four perspectives "organicism", "encyclopedism", "emergentism" and "evolutionary cybernetics" (Conceptions of a Global Brain: an historical review, 2011). Further discussion of the concept has been made by Marios Kyriazis (Systems Neuroscience in Focus: from the human brain to the global brain? Frontiers in Systems Neuroscience, February 2015). A Global Brain Institute has been established to focus such studies.

Use of the metaphor followed from the earlier articulation of a "world brain" by H. G. Wells (World Brain, 1938). A much more recent proposal using the term has been geared to the worldview of the intelligence community, although who therein might be motivated to comprehend its nuances is another matter (Robert David Steele, Model for Making Amazon the Profitable World Brain, Public Intelligence Blog, 2007).

A basis for simulating the operation of the brain in terms of the connectivity of its elements has been suggested in terms of the thousands of interlinked online profiles of the Yearbook of International Organizations and the Encyclopedia of World Problems and Human Potential (Simulating a Global Brain: using networks of international organizations, world problems, strategies, and values, 2001). These initiatives also had a historical connection to H. G Wells through his secretary, Peter Hunot, who later became the enabling editor of the first post-war edition of that Yearbook.

As previously argued. advantage can be taken of both the visual depictions of the multidimensional toroidal interconnection of supercomputer memory (potentially understood in terms of a hypercube) and the traditional circular arrangement of hexagrams perceived by Leibniz to be relevant to binary logic -- as discussed separately in some detail (Framing Cognitive Space for Higher Order Coherence, 2019).

Comparable perspectives on cubic organization
Torus interconnect schematic
(in cubic array)
3D reconstruction of schematic on left
(animation with indicative cube)
8-fold BaGua of trigrams
(according to Sung)
Torus interconnect schematic in Tofu supercomputer Animation in 3D of torus interconnect schematic in Tofu supercomputer Cubical representation  of BaGua pattern of I Ching
Reproduced from Wikipedia   Reproduced from Z. D. Sung, The Symbols of Yi King or the Symbols of the Chinese Logic of Changes (1934, p. 12)

The image communicated Leibniz is presented below left. It was received in a period in which conceptualization of the solar system in Europe was emerging from problematic patterns of planetary epicycles as indicated below centre. The latter would now be deprecated as the epitome of misperception. Such images may be usefully contrasted with the more complex insight into a hypercyclic system shown schematically below right (Perspective: thinking globally and acting locally -- epicycles or hypercycles? 2019).

Indication of contrasting modes of schematic comprehension
Shao Yung circle of hexagrams
as communicated to Leibniz (1703)
Planetary epicycles associated
with early comprehension of solar system
Hypercycle
Shao Yung circle of hexagrams Planetary epicycles Hypercycle
By Unknown - Perkins, Franklin. Leibniz and China:
a commerce of light
. Cambridge UP, 2004. 117., Public Domain, Link
Reproduced from Wikipedia Reproduced from Principia Cybernetica

In what follows, the multiple references to the traditional circle of hexagrams is as an influential integrative pattern. As a template, such a pattern coulld be understood as a coherent framing of an unusual degree of complexity. Exploration of the global brain could be understood as an exercise in mega-patterning, if not meta-patterning. This raises a variety of issues as discussed by Jeremy Lent (The Patterning Instinct: a cultural history of humanity’s search for meaning, 2017) and separately critiqued (Patterning Intuition with the Fifth Discipline, 2019).

Systemic feedback cycles of global brain interrelationships in 2D

As a pattern, in the quest for a comprehensible design of a viable system model, the complex coherence of the traditional Chinese cyclic configuration of conditions of change communicated to Leibniz suggests the value of depicting the patterns of transformations between those conditions -- as explicitly implied by the encoding system. The derivation and construction of that pattern, shown below left, is discussed separately (Alternating between Complementary Conditions -- for sustainable dialogue, vision, conference, policy, network, community and lifestyle, 1983).

The value of that pattern can be partly recognized in its generality and its relation to binary logic. However, and potentially of equal relevance, it can also be recognized in its use of metaphor as a mnemonic catalyst accessible through common language. The sophisticated technical language through which the global brain is otherwise understood can then be challenged as a valuable jargon, but one which fails to encompass the subtlety of psychosocial reality -- even to the point of denying its reality for many.

Given any acknowledgement of requisite variety, the challenge of comprehension calls for recognition that the technical perspective alone is a form of "subunderstanding", as argued by Magoroh Maruyama (Peripheral Vision: polyocular vision or subunderstanding? Organization Studies, 25, 2004, 3). This is exemplified by the constraints on sociopolitical decision-making at this time and the variety of implications that a wider spectrum of perspectives is required, as partially suggested by efforts to reframe the technical worldview (Robert Romanyshyn. Technology as Symptom and Dream, 2015; Erik Davis, TechGnosis: myth, magic, and mysticism in the Age of Information, 1998). Of relevance are then the characteristics of a global brain capable of encompassing the apparently incommensurable dimensions so evident in society (Using Disagreements for Superordinate Frame Configuration, 1992; Epistemological Challenge of Cognitive Body Odour: exploring the underside of dialogue, 2006; The unmentionable challenge to sustainable paradigm shifting and social transformation, 1998). The latter focuses on the consequences of the antipathy between change agents.

Appropriately that pattern frames an underlying question of how it should be read -- a much neglected intercultural challenge presented separately (Unquestioned Bias in Governance from Direction of Reading? Political implications of reading from left-to-right, right-to-left, or top-down, 2016). This is illustrated by the central and right-hand images below -- with brief explanation thereafter. The issue is otherwise in the chirality or sidedness fundamental to biological organization -- suggesting that it may well have psychosocial and epistemological implications (Kurt Mislow Paul Bickart, An Epistemological Note on Chirality, Israel Journal of Chemistry, 15, 1976, 1-2; Hazrat Mirza Tahir Ahmad, Chirality and Sideness in Nature, The Review of Religions, 1 December 2001).

The alternatives imply a need to alternate between the two directions -- in some kind of cognitive alternation dynamic. Interpretation of the distinctions between the 64 conditions have been experimentally derived from for various domains (Transformation Metaphors derived experimentally from the Chinese Book of Changes (I Ching) -- for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997).

Indication of transformations pathways between hexagram conditions in Shao Yung circle
Without condition descriptors Conditions read "top-in" Conditions read "top-out"
Shao Yung circle of hexagrams with added transformations Map of transformations between global, 'heads-together' networking conditions ('top-in') Map of transformations between local, 'back-to-back' networking conditions ('top-out')
     
Alternative maps of transformations between conditions of change
  Between global, 'heads-together' networking conditions ('top-in') Between local, 'back-to-back' networking conditions ('top-out')
The conditions are denoted by hexagrams in a traditional circular order (each facing its negative image). The 6 transformations shown interlinking these conditions are those described in the accompanying text (in which only one line of each hexagram code is modified; see below for multiple line modifications). The hexagram code is read here with the top line closest to the centre (in contrast to that on the right). thus determining the condition numbers added. Note that a 7th transformation from each condition is that to its negative across the circle; an 8th is to its inversion, in the equivalent position in that on the right.

Transformations
(curves)

Transformations
(straight lines)

(- - -) 3rd sub-condition (- - -) 6th sub-condition
(long) 2nd sub-condition (long) 5th sub-condition
(short) 1st sub-condition (short) 4th sub-condition
The hexagram codes appear here in the same order as in that on the left. but because each code is read here with the bottom line closest to the centre (in contrast to those on the left). the codes represent different numbered conditions in many cases. Only conditions 1,2, 27, 28, 29, 30, 61 and 62 do not change position

Transformations
(lines)

Transformations
(curves)

(- - -) 1st sub-condition (- - -) 4th sub-condition
(long) 2nd sub-condition (long) 5th sub-condition
(short) 3rd sub-condition (short) 6th sub-condition

The elaboration of the visually enhanced circular configuration presented above was made at a time when the implied pattern of transformations could be most readily presented by using straight lines within the circle and curves outside it. Other insights can however be suggested using a different design metaphor.

The pattern on the left below substitutes points (of perspective) for the hexagrams in that above, and represents most links as complete circles (cycles) rather than segments thereof. Unfortunately the earlier experimental use of scalar vector graphics to generate that pattern is only problematically supported by web browsers, especially if the possibilities of relevant animation are to be explored to enable comprehension of dynamics. The image has therefore been constructed (centre and right below) using the current X3D standard for computer graphics which facilitates both representation of dynamics and modelling in virtual reality (as illustrated in a later section).

Reconstruction of 64-fold pattern of transformation pathways suggestive of global brain processes (screen shots)
Scalar vector graphic variant Animation of colour variants (X3D) Animation of black/white variants (X3D)
64-fold pattern of transformation pathways suggestive of global brain processes 64-fold pattern of transformation pathways suggestive of global brain processes 64-fold pattern of transformation pathways suggestive of global brain processes
     

Note that the pattern of hexagrams encodes 6 transformations from each hexagram to others. Of these, 3 can be readily seen in relation to each in the central image as red, yellow and blue circles. A fourth and fifth are indicated by the transformations to proximate points around the circular configuration. The sixth across the circle is indicated by the cyan curve (through the centre) to the point diametrically opposite.

Cyclical patterns of N-foldness in static depictions of a global brain?

