Perspectives, insights and visions in relation to configurations of symbols

Reconciling Symbols of Islam, Judaism and Christianity (Part #10)

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"Perspectives" as "visions": Although the Abrahamic religions are inspired by a shared monotheism. This "principle" is so elusive that there is little deriving from it which enables them to reconcile their highly contrasting perspectives. The "perspective" of each is considered dangerously misguided by the others -- essentially missing the "point". A merit of the geometric models in 3D is that these offer, and require, multiple "viewpoints" to enable the whole to be comprehended. Use of a dynamic allows a sequence of patterns to be viewed from a single viewpoint -- as with a kaleidoscope. Understood as a mandala or rose window pattern, this is continuously shifting through a cycle of phases. Whilst this is indeed evident in 3D with the dynamic to be recognized as engendering a 4D model, it is obviously challenging to imagine the nature of the cycles in 5D (or more) and the patterns which emerge during those cycles.

It is useful to recognize the "visions" so central to religious experience as corresponding to some degree to recognition of particular patterns and cyclic phases. The puzzle is how such "visions" then engender such disparate articulations, with their associated assertions and possible institutionalization. More problematic is understanding how a "vision" can be so so radically transformative -- so fundamental -- as to render irrelevant those which may be articulated by others. Arguably the "rightness" associated with the experience of the "vision" could be understood as recognition of an especially complex form of symmetry, rendering other perspectives as secondary or tertiary -- basically derivative.

"Higher" dimensionality: As with the symmetry in 5D, 6D, and the like, it may be virtually impossible to articulate these other than through a variety of indications in whose underlying integrity others are called upon to believe. This could be considered the case with the multidimensional insights of fundamental physics whose nature can only be partially articulated in mathematical form -- for those who can interpret such script.

There is clearly a whole mystery as to how a perspective can shift in comprehension from 3D to 4D, from 4D to 5D, and so on. This is especially the case when the nature of "dimension" is called into question at each stage, beyond the formalism of mathematics -- as a perspective in its own right, with its own forms of fundamentalism, readily appreciated as alienating by some. Particularly intriguing is the sense in which "higher" dimensionality is called into question when this may rather be experienced as a more intimate experience rather than an elusive abstraction.

Shifting patterns: Missing from this sense of "vision" is the consequence of movement, recognized in the process through which the "vision" fades away and can be recalled only with increasing difficulty. This process is readily recognized through use of psychoactive drugs, the aftermath of the experience, and the difficulty of communicating it. The "perspective" which may encompass this fading away tends to be articulated in process philosophy and poetry regarding the sense of passing -- as with the surprise of emergence of revelation.

Together these may be framed by some sense of eternal return. Such elusive insights are essentially difficult to communicate and do not lend themselves to the kinds of declarative assertions typical of the Abrahamic and other religions. Arguably, it is the fixity of fundamental religious perspectives -- and deemed essential to their identity -- which is called into question to some degree.

Problematic inversion: The use of movement in the above models is especially valuable with respect to encompassing the "degradation" of a vision of much-valued symmetry. This is evident in the case of the highly controversial inversion of symbols such as the pentagonal star -- then readily associated with the most fundamental evil. Such an association is also evident in the case of the Christian cross. Traditionally use as been made of an inverted variant of the conventional Latin cross, known as the Cross of St Peter. As described by Wikipedia, this has more recently come to be associated with anti-religious groups.

Set within a process, the inversion is then better recognized as part of a cycle whose movement as a whole -- as with birth and death -- is essentially healthy in a larger sense, however tragically elusive this may remain. The larger cycle is also appreciated through an understanding of eternal return. Although elusive, the insight has been variously suggested:

• The First Shall be Last, and the Last First (Matthew 20:16)
• 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).

The poignancy of loss, and the nostalgia for past integrity, have merit in their own right -- better appreciated through the metaphor of the seasons. This metaphor is particularly valuable in a global context in which winter for some is experienced elsewhere as a time of summer. Any regrettable inversion perceived from one viewpoint of the above models, would be experienced otherwise from a different perspective.

A related issue, occasioning the greatest controversy, is the sense in which the rendering secondary of other perspectives can be interpreted from a fixed perspective as justifying attitudinal and social consequences which may take the form of "enslavement". The models models suggest that this may be interpreted in geometrical terms. The Abrahamic religions could be considered notorious in this respect for having condoned the enslavement of those of other faiths down the centuries -- and in new forms at this time.

Holomovement: explication and implication: The models above offer one interesting means of encompassing the sense of the holomovement which is a fundamental concept of quantum mechanics as articulated in the worldview of David Bohm (Wholeness and the Implicate Order, 1980). From this perspective, wholeness is not a static oneness, but a dynamic wholeness-in-motion in which everything moves together in an interconnected process, notably explicated as follows to include not just physical reality, but life, consciousness and cosmology:

• Our basic proposal was that what is the holomovement, and that everything is to be explained in terms of forms derived from this holomovement. (p. 178).
• The implicate order has its ground in the holomovement which is, as we have seen, vast, rich, and in a state of unending flux of enfoldment and unfoldment, with laws most of which are only vaguely known (p. 185).
• Our overall approach has thus brought together questions of the nature of the cosmos, of matter in general, of life, and of consciousness. All of these have been considered to be projections of a common ground. This we may call the ground of all that is. (p. 212).

