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Geometry of meaning: an alchemical Rosetta Stone?

Eliciting a Universe of Meaning (Part #15)

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Alchemy as a meta-metaphor: Being an "out of the box" process, alchemy is not "what one thinks it is" -- rather "it" is better understood as being about the process of thinking about "its". It might be said to be a process of being otherwise by being other wise (Human Intercourse: Intercourse with Nature and Intercourse with the Other, 2007; Intercourse with Globality through Enacting a Klein bottle, 2009). It may be best understood indirectly through metaphor (as with the encounter of Perseus with the Gorgon), as being a "science" of metaphor, if not a technology, perhaps as implied by the work of Erik Davis (TechGnosis: Myth, Magic, and Mysticism in the Age of Information, 1999).

Like the mercury which is a major focus of its traditional commentaries, alchemical processes are "cognitively tricky" -- emphasizing self-reflexivity through the mirroring offered by "quicksilver". Alchemy is essentially about itself as a meta-metaphor -- about the process of engendering reassuring transitional objects in which confidence may be invested for a time. Religion, science and the monetary system offer such temporary comfort through the states whose recognition they enable -- as distractants from more fundamental existential questions.

Insights into creative governance from technomimicry: Tentatively, the argument can be taken further in the light of the explorations of Arthur M. Young (The Geometry of Meaning, 1976). He was the designer of Bell Helicopter's first helicopter, the Model 30, and inventor of the stabilizer bar used on many of Bell's early helicopter designs. He sought to generalize insights into the control of the flight of a helicopter -- which he framed metaphorically through 12 standard physical "measure formulae" -- in the quest for the design a "psychopter".

Young's approach might also be framed in terms of technomimicry, as separately discussed (Engendering a Psychopter through Biomimicry and Technomimicry: insights from the process of helicopter development, 2011). It is through insightful "mimicry" of the technology that innovation essentially takes place -- mysteriously eliciting new meaning from nothing. The widely acknowledged mysteries of the creative process have implications the development of this argument in that it recognizes a complex of potentials and constraints indicated by apophasis and autopoiesis. This is consistent with the aversion of innovators to "explaining" the process and progress of their "work". The implications go further in the case of alchemy.

The essentially controversial intention of Young can usefully be framed in terms of the repudiated alchemical endeavour of "transmuting base metals into gold". He chose as his "base metals", a set of 12 standard formulae of physics, those most ironically characteristic of "Newtonian mechanics". His purpose was to elicit the design of a psychopter as a "winged self" (The Bell Notes: a journey from physics to metaphysics, 1979). The cognitive "transmutation" could be framed in terms of what is readily termed "generalization". It could be better understood in musical terms as "transposition of key" (Paradigm-shifting through Transposition of Key: a metaphoric illustration of unexplored possibilities for the future, 1999). Douglas Hofstadter "played" with such a musical metaphor in his original work (Gödel, Escher, Bach: an Eternal Golden Braid, 1979). He has developed the implications in his most recent work with Emmanuel Sander (Surfaces and Essences: analogy as the fuel and fire of thinking, 2013).

12 "measure formulae" distinguished and clustered by Arthur Young
(reproduced from The Geometry of Meaning, p. 102)
Actions States Relationships
Position -- L Moment -- ML Power -- ML2/T3
Velocity -- L/T Momentum -- ML/T Inertia -- ML2
Acceleration -- L/T 2 Force -- ML/T 2 Action -- ML2/T
Control -- L/T3 Mass control -- ML/T3 Work -- ML2/T2
Young indicates with respect to this table: The last column is displaced one place.., in order to have the three members on each line 120 degrees apart (p. 102) ... in the circular configurations presented below

Universality of 12-fold patterns: Young comments extensively on the significance of each of these 12 in terms of the cognitive processes of learning/action cycles. Of relevance to the above argument is the co-presence of "states" and "actions" -- the latter implying the process dimension otherwise lacking in a "state-focus". Recognition of a "relationship" dimension suggests a valuable means of transcending that duality. These distinctions have been interpreted separately for a variety of psychosocial contexts (Typology of 12 complementary strategies essential to sustainable development,1998; Characteristics of phases in 12-phase learning / action cycles, 1995; Typology of 12 complementary dialogue modes essential to sustainable dialogue, 1998).

