Challenges to Comprehension Implied by the Logo
of Laetus in Praesens
Laetus in Praesens Alternative view of segmented documents via Kairos

13 January 2020 | Draft

Satellite Constellation and Crown Chakra as Complementary Global Metaphors?

Experimental representation of crown chakra in virtual reality

-- / --

Petals as hearts in designing a 1,000-petalled crown chakra
Crown chakra as circular configuration of rotating heart-patterns
Construction of crown chakra in 3D using a twisted torus
Crown chakra embodying gimbal dynamics to frame the Axis Mundi
Axis Mundi, Yggdrasil, Omphalos and Sahasrara?
Sahasrara as indicative of cognitive interweaving and tensional integrity
Meta-pattern: petal-bird-heart dynamics as a metaphorical nexus?
Interdisciplinarity and integrative intelligibility
Integrative "orbital" implications: Crown and Sceptre / Sahasrara and Axis Mundi
Cognitive organization of a crown in the light of polyhedral nesting?
Multi-level crown chakra "temple" configuration?

Development of a suggestion in Symbolic Disconnection from the Stars and the Universe? (2019)


An earlier document focused on the imminent launch into orbit of the Starlink satellite constellation of some 12,500 communication satellites, and especially on their problematic psycho-social and symbolic implications (Symbolic Disconnection from the Stars and the Universe? 2019). There the suggestion was made that there was a potential complementarity in cognitive terms between a dense pattern of satellites orbiting the planetary globe and the pattern of insights represented in the many representations of the crown chakra of Asian tradition. The first is necessarily a "crowning" achievement of collective human initiative; the second is held to be the ultimate achievement of individual human cognitive development.

The concern here is how such distinctive phenomena might be understood as cognitively related -- despite being extremely remote and meaningless to most, however all-encompassing they are upheld to be. Especially challenging is the sense in which both offer coherence as contrasting configurations of differences, with the constellation of satellites embodying that in the pattern they form -- orientations, orbits, and levels. Curiously complementing those extremes is the strange embodiment of significance in the ultimate symbols of governance and collective identity, such as bejewelled crowns, sceptres and orbs -- or more simply as the emblematic pattern on a flag, possibly with stars echoing the configuration of satellites in the heavens. A strange triadic complementarity indicative of the elusive nature of unity?

The question here is whether these three distinctive patterns are complementary in any fruitfully meaningful manner. The challenge with respect to a complex constellation of satellites is how this is to be comprehended as a global phenomenon of personal significance. The challenge with respect to the implications of a crown chakra is the kind of insight it offers into integrative globality from an individual perspective and as implied by the symbolic functions of any crown. The earlier discussion noted an intriguing confluence between the geometrical design constraints of such a constellation and those of the sacred geometry with which the crown chakra is necessarily associated. Whether individually or collectively, what is implied cognitively by any such crown (Engaging with Globality through Cognitive Crowns, 2009)?

There are many depictions of the crown chakra -- necessarily in two dimensions, and typically as a feature of meditation devices such as the mandala and the rose window. These obviously imply a form of integrative comprehension -- necessarily of a "multi-dimensional" nature. There are many depictions of three-dimensional crowns -- variously constructed and bejewelled. There is now an opportunity to experiment with representations of the crown chakra in three dimensions, using the animation possibilities offered by widely available virtual reality applications, as previously indicated (Global Coherence by Interrelating Disparate Strategic Patterns Dynamically, 2019). Especially characteristic of such representations are the aesthetic choices -- raising the question of how these contribute to integrative comprehension.

Are the design challenges and opportunities of such representation suggestive of new ways of thinking about globality in general -- whilst at the same time potentially serving to enable a fruitful way of comprehending the dynamics of a dense coalition of satellites orbiting the Earth. What indeed are the symbolic connotations of such disparate global patterns with their various implications as "crowns"? Might they reinforce one another in some way?

The approach taken here follows from earlier exercises in representation in 3D animations of symbols much-valued in their static 2D depictions (Exploring Representation of the Tao in 3D: virtual reality clues to reconciling radical differences, global and otherwise? 2019; 24-fold Pattern Implied by Dynamics of the Lauburu in 3D: visualization of the interplay of sets of voices in discourse, 2016; Comprehension of Requisite Variety via Rotation of the Complex Plane: mutually orthogonal renderings of the Mandelbrot set framing an eightfold way, 2019; Cognitive Implications in 3D of Triadic Symbols Valued in 2D, 2017).

The question here is whether there is some collective cognitive interplay to be fruitfully explored at this time between a global constellation of satellites and traditional symbols such as the Axis Mundi, World Tree (Yggdrasil), and Omphalos -- and their reflection in the Sahasrara (crown chakra). How are these integrative patterns echoed in conventional symbols of governance -- such as crown, sceptre and orb? The possibilities of dynamic representation in 3D also raise new questions as to their potential cognitive significance, whether collectively or individually.

Petals as hearts in designing a 1,000-petalled crown chakra

The following images were presented in the earlier paper, with that on the right evoking this exploration.

Contrasting representations of global constellations
Starlink Constellation [phase 1]
first orbital shell: 72 orbits with 22 each, 1,584 satellites at 550 km altitude
Future constellation
of 12,500 satellites
encompassing Earth?
Crown chakra animation
with 1000 petals,
in 20 layers of 50 petals each.
Indication of Starlink Constellation -- phase 1 Future constellation of 12,500 satellites? Crown chakra animation
Lamid58 [CC BY-SA 4.0],
via Wikimedia Commons
Produced with Stella Polyhedron Navigator Developed from an image by
Colin-Bentham on DeviantArt

The crown chakra, as a "1,000-petalled lotus" poses the interesting challenge of how best to represent the "petals" in a form which lends itself to animation in 3D. Inspired by some representations, the design chosen here is that of the heart pattern -- geometrically defined. This choice is consistent with earlier arguments (Cardioid Attractor Fundamental to Sustainability, 2005; Symbolizing Collective Remembering Otherwise: encompassing the "headless hearts" and "heartless heads" through their dynamic entanglement, 2019; Cognitive heart dynamics framed by two tori in 3D, 2016).

There are a number of mathematical curves that produce heart shapes. Those most commonly recognized feature in Wolfram MathWorld, as shown below (accompanied there by the relevant equations).

Varieties of heart curve
Varieties of heart curve
Reproduced from Heart Curve (Wolfram MathWorld)

Rather than any of the variants shown above, that derived from the four circles in animation on the left below was used. A comparison is made in the other images with the geometry of the lauburu

The animation on the left derived from an image which suggested that the "petals" in the composition could be designed in the form of hearts -- understood geometrically in 2D as follows. Consideration of the heart curve as a symbol had earlier highlighted the following patterns (Symbolizing Collective Remembering Otherwise: encompassing the "headless hearts" and "heartless heads" through their dynamic entanglement, 2018).

Heart framed by circular geometry
Versions of lauburu and their superposition Eliciting the heart pattern from geometry of lauburu
(rotated 45 degrees, with superposition of both variants)
Left-facing (symbolizing death) Right-facing (symbolizing life)
Lauburu (Basque cross) left-facing Lauburu (Basque cross) right-facing Eliciting the heart pattern from geometry of lauburu
Superposition of left and right facing Lauburu (Basque cross)

Crown chakra as circular configuration of rotating heart-patterns

The 20 rings of 50 petals in the "1,000-petalled lotus" could then be configured as indicated in the three distinctively coloured examples below.

Rings of 50 heart patterns
Ring of 50 heart-patterns Ring of 50 heart-patterns Ring of 50 heart-patterns
Each such ring is constructed as a separate image

Clearly there are many design options associated with the colours used and the order in which the rings are stacked. Traditions of meditation may associate particular mnemonic importance with those choices. No effort has been made here to refine the choice.

The 20 rings of heart patterns (as above) could then be configured experimentally to produce the following animations -- with the rings variously rotated, given the considerable importance which may be associated with the direction of rotation. The first three animations assume that the fastest rotation is associated with the smallest rings at the centre. Especially significant to interrelating the rings is the extent to which the petal-hearts in adjacent rings overlap. Here the choice was made to configure them such that the tips of the petals of any inner ring touched the base of the adjacent outer ring. Greater overlap is an obvious possibility.

Clearly, as with the colours, arbitrary choices have been made with respect to the relative speed of rotation of the rings. The outer ring has been rendered stationary.

