Attribution of significance: considering meaningful pattern mapping

Psychosocial Learnings from the Spiral Form of Hurricanes (Part #8)

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The argument above drew attention to the need to render more explicit the extent and nature of the bonding between the helical strands -- again in the light of their vital function in double- and triple-stranded DNA. Expressed otherwise, the issue is whether the helical structure offers a useful means of holding and integrating functional distinctions -- a pattern which can be meaningfully mapped, as has been the case with the Human Genome Project.

An indication of the most common DNA forms in terms of geometry is presented below -- as seen through looking along the axis of the helix. The literature does not seem to indicate any focus on analogous patterns of bonding in the Triple Helix model.

End view of A-, B-, and Z-DNA conformations.

Reproduced as a detail of an image in Wikipedia (where side views of the helix are also given)

Memetic code and morphogenesis: Such patterns suggest a relation to the literature reflecting speculatively on the possibility of a "memetic code" as discussed separately (Identifying 20 "amino acids" of a memetic code potentially vital to psychosocial life? 2015) . Clearly this is a step beyond the current considerations of the Triple Helix model -- and is potentially indicative of the restrictive focus of that model in relation to innovation, if innovation is in any way to be considered analogous to morphogenesis.

In psychosocial terms the latter has been a particular focus of René Thom (Structural Stability and Morphogenesis, 1972), as variously discussed separately (Enabling morphogenesis and transformation through catastrophic questioning, 2013; Morphogenesis of globalization: enabling topological transformation, 2010). Of particular interest to that approach is the relation between those preoccupations and catastrophe theory -- especially given the disruptive power of "cognitive cyclones". Envisaged as it has been to enable innovation of relevance to the future, has the Triple Helix model been "future proofed" and "hurricane proofed"?

Whilst a "memetic code" remains elusive, if not questionable, there is considerable investment in patterns through which knowledge might be organized -- if only to facilitate the processes of search engine. Typically these avoid concern with the comprehensibility of such patterns and the coherence they supposedly imply.

It is in this sense that traditional preoccupation with coding systems in order to preserve collective memory merits attention, as extensively documented by Lynne Kelly (The Memory Code: the Secrets of Stonehenge, Easter Island and other Ancient Monuments, 2017; This ancient mnemonic technique builds a palace of memory, Aeon, 2017). Perhaps appropriately, any view along the axis of a helix (as above) recalls the preoccupation with circlets of beads (Designing Cultural Rosaries and Meaning Malas to Sustain Associations within the Pattern that Connects, 2000; Engaging with Globality through Cognitive Circlets, 2009).

The challenge is that such circlets are widely held to be meaningful -- whereas the Triple Helix is currently only meaningful to the very few, much challenged in communicating its potential to a wider audience (expected to subscribe to the framing it offers). A more provocative contrast could be made in the light of the strange significance associated with so-called "loving cups" ("pass cups", tygs) when 3-handled for ceremoial purposes, as is often the case across cultures and down the centuries. The 3 top-to-bottom links associated with the helical structure above render it reminiscent of that form.

The strange cognitive inversion implied by the contrast between rational articulation of academic and strategic models and the forms valued for their significance suggests that any "cognitive wormhole" is somehow irrationally fundamental to the creativity associated with radical innovation. This is evident to varying degrees in studies of creativity (Arthur Koestler, The Act of Creation, 1964; Daniel Dervin, Creativity and Culture: a psychoanalytic study of the creative process in the arts, sciences, and culture, 1990)

Triadic bonding between helical strands? Such indications frame the possibility of "populating" experimentally the triple helix in some comprehensible manner -- the issue being to ensure a triadic bonding between the three strands as variously indicative of stages and processes of interaction between academia, business and government, or the cognitive functions of which they are the institutional manifestation. An obvious approach is to link the strands with a set of triangles as being suggestive of a particular understanding of such psychosocial bonding.

Screen shots of triple helix with inclusion of three triangles only
"Top" view	Side view	View "through""

Clearly many more triadic bonds could be added in this way. How they are positioned precisely calls for (mathematical) attention to the relative position of the three strands so bonded. Multiple triangles viewed down the helix would bear some resemblance to the views above of DNA.

