-- / --
Curiously, and for seemingly unknown reasons, great importance is associated with organization in terms of 12-fold patterns in many sectors of society and in many cultures of the world (Checklist of 12-fold Principles, Plans, Symbols and Concepts: web resources, 2011). Obvious archetypal examples of continung significance include: 12 Olympian deities (Greece); 12 Dii Consentes (Rome); 12 Apostles; 12 Knights of the Round Table; 12 Tribes of Israel; 12 Imams. ***
Modern examples include the 12-Point Plan to Combat Terrorism, the 12-Point EU Action Plan to support the Millennium Development Goals, the 12-starred Flag of Europe, ***. Typically little distinction is made between the elements configured in this way -- the totality being somehow recognized as a symbol of completeness and perfection, requsite comlexity in the case of 12-member juries. Critically, at a time of great crisis for the "European project", there is no sense of what any distinctions might imply for the integrity of Europe. In this case, there is even concern that the nature of the strategic "pillars" of Europe offers relatively little guidance -- although these have always numbered less than 12.
When qualitative distinctions are implied, as in the case of the archetypal figures above, very little indication is provided as to the relationship between them. This could be considered extremely negligent when the 12-fold pattern is of a strategic nature -- then implying a lack of systemic insight into the relationships between the 12 elements of any plan and the institutions mandated to implement each of them. This neglect is currently as evident in the set of 17 Sustainable Development Goals (SDGs) of the United Nations as it was in the set of 8 Millennium Devlopmebt Goals which it superceded.
One obvious possibility is to map the names or symbols of the 12-fold set onto one of the polyhedra familiar to the Pythagoreans, namely onto the 12-sides of a dodecahedron or the 12-vertices of an icosahedron. This may well have been done in Ancient Greece, or in the Roman Empire which adopted that pattern. However any such mapping does little to distinguish the nature of the relationships between the psychosocial functions configured in this way -- irrespective of any temples erected in the past for the worship of individual deities, or the buildings now erected for the relevant agencies.
The challenge of such a "Rosetta stone" can be usefully presented as a puzzle, as illustrated by the Dogic. This is an icosahedron-shaped puzzle like the Rubik's Cube. It has a total of 80 movable pieces to rearrange, compared to the 20 pieces in the Rubik's Cube (The Ultimate 3D Puzzle: the rare, 20-sided dogic Mental Floss, 26 August 2015). Equivalents exist in dodecahedral form (Coolzon Megaminx Dodecahedron, MaoMaoyu Megaminx Cube, and Speed Cube Megaminx). The possibility of using such devices with respect to the UN's Rosetta Stone of global goals was explored separately (Interplay of Sustainable Development Goals through Rubik Cube Variations: engaging otherwise with what people find meaningful, 2017).
Such a puzzle could be understood as indicative of a fundmental insight. Any Rosetta stone of "meaning" may not be as static as is implied by use of the term "stone" -- as with the Philosopher's Stone . It may need to be dynamic in ways which are consistent with psychosocial dynamics, and especially with cognitive dynamics. Any sense of "mapping" meaning statically onto surface geometry is then challenged by the need to associate meaning with the dynamics between those surfaces understood in topological terms.
This reframing may be especially relevant to the indication of cycles and vital feedback loops between the psychosocial functions identified by the 12 elements distinguished in the pattern. Such static patterns are then to be considered as potentially indicative of an intuition recognition of dynamics whose integrative nature currently remains elusive -- hence the mysterous attraction of the 12-fold pattern.
The following approach is a further reflection on issues previously explored with respect to time (Cognitive Implication of Globality via Temporal Inversion, 2018). It is a further development of an approach previously explored (Representation of Creative Processes through Dynamics in Three Dimensions, 2014).
There is a case for repeatedly challenging any elaboration of a Rosetta stone (or a Philosopher's stone) -- or a Theory of Everything -- on the basis of criteria which can already be recognized, and in the light of criteria which may be of relevance.
Pattern that connects: This meta-pattern was described by Gregory Bateson in the following terms:
The pattern which connects is a meta-pattern. It is a pattern of patterns. It is that meta-pattern which defines the vast generalization that, indeed, it is patterns which connect. (Mind and Nature: a necessary unity, 1979)
As noted previously, there is the a case for recognizing the necessarily elusive nature of that pattern (Elusive nature of the pattern that connects, 2013). This highlighted the following:
Meta-model criteria: The following factors were discussed in a much earlier exercise (Criteria for an Adequate Meta-model: preliminary list, 1971):
Ordering of a dimension
Dynamic and evolutionary
Inconvenience: The possibility of an integrative pattern might usefully be explored in terms of its disruptive potential as an "inconvenient truth", as discussed separately (An Inconvenient Truth -- about any inconvenient truth, 2008) in terms of:
"Dimensions" and factors of a meta-model? How indeed are relevant dimensions to be distinguished and what is the nature of the set as a whole? Reframed, do they bear comparison with sets of "cognitive sins" and "cognitive virtues" -- even of "human rghts"? The following merit consideration as factors potentially calling for recognition, however they might be clustered or further articulated:
However the "dimensions" may be articulated, a relevantt question is how these are reflected in the articulation of the Rosetta stone itself -- rather than constituing external meta-comments from a meta-perspective of unknwon origin.