Crown chakra with rotation of 20 rings of 50 petals ("1,000-petalled lotus")
(fastest rotation in the smallest rings at the centre)
Anti-clockwise rotation of 20 rings Counter-rotation of 20 rings Clockwise rotation of 20 rings
Anti-clockwise rotation of 20 rings of 50 heart-patterns Counter rotation of 20 rings of 50 heart-patterns Clockwise rotation of 20 rings of 50 heart-patterns
video mp4 video mp4 video mp4
Technical note: The exercise above used an image of the heart and configured it in a ring (as noted) -- each coloured variant saved as a separate image. These images were resized and configured in an X3D application, each image applied to a thin disk, then stacked above each other in sequence. The resulting animations constitute a reasonably efficient "fudge" leaving other issues to be addressed.

Construction of crown chakra in 3D using a twisted torus

The disadvantage of the above approach is that the rings cannot be successfully rotated out of the 2D plane within which the rotation takes place, because of the problematic interference between the disks to which the images are applied in the graphics software.

A potentially more fruitful approach is then to construct the individual heart patterns in an X3D application -- rather than as 2D line drawings. These could then take a 3D tubular form (effectively a torus twisted into the form of a heart pattern) -- then configured into variously coloured rings (as above). The choice was made to use a hollow tubular heart rather than one that was filled. This gave rise to the following lace-like image.

Alternative dynamic representation of crown chakra
Horizontal rotation of 20 rings of 50 hearts moving independently Vertical rotation of total set of 20 rings of 50 hearts
Horizontal rotation of 20 rings of 50 hearts moving independently Vertical rotation of total set of 20 rings of 50 hearts
Technical note: These animations are relatively complex and heavy, hence a degree of jerkiness when rendered through virtual reality applications. A degree of optimization from earlier versions benefitted significantly from the advice of Sergey Bederov of Cortona 3D -- to whome thanks. Further optimization is possible, if not necessary for other purposes. (mp4 video of animation on right)

The design metaphor is potentially consistent with an associated meditation insight on the "emptiness of form" (Jayarava Attwood. Form is (Not) Emptiness: the enigma at the heart of the Heart Sutra. 2017; Paul Gerstein, Form Is Emptiness: an insider's guide to the Heart of Zen Buddhism, 2013; Donald S. Lopez Jr, Elaborations on Emptiness: uses of the Heart Sutra, 2016).

Crown chakra embodying gimbal dynamics to frame the Axis Mundi

Of potential interest to the dynamics of the crown chakra as it might be understood is to reframe the function of the central axis -- the line along which the centre is viewed. The possibility is clarified by the following animations of a gimbal. As noted by Wikipedia, a gimbal is a pivoted support that allows the rotation of an object about a single axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of the rotation of its support (e.g. vertical in the animation on the left below).

For example, on a ship, the gyroscopes, shipboard compasses, stoves, and even drink holders typically use gimbals to keep them upright with respect to the horizon despite the ship's pitching and rolling. Gimbals are of considerable importance to the stability of vessels in space. Gimbals have a history dating back to its description by the Greek inventor Philo of Byzantium (280–220 BC).

Gimbal dynamics
Illustration of a simple three-axis gimbal set; the center ring can be vertically fixed In a set of three gimbals mounted together, each offers a degree of freedom: roll, pitch and yaw
3-axis gimbal dynamics 3-axis gimbal dynamics
No machine-readable author provided. LucasVB assumed (based on copyright claims). [Public domain] Lookang many thanks to Fu-Kwun Hwang and author of Easy Java Simulation = Francisco Esquembre [CC BY-SA]

With this insight, each of the 20 rings in the crown chakra can be dynamically rotated out of the 2D plane on various axes to give a 3D configuration -- readily reminiscent of a pattern of orbital satellite dynamics. Of interest to the importance of the central axis, in reflection on the crown chakra, is the extent to which it is "stabilized" by the operation of the gimbal framework -- potentially reminiscent of the symbolic significance of the Axis Mundi and that of the sceptre of governance (considered below).

Representation of crown chakra with 20 rings rotating on various axes
General view Detailed view
Representation of crown chakra with 20 rings rotating on various axes Detail of crown chakra with 20 rings rotating on various axes
Technical note: See above

Understood as a gimbal, the dynamics recall those of the operation of a gyroscope and its importance to stabilizing the operation of a compass to enable navigation on a rocking vessel -- whether on the sea or in a spacecraft. Of relevance is then the implication for navigation in turbulent psychosocial space, as highlighted from a policy science perspective by Geoffrey Vickers (Freedom in a Rocking Boat: changing values in an unstable society, 1972).

The possibility of a dynamic of that kind has been evoked in the imaginatively design of a "machine" for spacetime travel in a science fiction movie (Contact, 1997). Such dynamics highlight the probable need for an elusive balance in any form of higher dimensional navigation (Gyroscopes for balance in higher dimensional navigation, 2018). The pattern might be understood as a compactification of the extra dimensions which physics now considers necessary to a meaningfully realistic modelling of reality. Representation of such "curled up" subtlety might now be enabled by AI, as described by John Pavlus (An Idea From Physics Helps AI See in Higher Dimensions, Quanta Magazine, 9 January 2020).

It could however be suggested that insight of this kind is enabled to a degree by the manipulation of circlets of prayer (and worry) beads (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000).

Axis Mundi, Yggdrasil, Omphalos and Sahasrara?

As noted by Wikipedia, in 20th-century comparative mythology, the term axis mundi (variously also cosmic axis, world axis, world pillar, center of the world, world tree) has been greatly extended to refer to any mythological concept representing "the connection between Heaven and Earth" or the "higher and lower realms". The concept was introduced by Mircea Eliade in the 1950s.

Planetary boundaries: In a period of global crisis, there is considerable irony to the topological association of the world with a doughnut given the use of the metaphor by Kate Raworth (Doughnut Economics: seven ways to think like a 21st-century economist. 2017; A Safe and Just Space for Humanity: can we live within the doughnut? Oxfam Discussion Papers, 2017; Introducing 'The Doughnut' of social and planetary boundaries for development, Oxfam International, 10 February 2012). This has evoked a preoccupation with doughnut economics in relation to achieving the UN's 17 Sustainable Development Goals. The metaphor featured in a gathering of the World Economic Forum (Kate Raworth, How to do business with doughnuts, 25 January 2018).

The irony is all the greater in that the widespread reference to nine "planetary boundaries" derives from a presentation to the Club of Rome by the Stockholm Resilience Centre (Johan Rockström, et al., Planetary Boundaries: exploring the safe operating space for humanity, Ecology and Society, 14, 2009, 2). Curiously the boundaries have been strictly defined in purely physical terms, as challenged in a commentary thereon (Recognizing the Psychosocial Boundaries of Remedial Action: constraints on ensuring a safe operating space for humanity, 2009; Exploring the Hidden Mysteries of Oxfam's Doughnut: recognizing the systemic negligence of an Earth Summit, 2012).

The extensive significance of nine in Norse mythology, most notably the nine worlds that are supported by Yggdrasil as the "World Tree" (Joshua J. Markby, Nine Realms of Norse CosmologyAncient History Encyclopedia, 20 December 2018). Ironically the Stockholm music label Acronym has separate recordings for both "Planetary boundaries" and "Yggdrasil" -- reinforcing any argument that the Stockholm Resilience Centre may have been influenced in some way in originally distinguishing nine such boundaries.

Yggdrasil (World Tree): The case for a 9-fold winding of a torus (as a "doughnut") is presented separately (Imagining Toroidal Life as a Sustainable Alternative: from globalization to toroidization or back to flatland? 2019). This is reminiscent of arguments regarding the Potential implications of alternation and rotation in psychosocial fields in the light of the remarkable insights of Nikola Tesla (Reimagining Tesla's Creativity through Technomimicry Psychosocial empowerment by imagining charged conditions otherwise, 2014).

In any quest for widespread popular comprehension of the "planetary boundaries", the argument above emphasized the intuitive (if not instinctual) appeal of toroidal motion. To what extent is this reflected in the appeal of many carousel-like fairground rides -- "merry-go-rounds" -- to which the animations above then bear a fruitful resemblance? It is probable that carousels in Nordic countries would use the 9 gods of Norse mythology in their rides.