The requisite cognitive diversity within such a pattern is fruitfully explored in the quest for "operacy" through the work of Edward de Bono (How to Have Creative Ideas, 2012). His 6-fold generalization can be interpreted as offering set of 6 binary dimensions with 12 polar variants (Six Frames For Thinking About Information, 2008).

Curiously there is a widespread tendency to favour a 12-fold articulation of conventional strategic initiatives, as documented separately from web resources (Checklist of 12-fold Principles, Plans, Symbols and Concepts, 2011). This cognitive disposition reinforces the potential of Young's approach, as separately explored (Eliciting a 12-fold Pattern of Generic Operational Insights: recognition of memory constraints on collective strategic comprehension, 2011; Enabling a 12-fold Pattern of Systemic Dialogue for Governance, 2011).

Magnum Opus of global civilization? Framed in terms of alchemy, Young effectively gives focus to its classical preoccupation with a Magnum Opus. This was occasionally framed in terms of 12 phases. The provocative challenge of this time of crises could then be framed through a question such as: How is any Magnum Opus of humanity's global civilization to be understood? Can the elements of such a Magnum Opus be distinguished as processes implicit in strategic reports purporting to respond to these challenges -- as in the following?

Do these sets of "recommendations", "shoulds", or "messages" imply a Magnum Opus? How are the processes in questions to be comprehended as interrelated? How are they to be communicated meaningfully and credibly -- such as to elicit confidence?

Zodiac as a memorable popular configuration: Young uses the traditional pattern of 12 zodiacal signs to provide a circular (mnemonic) encoding of the learning/action cycles in terms of their psychological implications. The pattern constitutes a commonly multifacetted container through which to engage with the infinite potential of a universe in all its senses. Young sees this pattern as constituting a Rosetta Stone of meaning -- readily associated with the philosopher's stone traditionally engendered by the Magnum Opus of alchemy. The current implications of such a "stone" metaphor can be variously explored (Transforming and Interweaving the Ways of Being Stoned: imagination, promise, rocks, memorials, petrification, 2012). It could be understood as a process of "enstating" or "instating".

The elements of the table above can then be presented in two configurations, as indicated in the images below -- with the addition of the psychological analogues to each element on which he comments extensively. Most of these terms correspond to the vocabulary of strategic change management -- as would be required for the governance of a psychosocial vehicle (just as their physical equivalents are for a helicopter).

Circular configuration of 12 "measure formulae" correlated with the pattern of the zodiac
(combining representations by Arthur Young  from The Geometry of Meaning, p. 102 and 119)
Four triangular patterns (triplicities)
(one triangle per table row)
Three square patterns (quadruplicities)
(one square per table column)
Zodiac tripliciities (Geometry of Meaning) Zodiac quadruplicities (Geometry of Meaning)

These two distinct cyclic patterns can be fruitfully seen as implying the experiential challenge recognized by a cyclist in riding a bicycle -- and in learning to ride. Verbal explanation does not convey the nature of viable dynamic balance, nor how this should be comprehended. The metaphor could be used to reframe the challenge of governance in "cycling" around the adaptive cycle. More intriguing is the potential consequence of the constraint on human memory described in the much-cited paper by George A. Miller (The Magical Number Seven, Plus or Minus Two: some limits on our capacity for processing information, Psychological Review, 1956). This would imply a sense in which the only means of "encompassing" a pattern of 12 is by "cycling through" combinations of 3 and 4 phases -- as indicated in the two schematics.

Correlating alchemical processes with the zodiac: With the reservations indicated above regarding the tricky cognitive nature inherent in the creativity of the alchemical process, there is a case for reviewing the 12 phases of the process as they have been traditionally associated  with the signs of the zodiac (although other patterns of phases are also identified). The names for these alchemical processes (as indicated by Wikipedia) have been added to the circular representation in the schematic below. This combines the triangular and square patterns of connectivity in the schematics above

Zodiacal encoding of 12 "measure formulae" with associated alchemical processes
Zodiac of Geometry of Meaning (Arthur Young)

Use of the signs of the zodiac in the above manner, if only for mnemonic purposes, is of course questionable because of their problematic associations with a deprecated methodology. However as forms which have held valued psychosocial distinctions over centuries they merit a degree of attention, especially if they have a degree of mnemonic value in engaging with complexity. It is however striking to consider that they may be seen as performing the same function as the distinctions provided by Rene Thom between "archetypal morphologies" -- notably for semiotic purposes. He presents the set of 16 indicated below, of which 12 merit comparison with the functions indicated by the signs of the zodiac, and possibly even their forms. The first 4 (top left, below) could be considered "primitives". Such a comparison is even more justified by Thom's subsequent consideration of the pattern below in terms of their cognitive implications as processes, following his semiotic generalization (Esquisse d'une Sémiophysique: physique aristotélicienne et théorie des catastrophes, 1989).