The triangles are especially indicative of the nature of triadic thinking, as cited above. The question then becomes how distinct significance might be attributed to any particular triangle linking the three strands. With respect to decision-making, the argument can be taken further by considering (if only speculatively) the relationship between the superposition of triangles (as perceived) and a particular relationship between the Star of David and the I Ching (Mapping of I Ching hexagram coding onto Star of David, 2008). Although resembling the Star of David in the simplest case, multiple inclusion of triangles between the helical strands would result in triads being variously oriented to one another, forming a more complex pattern.

As illustrated by the animation below, this has the advantage of highlighting a dynamic aspect to the triadic bond. It is appropriate to recall that the 64 different hexagrams distinguishing particular decision-making conditions within the I Ching are composed of an upper and a lower triad (of which there are 8 types). Speculative references to a complementary relationship between the I Ching and DNA patterns are noted separately (Archetypal Otherness -- "DNA vs. I Ching", 2007). As with the triskelion, the point to be emphasized is the enduring significance widely attached to the I Ching over millennia. Appropriate to this argument, the relevance tof the I Ching pattern is a feature of the recent study by Steven Rosen, (Quantum Gravity and Taoist Cosmology: exploring the ancient origins of phenomenological string theory, Progress in Biophysics and Molecular Biology, 2017)

Representation of I Ching hexagram codes mapped onto the Star of David (framed, for mnemonic purposes, by implications for innovation)
64 I Ching hexagrams configured as double triangles (as in animation on the right)	Animation suggestive of the dynamics of triadic bonding -- up and down the helix
		Consensus (about innovation)
	Comprehension (of innovation)		Coherence (of innovation)
	Confidence (in innovation)		Communication (of innovation)
		Complexity (of innovation)
[tentative: of interest is the convention regarding allocation of trigram lines to triangle positions and whether alternative allocations are anyway of significance in their own right

Some possible sense of the distinctive decisions is indicated separately (Transformation Metaphors derived experimentally from the Chinese Book of Changes (I Ching) -- for sustainable dialogue, vision, conferencing, policy, network, community and lifestyle, 1997). Framing the animation (tentatively) by implications for innovation offers the suggestion that particular conditions may only apply in certain circumstances.

Helical supercoiling: To the extent that the Triple Helix model is inspired by the helical structure of DNA, it is curious to note the seeming absence of any reference to the significance of DNA supercoiling which is of such importance in a number of biological processes. This refers to the over- or under-winding of a DNA strand, and is an expression of the strain on that strand. Technically the "twist" is the number of helical turns in the DNA, whilst supercoiling is defined in terms of the "writhe", namely the number of times the double helix crosses over on itself. Extra helical twists are positive and lead to positive supercoiling, while subtractive twisting causes negative supercoiling.

Such insight into patterns fundamental to biological mutation should encourage insight into their implications for innovation in wider society. The potential relevance has been argued separately (DNA Supercoiling as a Pattern for Understanding Psycho-social Twistedness, 2004). The argument has been developed further in the experimental visualization of helical coils (Visualization in 3D of Dynamics of Toroidal Helical Coils: in quest of optimum designs for a Concordian Mandala, 2016).

Any use of "supercoiling" in relation to mutation and innovation is a reminder of the possible inappropriateness of assuming that this can best be comprehended in 3D, especially if significant innovation might be better understood as being of higher dimensionality. Termed compactification, physics makes a case for higher dimensions being "wrapped" up on themselves, or "curled" up on Calabi-Yau spaces, or on orbifolds. Such thinking has been recognized as relevant to the cognitive organization of the transformation processes in music (In Quest of a Dynamic Pattern of Transformations, 2012; Carol L. Krumhansl, The Geometry of Musical Structure: a brief introduction and history, Computers in Entertainment, 2005). Especially relevant to this argument is the work of Dmitri Tymoczko (The Geometry of Musical Chords, Science, 2007) who notes:

A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by utilizing short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant chords possess different near-symmetries, and suggest different musical uses.

Given the cognitive intimacy of musical comprehension and appreciation, associating the higher cybernetic orders of self-referential feedback (noted above) with the cognitive implications of 3D helices might be usefully explored in terms of such dimensional compactification and supercoiling.

So framed, the external links between the "upper" and "lower" ends of the 3D helix depicted above, combined with the hexagram patterning of the Star of David, suggest further possibilities as indicated by representation of the latter in 3D (Framing Global Transformation through the Polyhedral Merkabah: neglected implicit cognitive cycles in viable complex systems, 2017).