Animation of indicative pathways in a global brain -- "global brainwaves"?
(using the pattern above as a template)

The animation uses a sequence of images to give a sense of pathways within and between more "worlds" of more "local" preoccupation

Pathways of larger dimension are indicative of emergence of more "global" integration of the hemispheres of the brain

 

Animation of indicative pathways in a global brain: global brainwaves?
Produced in anticipation of generation of more complex animations

** movement of balls / feedback loops / learning cycles / 16-fold strategies, etc

Various representations of cyclic dynamics with implications for a global brain

Smith chart in 2D and 3D variant: Cyclic dynamics can be indicated in a surprising manner through use of the 2D variant of the Smith Chart. This is a graphical aid or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist in solving problems with transmission lines and circuit matching. As discussed separately it can be used to explore the dynamics of cognitive transformations potentially typical of a (global) brain (Modulating cognitive transformations: electrical metaphors and semiconduction in In Quest of a Dynamic Pattern of Transformations: Sensing the strange attractor of an emerging Rosetta Stone, 2012).

Curiously, but potentially appropriately, the form of the patterns has resulted in their recognition using terminology with which the circle of hexagrams has been traditionally associated (Randy Rhea, The Yin-Yang of Matching, High Frequency Electronics, 2006). In relation to the discussion of wave forms, the 8 types of the 2D Smith Chart were presented separately (Animations variously suggestive of "being a waveform", 2013 in Being a Waveform of Potential as an Experiential Choice: emergent dynamic qualities of identity and integrity, 2013

8 elements of Tao symbol represented experimentally on a Smith Chart
(redrawn versions, using dashed lines, of the 8 figures by Randy Rhea in The Yin-Yang of Matching, High Frequency Electronics, 2006)
Type 1 (blue) and Type 3 (red) Type 2 (blue) and Type 4 (red) Type 5 (red) and Type 7 (blue) Type 6 (blue) and Type 8 (red)
8 elements of Tao symbol represented on a Smith Chart (Type 1 and 3) 8 elements of Tao symbol represented on a Smith Chart (Type 2 and 4) 8 elements of Tao symbol represented on a Smith Chart (Type 5 and 7) 8 elements of Tao symbol represented on a Smith Chart (Type 6 and 8)
Indication of a dynamic pattern of transformations
(through experimental animation of the 8 types above on a Smith Chart)
Animation indicative of a "complementary" pattern of transformations
(modifying the orientation of the 8 types on the Smith Chart above)
Comparison of 2D and 3D Smith Charts
Indication of a dynamic pattern of transformations (Smith Chart) Animation indicative of a complementary pattern of transformations Comparison of 2D and 3D Smith Charts

The 3D variant of the Smith Chart (above right) is also of relevance to this argument (The 3D Smith Chart and Its Practical Applications (July 2012); A 3-D Smith Chart Based on the Riemann Sphere for Active and Passive Microwave Circuits (June 2011)

Dynamics implied by the Basque Lauburu: As the traditional symbol of Basque culture, the lauburu invites recognition of the cognitive dynamics. Potentially implied with respect to the many reflective on 4-fold pattern. (Transformation pathways in multivocal discourse. 2016). The pattern may be experimentally superimposed on the Smith Chart (indicative of the geometry by which it is constructed). The animation is indicative of the possibility of more complex animations with rotation of the nested structures of smaller scale.

Dynamics potentially associated with Lauburu pattern
Lauburu construction Superposition of Lauburu on Smith Chart Animation of the image between 8 orientations
Superposition on I Ching
pattern
Anti-clockwise rotation over BaGua King Wen pattern Clockwise rotation over BaGua Fuxi pattern
Lauburu construction Experimental superposition of Lauburu on Smith Chart Experimental animation of Lauburu between 8 orientations Experimental superposition of Lauburu on circle of hexagrams Experimental rotation of alternative Lauburu patterns over alternative BaGua patterns Experimental rotation of alternative Lauburu patterns over alternative BaGua patterns

To be stressed as relevant to this exploration, each trigram in either BaGua pattern traditionally has fundamental metaphorical associations -- with the encoding indicative of how these are understood to transform into each other. Associating the Lauburu dynamically in the animations is suggestive of how its "deconstruction" is able to hold 12 distinctive sub-transformations.

Combining spiral patterns attributions of distinctions: Of particular interest are the Euler spiral and the Fibonacci spirals. The former, otherwise known as a clothoid, is valued for the transition it enables in practice between linear and circular movement, notably in the case of road design. The latter, as one of the approximations to a golden spiral, is of interest here through the manner of its construction by which the elements of an I Ching hexagram can be distinctively attributed, as shown below. A mirror variant can be associated with the pattern, as discussed separately (Designing Global Self-governance for the Future: patterns of dynamic integration of the netherworld, 2010).

Use of simple mirrored reflection of the pattern of construction of a Fibonacci spiral
Note that one consequence of this reflection (as may be seen on close inspection) is that the line codes change their significance
if those in the lower portion are read in the same direction as those in the upper portion.
This points to the possibility of dynamic alternation between such readings
Experimental superposition of Euler spiral  on circle of hexagrams" . Mirror reflections of Fibonacci spiral
Fibonacci spiral organization of I Ching codes (reversed) .
Alternation -- That which is, is not. That which is not, is
-
- perhaps indicative of the holomovement described by David Bohm

Pattern of genetic codes mapped by the circle of hexagrams: As a pattern, there is widespread recognition of the correspondence between the circle of hexagrams and the set of genetic codes, as discussed separately (Changing Patterns using Transformation Pathways, 2015; Indicative mutual constraints between codon and hexagram patterns, 2015). As indicated in the latter both 64-fold sets lend themselves to mapping onto the 64-edged the drilled truncated cube.

Additional patterns of connectivity
Map of selected complex transformations between network conditions Projection of all conditions (hexagrams) onto a circle
.
Depiction of Rumer's transformations
in relation to the circle of hexagrams
Depiction of transformations based on Rumer in relation to the circle of hexagrams
Map of selected complex transformations between network conditions Projection of all conditions (hexagrams) onto a circle Rummer's transformations in relation to the circle of hexagrams Rummer's transformations in relation to the circle of hexagrams
  Reproduced with permission of Anagarika Govinda (Inner Structure of the I Ching; the Book of Transformations Adapted from Wikipedia

Implication of 3D representation of a global brain

Polyhedral configuration? Given the multidimensional organization of supercomputer memory (as noted above), there is every possibility that whatever is to be understood as a "global brain" is likely to be characterized by some form of multidimensional architecture -- as arguments for hypercomputation have effectively recognized (Imagining Order as Hypercomputing: operating an information engine through meta-analogy, 2014). Such language merits comparison with the results of recent neuroscience research which indicates the remarkable possibility of cognitive processes taking up even up to 11-dimensional form in the light of emergent neuronal connectivity in the human brain:

Using mathematics in a novel way in neuroscience, the Blue Brain Project shows that the brain operates on many dimensions, not just the three dimensions that we are accustomed to. For most people, it is a stretch of the imagination to understand the world in four dimensions but a new study has discovered structures in the brain with up to eleven dimensions - ground-breaking work that is beginning to reveal the brain's deepest architectural secrets..... these structures arise when a group of neurons forms a clique: each neuron connects to every other neuron in the group in a very specific way that generates a precise geometric object. The more neurons there are in a clique, the higher the dimension of the geometric object. ...

The appearance of high-dimensional cavities when the brain is processing information means that the neurons in the network react to stimuli in an extremely organized manner. It is as if the brain reacts to a stimulus by building then razing a tower of multi-dimensional blocks, starting with rods (1D), then planks (2D), then cubes (3D), and then more complex geometries with 4D, 5D, etc. The progression of activity through the brain resembles a multi-dimensional sandcastle that materializes out of the sand and then disintegrates. (Blue Brain Team Discovers a Multi-Dimensional Universe in Brain Networks, Frontiers Communications in Neuroscience, 12 June 2017)

The question is whether any pattern of 64 distinctions, whether hexagrams or genetic codons, can be meaningfully configured in 3D. A valuable candidate for such an exploration is the drilled truncated cube (Proof of concept: use of drilled truncated cube as a mapping framework for 64 elements, 2015) *** with anim

Configuring a 64-fold pattern through mapping onto a 64-edged drilled truncated cube
With hexagram names Suggestive animations using Shao Yung circle
Drilled truncated cube of 64 edges with hexagram names Drilled truncated cube of 64 edges with hexagram names Drilled truncated cube with animation of single circle of hexagrams augmented by transformation pathways Drilled truncated cube with 6 circles of hexagrams associated with faces
       

Animations variously suggestive of "being a waveform", 2013 in Being a Waveform of Potential as an Experiential Choice: emergent dynamic qualities of identity and integrity, 2013

Enabling Wisdom Dynamically within Intertwined Tori: requisite resonance in global knowledge architecture, 2012

Mandelbrot set as indicative of the complexity of a global brain? Arguably the renderings of the Mandelbrot set are a corrective to tendencies to oversimplify the role of the global brain as an interface between order and chaos. The argument has been developed separately (Comprehension of Requisite Variety via Rotation of the Complex Plane: mutually orthogonal renderings of the Mandelbrot set framing an eightfold way, 2019).

The images below were previously presented in Imagination, Resolution, Emergence, Realization and Embodiment: iterative comprehension ordered via the dynamics of the Mandelbrot set (2005) in support of various arguments relating to that rendering (Sustainability through the Dynamics of Strategic Dilemmas -- in the light of the coherence and visual form of the Mandelbrot set, 2005; Psycho-social Significance of the Mandelbrot Set a sustainable boundary between chaos and order, 2005; Understanding the Monster through the Mandelbrot set -- Moonshine connectivity? 2007)

The illustrative images there were of 2D form. In the light of the arguments above with respect to rotation of the complex plane, there is then a case for considering how 8 distinctive cognitive significance might be associated with the octants of the 3D configuration of Mandelbrot sets as cognitive contexts of particularly quality. Insights may be distinctively associated with the BaGua trigrams (or encoded by them) as with those of oppositional logic. How then might these relate to that configuration -- as suggested by their association with the octants in the image above (and below)?