The implications of geometry for thinking were the primary focus of R. Buckminster Fuller (Synergetics: Explorations in the Geometry of Thinking, 1975 and 1979), as discussed separately (Geometry of Thinking for Sustainable Global Governance: cognitive implication of synergetics, 2009).
The following exploration is inspired by the approach of Arthur Young (The Geometry of Meaning, 1976). His 12-phase learning / action cycles. can be variously adapted (Typology of 12 complementary strategies essential to sustainable development, Typology of 12 complementary dialogue modes essential to sustainable dialogue). The particular merit of the approach is the explicit distinction between the 12 elements of the pattern offering insights into their cyclic relationship in practice
Young presents the results of his exercise in tabular and circular form as a 12-fold "Rosetta stone of meaning" -- on the basis of insights from physics and the challenge of driving a vehicle. The concern here is to consider the possibility of gaining greater insight into that pattern through the guidance it offers to configuration in three dimensions. In this adaptation, the focus is on distinguishing 12 distinct "mixes" of past, present and future as they are experienced (Varieties of experience of past-present-future complexes, 2001). Each mix offers a different quality of experience.
|Tabular adaptation of the Rosetta Stone of meaning of Arthur Young|
Observation; act of considering; position determination; reactive learning based on immediate registration of phenomena; assessment of distance; "sizing up"
"Matters of moment"
Recognition of moment(-ousness), relevance (as related to leverage), significance ; weight of facts; bringing matters into focus
Faith in paradigm of the moment; unexamined or habitual commitment to a process projection or understanding, irrespective of inconsistent disturbing factors. Moment of inertia.
|Conscious adaptive response Awareness Calendar time Linear time Arrow-of-time||T-1||L /T
Adaptive change; reaction; passive adaptation or change of position in response to changing circumstances
Recognition of the momentum (of an issue) resulting from a change, namely the consequential transformation of awareness or perspective
to act or initiate a process determining the future. "Angular momentum"
|Comparison with norms
or memory of previous experience
"Change of pace"
Spontaneous initiation of transformative action; commitment to a new course of action
Engendered, experienced or embodied as a result of transformative action; constructive (or disruptive) action potential; enhanced sense of being
"Work / Energy"
Achievement of a desired result by application of understanding (and adjustment of implicit beliefs) in response to external factors; working action on reality. "Torque"
with previous comparisons Patterns
Awareness of self-awareness
Cyclic time / Feedback
Control of transformative action. Cybernetics / Systems
Establishment of disciplined pattern of response; consolidated or harmonious control of action potential; holding forces in check
of acquired knowledge; know-how; integrated or embodied experience; capacity (including that of not acting); non-action
The table above, especially in Young's original format, is a reflection of conventional thinking in Newtonian terms. Higher derivatives (as suggested by the following extension) are necessarily a challenge to what can be unambiguously named, explained and experienced. With respect to the rate of change of acceleration, Young notes:
But what name and what meaning can we give to this? The name given by aeronautical engineers is jerk, probably because when acceleration is changed by automatic control, it does so in an all-or-nothing fashion which results in a jerk. But in the general case, as in human control, it need not be a jerk... a change in acceleration is what we mean by control... (pp. 15-16) [emphasis added]
Even with respect to ML/T3 in the last row above, Young notes that: Until recently there has been no conventional word for the third derivative of momentun, It is now recognized, however, and used in aeronautical engineering, where it is called power control. I would prefer to call it mass control (material extent of control) (p. 33). This confusion is evident in the discussion below with respect jolt, jerk, jounce and snap. Thus some authors treat jolt, jerk and jounce as synonymous, and corresponding to L/T3. Jounce may more commonly be understood as the rate of change of jerk (L/T4). Crackle is assertively recognized as the fifth derivative (L/T5), with pop a the sixth derivative (L/T6).
The lack of clarity is especially relevant to the confiusion in any psychosocial systemic analogue. Young's insight that, under human control, a jerk need not be a jerk, is fundamental to the argument which follows -- as with the implications in jargon usage of the term.
|Jargon terms for derivatives of tme|
The degree of confusion is compounded by how these distinctions may be experienced in relation to subtler interpretation of M and L, and with respect to whatever the "higher derivatives of time" are related, especially when termed "negative powers of time". The table as extended above therefore corresponds to a higher degree of subjectivity, with whatever degree of objectivity its elements may be recognized. Of particular relevance is the greater ease with which disruptive forms may be experienced, rather than the "higher" forms of control which constrain their manifestation -- as recognized by Young with respect to jerk..