Quadruple helix / Quadskelions -- Quintuple helix / Quinskelions? As indicated with respect to the parametric renderings of the triskelion, the possibility of "polyskelions" can be readily envisaged (J. Jacquelin, Parametric equations and specifications of a triskelion (triple spiral), Mathematics Stack Exchange, 30 January 2014). As adapted from the images there, these would take the following form. The coloured variants are included to emphasize the manner in which each could be understood as "engaging" with the environment and informed by it -- with the triskelion as the first in the sequence to suggest an "interior" and to function as a form of container.

Comparative renderings of "polyskelions"
Biskelion	Triskelion	Quadskelion	Quinskelion	Hendecaskelion
Adapted from depictions by J. Jacquelin (Parametric equations and specifications of a triskelion (triple spiral), Mathematics Stack Exchange, 30 January 2014).

The above panels offer a reminder that both the "skelions" and any helices can be of distinctive chirality, with whatever that may imply, as explored in another context (Unquestioned Bias in Governance from Direction of Reading? Political implications of reading from left-to-right, right-to-left, or top-down, 2016). Given that DNA can take both right and left-handed forms, is the Triple Helix model understood to be based on a right-handed or left-handed spiral -- and what would any such difference imply?

Engaging with otherness: binary, ternary, quaternary and quinary relationships ? (experimental animation)

Arrows are associated with the double spirals to indicate the nature of their systemic linkage with neighbouring spirals. The directions of the arrows alternate as an indication of input and output of information. In "emitting" the coloured arrows, the spirals are assumed to be associated with the same colours in all the images (as used above: left=blue, right=red, upper/lower=green, except in the 4-and 5-fold cases), The binary condition, typical of conflictual situations, is shown as transformed through an emergent third perspective (the triskelion), whether mediating (above), or engendering (reversed, as with an engendered child). Of particular interest is the manner in which systemic continuity is established paradoxically through the centres of each spiral (as "cognitive wormholes"). If any central whorls are occluded in some way, this would suggest an inauthentic relationship, even a systemically pathological condition. The animation would need to be further extended to take appropriate account of chirality.

The quadskelion could be considered relevant to the four-fold articulation of Nonaka (indicated above) as well as to possibilities of a Quadruple Helix model. Similarly the quinskelion form could be of relevance to proposals for a Quintuple Helix model. Of particular interest in that respect is the significance associated with the 5-fold star in iconography, notably of both Islam and the USA, and the challenge implied by the 6-fold, as discussed separately (Middle East Peace Potential through Dynamics in Spherical Geometry: engendering connectivity from incommensurable 5-fold and 6-fold conceptual frameworks, 2012). The manner in which 5-fold and 6-fold stars link the helical strands of particular models is especially suggestive -- perhaps to be understood in terms of the operation of an electrical commutator and rotary transformers.

There is a curious parallel with respect to health and healing between the pentagonal Wu Xing pattern, as a fundamental Chinese concept, and the Pythagorean symbol of the Hygiea (Beyond dispute in 5-dimensional space: Pentagramma Mirificum? 2015). That there is a degree of sensitivity to such pentagonal symbols is evident from the concern which can be aroused in the media by their inversion and association with questionable rituals.The hendecaskelion anticipates a rendering of a dodecaskelion with all the potential strategic implications currently associated with the 12-fold (Checklist of 12-fold Principles, Plans, Symbols and Concepts: web resources, 2011; Topological Clues to a Memorable 12-fold Systemic Pattern, 2011).

The presentation of spirals in the above argument has been limited to a particular number of "whorls", irrespective of whether the helix was triple or more complex. Any sense of the number of whorls appropriate to the meaning to be carried recalls the many considerations of "levels" in integrative processes, each level implying a higher inegrative order -- however that is to be understood by different belief systems and schools of thought, as may be variously discussed (Engaging with Insight of a Higher Order: reconciling complexity and simplexity through memorable metaphor, 2014; Engaging with Questions of Higher Order: cognitive vigilance required for higher degrees of twistedness, 2004; 9-fold Higher Order Patterning of Tao Te Ching Insights: possibilities in the mathematics of magic squares, cubes and hypercubes, 2003). In experiential terms, "whorl" 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).

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