Remembering as rediscovering or reinventing the wheel

Symbolizing Collective Remembering Otherwise (Part #16)

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The quest in this argument, as indicated by the title, is for symbols to function as catalysts to enable collective "re-membering" (In Quest of Mnemonic Catalysts -- or comprehension of complex psychosocial dynamics, 2007).

Music and orbifolds: Especially provocative with respect to the relationship between head and heart are the emerging insights regarding comprehension of music readily recognized as performing a bridging function intimately related to the process of remembering and triggering a heartfelt response. It is in this sense that explorations of the organization of music by the brain is especially valuable (Dmitri Tymoczko, The Geometry of Musical Chords. Science, 313, 5783, 7 July 2006, pp. 72-74; A Geometry of Music: harmony and counterpoint in the extended common practice, 2011). This is discussed separately (Engaging creatively with hyperreality through music, 2016).

With respect to the ring symbol, it is therefore of considerable interest to note the results of psychoacoustic experiments by C L Krumhansl and E J Kessler (Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys, Psychological Review, 1982) of the inter-key relations of all major and minor keys can be represented geometrically on a torus -- as shown by Benjamin Blankertz, Hendrik Purwins and Klaus Obermayer (Constant Q Profiles and Toroidal Models of Inter-Key Relations -- ToMIR, 1999) in the following image.

Geometric representation of the inter-key relations of all major and minor keys (derived from psychoacoustic experiments by Krumhansl and Kessler)

For other relevant publications see Music Cognition Laboratory

Memorials "in stone": One exploration of relevance is through the extent to which collective memory and remembrance may be a matter of variously "writing in stone" (Transforming and Interweaving the Ways of Being Stoned: imagination, promise, rocks, memorials, petrification, 2012). Given the interplay of love/hate dynamics suggested by the intervention of Cupid, another approach is a degree of recognition of the extent to which the heart calls for recognition of the daemonic (Interweaving Demonic and Daimonic Associations in Collective Memory, 2008).

Mandalas and spokes: The interplay between the ring and the heart is usefully "regulated" by what can be seen as "arrows" (whether electrical or otherwise), or as the spokes of a wheel. The latter obviously recalls the challenge of discovering or inventing the wheel. In this context, in a knowledge-based civilization variously challenged by comprehension -- whether for an individual or a group -- this may well be a case of "rediscovering the wheel" or "reinventing the wheel". The point stressed above, with regard to the tragedy of the "broken ring", suggests that it may indeed need to be rediscovered or reinvented in some way -- with the implication that this may imply the need to comprehend it anew. In cognitive terms, any such "wheel" has long been suggested by mandala-type structures. However the above argument suggests that the quest for a "three-dimensional wheel" might prove more fruitful (Concordian Mandala as a Symbolic Nexus, 2016; Use of Concordian Mandala for a 3D ordering of value polarities, 2016; Speculation on Potential Symbolic Relevance of the Concordian Mandala, 2016 ).

Cognitive wheels and spokes: In the sense of their functioning systemically as "arrows", spokes offer an interesting way of framing that process of comprehension and discovery. Beyond the solid wheeel of yore, can the wheel function with 2 spokes, with 3, with 4, or more? Of interest in that respect is the history of the design of wheeled war chariots which at their peak had 15 spokes -- reminiscent of the 16 Sustainable Development Goals. A delightful caricature can be explored with respect to the effective use of square wheels (Reframing the Square Wheels of Global Governance: transcending vain hopes of squaring the circle in global decision-making, 2017). This includes a commentary on the possibility of Governance "locomotion" enabled by loopwheels, telescopic spokes and multipedal legs?

Rotation of magnetic fields: With respect to the functional relationship between spokes and arrows in interrelating ring and heart, of particular interest is the well-studied manner in which spokes are alternatively under compression or tension as a consequence of parts of the wheel being in contact with the ground and then having to bear a greater proportion of the load. A richer metaphor is offered by the highly innovative work by Nikola Tesla on the relation between positive and negative in electromechanical systems, as discussed separately with animations (Potential implications of alternation and rotation in psychosocial fields, 2014).

Ring, heart and ouroboros: Part of the challenge of this exercise, as implied above, is to indicate interesting relationships between the ring, the heart and the ouroboros -- for the reasons mentioned. One such possibility is presented below-left, further to animations presented previously (Experimental animations in 3D of the ouroboros pattern, 2017). It follows from an earlier demonstration of the possibility of "stacking" 3D heart patterns using horn tori, as shown below-centre (Cognitive heart dynamics framed by two tori in 3D, 2016). That stacking is reminiscent of the architecture of stepped temples. With greater effort, the 2D animation on the left could be presented in 3D using the toroidal elements from the centre. Whilst the direction of rotation of the ouroboros is provocatively consistent with the traditional presentation of the "serpent eating its tail", it can of course be asked what the reverse rotation would imply -- especially in relation to the symbolism of the heart.