Mandelbrot set and its possible organization in 3D

Animations according to different colouring conventions)
Rotation in complex plane of mutually orthogonal Mandelbrot renderings Corresponding octant configuration
Animation of colouring conventions of Mandelbot set Experimental use of the Mandelbrot set Animation of mutually orthogonal configuration  of Mandelbrot  sets with trigram encoding Octant configuration with signs and trigram encooding
       

Horn torus, Lissajous curves: "global heart" symbol: Of some relevance to any understanding of "globality" is the contrast between a "global brain" and whatever meaning is to be associated with a "global heart" beyond the cardiovascular focus of journals and international initiatives of that name (Anodea Judith, The Global Heart Awakens: humanity's rite of passage from the love of power to the power of love, 2013; Global Heart Project) This is of particular concern in that focus on the "heart" metaphor is of far greater concern (to a quite distinct constituency) than that on the "brain" metaphor.

The issue is highlighted otherwise by recognition that the times are especially characterized by a struggle in global dialogue between the "headless hearts" and the "heartless heads" (Challenge of the "headless hearts" to the "heartless heads"?, 2018; Possibilities of reconciling the "headless hearts" to the "heartless heads", 2018). As indicated by Johan Galtung:

Peace appeals to the hearts; studies to the brain. Both are needed, indeed indispensable. But equally indispensable is a valid link between brain and heart. (The 1987 Right Livelihood Award Acceptance Speech, 1987)

In the light of the work of Edward Haskell, a degree of reconciliation may prove possible through exploration of the coaction cardioid (Cardioid Attractor Fundamental to Sustainability: 8 transactional games forming the heart of sustainable relationship, 2005).

There is of course extensive medical research into both the brain and the heart but with little reference to their respective role as fundamental symbols -- commensurate with the traditional significance attached to the Sacred Heart in Christian and Aztec cultures, for example. In exploring that of the global brain, there is therefore a case for recognizing the geometrical articulation of "heart surfaces" as indicative of radical location of "significant others" (Implications of a 3D heart symbol, 2018). Are the chambers of the heart to be understood as comparable to the organization of the brain? Does the brain "beat" in some way to enable a vital form of circulation?

The images below left are indicative of interactive demonstration of 3D heart shapes based on different equations. Of related interest is the possibility of configuring a heart through the interactive juxtaposition of horn tori as discussed separately (Cognitive heart dynamics framed by two tori in 3D, 2016). In that connect, Wolfgang Daeumler comments on the presentation of Lissajous curves on the surface, as illustrated by the animation (below). The visual form of these curves is often suggestive of a three-dimensional knot, and indeed many kinds of knots, including those known as Lissajous knots, project to the plane as Lissajous figures. The animation below is somewhat reminiscent of the hypersphere animations suggestive of higher-dimensional brain functioning (as presented above).

Forms in 3D of relevance to the heart and its implications for the dynamics of the global brain
Heart forms Horn torus and Lissajous curves
Kuska formula Trott formula Complementary curves
engendering upright and inverted heart symbols
Animation indicative of embedding of heart pattern within contiguous tori
3D Heart surface (Kuska) 3D Heart surface (Trott) Animation of two complementary Lissajous curves on horn torus Animation indicative of embedding of heart pattern within contiguous tori
Equations for Valentines from the Wolfram Demonstrations Project, by Michael Croucher after work by Eric W. Weisstein and Michael Trott. Adaptation, with permission, of animation by Wolfgang Daeumler (Horn Torus)

Patterns of "voices" suggested by 3D variants of the Lauburu: As shown below, animations in 3D of the Lauburu are suggested by the 2D geometry. Wish respect to the global brain, these can be understood as complementary patterns of distinct "voices" as described separately (24-fold Pattern Implied by Dynamics of the Lauburu in 3D: visualization of the interplay of sets of voices in discourse, 2016).

Screen shots and 3D animations of complementary "voices"
using the geometry of mutually orthogonal lauburu to frame pathways of emergence and reabsorption
Single-plane lauburu framework
8-voice dynamics
Double-plane lauburu framework
16-voice dynamics
Triple-plane lauburu framework
24-voice dynamics
Single-plane lauburu framework: 8-voice dynamics Double-plane lauburu framework: 16-voice dynamics Triple-plane lauburu framework: 24-voice dynamics
Video (mp4). Virtual reality (x3d, wrl) Video (mp4). Virtual reality (x3d, wrl) Video (mp4). Virtual reality (x3d, wrl)

Adaptation of 2D representation of Shao Yung circle through animation in 3D: An exploratory exercise is presented as a concluding animation below. Of interest, in addition to the comments presented there, is the sense in which the projection of 2D geometry into 3D offers the possibility of converting lines into planes, circles into spheres, rotating the circles, or forming toroids from the circles when the pattern as a whole is rotated.

Presenting the circles as spheres usefully recalls the sense in which each constitutes a "world" for its cognitive inhabitants -- otherwise to be explore through the bubble metaphor, as suggested by the images above (Pricking the Bubble of Global Complacent Complicity Hyperdimensional insights from the physics of bubble blowing, bursting and collapse? 2017).

As noted there, and separately, such rotation invites consideration of the insights of Nikola Tesla with respect to the rotation of magnetic fields -- understood here in psychosocial terms (Imagining Toroidal Life as a Sustainable Alternative: from globalization to toroidization or back to flatland? 2019; Reimagining Tesla's Creativity through Technomimicry: psychosocial empowerment by imagining charged conditions otherwise, 2014). Of particular relevance, discussed in the latter, are the Potential implications of alternation and rotation in psychosocial fields and Encycling positive and negative for future sustainability,

Any restriction to 3D is an unnecessary limitation on the potentially requisite complexity of any global brain. The argument can be developed by provocative reference to comprehension of the "branes" imagined in fundamental physics (Global Brane Comprehension Enabling a Higher Dimensional Big Tent? 2011; Towards a bigger tent: recognizing responsible time horizons in cyclic terms? 2015). The smallest circle in the Saho Yung adaptation are then suggestive of "little tent thinking" in a period when there is need to articulate their relation to "bigger tents".

As discussed separately, given the insights from physics, the serpents and dragons of mythology might be better understood as features of visual renderings of the Calab-Yau manifold of string theory, as shown below -- or of Hopf fibration, namely a hypersphere in four-dimensional space (Cognitive Osmosis in a Knowledge-based Civilization: interface challenge of inside-outside, insight-outsight, information-outformation, 2017). In their animated form, these featured as indications of Animations variously suggestive of "being a waveform" in an argument exploring the possibility that people could -- in the light of the understandings of physics -- experience themselves as waveforms (Being a Waveform of Potential as an Experiential Choice: emergent dynamic qualities of identity and integrity, 2013). Both featured in a discussion of Transforming vehicles of identity between global and toroidal forms (2016).

Animations of visual renderings suggestive of higher-dimensional cognitive osmosis in a global brain
Hypersphere (Hopf fibration)   Calabi-Yau manifold


The image on the right from Wikipedia, which originally appeared on the cover of Scientific American, Nov. 2007). Such manifolds are higher-dimensional analogues of K3 surfaces of significance in superstring theory. The extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi-Yau manifold.

The image was previously used in a separate speculative discussion of Global Brane Comprehension Enabling a Higher Dimensional Big Tent? Strategic implication in encompassing nothing and coming to naught (2011).

The animation of the original image made use of selected aesthetic possibilities of Photoshop -- of which many others might be employed to improve the suggestive quality of the animation.

Dynamic patterns of play engendered by Homo ludens and Homo undulans?

It can be argued that social processes are now characterized by two forms of play (Playfully Changing the Prevailing Climate of Opinion: climate change as focal metaphor of effective global governance, 2005). On the one hand, there is the game-playing that is so characteristic of political processes and strategic initiatives, and the mind sets associated with competitive business and sport. On the other hand there is the pursuit of pleasurable play in its many forms, framed as irresponsible hedonism by some with incompatible social change agendas. In both senses it might be said that humans have already evolved from Homo sapiens into an unfortunate variant of the Homo ludens foreseen by Johan Huizinga (Homo Ludens: a study of the play element in cultures, 1938).

Given the role of movement in some forms of play, and most obviously game-playing and dance, of related interest are arguments regarding the embodiment of mind (George Lakoff and Mark Johnson, Philosophy in the Flesh: the embodied mind and its challenge to Western thought, 1999; Mark Johnson, The Body in the Mind: the bodily basis of meaning, imagination, and reason, 1987; Maxine Sheets-Johnstone, The Primacy of Movement, 1999).

In envisaging future evolution beyond Homo sapiens, one possibility is suggested by Homo conjugens (Authentic Grokking: emergence of Homo conjugens, 2003; Emergence of Homo undulans -- through a "grokking" dynamic? 2013). The latter is the theme of a penultimate chapter of the very detailed study by Daniel Dervin (Creativity and Culture: a psychoanalytic study of the creative process in the arts, sciences, and culture, 1990)

Playfullness: Argued otherwise, together with humour, such processes hold the promise of valuable approaches to kinds of integration by which a viable global brain might be characterized, as noted above (Humour and Play-Fullness: essential integrative processes in governance, religion and transdisciplinarity, 2005).

The introduction draws attention to the remarkable role of music in providing a direct engagement by many with the complex subtlety otherwise articulated through the allusive hypothetical abstractions of a "global brain".The visualizations above offer some clues, necessarily obscure in their own right. The role of playful aesthetics has been remarkably framed by Hermann Hesse (The Glass Bed Game, 1943) which has inspired many attempts to give it form on the web. These follow from the tradition of Rithmomachy -- otherwise known as the philosophers game. That inspiration is also evident in many online video games, to whatever extent these endeavour to embody or suggest the integrative function to which The Glass Bead Game alludes.