Experimental animations of 9-fold pattern of planetary boundaries inspired by the "World Tree" (Yggdrasil)
Solid variant Wireframe variant
Yggdrasil-based annimation nine planetary boundaries Yggdrasil-based annimation nine planetary boundaries
Reproduced from Imagining Toroidal Life as a Sustainable Alternative (2019)

Omphalos: Axis Mundi is closely related to the mythological concept of Omphalos (navel) of the world or cosmos (as mentioned in the earlier discussion). It is especially curious to note how a constellation of satellites could be said to be anticipated to some degree in the formative archetypes of the past -- if only through its visual form. As represented by the marble Omphalos of Delphi, this has a carved knotted net covering its surface with its emplacement held to define the centre of the world. Reminiscent of orbiting satellites, according to the myths regarding the founding of the Delphic Oracle, Zeus, in his attempt to locate the center of the earth, launched two eagles from the two ends of the world, and the eagles, starting simultaneously and flying at equal speed, crossed their paths above the area of Delphi, and so was the place where Zeus placed the stone. Appropriately "eagle" is a favoured name for aerospace vessels -- as with the Moon landing: The Eagle has Landed.

For Nikolai Tolstoy, Omphaloi worldwide were characterized by similar ideological conceptions (The Mysteries of Stonehenge: Myth and Ritual at the Sacred Centre, 2016). For example, the Turoe Stone (also referenced as the "Irish Omphalos") is carved in a comparable manner. Understood metaphorically, Harry White proposes that the quest for the Irish omphalos, the stone that marks the centre of the Irish world requires a consideration of music not simply as a striking absence but as a vital contemporary Irish literature. (Words for Music In Search of the Irish Omphalos, 2008).

Comparison of carvings of Omphalos variants with Crown chakra (Sahasrara)
Omphalos of Delphi Turoe Stone (Irish Omphalos) Buddha with Sahasrara
Omphalos of Delphi Turoe Stone (Irish Omphalos) Buddha with Sahasrara

Sahasrara as indicative of cognitive interweaving and tensional integrity

There are numerous books and references to the chakra system and to the crown chakra as a model of human development. However controversial, many focus on balancing the contrasting emerges held to be associated with the chakras. In the case of the crown chakra, the common focus tends to be on how it can be appropriately balanced through music. This does not appear to have been especially helpful to clarifying the range of integrative cognitive functions with which the crown chakra is associated.

A valuable exception of some relevance to this argument is the study by Richard Jelusich who argues:

The seventh or "crown" chakra is the gateway to other levels of consciousness and existence. The crown chakra represents the "God spot" or the point where everything and nothing exists.... Just as much as it takes a whole first chakra to have a physical body and presence in this dimension, it takes a whole seventh chakra to have any concept of a true multi-dimensional reality -- because our concepts of many dimensions at best are flawed if you take as a first premise that we live in Oneness.... Similar examples that are representative of the zero-point are black holes... It is my opinion that the energy of the seventh chakra is similar to a toroidal (donut shaped) energy field. It operates in much the same way as a black hole (or white hole) in that much of the higher dimensional energies are coalesced into the physical plane through the lens of the seventh chakra. Nothing can escape the zero-point region because it represents the totality of reality...The access point through the seventh chakra represents the point where everything and nothing exists, and it is the grasping of this point that allows the transcendence of the limitations of a physical existence into the seamlessness of the Oneness that includes a physical existence... (Eye of the Lotus: psychology of the chakras, 2005): pp. 207-208)

In the light of the argument above, there is a case for exploring how the geometric pattern by which the crown chakra is represented may be suggestive of further insight. This could offer a means of avoiding any confusion engendered by the many other references to it and to the chakra system. The latter is typically deprecated in conventional science, despite the various allusions by science to the quest for wisdom through the advancement of knowledge -- whatever "wisdom" may be held to mean in that context, and especially in these challenging times for global governance.

As noted in the earlier paper, the launching of a constellation of some 12,500 satellites is claimed to be with the purpose of facilitating communication interconnectivity. The implication, as challenged there, was that this would somehow be associated with enhanced intelligibility -- whatever that might be taken to mean. The concern, as demonstrated by the operation of the search engines to which enhanced access would be provided by that constellations, is that it is questionable to what degree intelligibility is in fact enhanced -- as possibly to be contrasted with the facility of such modalities for enhancing global "dumbing down". Interconnectivity does not necessarily imply intelligibility -- except, and only to a degree, by the intelligence services using supplementary analytical software.

The concern with respect to any Sahasrara-like pattern is how it enables an integrative function. This preoccupation follows from an earlier discussion regarding possibilities (Interweaving Thematic Threads and Learning Pathways: noonautics, magic carpets and wizdomes, 2010). The question is how the vast array of topics of relevance to the perceived challenges of the times is to be organized, however "organization" is to be understood.

One relevant metaphor variously explored is that of the "global brain" (Envisaging a Comprehensible Global Brain -- as a Playful Organ, 2019). That metaphor has recently been framed in relation to the emergence of singularity -- readily to be interpreted as an understanding of a higher order of complex integration (Cadell Last, Global Brain Singularity: universal history, future evolution and humanity's dialectical horizon,Vrije Universiteit Brussel, 2018). The organization of music -- as comprehended -- may indeed offer clues to integration within the pattern of the crown chakra, as separately discussed (Global brain as an organ: playable, playful or neither? 2019).

The cognitive challenge could be framed otherwise in the light of the extant complex array of "disciplines" (Intellectual Disciplines and Sciences: cross-referenced to world problems, 1976 1845 / 1,000 ****). An evident problem being the often highly problematic relation between such disciplines -- typically extending to mutual deprecation and reframing as "pseudosciences" or the like, and epitomized by the violence-engendering relations between religions (as disciplines in their own right). The potential of the many approaches to interdisciplinarity and transdisciplinarity has not proved fruitful -- except in the claims made for its value in limited cases (Integrative Knowledge Project). 633 concepts ***

Exploiting the Sahasrara metaphor of a "1,000-petalled lotus", is the array of disciplines to be fruitfully understood as represented by an array of "petals"? Intriguing in that respect is whether efforts have been made (in the relevant traditions) to name and locate the individual petals -- and the extent to which these names reflect distinctive cognitive modalities suggesting a fruitful mapping of disciplines. Questionable in this respect is the relatively simplistic organization of depictions of the crown chakra -- in 2D, static, and emphasizing a hierarchical order. Such constrained understandings of order are notably challenged by emerging understanding of the psychosocial implications of quantum mechanics, as remarkarkably articulated for global organization by Alexander Wendt (Quantum Mind and Social Science: unifying physical and social ontology, 2015).

Another approach is suggested from a management cybernetic perspective by the work of Stafford Beer extending into understanding of the design of a viable system (Beyond Dispute: The Invention of Team Syntegrity, 1994; Brain of the Firm, 1988). A relevant feature of the understanding of "syntegrity" was its embodiment of the principles of tensegrity. The term was coined by Buckminster Fuller in the 1960s as a portmanteau of "tensional integrity". Arguably this offers a device for organizing -- interweaving and interrelating -- the tensions between the disparate cognitive modalities.

Whereas the dominant metaphor of the interconnectivity of the constellations of satellites is as an orbiting network, the potential may lie in the shift to a modality involving the embodiment of tensions in the tensegrity modality, as may be variously argued (From Networking to Tensegrity Organization, 1984). Such a possibility was explored in relation to disparate topics evoked at the first UN Earth Summit (Configuring Globally and Contending Locally: shaping the global network of local bargains by decoding and mapping Earth Summit inter-sectoral issues, 1992).

Of interest is the interplay, in geometric terms, between the 20-level organization of the crown chakra and the 30-fold emphasis of the icosahedral tensegrity basic to Beer's use of it in syntegrity. In 3D, this interplay is characteristic of that between the icosahedron and the dodecahedron -- as its geometric dual. This alternation, and its animation, featured in an earlier discussion (Time for Provocative Mnemonic Aids to Systemic Connectivity? Possibilities of reconciling the "headless hearts" to the "heartless heads", 2018). A tensegrity structure achieves its integrity through a continuing dynamic between tensional and comprehensive elements.

Meta-pattern: petal-heart-bird dynamics as a metaphorical nexus?

In metaphorical terms, the "petals" of the "1,000-petalled lotus" could as usefully be explored as "hearts" or as "birds". As patterns, all three are valued in allusions to the elusive insights in terms of which more integrative understanding might be achieved. As symbols they could be considered interchangeable under certain conditions. This is a common feature of the figurative language of poetry and other arts.

Petal dynamics? Although remarkably familiar, there is little that can be obviously (or usefully) said about the dynamics of a petal. Considerable value, if not the highest, is associated with the rose (most notably in the West) and with the cherry blossom (most notably in Japan). The lotus is the flower which is traditionally highlighted through the suggestion that the dynamics of its petals offers in relation to the opening and closing of awareness according to a circadian rhythm. Much is made in aesthetic terms of the fading of the rose and the cherry blossom over the life of the flower. There are now many lotus animations accessible via the web.

