Enhancing aesthetic appreciation through augmenting immersive reality

Evoking Castalia as Envisaged, Entoned and Embodied -- informed by the bertsolitaria process ? (Part #9)

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Mathematics and art: The cultivation and appreciation of the great game in Castalia is significantly enhanced through the further development of a variety of familiar mobile and web-enabled applications -- in addition to those cited above.

These notably reflect the aesthetic possibilities highlighted periodically at the annual conferences of The Bridges Organization on the connections between art and mathematics, extended in 2016 to include poetry (Kristof Fenyvesi, Bridges: A World Community for Mathematical Art, The Mathematical Intelligencer, 2015).

Despite a degree of recognition of mathematical beauty, mathematics is however inherently indifferent to aesthetics other than in terms of elegance as an imputed characteristic of any formal articulation (Philip J. Davis and Reuben Hersh, The Mathematical Experience, 1995). As a method, mathematics is however also inherently indifferent to comprehension of its complexities, as separately argued (Dynamics of Symmetry Group Theorizing: comprehension of psycho-social implication, 2008).

In Castalia, however, the cultivation of the experience of mathematics was fundamental to its aesthetic "organ-ization". The implications for collective engagement with conceptual structures had long been inspired by the early explorations of Douglas Engelbart (Augmenting Human Intellect: a conceptual approach, 1962).

Confluence of technologies: Such developments transformed conventional observation of the game into a higher order of cognitive engagement with it -- partly to be understood by public appreciation of chess and go. Some understanding can be suggested in terms of an unusual confluence of technologies including:

• video recording for purposes of web-casting to local and remote devices
• virtual reality devices, as heralded by their rapid deployment in 2016
• simultaneous interpretation and transcription of oral formulations, enabling multilingual web-casting
• enhanced tracking of:
  • body movement, as extensively developed for purposes of animation and special effects
  • tonal and melodic forms in use
  • "passing patterns" in the exchange of memes between participants, variously challenging or reinforcing each others perspectives
• inter-modal "translation" between oral, graphic and textual forms, notably reflecting the sonification techniques of the International Community of Audiory Display -- and suggestive of the possibility of decoding tweets into tonal and melodic form
• a variety of enhanced mapping techniques, whether into visual or soundscape forms
• a variety of classification techniques through which categories could be ordered and re-ordered (as a creative process in its own right), notably with respect to:
  • thematic content
  • melodic and tonal structure
  • rhyme and metre
• pattern recognition and fitting, notably constrained to enhance memorability
• evolution of artifical intelligence, with the possibility of encompassing sung versification as a mode of communication (Forthcoming Major Revolution in Global Dialogue: challenging new world order of interactive communication, 2013)

Poetizing systems diagrams and systematizing symbolic patterns? In formal design terms, there is a remarkable degree of resemblance between conventional systems diagrams and the integrative patterns elaborated within various cultural traditions (of which examples are depicted above).

Reference was made above to the use of song as a mnemonic aid to comprehension of the pattern of metabolic pathways. In Castalia the possibility is taken further through use of the intricate symbolic imagery (as depicted above), notably the Celtic knots as featured within the Book of Kells. Such imagery was associated in Celtic tradition with song, although any direct relation is considered to have been lost, especially the secret of generic rhyme.

In Castalia it is assumed that Celtic knots can be sung and in fact constitute an aesthetic system of notation -- of which many musical variants already exist. Especially intriguing in Castalia is the recognition of the intricacy of Celtic knots as encoding the Welsh poetic constraints of cynghanedd. With the latter understood as "harmony" or "chiming", a correspondence was thereby established between the visual symmetry of such a knot and that associated with a poem, whether sung or not.

Technically the association derived from decoding the pattern in topological terms, in the light of the extensive application of topology to the mathematical theory of knots of which an especially valuable articulation is provided by Jessica Connor and Nick Ward (Celtic Knot Theory, University of Edinburgh, 2012). This provides a proof that Celtic knots are alternating, and that alternating knots are Celtic. They notably conclude that: The connection between pure maths and something based entirely upon aesthetics was particularly interesting.

Of relevance is the recognition by mathematics of a form of musical isomorphism. The innovative insight in Castalia lay in associating the pattern of crossings and contrasting orientations with the complex rules of cynghanedd, regarding usage of vowels and consonants and the rhyming conventions.

This understanding then allowed conventional systems diagrams and concept maps to be rendered (and comprehended) in poetic verse form -- enabling them to be sung. This offered a new approach in Castalia to the elaboration of complex patterns of (dis)agreement fundamental to its social organization -- potentially a pattern of wider relevance, as noted above (A Singable Earth Charter, EU Constitution or Global Ethic? 2006).

The role of alternation in aesthetics is recognized as especially relevant as a requirement of sustainability in governance, as separately argued (Development through Alternation, 1983). Understanding of the fundamental challenges of governance within Castalia then invites exploration in terms of higher dimensional knots and their comprehension, both in mathematical and psychosocial terms (Andrew Ranicki, High-dimensional Knot Theory, 1998; R. D. Laing, Knots, 1972). Lines of an introductory "poem" from the latter include:

The patterns delineated here have not yet been classified by a Linnaeus of human bondage.
They are all, perhaps, strangely, familiar.
In these pages I have confined myself to laying out only some of those I actually have seen.
Words that come to mind to name them are: knots, tangles, fankles, impasses, disjunctions, whirligogs, binds.
I could have remained closer to the 'raw' data in which these patterns appear.
I could have distilled them further towards an abstract logico-mathematical calculus.
I hope they are not so schematized that one may not refer back to the very specific experiences from which they derive; yet that they are sufficiently independent of 'content', for one to divine the final formal elegance in these webs of maya.