It has been argued that the singing of the Basque bertsolaritza offer another indication (Evoking Castalia as Envisaged, Entoned and Embodied: the great game informed by the bertsolaritza cultural process? 2016). This is especially the case in the light of their focus on improvisation (Improvisation in Multivocal Poetic Discourse: Basque lauburu and bertsolaritza as catalysts of global significance, 2016). Reference was made above to the manner in which the Basque symbol of the lauburu offers an encoding of multiple "voices" which may be explored in 3D dynamics

Musical harmony: It is perhaps most remarkable to note how many of the complex subtleties, paradoxes and harmonic possibilities of any comprehension of a "global brain" are explored in music and through the instruments by which it is played. Especially intriguing is to note the "unresolved" challenges between alternative tuning systems and the initiatives by which these have been variously addressed. 7 vs 8 why 12? Interplay of "voices" ***

The variety of these initiatives could be understood as exercises in simulating engagement with globality in ways contrasting to those otherwise articulated through use of computer information technology. These complementary ways typically rely of aesthetics to a high degree in enabling comprehension.

One extensive discussion of this relationship is provided by the horn player Richard O. Burdick (I Ching as a Structural Foundation for Music). The author offers a relationship of musical scales to the circular representation of hexagrams of Shao Yong (Shao Yung, Shaoyong) (I Ching Music -- Shau Yung's Circle) as well of a range of recordings using the hexagram relationships as a formal template for their composition.

Distinction encoding and keyboards: Given the traditional circular configuration of hexagrams -- an inspiration to Leibniz and his development of binary logic -- it is remarkable to note the degree to which a variety of keyboards have been envisaged in response to the needs of musicians and their audiences. Exploratory innovation in such designs is a feature of the freedom of elaboration and use of virtual keyboards on the web -- notably circular keyboards. examples ****

Most of the circular designs appear to be just that, namely visual reconfiguration of the conventional 88-key piano keyboard. The designs of these keyboards could be understood as reflecting and embodying the alternative metaphors through which a "global brain" might be envisaged -- and played as an "organ". Irrespective of whether notions of "globality" as such are meaningful in the musical domain, the metaphors also suggest ways in which "the player" (in a "global brain") might engage with singularity and embody it dynamically.

Potentially most intriguing, if only as an exemplification of this trend, is the production of the Piano Arc keyboard with 294 keys (Mary Brainerd, The World’s First Circular Keyboard Puts The Old Straight 88 To Shame, Golden Music, 27 November 2014; Lady Gaga’s Lead Keyboardist Invents 360° Keyboard With 294 Keys; US Patent US20130192444A1). The design continues to evolve; depending on the model, the circle may have 288 keys. To facilitate transportabiluty, it may be made of 72 note (6 octave) quarter-circle sections that can be variously combined, whether into an arc of 144 keys (as in the Dual Wing model) or a 24 octave full circle of 288 keys (as in the  Brock360 model). The original model combined three 88 note keyboards, and a small control section.

Several videos illustrate the manner by which it may be played by one or more (Piano Arc Circular Controller Keyboard Synthesizer, YouTube, 2016; Flipping the chords to Drake on a piano arc via Brockett Parsons Artist). These are notably helpful in framing metaphorically the question as to how a player in a global context can engage with an extensive range of encircling keys, some of which are necessarily not visible (being "behind") at any one time. Options of significance are:

It is less evident how "24 octaves" might be played in practice.

These options effectively mirror the pattern through which distinct cognitive and strategic domains are governed and managed by specialization (virtually to a degree of pathological fragmentation). They frame the question as to the the cognitive skills to play the full pattern of octaves -- whether or not the resulting "music" can be heard or appreciated. Given a prominent strategic articulation of the global challenge of "doughnut economics", it is especially curious to note the recognition of that form in the design of a circular keyboard (Robert Klara. Can Lady Gaga’s Keyboardist Make His Donut-Shaped Keyboard Into a Brand? Adweek, 20 May 2015

Applying hexagrams to piano keys: Inspired by Burdick's ongoing explorations, the tentative approach taken here has been simply to math the pattern of 64 hexagrams to an 8-octave circular layout of piano keys, as presented in an animation below. An obvious design challenge to any such mapping is the distinction in musical terms between the notion of "octave" and the manner in which octaves overlap through an 8-fold succession of 7 white keys (namely 56). The mapping option taken was to treat each 8-fold hexagram "house" as overlapping the next "house" by one hexagram; the two variants being alternatively evident through animation. The overlap is indicated in the first position of the octave by a hexagram appearing in red in the animation (below)

Comparable images suggestive of "playful" engagement with a circle of possibilities?
Shao Yung circle of hexagrams 8-octave circular keyboard (96 keys)
(hexagram "houses" mapped to each octave)
20-octave circular keyboard (240 keys)
Hexagram circle of Shao Yong 8-octave circular keyboard (96 keys) 20-octave circular keyboard (240 keys)
     

Requisite helical cognitive engagement within a global brain?

Spiral periodicity of musical scales: The questionable effort to reconcile the circular configuration of 64 hexagrams with a circular pattern of 8 octaves (as in the animation above) highlighted the possibility that a more appropriate design could be achieved through a spiral form. The "overlapping" could then be a feature of helical recurrence at a distinctive pitch level -- a pitch helix, namely a visual representation variously explored in music theory (Diana Deutsch, The Paradox of Pitch Circularity, Acoustics Today 6, 2010, 3; Diana Deutsch, et al, Pitch circularity from tones comprising full harmonic series, The Journal of the Acoustical Society of America, 124, 2008, 1; Roy D. Patterson, Spiral Detection of Periodicity and the Spiral Form of Musical Scales, Psychology of Music, 14, 1986, 1).

In music theory, the spiral array model is an extended type of pitch space. This is a mathematical model involving concentric helices (namely an "array of spirals"). It is understood as representing human perceptions of pitches, chords and keys in the same geometric space as first proposed by Elaine Chew (Towards a Mathematical Model of Tonality, MIT, 2000; Mathematical and Computational Modeling of Tonality: theory and applications. International Series in Operations Research & Management Science. Springer, 2014)

Spiral mapping: The choice of a 2D spiral mapping metaphor for 64 hexagrams (below centre) featured in an earlier argument (Adaptive Hypercycle of Sustainable Psychosocial Self-organization: designing a mapping of a Chinese metaphorical pattern language, 2010).

The emphasis in this argument is on the ability of the human mind to engender and recognize patterns, as discussed in the light of the recent study by Jeremy Lent (The Patterning Instinct: a cultural history of man's search for meaning, 2017), as critically reviewed separately (Patterning Intuition with the Fifth Discipline, 2019). It is in this sense that quite disparate instances of patterning substance may be compared as arising from that proclivity, most notably as argued by George Lakoff and Rafael E. Núñez (Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2000).

A fundamental exercise in patterning, in contrast with the tabular convention is the helical periodic table of chemical elements (G. Schaltenbrand, Darstellung des periodischen Systems der Elemente durch eine räumliche Spirale, Z. anorg. allgem. Chem., 112, 1920). An extract is presented below right. It is important to note that there have been numerous attempts to organize in a comprehensible manner the chemical elements (Internet Database of Periodic Tables, Chemogenesis), with the struggle continuing (D. H. Rouvray and R. Bruce King (Eds). The Mathematics of the Periodic Table, 2005).

Comparable recognition of helical organization
Helical organization of pitch space Spiral organization of hexagrams Helical periodic table
Helical organization of pitch space Spiral arrangement of 64 hexagrams of I Ching Helical periodic table
Elaine Chew [CC BY-SA 4.0], via Wikimedia Commons   G. Schaltenbrand, 1920

Given the role of the torus variously highlighted above, possibilities of comprehensible representation of helical organization have been discussed separately in relation to its coiling (Visualization in 3D of Dynamics of Toroidal Helical Coils -- in quest of optimum designs for a Concordian Mandala, 2016). Also of relevance is the helical mapping of hexagrams onto a globe by József Drasny (The Image of the Cosmos in the I Ching: the Yi-globe, 2007) as discussed separately (Enhancing coherence through spherical triangulation, 2011).

Spiral dynamics:  In experiential terms, the spiral form can be explored through the framework of spiral dynamics (Don Edward Beck and Christopher Cowan, Spiral Dynamics: mastering values, leadership and change, 1996; Don Edward Beck, et al, Spiral Dynamics in Action: humanity's master code, 2018). This is a structured evolutionary model of adaptive intelligence which has spawned much discussion and (sometimes tangential) integration of concepts by other theorists, such as the AQAL integral theory of Ken Wilber.

Unfortunately most of the images clarifying the spiral stages (tiers) of development are subject to copyright. These are distinguished by colour: Beige: individual survival; Purple: tribal; Red: power and dominance; Blue: follows moral precepts of the group; Orange: autonomy and achievement; Green: egalitarianism and community; Yellow: integration and personal responsibility; Turquoise: collective individualism (Scott Jeffrey, How to Use Spiral Dynamics for Psychological and Leadership Development).

Symbolic traces: laurel wreath and Caduceus: It is intriguing to note the traditional and continuing importance attached to the laurel wreath as a symbol of victory and completion -- as well as of death. Curiously the many 2D images of the laurel wreath are intimately associated with the logos of globally oriented institutions, notably the United Nations and its agencies -- and as such their reproduction is severely constrained by intellectual copyright and paywalls. Of further interest is the seeming absence of variants in 3D -- meriting interpretation in the light of enabling comprehension of globality by such bodies. The animation of the Caduceus is an adaptation of a set of screen shots of a 3D model.