The nature of the attachment and detachment of awareness, with which flowers are associated metaphorically, is potentially to be recognized through the studies of wetting, namely the ability of a liquid to maintain contact with a solid surface:

Considerable attention has been given to the geometry of flowers, by Keith Critchlow as a development of his work on Islamic patterns (Islamic Patterns: an analytical and cosmological approach, 1976; The Hidden Geometry of Flowers: living rhythms, form and number, 2011). The process of arranging flowers, and the resulting arrangement, may well be described in dynamic terms -- especially in the Japanese art of ikebana. Less obvious from a geometrical perspective are the dynamics of opening and closing with which awareness may be associated.

A useful articulation of petal movements is offered by Wouter G. van Doorn and Uulke van Meeteren (Flower Opening and Closure: a review, Journal of Experimental Botany, 54, 2003, 389) who discuss four types of opening:

A later study by the lead author focuses on recent advances in understanding of the biological clock, and on the physiological background of opening and closure movements (Wouter G. van Doorn and Chanattika Kamdee, Flower Opening and Closure: an update, Journal of Experimental Botany, 65, 2014, 20). Less evident from such studies is how the dynamics is constrained and enabled by the geometry -- and what implications for the Sahasrara these offer through metaphor.

Significance variously implied: Much is implied through allusion in the Lotus Sutra, held to contain the final insights of Buddha and on which there are numerous commentaries (Nichiren Daishonin, The Lotus Sutra and Its Opening and Closing Sutras, Soka Gakkai; Minerva TY Lee, Lotus Sutra and its Opening and Closing Sutras, 2015). The fundamental importance in one context is indicated by George Joji Tanabe and Willa Jane Tanabe (The Lotus Sutra in Japanese Culture, University of Hawaii Press, 1989):

The Lotus Sutra permeated the everyday life of the aristocrats to such an extent that one can regard the idealized or symbolic expressions of the sutra's ideas in the decorative frontispieces as reflections of the Heian aristocracy's thorough grasp of the essential meaning of the Lotus Sutra. The depiction of the aristocrats within the decorative frontispieces, for example, attests to the incorporation of the world of the Lotus Sutra into their own lives....The most extreme example of the interpenetration of this world and the world of the Lotus can be found in the fan-shaped booklets of the Lotus Sutra at Shitennoji. In this work from the late Heian period, the Lotus Sutra and the opening and closing sutras are copied onto fan-shaped paper embellished with gold and silver flakes of foil, marbelized patterns, and block-printed underdrawings. (pp. 92-93)

Somewhat ironically, by contrast, the opening and closing of "lotus petals" is the subject of a patent with a visualization of particular dynamics of that device -- of questionable relevance to this argument.

A distinctive interpretation of the complex dynamics is implied by the study of over sixty Buddhist temples and associations representing a diversity of ethnic, national, and linguistic identities within five Asian Buddhist communities: Japanese-Canadian, Tibetan, Vietnamese, Cambodian, and Chinese (Janet McLellan, Many Petals of the Lotus: Five Asian Buddhist Communities in Toronto, 1999). How their dynamics are to be understood in terms of the dynamics of lotus petals is primarily evident by allusion.

Particular existential significance is attached to the remembrance poppy flower in the West, as a consequence of World War I, as extensively explored by Ann Elias (War and the Visual Language of Flowers: an antipodean perspective. War, Literature and the Arts, 20, 2008, 1-2; Exquisite Corpse: Flowers and the First World War, International Journal of the Humanities, 5, 2007, 3).

Comparable significance is poignantly indicated in the case of Japan, given the symbolism associated there with cherry blossom (sakura), as discussed separately with respect to resilient response to the catastrophes of the nuclear power "plant" at Fukushima and the effects of atomic bombing (Fukushima, cherry blossom and "mono no aware", 2011). As documented by Emiko Ohnuki-Tierney (Kamikaze, Cherry Blossoms, and Nationalisms: the militarization of aesthetics in Japanese history, 2002), the symbolic importance of cherry blossoms, through their brief flowering and poignant scattering, become the quintessential symbol of tokkotai sacrifice -- resulting in an "aestheticization of death".

On a larger time scale, but without distinguishing the dynamics of petals, the metaphor is applied to culture and civilization in general (Flowering of Civilization -- Deflowering of Culture: flow as a necessarily complex experiential dynamic, 2014). The latter notes the reference by Elias to the significance of flowers in philosophical articulated by Claudette Sartiliot (Herbarium Verbarium: the discourse of flowers, 1993):

... it is in their nature to embody double meanings, since flowers are male and female in one, and when cut they become mobile metaphors that do not denote any fixed identity. In war imagery they oscillate between the beautiful and the ugly, the masculine and the feminine, death and love, and the transcendent as well as the abject. They are simultaneously symbols of grief for the slain, and symbols of hope about life's renewal. Sartiliot describes the flower as a unique entity that: seems to have no topos, no clear or real place, no role. If flowers are traditionally -- and as literary emblems, primordially -- associated with feminine beauty, life, and innocence, they shift in the same texts into their opposite.

Elias then concludes:

Nationalism depends on the symbolism and aesthetic of red which enfolds not only visceral references to the dead but also historical references to Flanders fields. However, the red poppy that increasingly emerges today as symbol of contemporary war, and its aftermath, is the cultivated narcotic poppy from Afghanistan. The Flanders poppy and the Afghanistan poppy symbolise two different eras of warfare, but in both cases, their image embodies the melancholy of the human condition which is the struggle between war and peace.

Heart dynamics: Considerable significance is variously associated with the "heart". In contrast to the "head", its existence and operation are widely used as a metaphor -- as continues to be the case in reference to the Sacred Heart and to the Holy Blood, curiously curiously recalling preoccupation with both in the Mayan and Aztec cultures of centuries past (Bloodletting in Mesoamerica. Wikipedia).

The fundamental strategic strife at this time has been framed as that between the "heartless heads" and the "headless hearts". More specifically the economist Paul Collier has argued that: the debate on migration is polarised into two strident positions, a heartless and the headless (On Immigration, Head to Head: Al Jazeera, 7 August 2015). A "crown" of some kind might herald the emergence of a form of wisdom transcending such a binary framework and the conflict it sustains.

There is therefore a case for exploiting the structure and dynamics of the 4-chambered heart in metaphorical terms (unconstrained by its actual operation in practice). An animation is presented below to frame such a possibility and how it may indicate a bridging modality between heart and head as metaphorically understood. Each of the 4 chambers may be understood as expanding or contracting, as shown in the animation. Arguably, when all are "filled" (depicted as the 4-circle condition), this can be used to suggest dominance of "heartfulness". At the other extreme, when all are empty (depicted by the diamond shape, with no completed circles), this can be used to suggest dominance of the "head" modality -- and the absence of "heart".

There are of course many intermediary conditions -- effectively "shades of grey". These can be usefully indicated by the simple coding system in the table below -- with 0 indicative of "full" and 1 indicative of "empty". Thus 0000 then indicates the extreme of "heartfulness" and 1111 indicates the extreme of "headfulness". For simplicity's sake, the animation only includes the 8 conditions in grey.

Schematic animation of 4-chambered heart (with intermediary conditions)
Animation of a metaphorical 4-chambered heart "Heart cognition" dominant
("headless hearts")
  "Head cognition" dominant
("heartless heads"
Animation of a metaphorical 4-chambered heart                  
0 0 0 0   1 0 0 0
0 0 0 1   1 0 0 1
0 0 1 0   1 0 1 0
0 0 1 1   1 0 1 1
0 1 0 0   1 1 0 0
0 1 0 1   1 1 0 1
0 1 1 0   1 1 1 0
0 1 1 1   1 1 1 1

A potentially more insightful pattern can also be envisaged as suggested by ae schematic (left below) -- but more readily comprehended through animations (centre and right).

Transformations between elements of the heart pattern
(animations indicative of selected patterns and combinations of movements)
Animation schematic Pattern of 8 diagonal movements of 4x2 circular elements Pattern of 16 clockwise movements of 4x4 circular elements Pattern of 16 anti-clockwise movements of 4x4 circular elements Combination of 32 clockwise and anti-clockwise movements
Transformations between elements of the heart pattern Pattern of 8 diagonal movements of 4x2  circular elements of heart patterns Pattern of 16 clockwise movements of 4x4  circular elements of heart patterns Pattern of 16 anti-clockwise movements of 4x4  circular elements Combination of 32 clockwise and anti-clockwise movements of circular elements of hart patterns
Technical note: Rendering the animations even more relevant to highlighting the heart pattern could be achieved by enabling the progressive "disappearance" of the green and mauve curves -- as they reach their lower positions in the dynamic, with the additional possibiity of ensuring the "disappearance" of the upper yellow curves highlighting the diamond. The periodic emergence of the heart or diamond, and their coherence, could be further emphasized by enabling the movement of small spheres along either pattern at that moment in the dynamic. The animations would then alternate between a highlighted heart or diamond.