Potentially more suggestive is possible equivalence between a rendering of the Mandelbrot set (oriented otherwise) and the heart pattern. Different colouring conventions can then be used to indicate different conditions "within the heart", as in the animation below-right. The renderings were produced using the remarkable Xaos application -- an interactive fractal zoomer program. The images were previously presented in Imagination, Resolution, Emergence, Realization and Embodiment: iterative comprehension ordered via the dynamics of the Mandelbrot set (2005) in support of various arguments relating to that rendering (Sustainability through the Dynamics of Strategic Dilemmas -- in the light of the coherence and visual form of the Mandelbrot set, 2005; Psycho-social Significance of the Mandelbrot Set a sustainable boundary between chaos and order, 2005; Understanding the Monster through the Mandelbrot set -- Moonshine connectivity? 2007)

Interrelating ring, heart and ouroboros (animation rotating right)	Stacking 3D heart patterns (based on horn tori)	Mandelbrot set (entamind) docs00s/cardrep3.php (animation of different colouring conventions)

The sequence of images in the animation on the right could of course be presented in a circle -- as an Ouroboros -- as with the animation on the left.

A case can be made that patterns suggestive of the mysterious nature of the relation between head and heart can be variously found, if only speculatively. Contrasting examples are presented below. The clothoid (or Euler spiral) is for example valuable in clarifying the transition between linearity and curvature. Shown with a reflection this is potentially significant to communication more generally (Reframing communication relationships, 2012; Clothoid as a psychosocial transition curve: from linear to circular, 2012). The geometry of the heart pattern may be further transformed, as shown, in order to engender a ring (proportioned again by phi). Given their role in affairs of the heart, the human ovaries offer a strange resemblance to the heart pattern, especially given the powerful circular attractor of the vagina.

With the widespread significance attached to bull symbolism, especially in the past, the head can also be recognized as recalling the heart pattern -- strangely extended by the ring, so frequently inserted in its nose as a means of control. This invites a variety of considerations (Theatre: spectator, spectacle of the feminine and the Bull Ring, 2014; Game-playing, bull-leaping and laurel wreaths, 2014). Also strangely relevant is the particular sense in which very extensive use is made of "bull" in relation to the ever increasing incidence of spin and fake news. With respect to this argument, such usage could be considered a typical response of those of the head modality to those of heart modality -- and vice versa. Hence the curious challenge of "bullfighting" at this time (Viable Global Governance through Bullfighting: challenge of transcendence, 2009; Transformation of Global Governance through Bullfighting: visual symbols and geometric metaphors, 2009).

Mnemonic catalysts for reflection on the relation between head and heart symbols?
Clothoid transition curves	Heart pattern geometrically transformed	Human ovaries and vagina	Bull head with a ring in its nose

Such images raise the question as to whether their potential equivalence merits exploration in terms of various approaches to symbolic equivalence, notably in the light of the Symbolic Equivalence Test developed by Frank Barron (Putting Creativity to Work, 1988), as discussed by Joseph Glicksohn, et al (A Note on Metaphoric Thinking and Ideational Fluency, Metaphor and Symbolic Activity, 8, 1993, 1). Equivalence between symbols is necessarily a feature of pattern recognition and can also be explored in terms of correspondences (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007).

The test features in a study by the US Department of Defense (Cognitive Agility Measurement in a Complex Environment, April 2017) concerned with levels of military decision makers in order to support the Army's line-of-effort in quest of "cognitive dominance" -- an aspect of full-spectrum dominance. This can be imagined otherwise (Embodying Global Hegemony through a Sustaining Pattern of Discourse: cognitive challenge of dominion over all one surveys, 2015).

In a global civilization readily characterized as faced with fundamental communication problems, it is appropriate to explore resources creatively developed by those responding to the implications of systemic nonsense -- as discussed separately (Nonsense commensurate with dysfunctionality (2014). Reference was made there to one of the widely known "nonsense poems" by Edward Lear (The Owl and the Pussy-Cat, 1871). In relation to this argment, this can in fact be read as a relatively unique description of the possibility of a distiinctly improbable "marriage" between the head modality and the heart modality -- with a prescient environmental sensitivity. Their marriage is sealed with a ring acquired with an appropriate measure of "nonsense" from any conventional perspective.

Aside from more obvious sexual connotations, one remarkable no-nonsense commentary on the possible hidden significance of the poem is offered by David Cowles (Owl and Pussycat, Aletheia, 26 March 2014). With respect to the ring he wonders:

Could it be that the ring was actually a Möbius strip, a one sided, 2 dimensional object? A Möbius strip is 'non-orientable', a topology in which there is no fixed beginning or end and no fixed orientation. Many eschatological cosmologies, for example Dante's in the Divine Comedy, include a non-orientable topology. A Möbius strip has the unique property that allows you to travel around it continuously, always coming back to the starting point; however, each time you return to the starting point, your orientation is reversed.

Further insight is offered to the effect that:

Three dimensional objects that contain a Möbius strip are called "Klein Bottles". In our world of 3 spatial dimensions, Klein Bottles are not physically realizable, but if they were, they could hold no liquid. Why? Because like all non-orientable objects, they are one sided and therefore have no inside or outside. In this admittedly speculative interpretation, the "runcible spoon" [a feature of the marriage celebration] is the three dimensional correlate of the Piggy-wig's two dimensional ring. It suggests that there is a consistently non-orientable topology in the eschatological kingdom, "the land where the Bong-tree grows" [the place where the marriage proved possible].

The current psychosocial significance of the Klein bottle is central to the work of Steven Rosen (Topologies of the Flesh: a multidimensional exploration of the lifeworld, 2006).

The mysterious interplay between head and heart modalities, in a period in which the "circle of trust" has been breached, is curiously symbolized by the widespread use of so-called awareness ribbons (List of awareness of ribbons).

Symbol of mourning

The form of the many such ribbons echoes both that of a broken Möbius strip and an inversion of the heart symbol -- with ring -- as variously indicated above.

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

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