Archetypal morphologies
from Rene Thom (Structural Stability and Morphogenesis: an outline of a general theory of models, 1972, p. 307)

Archetypal morophologies archetypal morphologies

As noted by Thom with respect to his approach:

It may seem difficult to accept the idea that a sequence of stable transformations of our space-time could be directed or programmed by an organizing center consisting of an algebraic structure outside space-time itself. The important point, as always, is to regard it as a language designed to aid the intuition of the global coordination of all the partial systems controlling these transformations. (1972, p. 119)

One of the basic postulates of my model is that there are coherent systems of catastrophe (chreods) organized in archetypes and that these structures exist as algebraic entities independent of any substrate, but it must not be forgotten that the substrate does have a part fundamental in the dynamic of these forms. (p. 316)

From where, then, does our feeling of beauty come? From the idea that the work of art is not arbitrary, and from the fact that, although unpredictable, it appears to us to have been directed by some organizing center of large codimension, far from the normal structures of ordinary thought, but still in resonance with the main emotional or genetic structures underlying our conscious thought. (p. 316)

So what I am offering here is not a scientific theory, but rather a method: the first step in the construction of a model is to describe the dynamical models compatible with an empiricially given morphology, and this is also the first step in understanding the phenomena under consideration. It is from this point of view that these methods, too indeterminate in themselves, lead not to a once-and-for-all explicit standard technique, but rather to an art of models. (p. 323)

Many of my assertions depend on pure speculation and may be treated as day-dreams, and I accept this qualification -- is not a day-dream the virtual catastrophe in which knowledge is initiated? At a time when so many scholars in the world are calculating, is it not desirable that some, who can, dream? (p. 325)

The implications of Thom's work, notably in relation to psychological types, are discussed separately Potential emergence of coherent transformational connectivity (in the context of In Quest of a Dynamic Pattern of Transformations: sensing the strange attractor of an emerging Rosetta Stone, 2012). Thom is of course renowned for his work on catastrophe theory, to which the above morphologies are naturally related. This suggests that the creative process is a succession of elementary catastrophes -- phases which can be characterized and denoted by the zodiac signs. Cognitively these catastrophes are potentially related to questions, as discussed separately (Conformality of 7 WH-questions to 7 Elementary Catastrophes: an exploration of potential psychosocial implications, 2006).

Rather than seeking inspiration from the helicopter, whose operation few understand, the 3-fold and 4-fold circular patterns above could be compared to the front derailleur and rear derailleur on a multi-gear bicyle. One derailleur offers 4 possible gears -- to be compared with the 4 catastrophes with 1 active variable (fold catastrophe, cusp catastrophe, swallowtail catastrophe, butterfly catastrophe). The other derailleur offers 3 possible gears -- to be compared with the 3 catastrophes with 2 active variables (hyperbolic umbilic catastrophe, elliptic umbilic catastrophe, parabolic umbilic catastrophe). Together, any one of the 4 with any one of the 3, this offers 12 possibile "cognitive gears" -- 12 operational modalities between which to choose according to circumstances.

Thom's highly innovative transdisciplinary work is now largely deprecated, strangely echoing repudiation of Isaac Newton's preoccupation with alchemy. There is some irony to Thom's use of chreod, given a related notion (creode), and the challenge of comprehension of the geometrical consideration he proposes, as with that of fundamental symmetry more generally (Dynamics of Symmetry Group Theorizing: comprehension of psycho-social implication, 2008). Provocatively, creode could be explored as indicative of a "way" of creative comprehension -- combining credo. creativity, and credibility -- namely "something to believe in". This suggests an exploration of an interweaving of mathematics and theology (Mathematical Theology -- Future Science of Confidence in Belief Self-reflexive: global reframing to enable faith-based governance, 2011).

