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16 May 2019 | Draft

Patterning Intuition with the Fifth Discipline

Critical review of the conclusion of the 5-fold Patterning Instinct

-- / --


Introduction
Patterns, their visualization and their comprehension
Possible cognitive implications of 5-foldness
Tracing complex feedback loops
Requisite fifth-order thinking?
Trajectories to our future -- and their recursive implication?
Clues to systemic implications of 5-fold cognitive organization?
Cognitive glass ceilings impeding integrative comprehension
Beyond the 4-fold cognitive modality: integrating the 5-fold, 6-fold and 7-fold?
Eliciting systemic answers from a 5-fold web of meaning?
Pattern spiralling challenge of biomimetics
Polyhedral possibilities of interrelating patterns comprehensibly: a "cognitive gearbox"?
Speculation regarding a requisite "sixth discipline" and more
References

Review of the concluding section of The Patterning Instinct: a cultural history of man's search for meaning (2017) by Jeremy Lent


Introduction

This book has been widely praised, as indicated by reviews such as the following (emphasis added):

The foreword concludes:

Cognition is embedded in matter at all levels of life... cognition is not a representation of an independently existing world but rather a "bringing forth" or "enacting" of a world through the process of living. Jeremy Lent applies this insight to history, recognizing the power of the human mind to construct its own reality and arguing that "the cognitive frames through which different cultures perceive reality have had a profound effect on their historical direction"... From this perspective, Lent proposes new answers to some age-old questions of human history... In our time of global crisis, which desperately needs guidance through new and life-affirming metaphors, the answers to these questions are more important than ever (Fritjof Capra, author of The Systems View of Life)

The focus in the following review is on the potential implications for the future, as implied by the highlighted indications above. Given the framing offered by Fritjof Capra in the foreword, it is appropriate to note that his own recent study was subject to a separate critical review (Transcending an Asystemic View of Life, 2014). Many of the arguments made there are of some relevance to those made here with respect to The Patterning Instinct.

The book is organized into five parts, and it is in the final part that the highlighted implications should become most apparent. The parts are understood as a "cognitive history" -- a sequence corresponding to "the core pattern of meaning by which people made sense of their world":

  • Part 1: Everything is Connected
  • Part 2: Hierarchy of the Gods
  • Part 3: The Patterns Diverge
  • Part 4: Conquest of Nature
  • Part 5: The Web of Meaning?

In considering Trajectories to Out Future (the chapter title of Part 5), it is appropriate to note that it mainly echoes speculation on strategic scenarios in other studies, notably by futurists. The valuable insights into patterns elicited in the other parts do not seem to carry over into any form of cognitive empowerment with regard to immediate challenges, or those to come.

In this sense, somewhat ironically, the book is best appreciated and deprecated for its enthusiasm -- given the shifting ambiguity with which that has been understood over the centuries and to this day (Susie Tucker, Enthusiasm: A Study in Semantic Change, 1972). More cautious in this respect is Brendan Montague (Beating the system - metaphorically, The Ecologist, 3 July 2018). It can be appreciated as a decorous progress through humanity's past, reminiscent of a pavane -- a stately dance in musical terms.

The concern with regard to Part 5, in a book which offers a remarkable historical survey of patterning, is what it enables with respect to the future at this time. Is consideration of the future thereby transformed into a "historical afterthought"? What is to be gleaned from cognitive history? What are the "take-away" insights for action now?

This critique raises the question as to whether patterning is instinctive (as implied by the title of the book) or whether it is better understood as intuitive (the implication of its organization into five parts). To the extent that humanity is held to be unconscious, patterning is necessarily instinctive (John Ralston Saul, The Unconscious Civilization, 1995). However, to the extent that a collectively self-conscious humanity is required to make conscious choices with respect to its future, survival may well depend upon intuitive patterning (Post-Apocalyptic Renaissance of Global Civilization: engaging with otherness otherwise? 2018).