It is appropriate to note that whilst the heart is much valued as indicative of compassion (together with the symbolism of blood), the diamond-like shape at the other extreme is also much-valued as indicative of cognitive brilliance and wealth, as explored separately (Patterning Archetypal Templates of Emergent Order: implications of diamond faceting for enlightening dialogue, 2002). This is exemplified by its symbolism in Diamond Way Buddhism, the Diamond Realm of Vajrayana Buddhism, and in the associated Diamond Sutra. in all of which the emptiness of form is appropriately features (as noted above). Such animations offer a framework for reflection on the significance attached to such metaphors as "whole-hearted" and "broken-hearted".

Given the nature of the above argument, there is a curious irony to the worldwide familiarity with the form of "hearts" and "diamonds" in the playing card suit. The implications can be variously discussed (Symbol systems and playing cards, 2007; Cognitive engagement with complexity through articulation of the heart pattern in playing cards, 2018; Radical Localization in a Global Systemic Context: distinguishing normality using playing card suits as a pattern language, 2015). Arguably the four categories of the above table are intuitively indicated by the four distinctive playing card patterns -- rather than by only the two extremes. The four distinctive forms can be understood as derivatives of the 4-circle pattern, as shown schematically below (and lending itself to an integrative animation)

Pattern of derivation of set of 4 playing card suits
Pattern of derivation of set of 4 playing card suits

The original significance of the 4 distinctive playing-card cards, as presented, has seemingly been lost (Adrienne Bernhard, The Lost Origins of Playing-Card Symbols, The Atlantic, 24 August 2017). More relevant to this argument is their current association with the dynamics of the psyche, as noted with respect to the Tarot deck variant (Josh Jones, Carl Jung: Tarot Cards Provide Doorways to the Unconscious, and Maybe a Way to Predict the Future, Open Culture, 31 August 2017). Given the derivation suggested above, and the central role of Sahasrara (as shown), it is tempting to see the four derivatives as associated with other chakras in that pattern: Ajna (diamond?), Vishuddha (clubs?), Anahata (heart?), and Manipura (spade?). With the integrative challenge of achieving sustainable governance, possibly exemplified by the crown chakra, those four could perhaps be understood as associated with academia, innovation, health, and employment -- especially in the light of current efforts to interrelate them creatively through the Triple Helix, the Quadruple Helix, and the Quintuple Helix models.

Given the symbolic implications of the vital flow of blood ensured by the beating of the heart, it is appropriate to recognize that this is complemented by another type of flow ensured by the brain. In the quest for comprehension of what might "flow" in that case -- beyond the preoccupations of flow psychology -- explorations of the so-called "circulation of the light" merit consideration, This has notably been highlighted by Carl Jung and Richard Wilhelm with respect to a Chinese classic, The Secret of the Golden Flower (Tai Yi Jin Hua Zong Zhi). This perspective is discussed separately (Circulation of the Light: essential metaphor of global sustainability? 2010). With respect to "flow", the argument can be developed otherwise (Metaphorizing Dialogue to Enact a Flow Culture: transcending divisiveness by systematic embodiment of metaphor in discourse, 2019).

The pattern of movements used to frame heart and diamond in the animations above suggest the intriguing possibility that they could be used to hold both the 16-fold pattern of Boolean logical operations (noted below) and their relation to the 64-fold pattern encoded by the I Ching hexagrams -- thereby providing a dynamic integration of "head" and "heart". Calling for future consideration is the strange confluence of the geometry of satellite configuration and that of sacred geometry, as indicated in the introductory paper with respect to the 72-fold constraint in both.

How are the 72 orbital planes of the StarLink constellation to be imagined as related to the pattern of the crown chakra, with its 50 petal-hearts per ring? Is it a trivial coincidence that in the construction of the latter, each petal-heart is separated from the next by 7.2 degrees (360 divided by 50)? Also curious is the recognition that the human heart beats some 72 times per minute. As noted in the introductory comment, any such pattern of coherence lends itself to further speculative exploration (Engaging with Hyperreality through Demonique and Angelique? Mnemonic clues to global governance from mathematical theology and hyperbolic tessellation, 2016). The cognitive origins of such patterns and their recognition are the theme of the argument of George Lakoff and Rafael Nunez (Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2000) -- and of a separate discussion (Patterning Intuition with the Fifth Discipline, 2019).

Bird dynamics: flying and flocking: There is no lack of appreciation of birds -- from the many symbolic depictions of eagles on flags indicative of national identity (see below) to the widespread use of the dove as a symbol of peace. Although necessarily depicted statically and in 2D, their dynamics -- of which the static depictions are faintly indicative -- are widely appreciated by bird watchers. The flight of birds has been a primary factor in providing insight to the development of flight by technology -- through a discipline now formally defined as biomimetics.

Following the insights derived for airplane flight in general, and the helicopter in particular, it is appropriate to note the creative adaptation of biomimetics to the potential development of a "psychopter" by Arthur Young, as separately discussed (Engendering a Psychopter through Biomimicry and Technomimicry: insights from the process of helicopter development, 2011).

Seemingly inspired by bird flight, it is however curious to note the considerable importance associated with "wings" in politics and governance whether their reference to "right-wing" and "left-wing". Noteworthy is the apparent aspiration of each for "one wing governance" -- given the considerable challenges of "bipartisanship" and the desperate need to ensure that projects "get off the ground" and "fly". Sustainability could well be explored in terms of "sustainable flight".

Following the relatively complex dynamics of the heart, the complexity of ensuring sustainable flight is indicated by the fact that in the case of birds this calls for the coordination of over hundred muscles -- presumably with their correspondences in the technology of airplane flight. Appreciation of such articulation is less than apparent in the binary discourse of governance with its aspirations for "one-wing governance" and framing the alternative as redundant or non-existence ("There Is No Alternative! "). The implications of perspective have been fruitfully articulated in aesthetic terms by the much cited poem of Wallace Stevens (Thirteen Ways of Looking at a Blackbird, 1917). The theme can be exploited further (Anticipating When Blackbirds Sing Chinese: conversion from tweets to songbites to ensure integrity of communication, 2014).

Use of the wing metaphor and its dynamics can be variously discussed, notably with respect to the dramatic challenge of "extremes" (Coordination of Wing Deployment and Folding in Politics: bird flight and landing as complementary metaphors of global strategic coherence, 2018; Counteracting Extremes Enabling Normal Flying: insights for global governance from birds on the wing and the dodo, 2015). The latter includes sections on Bird flight as offering a global transformation of systemic perspective, on Styles of flight as styles of governance, and on the Lost art of bird watching?. Somewhat ironically, as augury, the latter figured prominently in the governance of the Roman Empire -- an epitome of sustainability by comparison with current empires. As a lost art, any trace is embodied in static symbols such as the following.

Heraldic eagles of empires past and present
France (Napoleonic) Germany USA Russia (1917) Spain
Heraldic eagle of France Heraldic eagle of Germany Heraldic eagle of USA Heraldic eagle of Russia Heraldic eagle of Spain

Eagle versus Dove? Whilst the flying capacity of the eagle is implied by such symbols, it is ironic to discover that controversy surrounded the choice of that bird as a national symbol in the USA -- in contrast with the original proposal for the flightless turkey (Eagle vs. Turkey: America's First Bird Controversy, The National Wildlife Federation, 2007; National Symbol - Turkey vs. Eagle, BirdNote). In a strange twist of history, the turkey now features controversially in a massacre of some 240 million each year (Nicole Breedlove, Happy National Genocide (Thanksgiving) Day! Huffington Post, 25 January 2014; Nafeez Ahmed, Thanksgiving: celebrating the hidden holocaust, Insurge-Intelligence, 23 November 2017; The Massacre For Which Thanksgiving Is Named, Native Amerian Roots, 22 November 2009). Reportedly nearly 88 percent of Americans surveyed eat turkey at Thanksgiving. For 2017, it is estimated that 44 million of turkeys were enjoyed at Thanksgiving, 22 million at Christmas and 19 million at Easter (Turkey History and Trivia, National Turkey Federation).

Given the widespread and long-stranding preoccupation with peace -- as so notably symbolized by the dove -- it is more than remarkable that there is seemingly so little interest in the complex dynamics enabling the dove to fly. If peace is somehow to "get off the ground" and "fly", does the flight of the dove offer more fruitful clues?