It was for this reason that a 3D variant was produced in order to enable distinctive manipulation of the two opposing fronds. Somewhat ironically, the leaves were adapted from an exercise in modelling the Tao (yin-yang) symbol in 3D, notably with the aid of Sergey Bederov, Senior Developer at Cortona3D, as described separately (Stages in imagining a 3D Tao symbol in virtual reality, 2019. The droplet-like shapes composig the symbol have been distorted in the 3D images below.

Helical insights from 3D representation of Laurel wreath and Caduceus
Laurel wreath: static symbol of binary completion or sacred flame Laurel wreath spiral upright
rotation
Laurel wreath spiral inverted
rotation
Rotation of Caduceus in 3D
Laurel wreath 3D Laurel wreath spiral upright Laurel wreath spiral invert Rotation of Caduceus in 3D

Dragon dance, bullfighting and storyboarding: Of particular interest is the sense in which the conventional static laurel-wreath can be understood as implying a dynamic only evident in 3D as shown in the central animations below. Both are reminiscent of the double dragon dance in quest of a pearl -- so central to Chinese culture and widely depicted in its iconography. The double spiral symbolism is also evident in the Caduceus of Western culture, now a symbol of both healing and commerce. Traditional depictions of the quest for the pearl are reminiscent of the strangely elusive role associated with "global" and even more specifically with the function of a "global brain". Framed as shown by a helical pattern, the challenge to its comprehension is all the greater if avoidance of premature closure is to be recognized as fundamental (Engaging with Elusive Connectivity and Coherence: global comprehension as a mistaken quest for closure, 2018).

With respect to the dance between the two branches of the laurel wreath, this was explored visually in a separate storyboarding exercise regarding the dance between matador and bull. The form of the wreath may be related metaphorically to the tradition of engagement with bull horns, whether in worship in sport or in bullfighting (Transformation of Global Governance through Bullfighting: visual symbols and geometric metaphors, 2009; Game-playing, bull-leaping and laurel wreaths, 2014). Such horns are a useful reminder of the dangerous horns of the dilemmas so characteristic of governance.

Whether the drama is focused on the quest for a pearl or mastery of the bull, the global brain narrative, with its trend toward singularity-collapse, can be understood as fundamentally a dramatic pretence (as suggested above). Is the high drama comparable with the mutual entanglement of the classic tales (Entangled Tales of Memetic Disaster: mutual implication of the Emperor and the Little Boy, 2009; "Big Brother" Crying "Wolf"? But them "wolves" are a-changin' -- them's becomin' "werewolves"! 2013)? Is comprehension of the "pearl" then conflated with comprehension of "singularity" -- confused by misleading warnings and vainglorious posturing, as highlighted by those tales?

Elusive incommensurability of opposites: The conventional laurel wreath is particularly valuable in implying both the possibility of circular completion whilst indicating a form of junction at the base and a mysterious gap at the top -- where the two branches do not connect. The presentation in 3D of the branches moving in relation to each other such as to suggest a spiral form is indication that any connection between opposites is a fundamental challenge to comprehension -- a paradox exemplified by their mirroring of each other.

The challenge is clarified otherwise in the image of the caduceus on the right. Again the nature of the connectivity in cognitive terms is elusive, if not a matter of fundamental risk, as implied by the snake-like forms. The gap merits consideration as a form of cognitive abyss.

One approach to such connectivity is through "correspondences", beyond the simpler assumptions of correlative thinking (A. C. Graham, Yin-Yang and the Nature of Correlative Thinking, The Institute of East Asian Philosophies, 1986). Perhaps appropriately, the validity of correspondences as a bridge is itself a matter of controversy (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007).

Challenge of representation and comprehension: The Shao Yung circle of hexagrams can be presented in 3D (below centre). The rotation highlights a potential problem of representation using current X3D norms in that the hexagrams may be "reversed" when particular techniques are used. Thus one perspective on the circle, during the rotation, corresponds correctly to the original; the other is incorrect. This is inadvertently indicative of a potential problem of comprehension. The misrepresentation can be corrected with other techniques. The issue is of relevance in that the left hand branch in the original is characterized by 4 sets of hexagram "houses" with an unbroken line at the bottom; the 32 hexagrams in the 4 "houses" in the right hand branch have a broken line at the bottom. Marking the start of each "house" by rendering the hexagram in red helps to clarify the issue.

The opposing "branches" of the circle can be angled with respect to each other in 3D, as was done with those of the laurel wreath above. Two variants are presented below which serve to indicate other potential challenges to representation and comprehension -- despite the technical problem of reversal in the central image having been rectified. These arise from how the opposing branches are angled with respect to each other. The variant on the left corresponds more closely to the original; that on the right has one branch reversed.

Use of a central sphere in the angled variants serves to recall the pursuit of the pearl in the traditional dragon dance. The issues of representation serve to highlight the challenges of mutual comprehension between opposites -- most notably between right and left.

Rotation in 3D of angled hexagram branches illustrating challenge of "reading"
Angled hexagram "branches" Circle of hexagrams in 3D Angled hexagram "branches"
Rotation in 3D of correctly angled branches of circle of hexagrams Rotation of circle of hexagrams in 3D indicating representational problem Rotation in 3D of incorrectly angled  of circle of hexagrams
     

The possibility of confusion in the comprehension between opposites is further illustrated in 3D by the presentation in rings of the rows of the Shao Yung central square arrangement (below left). The order needs to be variously "twisted" and "inverted" to achieve correspondence between the upper and lower trigrams in the stack of rings. This is a reflection of the mirror imaging embodied in the sequa re arrangement.

Reconciliation of 3D organization of hexagrams in rings (by row) with Shao Yung square (by row)
Shao Yung square arrangement Rings by row
(no twist)
Rings by row
(with inversion of upper set)
Rings by row
(with inversion and twist)
Shao Yung square arrangement  (upper)
Shao Yung square arrangement  (lower)
       

Challenge of 7-fold versus 8-fold organization: octaves versus hexagrams: As noted above with respect to the grouping of 7 major scale keys into an "octave", the 8-fold organization is achieved because one of the keys is comprehended as common to a second octave. This "confusion" is resolved by recognizing that the pattern is helical as shown in the central image below -- in contrast with that on the left. The question then arises as to whether the challenging "twist" in the organization of the matrix of hexagrams (above left) is clarified by organization in a helical pattern.

One experiment with such an organization is presented below right in which the upper portion of the matrix is mapped onto the red helix and the lower onto the green. The convention adopted is to position the hexagram with unbroken lines at the lowest position of the green helix, with the hexagram of broken lines in the highest position of the red helix -- offering a degree of correspondence with the matrix. In this variant it is either the lower or the upper trigram which is common between the distinctive helix turns -- whether vertically or horizontally. Other variants can be explored.

Comparison of 3D helical organization of musical pitch with a helical pattern of hexagrams: the challenge of 7 versus 8
Ring configuration of pitch succession Helical organization of musical pitch Double helical organization of hexagrams
Ring configuration of musical octaves Helical organization of pitch space Double helical organization of hexagrams
The animations have been constructed using X3D Edit, allowing parameters to be variously modified using a text editor. The models here (and above) have many technical defects which could be readily circumvented with greater skill.

Chirality (handedness); The example of double helical organization of hexagrams (above right) is arguably an instance of a pattern exhibiting a relatiely high degree of coherent complexity coducive to comprehension ("CCCC"?) -- and as such potentially indicative of the organization of the global brain. As a resonance hybrid, this might however be more appropriately associated with alternation between alternative helical patterns.

Examination of the variant shown highlights the issue of chirality -- namely the direction of rotation of the helix, with the two variants being mirror images of each other. This is a primary characteristic of DNA (Emily Singer, New Twist Found in the Story of Life’s Start, Quanta, 26 November 2014; Youri Timsit, DNA Self-Assembly: From Chirality to Evolution, International Journal of Molecular Sciences, 14, 2013, 4 Vsevolod A. Tverdislov. Chirality as an Instrument of Stratification of Hierarchical Systems in Animate and Inanimate Nature, 2012).

With the origin of life held to be associate with preference for one chiral form, the question might be asked whether the emergent organization of the global brain is to be similarly understood or whether it takes the form of a resonance hybrid. The insights of biology into the fundamental role of DNA supercoilding are potentially relevant to any development of the psychosocial argument with respect to the enoding offered by hexagrams (Ruggero Cortini, Chiral theory of DNA supercoiling, Imperial College, 2013; Paolo Bettotti, et al, Structure and Properties of DNA Molecules Over The Full Range of Biologically Relevant Supercoiling States, Scientific Reports, 8, 2018, 6163).

In response to the current tragedy of polarization in society and their challenges to governance, such indications suggest that what is required is not so much an approach to "conflict resolution" -- potentially oversimplistic under the circumstances -- but rather a focus on chirality and its "resolution". These may only be comprehensible through topological forms of higher dimensionality, as suggested by fundamental physics. In that respect, issues relating to compactification of "extra dimensions" are then a primary challenge to their comprehension.

Double helix, triple helix and juggling patterns: Through the biological role of DNA, the fundamental importance of helical organization has evoked considerable attention. Relatively little attention has been given to its psychosocial implications, if only in metaphorical terms (Climbing Elven Stairways: DNA as a macroscopic metaphor of polarized psychodynamics, 2007; Walking Elven Pathways: enactivating the pattern that connects, 2006). Reference to the triple-stranded variant of DNA is less widely made.