Patterns, their visualization and their comprehension

Feedback loops: In the concluding paragraphs to the Preface of the book, Jeremy Lent notes:

Given that human societies are themselves complex systems, can we use this framework to understand the great critical transitions in our history? I believe we can, with the caveat that when we apply this framework to human society, there is yet another crucial feedback loop to consider. Because of our unique cognitive capacity, human social systems need to be understood as a pair of two tightly interconnected, coexisting complex systems: a tangible system and a cognitive system. The tangible system refers to everything that can be seen and touched.... The cognitive system refers to what can't be touched but exists in the cognitive network of the society's culture: its language, myths, core metaphors, know-how, hierarchy of values, and worldview. These coupled systems interact dynamically, creating their own feedback loops, which can profoundly affect each other and, consequently, the direction of society....Much of the book is devoted to tracing these complex feedback loops. (pp 24-25; referencing an extensive note, p. 459; emphasis added)

The emphasis on feedback loops in the book is consistent with a particular bias of this reviewer as instigator of the online Encyclopedia of World Problems and Human Potential. That is especially focused on the feedback loops between thousands of problems, and between any corresponding strategies -- in the light of human values (Feedback Loop Analysis in the Encyclopedia Project, 2000). Considerable effort has been devoted to their visualization. It is therefore extremely surprising to note the absence in the book of any effort at depiction of the feedback loops that the book claims to trace. Most illustrations are of historical artefacts with the strange exception of the I Ching pattern of hexagrams -- ironically a notably focus in that Encyclopedia and in further commentary on it.

Pattern recognition: This frames a fundamental question as to the nature of patterns, how they are to be recognized, and how people might be expected to engage with them. There is a very strong argument that such processes are dependent to a considerable degree on representations in visual and other forms -- however these may be susceptible to textual commentary (Metaphor and the Language of Futures, 1992).

In these strange times it is appropriate to note both the tremendous importance of music of every kind to many and the value of sonification for pattern recognition in some sciences. As author of a study on Tomorrow, Who Will Govern the World? (2011), of some relevance in the latter respect is the insight of Jacques Attali that cultures articulate their social organization through the musical structure favoured in their immediate past (Noise: the political economy of music, 1977). Thus he specifically relates the currently dominant pattern of organization to that of classical Western music. Any argument, with respect to "tomorrow", should then take account of the pattern of music currently favoured by the voters of today. The patterns of music can then be understood as "heralding" the future, suggesting the possibility of sonification of the succession of patterns in The Patterning Instinct (Structuring Mnemonic Encoding of Development Plans and Ethical Charters using Musical Leitmotivs, 2001)

Pattern language: In the case of the Encyclopedia, consideration was given to experimentation with various patterns, notably including the I Ching and those in the classic text by Christopher Alexander (A Pattern Language, 1977), and its possible (5-fold) elaboration (Pattern Language Experiments: Metaphor Project; 5-fold Pattern Language, 1984). Alexander's work has inspired much further consideration of the nature of pattern language. Despite its title, The Patterning Instinct includes no reference to the challenge of pattern recognition in general nor to the specific challenge of recognition of the "patterns of meaning" which are a key focus of the book. For a book whose concluding part is entitled The Web of Meaning?, its preoccupation with the connectivity of insights is implied rather than explicit.

For Alexander, a pattern has been intimately related to "a quality without a name", namely a place it was "good to be". Although his focus was on the external environment, the 5-fold experimental elaboration evokes the possibility that this might have a cognitive analogue of which the physical is a valuable metaphor. The visualization of such patterns was considered in a commentary on Alexander's subsequent reflection on his work on the nature of order (Harmony-Comprehension and Wholeness-Engendering: eliciting psychosocial transformational principles from design, 2010). The framework of the elaborated 5-fold pattern language was presented there as follows (below left) together with many examples of the dynamics of pattern transformation (exemplified by that below right):

Indicative configuration of a 5-fold pattern language
(with those of the psychosocial realm above the dotted line)
Example of a simple icosahedral transformation
Icosahedron morphing into Dodecahedron
(made with Stella Polyhedron Navigator)
Indicative configuration of a 5-fold pattern language Morphing icosahedron

From this perspective it is intriguing to note that The Patterning Instinct lacks explicit concern with how patterns are comprehended, whether by an individual or a culture -- surely to be recognized as a fundamental issue for the "cognitive history" it claims to be. This concern may be implied by the arguments made (and the praise for its "readability"), but "comprehension" is not considered worthy of an index reference. This criticism is especially relevant to the implications of that study for the future, namely the focus of Part 5. How indeed are individuals or cultures to learn from the patterns of a "cognitive history" and apply them to any framing of relevance to the future and the possibility of engaging with it? Also problematic is the absence any reference to "learning" in the index.