Rather than any focus on geometry, it could be argued that the dynamics enabling emergence of an integrative perspective are remarkably indicated in aesthetic terms by the famed poem by the Sufi poet Farid ud-Din Attar, namely The Conference of the Birds. Finally therein, only thirty birds make it to the abode of Simorgh -- learning that they themselves are the Simorgh. The name “Simorgh” in Persian means thirty (si) birds (morgh). The poem, as with the argument above, calls into question any conventional hierarchical (epitomized by "sovereign") and any static approach to such organization.

This emphasis on multiple birds offers a clue to the dynamics of the potential cognitive integration associated with the crown chakra -- perhaps to be explored as a "1,000-bird flock". There have been extensive studies of the remarkably elegant dynamics of bird-flocking. This has been insightfully simulated in 2D and 3D as the behaviour of "boids" by Craig Reynolds (Boids Background and Update, 2001) -- on which numerous commentaries continue to be made. Beyond their relevance to swarm intelligence and crowd psychology, the issues highlighted relate to preoccupations with the integrative nature of collective intelligence. (James Surowiecki, The Wisdom of Crowds: why the many are smarter than the few and how collective wisdom shapes business, economies, societies and nations, Doubleday, 2004).

Contrasting animations suggestive of clues for governance from bird flight
Indicative of a multi-wing configuration Distinguishing governance factions by feather colour on right and left wing
(complementarity and role switching over time in response to issues)
Animation indicative of a multi-wing configuration Animation distinguishing governance factions by feather colour on right and left wing
Reproduced from discussion in Counteracting Extremes Enabling Normal Flying (2015)

Interdisciplinarity and integrative intelligibility

In the quest for enabling functions beyond the communication interconnectivity promised by a constellation of 12,500 satellites, current approaches to interdisciplinarity and transdisciplinarity could be challenged in the light of insights from boid flocking simulations. Could disciplines, cognitive modalities or fundamental insights be fruitfully considered as comparable to boids? In that light are current approaches to interdisciplinarity to be compared with the title of a study by Pablo Triana (Lecturing Birds on Flying: can mathematical theories destroy the financial markets? 2009).

Of curious relevance to this argument is the promotion of the fish-scale model of interdisciplinarity originally articulated by Donald T. Campbell (Ethnocentrism of Disciplines and the Fish Scale Model of Omniscience, 1969), and included as the concluding chapter of a compilation (M. Sherif and C. W. Sherif (Eds.), Interdisciplinary Relationships in the Social Sciences, 1969). This has subsequently been included in a compilation (Sharon J. Derry, et al., Interdisciplinary Collaboration: an emerging cognitive science, 2014). The editors of the latter volume comment with respect to its republication as the introductory chapter:

... the late Donald Campbell argues that successful interdisciplinarity begins with academic hiring and that universities should form a continuous texture of narrow specialties that overlap. With tongue in cheek, Campbell named his theory the fish-scale model of omniscience. This theory points to important connections between intergroup organization, group processes, and the institutionalization of interdisciplinarity. If the goal of interdisciplinary scholarship is a comprehensive, integrated multiscience, then the obstacle to overcome is the ethnocentrism of disciplines.

The "fish-scale" relevance, as variously illustrated by Campbell, is remarkably reminiscent of traditional representations of the arrangement of the "petals" in the crown chakra -- with the added suggestion that their configuration is somehow associated with "omniscience".

The use of such a static depiction can be challenged (as above) and the Boid dynamic is insightful in that respect. As noted in the Wikipedia description (which includes an animation), as with most artificial life simulations, Boids are an example of emergent behavior; that is, the complexity of Boids arises from the interaction of individual agents (the boids, in this case) adhering to a set of simple rules. The rules applied in the simplest Boid world are as follows (although more complex rules can be added, such as obstacle avoidance and goal seeking):

Does this capture the relational dynamics of disciplines and their practitioners -- constrained as they are by a quest for originality, productivity and the restrictions of copyright? Although "only in passing", reference is now seemingly made to the relevance of this model to university disciplines (Susan Stepney, Real world complex systems and cross-disciplinary research, 2017; Gianfranco Minati, Nonclassical Systemics of Quasicoherence: from formal properties to representations of generative mechanisms -- a conceptual introduction to a paradigm-shift, Systems 7, 2019, 4, 51)

Ironically satellites may well be termed "birds" -- and are presumably nicknamed "boids" -- with the dynamics of their relationships in a constellation presumably to be understood as constrained by similar rules. Of some relevance are studies such as that of Bibhya Sharma, et al. (Motion Planning and Control of a Swarm of Boids in a 3-Dimensional Space, International Journal of Computational Science and Engineering, 8, 2014, 2)

Assumptions regarding three-dimensionality clearly miss the sense in which Campbel's "omniscience" may be necessarily of higher dimensionality -- even hyperdimensional -- calling for some form of "hypercomprehension", as can only be speculatively and intuitively explored (Hyperaction through Hypercomprehension and Hyperdrive: necessary complement to proliferation of hypermedia in hypersociety, 2006; Higher degrees of comprehension and their "compactification"? 2018; Imagining Order as Hypercomputing: operating an information engine through meta-analogy, 2014)

Richard Jelusich argues: It is my opinion that the energy of the seventh chakra is similar to a toroidal (donut shaped) energy field (Eye of the Lotus: psychology of the chakras, 2005): pp. 207-208). This recalls the transcendental importance attached to the halo in the iconography of various traditions.

Integrative "orbital" implications: Crown and Sceptre / Sahasrara and Axis Mundi

As traditional symbols valued in the comprehension of governance, and representation of its authority, there is clearly a case for asking whether any such symbols are currently "fit for purpose" -- as with the crown, mace, orb and sceptre. Whilst there are complex ceremonial rituals and protocol in relation to them, typically they are held to be static -- even if they are carried from place to place and variously manipulated. The symbols themselves are not dynamic in any sense, whatever the dynamics they may be said to imply in relation to governance. In the case of the vajra, reference is made to its association with a thunderbolt. As noted above, both mace and vajra are held to be potential weapons and derive their power from that traditional association (and for that reason is the name of the primary multirole fighter of the Indian Air Force).

Mace: The current period is clearly witness to a challenge to the globalization imperative ("orb comprehension"?) by populist movements in a range of countries. The latter are variously preoccupied with local priorities and perspectives (a complementary understanding of "orb"?). This is curiously paralleled by challenges to the traditions of male dominance and patriarchy, exemplified by feminism and the tragedy of sexual abuse by the clergy. However it is also accompanied by desperate efforts "to be great again", whether focused through competitive business, sport, or the construction of ever taller skyscrapers, or ever more impressive vehicles. The reactivation of the arms race, and the quest for full spectrum dominance, are part of the "mace-based" pattern which is increasingly called into question by many. The process is especially evident in the desperate attempts to ensure exclusive possession of resources on the Moon or Mars -- despite obvious inadequacies in governance of the resources of the Earth.

It is in this sense that comprehensible connectivity between global and local merits attention. Especially striking is the articulation of the challenge in terms of the unreconciled issues of indigenous peoples historically dominated by a "mace-based" pattern, as noted separately (Global-Local dynamic: mace-based governance challenged by a feather? 2019). These have been creatively framed in the study by Stacie A. Swain (Armed with an Eagle Feather Against the Parliamentary Mace: a discussion of discourse on indigenous sovereignty and spirituality in a settler colonial Canada, 1990-2017, University of Ottawa, 2017).

It is however most curious that any comprehensible dynamic is currently most obvious in baton-twirling, readily deprecated as trivial in relation to governance, despite the extremely serious consideration given to its role in formal parades. Clearly use of a "lightsaber" is far more evocative for many. Is it time for a "lightmace" or a "lightsceptre" -- especially given the traditional "thunderbolt" associations of the vajra symbol? Given the 5-sense argument, use of such a weapon in a martial art offers associations to both the classic strategic manual (The Book of Five Rings, 1645) and to the use of sword-surrogates as in stick-fighting, quarterstaff and kendo.

Focusing comprehension of the Axis Mundi through design? To the extent that the mace or sceptre is symbolically indicative of the Axis Mundi, there is a case for exploring new ways of representing it, as discussed separately (Imagining local-global connectivity through innovative mace and vajra design, 2019). As an example, the latter discussion gave rise to the following design.