Attention has however recently been focused on the Triple Helix Model of Innovation which refers to a set of interactions between academia, industry and governments, to foster economic and social development. This focus may imply that it is a specific instance of forms of psychosocial organization which merit attention -- gi en the importance various attached to triadic organization and symbolism, as discussed separately (Contrasting the implications of "triple helix" -- cognitive and otherwise, 2017; Psychosocial Learnings from the Spiral Form of Hurricanes: implications of the triple helix and the 3-fold triskelion as "cognitive cyclones"? 2017).

The Triple Helix model have evoked attention to more complex possibilities. Especially noteworthy is consideration of a Quadruple Helix approach by the a Committee of the Regions of the European Union (Using the Quadruple Helix Approach to Accelerate the Transfer of Research and Innovation Results to Regional Growth, 2016). A Quadruple and quintuple innovation helix (Q2IH) framework has been developed. Of potential relevance is the relationship to more conventional devices for articulating strategic preoccupations, as discussed separately (Symbolic stars vs Strategic pillars; Polyhedra vs Helices; Logic vs Comprehension?, 2017). This frames the question of possible Biomimetic embedding of N-tuple helices in spherical polyhedra (2017).

Curiously, but appropriately (given the challenges of governance), a triple helix is characteristic of the "braiding" of one juggling pattern (as illustrated below) as mathematically understood (Governance as "juggling" -- Juggling as "governance": dynamics of braiding incommensurable insights for sustainable governance, 2018).

Comparison of helical molecular structure with patterns of innovation and juggling
Variant of the double helix
Triple-stranded DNA Triple Helix
3-ball juggling pattern as a braid
Triple Helix (Australia) 3-ball juggling pattern
Reproduced from Wikipedia DubOOIan [CC BY-SA 4.0] University of Melbourne Monash University, Melbourne

Supercoiling of higher degree as characteristic of global brain organization? It is intruiging that organic life appears to resolve the challenges of chirality through processes associated with supercoiling of DNA. As noted by Wikipedia, supercoiling is important in a number of biological processes, such as compacting DNA, and by regulating access to the genetic code, DNA supercoiling strongly affects DNA metabolism and possibly gene expression Additionally, certain enzymes are able to change DNA topology to facilitate functions such as DNA replication or transcription (Brad A. Krajina, et al, Large-Scale Conformational Transitions in Supercoiled DNA Revealed by Coarse-Grained Simulation, Biophysical Journal, 111, 2016, 7; Twists and Turns of Life: patterns of DNA supercoiling, ScienceDaily, 4 April 2016).

As noted by the latter:

The classic double helix structure that one associates with DNA is but an extremely limited view of its physical 'shape'. The molecule that holds the codes of life is capable of further winding itself into myriad complex shapes called 'supercoils' that are capable of affecting gene expression patterns.... DNA molecules are wound and rewound into complex structures that condense their immense lengths to a fraction of their actual size in order to fit their long strings of information into microscopic cells. But this 'packed' DNA that fits neatly into a cell also needs to be 'unpacked' periodically for gene expression and replication.

This frames the question as to whether analogues of some kind may prove vital to comprehension of the problematic challenges of polarization in psychosocial processes (DNA Supercoiling as a Pattern for Understanding Psycho-social Twistedness, 2004). More intriguing is why so little attention is given to that possibility -- given the crisis of polarization in society. In this respect, given current preoccupation with the Triple Helix model of innovation, a suitable provocation is offered by the insight from biomolecular dynamics: The triple helix does not represent the most thermodynamically stable structure that can be adopted by two complementary...strands. (DNA Supercoiling Is Required for Intramolecular Triplex Structures, Science Direct).

Supercoiling of DNA Continuous 9-winding helical spiral Double helical spiral 5-coil pattern
DNA supercoiling Continuous toroidal knot with 9 windings Pseudo-counter-coil with helices out of phase and  spheres travel  in opposite directions) Pseudo-counter-coil in 5-fold pattern of helixes
User:Notahelix, User:JoKalliauer [CC BY-SA 3.0], via Wikimedia Commons Reproduced from Towards a 3D visualization of toroidal counter-coiling dynamicss, 2016

It is presumably within this topological context that the mysteries of psychosocial mutation and morphogenesis are to be clarified -- notably in the light of te insights of René Thom (Structural Stability and Morphogenesis: an outline of a general theory of models, 1972). The possibility is an invitation to further specualtion (Reframing the Dynamics of Engaging with Otherness: triadic correspondences between topology, Kama Sutra and I Ching, 2011). Is the Shao Yung circle of hexagrams itself to be understood as a supercoil?

Global brain comprehension from an "axial" perspective? Little reference is made to the axial perspective of helical organization, as notably illustrated in the case of DNA (below left; and see especially Reginald Brooks, GoDNA: The Geometry of DNA. 2001). It could be argued that a significant number of centrosymmetric logo-style devices, by which organizations and strategic initiatives are identified, could be understood as "axial" perspectives on complex helical structures that are less readily presented or comprehended (World Guide to Logotypes, Emblems and Trademarks of International Organizations). Could the UN's 8-fold Millennium Development Goals and the 16 (+1)-fold Sustainable Development Goals be more appropriately addressed through recogition in terms of their 8-fold and 16-fold helical entanglement respectively?

As yet to be explored is whether and how appropriate helical arrangement of hexagrams offers an axial view of the distiguishing trigrams in the final turn of the helix in a manner corresponding to the alternative BaGua arrangements shown below centre.

Comparable representations of axial views implying helical entanglement ?
Axial view of DNA
Logo of Scientific and Medical Network Alternative BaGua trigram arrangements Sustainable Development Goals Spiral keyboard
Fuxi - Earlier Heaven King Wen -- Later Heaven
Axial view of DNA SMN Logo BaGua -- Fuxi - Earlier Heaven BaGua -- King Wen -- Later Heaven Sustinable Development Goals Spiral keyboard
    Reproduced from Wikipedia United Nations Spiral keyboard, Wifflegif

Given their valued cognitive role, many mandalas and yantras might well be understood from that perspective -- potentially as "standing waves" -- each possibly to be understood in terms of a "brain scan".

Animations of standing wave as vibrations of a circular membrane
Standing wave in two dimensions. Higher harmonic standing wave on a disk
Standing wave in two dimensions. Higher harmonic standing wave on a disk
Oleg Alexandrov [Public domain], via Wikimedia Commons;

Spiral and helical staircases: Whilst many of the helical patterns indicated above can be considered abstractions, it is remarkable that experience of helical movement in a spiral staircase is widely recognized and appreciated. This common experience is especially relevant to this argument in that it is consistent with the above-mentioned arguments regarding the embodiment of knowledge through movement. It is potentially for this reason that such staircases have long been a feature of buildings of symbolic significance, as discussed by George L. Hersey (The Monumental Impulse: architecture's biological roots, 2001). Wikipedia offers a List of ancient spiral stairs. He notes the degree of interest of Leonardo da Vinci in this pattern and its relationship to the helical structure of many snail shells. Leonardo was also the architect of a much-famed staircase (Da Vinci Designed a Double Helix Staircase at the Château de Chambord, Ancient Origins, 2018).

Both double spiral and double helix staircases are possible, with two independent helical stairs in the same vertical space, allowing one person to ascend and another to descend, without ever meeting if they choose different helices. Fire escapes, though built with landings and straight runs of stairs, are often functionally double helices, with two separate stairs intertwined and occupying the same floor space.

In contrast with the abstractions above, it is also remarkable that a number of websites enable anyone to design a spiral staircase (but not a double helical variant), with an extensive choice of parameters and possibility of visualization of the result:

Brainwaves and feedback loops in a global brain?

As mentioned above, early studies of a viable organizational brain focused on the cybernetics of its control (Stafford Beer, Brain of the Firm: the managerial cybernetics of organization, 1981). Beer endeavoured to apply those insights to the organization of the governance of Chile under Salvador Allende through the Cybersyn Project (1971-1973) -- necessarily uncompleted as a consequence of the controversial intervention by the USA. This focus emphasizes the role of feedback loops. As noted above, these have also been a feature of the profiling of thousands of interconnected entities of relevance to governance (Simulating a Global Brain: using networks of international organizations, world problems, strategies, and values, 2001; Feedback Loop Analysis in the Encyclopedia Project, 2000; Tomas Fulopp, Loop Mining in the Encyclopedia of World Problems, 2015).

In a period in which the policy sciences now recognize the complexity of so-called wicked problems -- effectively dynamic knots in topological terms, there is a case for recognizing the complex of loops which characterize a global brain (Encycling wickidity in the light of polyhedral viruses and their mutation, 2015). The latter featured in a critical review of the 17th International Futures Conference on Tackling Wicked Problems: where futures research, education and action meet (Turku, 2015).

Given promotion of the global brain metaphor, it is then indeed appropriate to ask in what manner its organization might appropriately feature "brainwaves" -- however these might be understood as an aid to comprehension of its emergent integrity. Are there clues relating the patterns of loop and wave in a fruitful manner? Curiously it is the topology of knots which offers one valuable lead.

Given that both brainwaves and feedback loops are abstractions, even metaphors -- although of a different kind -- it could be usefully asked to what extent both are usefully understood as sinusoidal and comparable in some way with "waves" more generally understood, especially in the light of the above-mentioned arguments of Alexander Wendt. Should a feedback loop indeed be understood as a form of closed wave, or even a standing wave -- or the global brain as a quantum computer? Thus for Wendt:

Quantum brain theory hypothesizes that the brain is able to sustain quantum coherence - a wave function - at the macro, whole-organism level (Chapter 5). How the brain might do this is not agreed on by the theory's advocates, who have explored the possibility from different angles. The pioneering and most well-known approach is due to Stuart Hameroff and Roger Penrose, but as we will see there are other approaches as well. Notwithstanding their differences, however, their conclusion is the same -- that the brain is a quantum computer. Whether quantum brain theory is true is speculative and deeply controversial, but it has attracted a growing number of advocates. (Quantum Mind and Social Science: unifying physical and social ontology, 2015, p. 30)

There is a considerable literature on the relation between brainwaves and individual experience -- with more speculative arguments concerning the implications for group experience. There is every reason to suspect that "brainwaves" of some kind are characteristic of the global brain -- if only to be understood as cybernetic feedback cycles, especially psychosocial systems.

