Indicative representation of resonance between complementary frameworks

Alternating between Complementary Images of Coronavirus (Part #9)

The image above, being essentially static, can only imply the dynamics associated with resonant alternation between contrasting perspectives. Some further indication can be sought through metaphor (Metaphors of Alternation: an exploration of their significance for development policy-making, 1984).

As noted above, the possibility of representation can be most readily suggested through music, as discussed separately (Hearing the Variety of Voices in Climate Change Discourse: recognizing the challenge of soundscape comprehension in controversy and emergency, 2019). The latter distinguishes the following, of which the interplay in each case is familiar to most and readily comprehensible:

voice types: Climate change discourse according to classification of singing voice types?
types of singing: Types of singing as indicative of modes of climate change discourse

However any sense of coherent alternation between voices as instruments, or instruments alone, is central to orchestration, as discussed in that context (Orchestration of a requisite variety of voices in response to climate change? 2019).

Encoding of 8-fold patterns: It could be assumed that orchestration, choreography and composition also offer examples of visual representation of interplay consistent with a sense of complementarity. That earlier exploration concluded with a discussion of Patterns of resonance and their characteristic experiential challenges, illustrated by the following animations indicative of the resonance inherent in the 8-fold encoding offered by the Chinese BaGua system. This is especially the case given the nature of the transformation between its 8 conditions to which the encoding gives precision, as indicated in the animations below-left. Both the conditions and the transformations are traditionally described through metaphor.

The animations below-right are reproduced from a discussion of Transformation pathways in multivocal discourse (2016) featuring the Lauburu pattern (or Basque cross). The latter featured in an experimental depiction of 8-fold, 16-fold and 24-fold patterns (24-fold Pattern Implied by Dynamics of the Lauburu in 3D: visualization of the interplay of sets of voices in discourse, 2016)

*Use of 8-fold BaGua* to suggest the resonant dynamic relationships between voices**
Alternative experimental animations indicative of transformations between BaGua "voices"		Experimental rotation of alternative Lauburu patterns over alternative BaGua patterns
Later Heaven (King Wen) pattern of transformations	Earlier Heaven (Fuxi) pattern of transformations	Anti-clockwise over Later Heaven (King Wen) pattern	Clockwise over Earlier Heaven (Fuxi) pattern

The argument with respect to climate change can be generalized in more speculative exploration of the global brain -- itself to be imagined as a form of resonance hybrid. This considered the helical organization of patterns such as those above, in the light of the role of the musical octave as the epitome of comprehensible resonance for many (Requisite helical cognitive engagement within a global brain, 2019).

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

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

The animation on the right below uses a sequence of images to give a sense of pathways within and between more "worlds" of more "local" preoccupation (Various representations of cyclic dynamics with implications for a global brain, 2019). Cyclical patterns of N-foldness in static depictions of a global brain? Pathways of larger dimension are indicative of emergence of more "global" integration of the hemispheres of the brain

Experimental animations representing dynamics of resonance
Representation through combinations of Smith Chart with Lauburu and Tao pattern			Pathways in a global brain?
8 elements of Tao symbol represented experimentally on a Smith Chart	Superposition of Lauburu on Smith Chart	Animation of the Tao image between 8 orientations	Indicative of "global brainwaves"?

Reproduced from Various representations of cyclic dynamics with implications for a global brain (2019)

Clues from improvisation: The challenge with any representation of resonance of strategic significance is how cognitive implication is indicated. Given the obvious requirement in music improvisation and challenging poetic exchanges, an extensive discussion of the matter focused on the former as framed by the Lauburu as an integrative symbol for the Basque bertsolaritza tradition (Improvisation in Multivocal Poetic Discourse: Basque lauburu and bertsolaritza as catalysts of global significance, 2016)/

Clarification as to how participants, using different instruments, might improvise together within a group is offered in a key text by Vinko Globokar (Reacting: role of a performer, 1970). The distinctions were tentatively mapped onto a Lauburu, as shown below right, with related uses of that framework in the original discussion.

Imitation: After a variable lapse of time, a performer reproduces exactly what is heard. This being the most direct and instinctive mode. Clearly, the spontaneity as well as the quality of the response will depend on the contents and character of the pattern, on the degree of its complexity and on the degree of its perceived difficulty.