The cognitive implications were later evoked with Jiddu Krishnamurti (The Ending of Time, 1985; Limits of Thought, 1999).

Multiplicity of religion and deities: The focus of this argument is on the unreconciled relationship between the Abrahamic religions -- given the points, lines and sides they engender in society. Arguably it could be said that the variety of polyhedra has not been ordered in any usefully definitive manner. However that variety, as with the multiplicity of stellar bodies, suggests the merit of recognizing focal points in addition to the Abrahamic religions.

One effort in extending the framework is the argument of Stephen Prothero (God Is Not One: the eight rival religions that run the world -- and why their differences matter, 2010; A Nation of Religions: the politics of pluralism in multireligious America, 2006). In terms of geometry, the more fundamental point is made by the existence of an alternative focus, as with that of Jason Boyett (12 Major World Religions: the beliefs, rituals, and traditions of humanity's most influential faiths, 2016). How best to ask questions about religious pluralism -- or about the disciplinary pluralism of academia and beyond? As noted above, efforts at encompassing the variety in the case of religions through mind-mapping is still at an early stage (University of Glasgow, Philosophy of Religion Mind Mapping Project). Mapping the relationships between the disciplines is at an equally primitive stage -- unfruitful with respect to any interdisciplinary endeavour.

It is in this sense that the multiplicity of deities and other elusive entities identified by other religions merits careful consideration rather than unthinkingly automatic rejection. Just as the Abrahamic religions have their angelic and demonic hordes, other religions have a multiplicity of spiritual entities -- Hinduism being most frequently (and critically) cited in this respect (Krishnan Ramaswamy, et al., Invading the Sacred: an analysis of Hinduism studies in America, 2007).

Whilst the Abrahamic religions may each pride themselves on their unitary nature, it is only too evident that they engender a multiplicity of denominations and schismatic forms -- variously inspired by individuals as a consequence of revelatory visions. Within those frameworks it is therefore interesting to note how this multiplicity may in each case be ordered, as partially explored separately (Engaging with Hyperreality through Demonique and Angelique? Mnemonic clues to global governance from mathematical theology and hyperbolic tessellation, 2016).

Metaphorical limits and clues: It is intriguing that the governance of global civilization is currently so constrained by vision-related perspectives -- even to the point of highlighting the "optics" in the political context (Optics, The New York Times, 7 March 2010). At the same time much is valued in music and other modes by the peoples of the world. The argument can be made that the future merits consideration through a variety of metaphors corresponding to the variety of senses -- vision, touch, taste, smell, and sound (Metaphor and the Language of Futures, 1992). Why indeed, for example, is no real effort made to articulate the "visions" of global governance in music and song, as argued separately (A Singable Earth Charter, EU Constitution or Global Ethic? 2006; Knowledge Gardening through Music: patterns of coherence for future African management as an alternative to Project Logic, 2000).

As a metaphorical alternative, especially relevant is the work of musicologist Ernest G. McClain (The Pythagorean Plato: prelude to the song itself, 1978; Meditations through the Quran: tonal images in an oral culture, 1981; Children of Abraham, 1984/2007). The latter is introduced in the following terms:

The tension today between Muslim, Jew, and Christian who claim descent -- and in that order -- from Father Abraham can be traced in part to the effort of Bible authors to illuminate three very different aspects of Deity. This is the story I missed in the first edition of my book, and for which I now try to make amends writing from a musical perspective that has endured for more than 5000 years.

The unusual feature of this detailed scholarly study is that all those named in the scriptures, and the proportions of the structures indicated, are interpreted in musical terms as tones and tuning systems. This includes an understanding of "slaves" and "enslavement", which the scriptures variously envisage -- thereby inviting controversial deprecation. A musical metaphor tends to switch cognitive enegagement from "interest" to "resonance", namely whether an articulation elicits some form of cognitive resonance, as indicated by speculation on the music of the spheres.

Sensual pattern? In the light of the above argument, this 5-fold "sensual" pattern can be "confronted" by the 6-fold pattern extensively articulated by Edward de Bono (Six Frames for Thinking about Information, 2008), Six Thinking Hats, 1985; Six Action Shoes, 1991; Six Value Medals, 2005). It is argued there that each "frame" is a direction or method in/with which to look, based on a different shape - triangle, circle, heart, square, diamond, slab. However each might also be understood as a generic equivalent to his distinction of the modalities of "thinking", "values" and action" (slide show). The attribution of Edward de Bono's categories in the table below is a tentative exercise, especially since it is their generic form which is of potential interest as a memetic complex of functions integrating thinking, action and values.

Here again, however, the "looking modality" is usefully to be called into question through the other senses. It is obviously the case that the Abrahamic religions variously take account of such modalities --beyond their theological assertions -- as in the use of hearing/music or smell/incense, for example. Their use may be even more developed in other religions.