In the case of the individual, one explanation of brainwaves suggests that:

It is a handy analogy to think of brainwaves as musical notes - the low frequency waves are like a deeply penetrating drum beat, while the higher frequency brainwaves are more like a subtle high pitched flute. Like a symphony, the higher and lower frequencies link and cohere with each other through harmonics. (What are Brainwaves? Brainworks)

Distinctions are commonly made, with their respect to their experiential implications, between:

Possible pattern of global engagement with time in the light of distinctive "brainwaves" (tentative)
  Brainwaves
Anticipatory planning period variously experienced / understood
cycles / sec (Hz) cycles / 100 secs
  Min. Max. Max Min Seconds? Minutes? Hours? Days? Months? Years? Generations?
Delta 0.3 3 333.3 33.33 333 to 33 333 to 33 333 to 33 333 to 33 333 to 33 333 to 33 333 to 33
Theta 3 8 33.3 12.5 33 to 12 33 to 12 33 to 12 33 to 12 33 to 12 33 to 12 33 to 12
Alpha 8 12 12.5 8.33 12 to 8 12 to 8 12 to 8 12 to 8 12 to 8 12 to 8 12 to 8
Beta 12 38 8.33 2.63 8 to 3 8 to 3 8 to 3 8 to 3 8 to 3 8 to 3 8 to 3
Gamma 38 42 2.63 2.38 3 to 2 3 to 2 3 to 2 3 to 2 3 to 2 3 to 2 3 to 2

Such a table frames the question as to how cyclic correspondences might be found in psychosocial systems. This has been a focus of social cycle theory, although how this might be driven by psychological and cognitive processes comparable with "global brain waves" is necessarily far from clear -- and seemingly unexplored. Examples of the literature include the following:

In summarizing contemporary theories, Wikipedia notably distinguishes from models focused specifically on American society:

(3–5 yrs) Just-in-time?
Framework for comparison of engagement with time in terms of psychosocial and economic cycles (tentative)
  Psychosocial cycle Economic cycle
Business cycle
Collective reaction time
      Planning period Feedback cycle Learning cycle Cycle of violence Crisis response
Delta

Demographic cycles
Dynastic cycles
Cultural memory

Grand supercycle Very long-term Very long-term Very long-term Very long-term Indeterminate response?
Theta "Long cycles" (70-100 yrs)
Kondratiev wave (45-60 yrs) Long-term Long-term Long-term blood feud? Much delayed
Alpha   Kuznets swing (infrastructural investment) (15-25 yrs) Medium-term Medium-term Medium-term Medium-term Delayed response
Beta   Juglar cycle (fixed investment) Short-term Short-term Short-term Short-term Proportionate respone?
Gamma News cycle? Kitchin cycle (inventory)Very short-term Just-in-time? Very short-term Rapid reaction

Given the unexplored bias in the use of the conventions of statistical graphing in 2D, "waves" -- especially those in sinusoidal form -- are necessarily presented as a dynamic in 2D. The following animation is a valuable indication of how a 3D helical form may result when waves recognized in distinct dimensions are combined. Rather than crises being associated with "waves" in 2D, they may take helical form as is so evident in the dramatic global impact of hurricanes. These frame the question of the nature of "hurricanes" in the global brain, as suggested above (Psychosocial Learnings from the Spiral Form of Hurricanes, 2017).

Animation of helical wave structure derived from mutually orthogonal sinusoidal x and y components
Helical wave structure  emerging from mutually orthogonal  sine waves
de:Benutzer:Averse [CC BY-SA 2.0], via Wikimedia Commons

Pathology of the global brain?

Central to this argument is the brain, metaphorically understood, as usefully summarized by Charlie Gere (Brains-in-vats, giant brains and world brains: the brain as metaphor in digital culture, Studies in History and Philosophy of Science, 35, 2004, 2). Given the current argument for the "brain death" of global institutions, it is then vital to ask whether there are insights from that metaphor into the possible pathology of the global brain.

One bridging approach is that offered in the light of exploration of "small-world network" insights (Danielle Smith Bassett and Edward T Bullmore, Small-World Brain Networks, The Neuroscientist, 12, 2007, 6). The latter argues:

Many complex networks have a small-world topology characterized by dense local clustering or cliquishness of connections between neighboring nodes yet a short path length between any (distant) pair of nodes due to the existence of relatively few long-range connections. This is an attractive model for the organization of brain anatomical and functional networks because a small-world topology can support both segregated/specialized and distributed/integrated information processing. Moreover, small-world networks are economical, tending to minimize wiring costs while supporting high dynamical complexity.

The problematic conditions to which the human brain is vulnerable then offer clues to conditions to which the global brain might be subject at various stages in its emergence and evolution. A previous exericise is suggestive of possibilities (Memetic and Information Diseases in a Knowledge Society: speculations towards the development of cures and preventive measures, 2008). This suggests the need for a neuropathology of the global brain and the networks with which it is associated -- especially given the importance now associated with neural learning or deep learning. Thus artificial neural networks (ANN) or connectionist systems are computing systems that are inspired by, but not identical to, biological neural networks that constitute animal brains.

A comprehensive list of human brain-related disorders is provided by the Brain Foundation. These can, for example, be variously clustered as:

Alzheimer’s disease
Autism and neural development diseases
Autoimmune diseases
Dementias
Tumours (brain cancer, etc)
Seizure disorders (epilepsy, etc)

Infections
Mental disorders
Movement disorders (Parkinson’s, taxias, etc)
Neuromuscular diseases
Stroke and vascular diseases
Trauma

Given preference for the brain metaphor, it is surely naive not to anticipate some form of pathology -- to which the global brain may already be unknowingly subject, given avoidance of such consideration. The argument above with respect to "small-world networks" is for exampe indicative of the narrow focus of the particular worldviews promoted by most disciplines -- readily to be construed as potentially pathological, given their inability to articulate or enable an interdisciplinary or transdisciplinary perspective to address the current problematic conditions of global society and its governance. Provocatively it might be asked the extent to which such worldviews are framed in a manner comparable with "blood clots" on the global brain -- increasing its suceptibility to "strokes". Ironically current research on "global brain ischemia" has implications only for the individual human brain.

Notably problematic is the manner in which communication within the emerging global brain is highly constrained by intellectual copyright. Understood in metaphorical terms, "copyright" could be recognized as fundamental to the regenerative capacity of global society, as has been so clearly understood in the case of living organisms through the process of DNA replication. This is the biological process of producing two identical replicas of DNA from one original DNA molecule. Does the current role of intellctual copyright enable or inhibit this process in the global brain at this critical time -- as effectively acknowledged by current controversy in that regard (Google and the World Brain, 2013)?

With respect to global governance, insights into movement disorders of the individual offer multiple insights into the widely acknowledged challenges of coordination in governance -- tragically comparable with the forms of spasticity derived from cerebral palsy, as separately evoked (Reframing the Square Wheels of Global Governance, 2017). Is this the primary condition of the emerging global brain at this time?

Global brain as an organ: playable, playful or neither?

Metaphorical images of a global brain? A much-cited framework by Gareth Morgan distinguishes 8 ways in which organization tends to be comprehended: machines, organisms, brains, cultures, political systems, psychic prisons, flux and transformation, and instruments of domination (Images of Organization, 1986). This was followed by a study of its implications (Imaginization: new mindsets for seeing, organizing and managing, 1993). Clearly whatever is implied as an integrative nexus by "global brain" draws to different degrees (and for different audiences) on several of these images. A key author emphasizes the biological metaphor of "organ" (Francis Heylighen, The Global Superorganism: an evolutionary-cybernetic model of the emerging network society Social Evolution and History, 6, 2007). Does the Gaia hypothesis reflect one insight into the nature of such a superorganism?

"Global brain" as a surrogate for global "unity"? It is typical for global instititutions to articulate desperate calls for "unity". Unfortunately the promoted understandings for such integrative coherence are typically naively simplistic -- and are notably unattractive to the populations of the world. This is not helped by the promotion of the evolution towards a form of singularity which is both obscure and fraught with unanswerable questions -- especially when variously conflated with emergence of a global brain as constituting some kind of more viable alternative.

Arguably the current plight of a NATO -- framed as "brain dead"-- is indicative of the institutional challenge (Are the UN and the International Community both Brain Dead? 2019). A case could be made for articulating and comprehending global institutions as forms of necessarily higher dimensionality (Envisaging NATO Otherwise -- in 3D and 4D? 2017). More specifically however, the singularity of any global brain could be challenged in musical terms -- notably the common expectation that "unity" requires that everyone should "sing from the same hymn sheet".

A musical framework is valuable as a reminder of the forms of emergent unity which are associated with polyphony and its harmronic orchestration. "Unity" is not a question of hitting all 64 notes on a keyboard simultaneously as might be held to be the essence of what is proposed. More intriguing is the sense in which unity is an emergent mode of organization associated with the process of playing music.

Is it through that metaphor that the emergence of a global brain -- and its essentially dynamic nature -- might be better understood?