Indicative experimental animations of wireframe versions of a mace-vajra
Rotation out of the plane of the screen "Sceptre-mode" Rotation in the plane of the screen
Rotation of wireframe versions of a mace-vajra Sceptre-mode of mace-vajra
Virtual reality interactive 3D variants: x3d, wrl. Video variants (mp4): rotation-out-of-plane; rotation-in-plane; rotation-vertical

Of some relevance to the possible representation of the 1,000 "petal-hearts" of the crown chakra in 3D (as discussed below), the ends of the mace-sceptre-vajra above use a form which can be understood as a rotation of the heart pattern in 3D.

Crown: It can be readily argued that past and current use of any crown is a symbolic indication of the crown chakra -- implying for observers and the wearer a form of integrative thinking, a link to transcendent dimensions (if not deity), and consequently a legitimation of the highest value. It is in this sense that its bejewelled nature merits reflection given the cognitive value with which the jewels it embodies are associated, as argued separately (Gemstones as an accessible metaphoric exemplar of the dynamics of coherence, 2002).

It is in this sense that the value attached to a ring may be understood in terms of recognition of its function as a "mini-crown". Whilst wearing a crown or carrying a mace may now be held to be excessive in many contexts, as with the ring, a related device may be more commonly used, for example symbolic livery collars, mayoral collars, collars of orders of knighthood, collars of Freemasonry. chains of office, or sashes, as discussed and illustrated separately (Wampum and its modern variants, 2014).

Given the geometrical emphasis in the explorations above of the crown chakra, there is a case for approaching understanding of its cognitive functions through considering future approaches to crown design -- reflective to a higher degree of the integrative functions with which it is assumed to be associated. The matter is considered separately in greater detail (Modifying the cyclic symmetry of the star torus, 2019). This gave rise to the following experimental designs, and consideration of further possibilities (Imagining further implications: helical coil, toroidal knot or crown?, 2019).

Illustrative use of geometry of star torus for mapping purposes
(use browser facilities to enlarge animations and labelling)
5-fold 8-fold 12-fold 16-fold
Pattern of 5-fold cyclic symmetry of star torus with WuXing labels Pattern of 8-fold cyclic symmetry of star torus with BaGua labels Pattern of 12-fold cyclic symmetry of star torus with information functions Pattern of 16-fold cyclic symmetry of star torus with UN SDG goals
Reproduced from Global Coherence by Interrelating Disparate Strategic Patterns Dynamically (2019). Animations generated with Stella Polyhedron Navigator

There is a potential irony to the focus on any pattern suggestive of a crown chakra given the technology now employed in both encephalography and in research on enabling control of devices via a brain-computer interface. (Emma Woollacott, How to control a machine using your mind, BBC News, 2 February 2018; Simon Chandler, Brain-Computer Interfaces And Mind Control Move One Step Closer To Becoming Reality, Forbes, 24 September 2019). One example is indicated below.

Challenging correpondences evoking reflection?
Pattern of electrodes in an EEG recording setup World surveillance
by the global brain?
Enhanced image of Apollo (of
related significance)
Pattern of electrodes in an EEG  recording setup World surveillance by the global brain? Apollo on cover of Yearbook of World Problems and Human Potential
Thuglas at English Wikipedia [Public domain] Adaptation of image on left Cover of the Yearbook of World Problems and Human Potential (1976)

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. As summarized:

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)

Rocketry and Sushumna? In exploring the possibility of cognitive complementarity, it is appropriate to speculate on the curious correspondence between rocketry as a collective undertaking and the transfer of cognitive focus from the base of the spine to the crown chakra -- held to be an individual process. This transfer is the focus of considerable attention in a variety of yoga-related disciplines where it is described in terms of Kundalini. It could be argued that the disciplined thinking and practice in rocket technology has an intriguing correspondence to some such energy transfer "up the spine" in the cognitive case. Is the insight required for the latter to be provocatively compared to rocket science?

Forcing a rocket up against the pull of gravity (a form of bondage), requires enormous force (created by burning of propellants, as a source of energy). The process of expulsion of heated gases is forceful but requires considerable care. Any disturbance can cause instabilities and the rocket may then deviate from its path or even explode. The process of raising Kundalini upwards is similarly alleged to be a highly disciplined process. It requires breaking bonds with sensory delights -- a liberation from more naive perceptions of life, the body and associated desires. Rigourous and sustained correct practice is claimed to lead to opening of Sahasrara. However deviations or errors in practice are even understood to lead to madness of th practitioner.

In symbolic terms both can be recognized as efforts to "get off the ground" and "into orbit" -- thereby establishing an imaginative link between an Earthly and Heavenly worldview, metaphorically understood.

Cognitive organization of a crown in the light of polyhedral nesting?

The recent indications from the Blue Brain Project, reinforce the case for exploring the cognitive organization of the crown chakra in polyhedral terms.

One approach follows from the considerations of oppositional geometry, especially in the light of the 16-fold pattern of Boolean logical operations and their representation (Oppositional Logic as Comprehensible Key to Sustainable Democracy: configuring patterns of anti-otherness, 2018; Oppositional logic and its requisite polyhedral geometry, 2019). The arguments are summarized separately (Neglected recognition of logical patterns -- especially of opposition, 2017) and are the focus of a forum on Oppositional Geometry: mathematics and philosophy of opposition- -- with a specific focus on "oppositional logic", as discussed with reference to the following patterns of relationship configured in terms of polyhedra -- with a 4D implication. The logic alphabet developed by Shea Zellweger, as a visually systematic way of representing each of the sixteen binary truth functions, has been a particular inspiration. Correspondences could be sought with the 16-fold dynamics of the heart as illustrated above.

Cubical representation
of BaGua pattern
of I Ching

The Logic Alphabet Tesseract
- a four-dimensional cube (see coding).
by Shea Zellweger

Topologically faithful 4-statement Venn diagram
is the graph of edges of a 4-dimensional cube
as described by Tony Phillips
Organization of contingent bitstrings
on a rhombic dodecahedron
Cubical representation  of BaGua pattern of I Ching The Logic Alphabet Tesseract by Shea Zellweger Topologically faithful 4-statement Venn diagram Rhombic dodecahedron with contingent bitstrings
Reproduced from Z. D. Sung, The Symbols of Yi King or the Symbols of the Chinese Logic of Changes (1934, p. 12) Diagram by Warren Tschantz
(reproduced from the Institute of Figuring) .
A vertex is labeled by its coordinates (0 or 1) in the A, B, C and D directions; the 4-cube is drawn as projected into 3-space; edges going off in the 4th dimension are shown in green. Adapted from Lorenz Demey and Hans Smessaert (2017)

Given reference to the paradigm shift implied by Eppur si muove, it is appropriate to confront a seminal image of Galileo's time by Johannes Kelpler (left below) with a dynamic model in 3D (below right). The latter offers a unique embedding of the Platonic polyhedra within a rhombic triacontahedron the Platonic polyhedra depicted by Kepler (dodecahedron (blue), icosahedron (red), cube (grey), octahedron (yellow), with tetrahedron (cyan) and tetrahedron (magenta).

Nested polyhedral model
of solar system of Johannes Kepler
in Mysterium Cosmographicum (1596)
Rhombic Triacontahedron (green) as a nesting framework
(virtual reality variants static: vrml or x3d;
mutual rotation: vrml or x3d; "pumping": vrml or x3d;
videos: "pumping" mp4; "rotation" mp4)
Kepler solar systemnested polyhedra Platonic polyhedra nested within Rhombic triacontahedron
Reproduced from Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity (2017)

Commentary on the model on the right, and the justification for use of the rhombic triacontahedron, are presented separately (Nesting polyhedra to enable comparison of patterns of discourse, 2015; Dynamic relationship between polyhedra engendered by circles -- variously implying forms of unity, 2017). Especially noteworthy are the distinctive implications of mutual rotation and a "pumping" action resulting from relative changes of scale of the nested polyhedra. From a cognitive perspective, are such dynamics to be understood as implied by a crown?

The argument above noted the 20-fold pattern of levels in the "1,000-petalled" crown chakra and considered the insights regarding the 30-fold viable integrity in discourse, highlighted from a cybernetic perspective by Stafford Beer.

Speculatively it might then be asked how the 30 birds in quest of the Simorgh in The Conference of Birds relate to this mix of 20-fold and 30-fold. Given the argument for a dynamic (rather than a static) understanding of crown chakra comprehension, it is intriguing to note their relationship in the morphing dynamic between two symbolically fundamental polyhedra which are geometric duals -- namely the dodecahedron and the icosahedron. Both have 30 edges, but the former has 20 vertices and the latter necessarily has 20 faces (as its dual).