Lauburu as a generative metaphor: Especially intriguing is the manner in which the generic form of the Basque lauburu is effectively used as a template onto which the dynamics of the game can be mapped and tracked.

However, rather than being understood as a fixed mapping surface, this is better recognized as a strangely elusive form of "instrument" to be variously "played" by adjusting parameters in order to enable and enhance comprehension. Rather than fixed, the "form" is then to be understood as "plastic" -- possibly to be compared metaphorically to a standing wave or a resonance hybrid. The instrument is then what the player makes of it as an interface for engagement with the game -- possibly via virtual reality.

The images below indicate how the form of the lauburu can be used as a mapping template in two dimensions. In contrast to conventional use of category boxes linked by lines, here the emphasis is switched to areas bounded by curves or variously associated with curves -- of global rather than local signifiance in engendering the form.

The encircled zones can be used as conceptual containers -- or concepts can be associated with curves, readily segmented within the pattern to handle greater detail. Consistent with the sense of cognitive "skins" described above, concepts are associated with zones in two of the images, whereas the possibility of distinguishing the curves (and their parts) by number is indicated in the third.

Use of the generative geometry of the lauburu as a concept container
Chinese Ba Gua trigrams	Systematic encoding	Musical notations

The widespread use of mobile devices helps to clarify further distinction:

• possession of the device
• connectivity of the device (to a local server or the web)
• access to online facilities (constrained by paywalls, copyright, and security)
• relative skill in use of the device
• specific skill with respect to a particular application
• ability to reprogram the device or applications
• handheld mobile

Lauburu and cognitive organ-ization: Use of this strange device, especially by the skilled, then enables the process of poetic or sung expression to be followed visually as evolving aesthetic patterns in the moment. These can then in turn be interactively "played", notably through their transformation into other modes -- however shared (if at all).

In this sense the device might be described metaphorically as a "cognitive wind harp". The harp metaphor is usefully reminiscent of a role-playing game Harp SF (separately reviewed). As noted by The Encyclopedia of Science Fiction, other such musical devices have been imagined by science fiction -- although with relatively little development of the cognitive implications. Some have been extensively explored in the dystopian novel by the poet Anna Smaill (The Chimes, 2016). There life is orchestrated by a vast musical instrument that renders people unable to form new memories. For Kim Stanley Robinson, a vast calliope-like instrument with a single player -- a great interplanetary "orchestra" -- features as part of a complex metaphor, combining music and mathematics, in which musical structure and cosmic structure are seen as analogous (The Memory of Whiteness, 1985). Such imagery is also evoked by David Zindell (Neverness, 1988).

Further insight into the nature of the device can be gained by considering various ways of using the lauburu as a mapping "surface" in two or three dimensions -- or more, as explored by topology. The map is then potentially to be understood as a dynamically engendered "soundscape", for example, rather than a fixed "landscape". What is mapped onto it may however be largely a matter for the participant-beholder as co-creator.

Such consideration can be usefully framed by recognizing potential cognitive correspondences with similar forms, possibly more familiar (although equally elusive in their implications) -- and into which (or between which) any mapping could be transformed. Such transformation would be consistent with the conventional understanding of map projections. The appropriateness of correspondences is of course variously appreciated and disputed (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007) as with viable transformation pathways and their embodiment

Cognitive implication through immersion in augmented reality: Development of use of the lauburu is taken further in Castalia through its articulation in three and more dimensions. This offers a richer array of mapping contexts -- planes and volumes -- with which cognitive operations can be associated. The capacity to benefit from these depends to some degree on augmented reality technology, especially when this offers immersive experience through which interlocuteurs can engage with each other, as variously described (Project Anywhere: digital route to an out-of-body experience, The Observer, 7 January 2015). Such augmentation is essential when dealing with higher dimensional topologies -- landscapes over which more complex discourse takes place.

The following images of elaboration of the lauburu in three dimensions to hold the dynamics between 6 or24 "voices".

Screen shots of 3D variants of lauburu
Representation of 6 "voices"	Representation of 24 "voices"

Potential implication of such patterns can be distinguished as follows, in the light of a separate discussion (Metaphorical Geometry in Quest of Globality in response to global governance challenges, 2009). Of particular relevance is the consideration of lines as strings (Polarities as Pluckable Tensed Strings: hypercomprehension through harmonics of value-based choice-making, 2006).

Cognitive implications in 2D	Cognitive implications in 3D
Lines	Planes
strings as in stringed instruments psychological and aesthetic associations (rhyming, etc) correspondences (especially following from parallelism) systemic links, feedback loops transformation pathways, by analogy to metabolic pathways sine curves ****	sounding boards, exemplified by metaphorical use of drummng sides, exemplified by taking sides in an argument
Circles	Spheres
categories, as in cognitive and other forms mind mapping representation of tones or "voices"	resonance chambers world views and cognitive domains spheres of cognitive influence (Sloterdijk, 20014-2016)

Encoding dynamics: In Castalia the form of the lauburu is used to hold the dynamics of the variety of patterns, whilst suggesting the cognitive shifts and twists of any process, understood as a dance or otherwise. Especially intriguing is an extension of the meaning long associated with "surfing the web" to surfing the "songlines of the noosphere" (as noted earlier). The value of the metaphor lies in the cognitive engagement with waves of information and the skill with which this may be done -- as effectively encoded in the complex of skills of sea surfing.

Indicative animation of activated patterns using lauburu geometry

Superposition of a reduced version of the geometrical construction of the lauburu as a whole within each branch of the lauburu (as with a fractal)	Shading of the geometry of the lauburu (left-hand image) to highlight one orientation of the Tao symbol and emergence of the "eyes" from the geometry

Experimental animation of the right-hand image above between 8 orientations indicative of the possibility of more complex animations with rotation of the nested structures of smaller scale

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