In that spirit, the framework adopted by Arthur Young is especially relevant through his preoccupation with cycles of learning -- and the cyclic framework he develops. His inspiration derived from the innovative insight he acquired in developing the original Bell helicopter with its unusual piloting challenges -- subsequently generalized by him in philosophical terms to include the speculative possibility of designing a "psychopter" (The Bell Notes: a journey from physics to metaphysics, 1979). For Young, the fourth derivative is unnecessary -- an understanding which may however have undermined his exploration of the operation of a psychopter in relation to gravity, otherwise understood. He argues with respect to control as the third derivative:
What causes us to turn the automobile, or to start it in the first place, or finally to sop it? The answer is "the destination". The destination is a place, or position. Thus the fifth step, the fourth derivative of position, that which determines control, is the same as the first step. This position is not the same position we started with but has the same category of measure (distance or length... (p.17).
This sense that there may be learning processes which could offer a new kind of overview (or integrative perspective) justifies a degree of speculation in that regard (Engendering a Psychopter through Biomimicry and Technomimicry: insights from the process of helicopter development, 2011; Intuited complementarity: environmental cycles and learning cycles? 2018).
Dimensional compactification: There is a degree of metaphorical irony to any progression down the rows of Young's table to the extent that this is paralleled by a form of compactification of dimensionality when represented (as argued with respect to string theory in fundamental physics). The uppermost row (in "substantive" text form) is typically verbose in encompassing one or more themes (as with this text). The second is more experiential and with greater dimensionality, as with "one image is worth a thousand words" -- or "skimming a text to gain an impression". In characterizing the third row in terms of an idea or conceptualization. however multifaceted, this tends to be even more compact, however held or grasped. The excitement characteristic of the fourth row is even more experientially succinct -- whatever the potential it embodies.
There is a further irony to the progression in relation to what might be termed the "trilemma of compactification":
With respect to compactification, Young's tabular presentation highlights a progression in temporal reciprocation (or inversion) which features in an appropriately titled subsequent study (Nested Time, 2004). Thus the first row, as production capacity, is effectively timeless as a product of 1/T0, the second identifies change over time as a product of 1/T1 (or T-1), the third identifies rate of change as a product of 1/T2 (or T-2), whilst the fourth is a measure of control as a product of 1/T3 (or T--3).
The 12 conditions which Young associated with the zodiac can be usefully mapped into an icosahedron (given its 12 vertices) as shown below -- as one significant approximation to a sphere. This could then be considered both as a 3D presentation of the zodiac and as an indication of the distinct control functions envisaged by Young with respect to any "psychopter". Given his helicopter inspiration, the animations are reminiscent of requirements of aircraft control in 3D (yaw, pitch, and roll). As in the above animation, a distinction is made below between 4 sets of contrasting threefold quality ("triplicities") and 3 sets of contrasting fourfold modality ("quadruplicities"). In the right hand animation, the rectangles have long been recognized as having the proportion of golden rectangles.
|Animations of mappings of selected sets into an icosahedron
(generated from the Stella Polyhedron Navigator software by its developer Robert Webb,
from a great icosahedron augmented by an icosahedron, then hiding selected faces)
|Triplicities||Modalities / Quadruplicities|
The "negative" signs are clustered by two of the traditional triplicities (termed earth and water); the "positive" by the two other triplicities ("fire" and "air"). The two types are combined in the following animation (again the work of Robert Webb) -- but with addition of a circumsphere and attribution of labels to the 12 vertices (not to be attributed to Robert Webb).
Each triplicity or quadruplicity is a distinct configuration of "positive" and "negative" -- as otherwise represented in the preceding 2D circular animation. As argued here, these are indicative more generally of contrasting values -- dualities, polarities, binaries. The vertices are then distinguished in terms of a 4-fold pattern (of 3 quadruplicies), a 3-fold pattern (of 4 triplicities), a 2-fold pattern (of positive and negative). For mnemonic purposes the singular quality of each vertex is also labelled with the zodiac sign -- given widespread familiarity with each.
|Experimental animation of 3D zodiac of triplicities (E, A, F, W) + quadruplicities (C, F, M)
(with indication of positive and negative)
The following images are screen shots from the above animation. They distinguish the four individual triplicities and the 3 individual quadruplicities/modalities as they were combined in the earlier animations. A yellow circle has been added linking the points of the triangle or rectangle -- suggestive of a feedback loop relating the conditions indicated by the vertices. The directions of the associated arrows suggest 2-way feedback. Note that the triangle or rectangle of each figure would appear differently in relation to the other forms if viewed from its other side. The characteristics by which the vertices are labelled include those associated with the work of Arthur Young, as indicated with the earlier circular animation above.
|Quadruplicities/Modalities commonly denoted as Cardinal, Fixed and Mutable
(screen shots of respective rectangles from rotations of the above animation)
|Cardinal (Young's four acts)||Fixed (Young's four states )|
|Mutable (Young's four relationships)|
|Triplicities commonly denoted as Earth, Air, Fire and Water
(screen shots of respective triangles from rotations of the above animation)
Although not explicitly associated with the 12 positions of the zodiac, it is appropriate to consider how the 6 polarities could be understood in terms of the arguments of Edward de Bono (Six Frames For Thinking About Information, 2008).
Young from driving to cognitive
standing wave and sustainability
triplicity -- M L T -- three extreme contrasts -- cannot be more different
generalization -- generic
enstoning / philosophers stone
Arthur M. Young:
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