Musical organ metaphor? With respect to any comprehension of the organization of the global brain, the association between "organization" and "organ" -- as a musical instrument -- has not been cultivated, except by inference in The Glass Bead Game of Hermann Hesse. It might be assumed that a global brain is the context par excellence for some form of infinite game as envisioned by James P. Carse (Finite and Infinite Games: a vision of life as play and possibility, 1987; Niki Harré, The Infinite Game: how to live well together, 2018). Greater insight is to be found in recognition of the pipe organ as a metaphor (Agnes Armstrong, Pipe Organs as Metaphors: voices of times and traditions, University at Albany). For Armstrong:

Pipe organs serve as metaphors on a number of levels. In a basic way, the instrument can be seen as a metaphor for the people who design and build it. The very structure of a pipe organ is a representation of a human being, with scores of moving parts and a wind-breathing system, all integrated into a complex machine. Producing sounds organized in several dimensions, it speaks a musical language which communicates with its auditors. The bellows are the lungs of the instrument. The pipes themselves are referred to in anatomical terms, their components being labeled as body, foot, mouth, and lip. As for the tonal aspect of the organ, just contemplate the plethora of pipes - pipes of every size and kind, of every shape and color - tall or small, slender or wide, from booming diapasons to lilting flutes to brilliant trumpets - "families" of pipes. Organ pipes are a metaphor for humanity. Pipes in a newly-constructed organ must "settle in" and "make their own community" - large organs in large cities, smaller organs in towns and villages. While great organs - as great cities - offer rich and extensive opportunities for both player and listener, less elaborate instruments suggest the limitations of small towns everywhere. More importantly, each pipe organ is a metaphor of the particular society and culture in which it is created.

Music of the spheres? The link between an institutional understanding any musical organization (despite the etymological origins), seems to have been lost in the mists of time with early references to music of the spheres and singing the organum. As noted by Nicolas Reeves, From the Harmony of the Spheres to Spherical Harmonics: the potential of wave-based morphogenetic processes for musical and architectural composition, Plymouth University) :

Putting things into order, even those that are non-measurable: this project describes the long, global evolution of knowledge during the Middle Age, over the background of a cosmos that was already perfectly ordered by Ptolemy’s circular harmonics. The underlying hope was the order of the cosmos would pervade all the cosmology of the time, and that the world would become progressively more explicitable through the power of reason, within the limits defined by the religious establishment for which the cosmos rested axiomatically on a mystery that escapes human understanding. Along with this hope, the idea of the reverse process began to emerge: in art disciplines that implied a form of composition, such as music or architecture, complex object could be constructed through the ordered and hierarchized combinations of simple elements. These objects would be entirely understandable, or in other words, transparent to the mind: every stage of their construction would be mastered and understood. The structure of the whole object, as complex as it may be, would reveal by itself the nature, status and role of each of its components: such complex assemblages would translate the hope of a world that could be completely deciphered. This underlying notion has been described as the origin of the considerable changes that occurred in the two arts, which finally led to the emergence of Gothic structures on one hand, and of polyphonic singing – the organum – on the other. (The Gradual Landing of the Heavenly Spheres, Ch. 6, pp. 159-160)

Of particular relevance to the above argument are chapters on Morphogenesis by Spherical Waves and Mathematical Considerations and Computer Transposition. The first recalls the magnum opus by Peter Sloterdijk (Bubbles, Spheres, Foams, 2011-2016).

Organizing as choreography? Missing from current common use of "organize" (as a verb) is the sense explored only in metaphor of ordering according to some understanding of musical principles and harmony -- choreography. Understood in this way, social organization is a process of imagining, designing and building an organ which can then be played in some way -- engaging others in the patterns engendered. Organizations can indeed be described metaphorically as symphony orchestras, although this understanding does not appear to inform those involved in any way however much they listen ritually to orchestral music on their ceremonial occasions. The situation is epitomized by the use of symphonic music and choirs as emblematic of major international institutions, as with the Anthem of Europe. The possibility of such "organization" is totally ignored (A Singable Earth Charter, EU Constitution or Global Ethic? 2006; Participative Development Process for Singable Declarations: applying the Wikipedia-Wikimedia-WikiMusic concept to constitutions, 2006). Despite early insight into Musica Universalis, the global brain has yet to be fruitfully rendered into music or song.

Playing games with a global brain? Given the fantasies currently cultivated by science fiction and techno-optimists, it is to be expected that some form of dialogue with a global brain will be soon enabled by artificial intelligence. Search engines are a precursor of this, as with virtual assistants such as Alexa, Siri and the like (Forthcoming Major Revolution in Global Dialogue: challenging new world order of interactive communication, 2013).

A playful dimension is already evident through online gaming and the exploits of AI in playing for mastery in chess, go and poker. It can be readily imagined that this will extend to music and song. Clearly there are emerging possibilities whereby for "playing with" a global brain.

A poignant comparison might however be made with the widely cited playing of Dueling Banjos, featured as an unforeseen improvisation in the acclaimed movie Deliverance (1972). The "duel" therein of a city adult with a mentally challenged, inbred country boy frames the question as to whether humanity is to be compared with the former or the latter -- in any future "duel" with global AI. However a further twist to the question is offered by the subtext of the movie presentation. Much was contrived in depicting the banjo playing by the boy. The duel was prescripted and appropriated without permission from the original composer, who succesfully claimed copyright and damages in a subsequent lawsuit.

Humour and the global brain? With respect to any quest for the nature of "global brainwaves" a valuable criterion may well prove to be whether the playfullness this is in any way associated with humour. Despite optimistic speculation with regard to the future creativity of AI (even of an aesthetic nature), there remains the question of how a global brain may engender and appreciate humour. As with literature on the capacity of deity to engage in such processes, is there the possibility that a global brain might frame its engagement with humanity through humour -- even "crazy wisdom"?

Given the acknowledged tendency for many in the computer-related world to be on the Asperger spectrum -- and professionally appreciated for the focus that this brings -- of relevance is a particular implication for any promotion by them of the global brain metaphor. The characteristically constrained ability of those on the spectrum to appreciate humour raises questions as to how the dimension of humour is imagined by them in relation to the global brain. (Jason McCormick, Asperger's Syndrome and Humor, Asperger-Autism Network; Damon Rose, Do autistic people 'get' jokes? BBC News, 15 December 2018; Susan Teresa Ruggeri, The Experience of Humour in Asperger’s syndrome, University of Wolverhampton).

Missing is seemingly any insight into the implications in terms of "organization", namely the more fruitfully comprehensible ordering of the global brain.

Playing ball with a global brain? A contrasting image is offered by the organization of the global brain as a "ball" of some kind -- with "global" as remotely reminiscent of the geometrical implications of the music of the spheres (Metaphorical Geometry in Quest of Globality -- in response to global governance challenges, 2009). In this sense it is strange to note the evolution of the logical preoccupations of Leibniz into spherically symmetrical configurations of the preoccupations and organization of oppositional geometry (Oppositional Logic as Comprehensible Key to Sustainable Democracy: configuring patterns of anti-otherness, 2018; Neglected recognition of logical patterns -- especially of opposition, 2017). Of particular value to such explorations is the rhombic dodecahedron (Lorenz Demey and Hans Smessaert, Geometric and cognitive differences between logical diagrams for the Boolean algebra B4, Annals of Mathematics and Artificial Intelligence, 83, 2018, 2).

The irony is all the greater at this time given the worldwide focus on the association football with a stitching pattern based on the truncated icosahedron. In the strangest of senses, the elusive cognitive dilemmas of the global brain are projected into the manner in which a ball is kicked around in patterns of play -- skillfully cultivated and studied as passing patterns in the quest for competitive advantage.

Envisaging global brain representation in 3D through use of animation (tentative)

The pattern of hexagram relationships derived above fom the original Shao Yung circle offers a useful template to explore animation in 3D. As a template it can be reframed as a form of instrument for visual effects to which sound effects could be added -- then a form of musical instrument, if not an organ or a harp.

The pattern recalls the two hemispheres of the human brain. The division into 8 groups (yellow) of 8 circles (red), is potentially clustered into 4 groups of large circles (blue). Each such 2D circle can be represented as a sphere -- evident through rotation of the whole. That approach could have been extended to render the circle as a whole into a global form.

Each sphere is rendered relatively visible or transparent in the dynamic of the animation. This effect could have been articulated further to distinguish the 64 red spheres individually, for example.

The result is aesthetically crude and merely intended as an indication of how the animation could be "composed" or "played" -- a proof of concept. Understood in cognitive terms, the 4 blue spheres are indicative of the common 4-fold distinction of modalities. Similarly the 8 yellow spheres recalls the 8-fold distinction of modalities -- a variant of the 8-fold way. The 64 red spheres recall the decision-making distinctions made in the pattern of the I Ching.

The spheres can be understood as cognitive "worlds" within which people may primarily function, whether the red-level only, extending to the yellow level, or the blue level -- each such level bridging a greater range of modalities. A pattern of "worlds within worlds" consistent with intuitive reference to the "music of the spheres"

Understood in mechnical terms, the animation recalls the function of a combustion engine -- whether 4-cylinder, 8-cylinder, or more. The dynamics are then suggestive of the pattern in which the cyinders "fire" -- especially if greater attention was given to the rhythm. If the circles were rotated, rather than represented as spheres, this would give the effect of fans rendering the pattern "flight enabled" as with the operation of some drones.

As an alternative, each circle could be transformed into a torus rather than a sphere suggesting pathways through which the distinctive "cognitive worlds" travel (Imagining Toroidal Life as a Sustainable Alternative: from globalization to toroidization or back to flatland? 2019).

Global brain representation in 3D through use of animation
The animation has been constructed using X3D Edit, allowing parameters to be variously modified using a text editor

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