These distinctions can notably be seen as relevant to the dynamics between the Abrahamic religions, as articulated by de Bono (Water Logic: the alternative to I am right you are wrong, 1993). The above models could be explored in the light of this confrontation as giving rise to "sensepoints" rather than "viewpoints" -- with the perspectival equivalent for which a neologism may be required, although the concept of "point" might itself call for rethinking. Both the dimensions of the table and their conjunctions in the cells of the table merit careful consideration as metaphors beyond the conventional significance of the terms.

Metaphorical confrontation of 5 "senses" and 6 "frames" to distinguish 30 "sensepoints" (indicative juxtaposition of categories calling for refinement)
	"hats"	"shoes"	"medals"	symbols		5 senses
	thinking	actions	values	"frames"		"vision"	"touch"	"smell"	"taste"	"hearing"
6 frames (Edward de Bono)	managing (blue)	routine procedures (navy)	goals (silver)	"triangle"	purpose
	information (white)	information gathering (grey)	quality implications (steel)	"circle"	accuracy
	discernment (black)	hard work (brown)	ecological impacts (wood)	"square"	alternative "points of view"
	emotions (red)	emergency actions (orange)	what matters (gold)	"heart"	matters of interest
	optimistic response (yellow)	empathy (pink)	perceptions (brass)	"diamond"	value
	creativity (green)	authority (purple)	innovation (glass)	"slab / rectangle"	outcomes conclusions

Together, in geometrical terms (as argued above), this 5x6 pattern frames 30 "points" in the case of an icosidodecahedron, or 30 edges in the case of an icosahedron/dodecahedron, or 30 "sides" in the case of rhombic triacontahedron -- with the implications of the other features of such polyhedra. Such a pattern has been explored from a management cybernetic perspective by Stafford Beer in relation to syntegrity and modelling a viable system (Beyond Dispute: the invention of team syntegrity, 1994).

Edward de Bono's "frames" can be compared with other metaphorical uses of the simplest geometrical forms (Engaging with Globality through cognitive lines, circlets, crowns or holes, 2009; Radical Localization in a Global Systemic Context: distinguishing normality using playing card suits as a pattern language, 2015). He has also made use of a 5-fold pattern of tools, termed the Five Stages of Thinking. In presenting his particular articulation it should be stressed that it is the generic tendency to identify such categories which is of relevance -- his articulation being only one that has been widely publicized (Jeremy Lent, The Patterning Instinct: a cultural history of humanity's search for meaning, 2017).

Four dimensional integration? Of further interest are the cognitive implications of such a 30-fold pattern in 4D where it might indeed take the form of 30 so-called "cells". The quest for insight on this matter detected a page of commentary on discrete Hopf fibrations (which had been partially deleted from Wikipedia). Both there, and in the remaining text in the user section of Wikipedia (Regular polychoric rings), it is noted that:

The 600-cell partitions into 20 rings of 30 tetrahedra each in a very interesting, quasi-periodic chain called the Boerdijk-Coxeter helix. When superimposed onto the 3-sphere curvature it becomes periodic with a period of 10 vertices, encompassing all 30 cells.

Whatever the future cognitive implications for such insights, the deleted page includes the animation (below centre), also presented here as an indication of the elusive quality of thinking that may be appropriate to integrative insight into the reconciliation of the Abrahamic religions.

Geometric clues to reconciliation of Abrahamic religions in 4D
3D projection of a 4D tesseract performing a simple rotation about a plane which bisects the figure from front-left to back-right and top to bottom	Challenging implications of discrete Hopf fibrations	3D projection of a 4D tesseract performing a double rotation about two orthogonal planes
Reproduced from Wikipedia	Reproduced from discrete Hopf fibrations	Reproduced from Wikipedia

Using the language of "cells" in 4D, the 3 Abrahamic religions could be understood as embedded in a tesseract -- which has 3 cubic cells (3-faces) per edge, as depicted in two animations above. The extensive commentary in Wikipedia notes that the the tesseract is the four-dimensional analogue of the cube -- with the tesseract being to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells. These could be explored as the 8 global religions noted by Prothero. The tesseract can howeve be understood as constructed with 3 cubes folded together around every edge -- possibly an indication of the distinctiveness attributed to the the 3 Abrahamic religions.

Use of the phrase "folding together" recalls that of fundamental physics in referring to the extra dimensions needed for a unified description of physical reality. String theory has one notable feature that requires extra dimensions for mathematical consistency. Spacetime is 26-dimensional in bosonic string theory, 10-dimensional in superstring theory, and 11-dimensional in supergravity theory and M-theory Understood in terms of "compactification", it is assumed these extra dimensions are "wrapped" up on themselves, or "curled" up on Calabi-Yau spaces, or on orbifolds. As noted above, this may imply a form of cognitive intimacy more familiar to aesthetic and mystical experience than the formalisms of physics -- and more cognitively accessible than the latter imply.

Missing with respect to the reconciliation of the Abrahamic religions is the equivalent to the quest for any such "M-theory". It is intriguing that the tesseract itself can be recognized as holding patterns of fundamental significance to those religions -- notably the 3-fold, the 4-fold, the 6-fold, the 8-fold, the 10-fold and the 12-fold.

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