Given the unresolved dynamics between various cognitive "ways", there is indeed a case for more radical reflection, as implied by Stephen Prothero (God Is Not One: the eight rival religions that run the world -- and why their differences matter, 2011). Prothero's pattern could be fruitfully challenged as corresponding to different styles of "catastrophe" (with one "too many"), or as a subset of 12 "religions" (with four "unrecognized"). Widely recognized as "gods ruling the world", the missing four" might include: "money", "combat" (sport, military), "distraction" (alcohol, drugs, etc), and "sex". Classical Greece and Rome may have been more perceptive in recognizing 12 "gods"-- the Dodekatheon and the Dii Consentes respectively.

Enabling a sense of the dynamics of the creative process: There is huge irony to the use of the circular schematic above to configure the phases of the creative process. This derives variously from:

  • the conventional deprecation of the significance traditionally attached to the zodiac -- especially through its continuing value in horoscopes, deprecated to an even higher degree
  • the fact that as a configuration (valued for its popular use in horoscopes), the zodiac configuration is more familiar to a wider proportion of the world's population than the reports and proposals on the global crisis, of such as the Club of Rome or The Royal Society, can ever hope to be
  • the apparently "static" nature of the presentation above -- despite the earlier arguments -- and the manner in which it is designed to encode processes which can only, at best, be inferred through that form

As with maps of metabolic pathways and systems diagrams, including those of the world models promoted by the Club of Rome, the cognitive challenge is how to give a sense of those dynamics in a manner which enables cognitive entrainment -- as is so readily evident in the case of music. With respect to creatively eliciting a universe of meaning, and sustaining it, the cyclic processes of the imagination can be fruitfully framed as the "circulation of light" -- given the metaphorical significance attributed to light (Circulation of the Light: essential metaphor of global sustainability? 2010).

Following the transformation of alchemical operations, via chemistry, into chemical engineering, a case can be made for imagining the sequence of creative processes in terms of the systemic process thinking essential to the productivity of chemical plants. Such systemic thinking remains to be engendered with respect to the creative process itself -- as with the cognitive implication of the dependence of a global civilization on "oil". To be emphasized, however, is the sense in which creativity is an imaginative process beyond the bounds of science -- and essentially disruptive of the tangible states and processes which it defines.

Animation suggestive of the experiential system of interwoven creative processes
-- creativity embodied in alchemical processes encoded by the forms of zodiacal signs
Zodiac of alchemical processes with Geometry of Meaning

The animation is a reminder of the manner in which a helicopter pilot is obliged to embody instinctively and intuitively the various skills and insights required to control the vehicle (as was the inspiration of Arthur Young). The implication is that a similar pattern of skills, but of a subtler cognitive order, is required for other form of (self)governance, whether of the individual or of a collectivity. Is governance too readily assumed to be less challenging than flying a helicopter -- perhaps too readily compared with riding a bicycle, driving an automobile, or ;piloting "the ship of state"?

In a civilization inundated with ever more attractive multimedia presentations, an animation is also a reminder of the need to embody the insights of any global strategic proposal into cognitive "attractors" -- as a civilizational Magnum Opus -- if they are creatively and imaginatively to elicit meaning. The further implication is that they may well need to take the form of "strange attractors" in order to be of requisite complexity to enable meaningful engagement with psychosocial reality. Related issues have been discussed separately (Psychosocial Implication in Gamma Animation: epimemetics for a Brave New World, 2013).

The personal implications of creativity in eliciting meaning have been explored separately -- in the light of the elegance essential to comprehension of the subtler forms of coherence of complexity commensurate with that of the universe (Being a Poem in the Making: engendering a multiverse through musing, 2012; Enactivating Multiversal Community: hearing a pattern of voices in the global wilderness, 2012).

The explorations of "the universe" by astrophysics suggest ways of thinking about the interpenetration of "multiple universes" essentially insensible to each other's existence. Currently such brane cosmology frames "the universe" as being restricted to a brane inside a higher-dimensional space. The question for the individual is how to benefit from such insights and what they may imply for any communication between the "universes" variously cultivated and inhabited by individuals and groups, as discussed separately (Global Brane Comprehension Enabling a Higher Dimensional Big Tent? 2011). One curious implication is the possibility of a more fruitful approach to the imperceptible nature of "what matters" in another universe, as speculatively explored (Import of Nothingness and Emptiness through Happening and Mattering, 2008).

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