Integration: Rather than imitation, it is possible for the performer to integrate into material serving as a pattern, to follow it, to embody it, to move in the direction it suggests. The performer can always find a possibility of doing so one way or the other, and so the degree of complexity of information does not play a decisive role.

Hesitation: This is the mode tending most to create distance and disengagement. Starting from being "tied" to a particular pattern, the performer reaches a mode of actively creating pauses -- extremely alive and tense. Parts of the pattern are taken and positioned in time, transformed subjectively. This may produce an inner tension in the performer which complete prescription would probably have been incapable of provoking. Idleness in music, which otherwise makes for a dead situation, then becomes extremely "constructive".

Countering: Contrary to the above, doing the opposite from might be expected by any pattern, the performer rapidly analyzes the situation to determine an alternative. Ultimately, he does not "choose" but reacts. A pattern characterized by maximum loudness, static, in a deep register, will be "opposed" according to the individuals in one, two or even all three parameters at the same time

Mapping modes of improvisation onto lauburu

It is appropriate to ask in any dynamic relating to a crisis, such as the COVID-19 pandemic, to what extent authorities design into policy elaboration those 4-fold distinctions. The impression created by authorities has been unquestionable assertion -- from which any contrary perspective has been skillfully (if negligently) designed out. As noted separately, it is characteristic of more mature strategic assessments to benefit from simulations of at least two opposing strategies, especially in evaluating military options -- typically a so-called "Red Team" and a "Blue Team" (Misrepresentation of the scope of the crisis? 2020).

Indication of resonance using a 3D Lauburu framework: Given the availability of 3D modelling facilities, it is possible to explore a form of interplay between 8, 16 and 24 voices, as discussed separately and indicated below (24-fold Pattern Implied by Dynamics of the Lauburu in 3D: visualization of the interplay of sets of voices in discourse, 2016).

Screen shots and 3D animations of complementary "voices" using the geometry of mutually orthogonal lauburu to frame pathways of emergence and reabsorption
Single-plane lauburu framework 8-voice dynamics	Double-plane lauburu framework 16-voice dynamics	Triple-plane lauburu framework 24-voice dynamics

Video (mp4). Virtual reality (x3d, wrl)	Video (mp4). Virtual reality (x3d, wrl)	Video (mp4). Virtual reality (x3d, wrl)

Resonance indicated by an 8x8 magic square: As one of the Founding Fathers of the United States, Benjamin Franklin was a recognized polymath and one of the most influential personalities of his time. He is recognized as having been the most intimately involved in the elaboration of the US Constitution.

One of Franklin's far less recognized accomplishments, however, was his exploration of magic squares, and even magic circles, as noted by Paul Pasles (Franklin Squares 2006; Benjamin Franklin's Numbers: an unsung mathematical odyssey, Princeton University Press, 2007) and by Maya Mohsin Ahmed (Unraveling the secret of Benjamin Franklin: constructing Franklin squares of higher order, 23 September 2015).

The methods by which he generated such squares so readily, charactericized by so-called bent diagonals, remain unknown (Harvey Heinz, Most-perfect Bent diagonal Magic Squares, 2009; Daniel Schindel, et al., Enumerating the bent diagonal squares of Dr Benjamin Franklin, Proceedings of the Royal Society, 462, 2006), pp. 2271-2279; Paul Pasles (The Lost Squares of Dr. Franklin, The American Mathematical Monthly, 108, 2001, 6).

Franklin's 8x8 magic squares: animations of movement of selected bent diagonals
Vertical movement	Combined movement	Horizontal movement

Reproduced from Salvation Enabled by Systemic Comprehension -- Via aesthetics of magic squares? (2015)

Franklin called his 16x16 magic square the most magically magical of any magic square ever made by a magician -- with which many mathematicians and mystics would now be held to agree (Peter Loly, Franklin Squares: a chapter in the scientific studies of magical squares, University of Manitoba, 2006; William H. Richardson, Ben Franklin's Amazing Magic Square [including animation], Wichita State University; Ben Franklin's 8x8 Magic Square, Wichita State University).

Franklin's 16x16 magic squares: animations of movement of selected bent diagonals
Vertical movement	Combined movement	Horizontal movement

Reproduced from Salvation Enabled by Systemic Comprehension -- Via aesthetics of magic squares? (2015)