Variable geometry illustrated by animations of morphing between icosahedron and dodecahedron
(illustrating various morphing techniques)
by sizing by augmentation by truncation by expansion by tilting quads by tilting triangles by tilting to rectification by tilting to compound
Morphing icosahedron by sizing Morphing icosahedron by augmentation Morphing icosahedron by truncation Morphing icosahedron by expansion Morphing icosahedron by tilting quads Morphing icosahedron by tilting  triangles Morphing icosahedron by tilting to rectification Morphing icosahedron by tilting to compound
Animations produced by Stella Polyhedron Navigator (see description of dual morphing)

The animations above are reproduced from a discussion of the European Parliament whose elusive integrity is implied by the 12-starred European Flag -- perhaps to be understood as a "crown" of a kind (Experimental Visualization of Dynamics of the European Parliament in 3D, 2019; Coherent Representation of the European Union by Numbers and Geometry: mapping structural elements and principles onto icosahedron and dodecahedron, 2019). These note the curious proclivity for a 20-fold operational focus in practice (Requisite 20-fold Articulation of Operative Insights? Checklist of web resources on 20 strategies, rules, methods and insights, 2018). Equally curious, given the 12-fold pattern shared by the dodecahedral faces and the icosahedral vertices), is the remarkable enthusiasm for 12-fold set of principles (Checklist of 12-fold Principles, Plans, Symbols and Concepts: web resources, 2011; Eliciting a 12-fold Pattern of Generic Operational Insights: Recognition of memory constraints on collective strategic comprehension, 2011).

Understood in terms of the case for the variable geometry of institutions, is there a strange alternation between the 20 directional journeys of birds (strategic "flights") and the 30 distinctive outcomes -- as required for some form of transcendent integrative viability? As with wave-particle complementarity, this ambiguity would then be curiously consistent with the long-articulated insight that purpose is especially related to the journey itself and not to the destination, namely that the journey is more important than the destination -- or the contrary:

Of related interest is the pattern of annual migration pathways of many birds, as now reflected in the orbital patterns of satellites -- and potentially to be disrupted by them.

Multi-level crown chakra "temple" configuration?

To the extent that a gobal constellation of communication satellites can be understood as a configuration of the "Heavens" -- in contrast with the cognitive framework purportedly offered by the crown chakra -- it is of relevance to explore an intermediate pattern. This is most obvious in the architecture of temples, and especially those of Asian tradition of multiple levels. It is therefore interesting to explore how representation of the crown chakra might be reflected in an externalization into a form of temple -- the "body as the temple of the spirit" (1 Corinthians 6:19).

Of potential cognitive relevance, in the light of the role of the icosahedron noted above, is the manner in which the a 3-dimensional 9-fold enneagram configuration is nested within it, as noted by Stafford Beer (Beyond Dispute: The Invention of Team Syntegrity, 1994) -- discussed and visualized separately (Imagining the nature of cognitive "flight" in terms of the enneagram, 2014). Such organization merits exploration in the light of the marked tendency for 9-level temple designs.

As above, little design effort is given to he animations below to the aesthetic attribution of colours, proportions, and relative rates of rotation. With respect to the architecture of any "temple", consideration could be given to the manner in which the proportions form either a spire or a dome. The relative proportions could follow a pattern such as that of the Fibonacci series, for example.

Experimental "temple" stacking of 20 rotating rings crown chakra each of 50 heart-patterns
(side view of animations pesented above)
20 Rings of 50 heart-patterns in "temple" form 20 Toroidal heart-petals rings of 50 heart-patterns in "temple" form
Technical note: See above

Exploration can be taken further through considerring how the heart pattern, and its dynamics, can be represented in 3D, as discussed separately (Cognitive heart dynamics framed by two tori in 3D, 2016). Here the 4-circle pattern above is changed such that the ratio of separation of centres of the smaller circles to that separating the larger is based on phi -- the golden ratio. The argument then explores the rotation of that pattern to form a torus -- but specifically a horn torus, as shown in the right below, adapted with permission from an animation by Wolfgang Daeumler (Horn Torus). This forms was used in the vajra model above.

Approaches to representation of heart-pattern in 3D
Animation of heart pattern framed by 4 circles

Animation of dynamics of 4 conditions of the heart-pattern Embedding of heart pattern within contiguous tori
(animation of wireframe rendering)
Heart defined in terms of phi 2D animation of dynamics defining the 4 conditions of the heart-pattern Animation indicative of embedding of heart pattern within contiguous tori

The experimental vajra models indicated above can be used within a "temple" variant of the crown chakra as a form of indicator rotating over the 2D heart patterns at each level. The 3D heart pattern can then be understood as a rotation of the 2D pattern -- "activating" the position indicated. It is of course the case that the heart pattern used in this exercise (based on phi) has proportions distinct from those in the crown chakra pattern.

The rotating vajra model is only included for a selection of levels of the crown chakra -- both to clarify the illustration and because the animations are already relatively heavy. The animation on the right below offers an indication of an animation of a stack of variously rotating vajra models -- omitting the crown chakra rings. In that case (and on the left), the connectors between the heart patterns in the vajra model -- based on the Mobius strip (as shown above) -- are allowed to rotate, rather than being stationary in the animation in the centre.

Experimental use of 3D heart-patterns in vajra-model rotating within crown chakra using a "temple" perspective
Rotation of vajra set over crown chakra Rotation of vajra set over crown chakra Rotation of 3D vajra stack alone
Experimental use of 3D heart-patterns in vajra-model rotating within crown chakra Experimental use of 3D heart-patterns in vajra-model rotating within crown chakra Experimental use of 3D heart-patterns in a set of rotating vajra-models
Technical note: See above
Although symbolically dubious, such experments highlight the question of how complex an animation can b made as a means of holding a complex pattern -- such as to render it comprehensible, memorable an communicable. Some temple architecture has clearly responded to this challenge (Jeffrey Balmer and Michael T. Swisher, Diagramming the Big Idea: methods for architectural composition, 2019). Consistent with rote learning, it is somewhat ironic that architecture may evole a process of meditative perambulation, as with sacred mountains (Kailash, etc) -- a dynamic suggested by the rotation of the vajra models in animations above. Provocatively one might wonder as to the appropriate design of a "Temple of Sustainable Development" (Greg O'Hare, Climate Change and the Temple of Sustainable Development, Geography, 87, 2002, 3).


Jayarava Attwood. Form is (Not) Emptiness: the enigma at the heart of the Heart Sutra. 2017 [text]

Jeffrey Balmer and Michael T. Swisher. Diagramming the Big Idea: methods for architectural composition. Routledge, 2019

Stafford Beer:

Joseph Campbell. The Inner Reaches of Outer Space: metaphor as myth and as religion. Alfred van der Marck Editions, 1986

Keith Critchlow:

Loai Dabbour. Geometric Proportions: the underlying structure of design process for Islamic geometric patterns. ResearchGate, December 2012 [abstract]

Sharon J. Derry, et al. (Eds.). Interdisciplinary Collaboration: an emerging cognitive science. Psychology Press, 2014 [contents]

Ann Elias:

Paul Gerstein. Form Is Emptiness: an insider's guide to the Heart of Zen Buddhism. MindSource Press, 2013

Richard Jelusich. Eye of the Lotus: psychology of the chakras. Lotus Press, 2005

Julie Thompson Klein:

George Lakoff and Mark Johnson:

Donald S. Lopez Jr. Elaborations on Emptiness: uses of the Heart Sutra. Princeton University Press, 2016

Janet McLellan. Many Petals of the Lotus: Five Asian Buddhist Communities in Toronto. University of Toronto Press, 1999

V. Walter Odajnyk. Gathering the Light: A Jungian View of Meditation. Fisher King Press, 2011

Kate Raworth:

M. Sherif and C. W. Sherif (Eds.). Interdisciplinary Relationships in the Social Sciences. Routledge, 1969

Henryk Skolimowski. The Participatory Mind: a new theory of knowledge and of the universe. Penguin/Arkana, 1994

James Surowiecki. The Wisdom of Crowds: why the many are smarter than the few and how collective wisdom shapes business, economies, societies and nations. Doubleday, 2004

George Joji Tanabe and Willa Jane Tanabe. The Lotus Sutra in Japanese Culture. University of Hawaii Press, 1989

Pablo Triana:

Geoffrey Vickers. Freedom in a Rocking Boat: changing values in an unstable society. Allen Lane, 1972

Alexander Wendt. Quantum Mind and Social Science: unifying physical and social ontology. Cambridge University Press, 2015

Richard Wilhelm. The Secret of the Golden Flower: A Chinese Book of Life. Psychology Press, 1999

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

For further updates on this site, subscribe here