Omissions: Curiously the book includes no reference to the work of Christopher Alexander nor to the now well-explored theme of "pattern language" as enabling appropriate design. Commenting on the book, other authors have however mentioned that relationship (Helene Finidori, Configuring patterns and pattern languages for systemic design, PUARL Conference, 27 October 2018; The Future of Patterns, PUARL Conference, 27 October 2018). However those indications focused to a far greater degree on Alexander's work than on Lent's contribution. There are however multiple references to "patterns of meaning" in the book, indicated as associated with "root metaphors", but not to the seminal work of Donald Schön on generative metaphor (Generative metaphor and policy-making, 1979). The Patterning Instinct seemingly avoids the challenge of how the patterns recognized enable any design of humanity's future.

In skillfully framing a focus on cognitive history, why ignore the work on "big history" and macrohistory, given that The Patterning Instinct is an exercise in both, and that Lent has become a macrohistorian (Johan Galtung and Sohail Inayatullah, Macrohistory and Macrohistorians: perspectives on individual, social and civilizational change, 1997)?

The indexing of the book is strangely inadequate with respect to terms on which emphasis is placed or implied in the introduction, most notably "feedback loops" and everything with which they might be considered to be connected in systemic terms, such as "pattern recognition", "cybernetics", "self-reference", and "learning". By contrast the book has 84 pages of detailed bibliographical footnotes notes (ordered by chapter but not otherwise), whose authors (and themes) do not appear in the index. The book is therefore best studied in its electronic version in order to benefit from the search facilities to track what are to be understood as feedback loops.

Possible cognitive implications of 5-foldness

Patterns of N-foldness: In the Introduction, framed as Shaping Our History, the explanation by Jeremy Lent as to why the book is organized into five parts is given as follows -- without further justification:

The path from the earliest search for human meaning to our current precarious situation is what we'll be tracing in this book... The path can be segmented into different periods, each characterized by the core pattern of meaning by which people made sense of their world. These periods, with their patterns of meaning, give the book its structure. (p. 32)

Why was a 5-fold articulation considered appropriate to the organization of the book -- to the "shaping" of the cognitive history of humanity? Given the cognitive hypothesis, Lent was clearly free to organize the flow of history as he saw fit. More intriguing is why 5-foldness "worked" for the author, rather than 6-foldness, or 12-foldness. One strange possibility, in the absence of any other explanation, is that Lent was overly influenced by the so-called Rule of Five which prevails to a curious degree in academic writing in the country of his adoption, as described by David Labaree (The Five-Paragraph Fetish, Aeon, 15 February 2018), noting:

The transition from the college research paper to the doctoral dissertation is not as big a jump as you might think. The Rule of Five lives on in the canonical structure for the dissertation.... Guides on dissertation-writing specify the content of each of the five chapters in detail, with this detail looking remarkably similar across guides.

In the light of any concern with the self-referential aspects of feedback loops, how does Lent see himself as positioned within the cognitive history he analyzes? Does the influence of "scholastic bias" merit consideration, as discussed separately?

This poorly researched question has been explored more generally (Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation, 1980; Comprehension of Numbers Challenging Global Civilization: number games people play for survival, 2014). The mysteriously unquestioned process by which a pattern of a certain complexity is chosen is discussed with respect to 12-foldness and 20-foldness in the following, with many examples:

Is the choice of a particular pattern of N-foldness primarily intuitive rather than instinctive? This would suggest the need for exploration of "patterning intuition" (hence the title of this review).

Examples of 5-fold patterns: There are of course many concept schemes organized according to a 5-fold pattern, raising the question of their cognitive implications and how these might have influenced the organization of the book -- if only unconsciously. Examples include:

Rather than consider the 5-fold organization of The Patterning Instinct as an arbitrary convenience, these suggest that it may have fundamental implications of significance to its theme. This is considered further below. The choice of any given number of patterns, for purposes of organization of the cognitive history of humanity, may be less than innocent.

Collective learning and a "5th discipline": Global civilization as a whole has long been framed as a learning society, most notably in UNESCO programs where this is articulated in an extensive set of reports (Lifelong Learning in a Learning Society). How might the cognitive systemic pattern of 5-foldness relate to that dynamic, as suggested to some degree by the argument of Peter Senge (The Fifth Discipline: The Art and Practice of the Learning Organization, 1990)? That book was identified by the Harvard Business Review as one of the seminal management books of the previous 75 years.

The five parts of the book might be tentatively related to Senge's five disciplines (collectively understood), as suggested by the following table.

5 core patterns of meaning (Lent) 5 disciplines of a learning organization (Senge)
Part 1: Everything is Connected

"Personal mastery is a discipline of continually clarifying and deepening our personal vision, of focusing our energies, of developing patience, and of seeing reality objectively."

Part 2: Hierarchy of the Gods "Mental models are deeply ingrained assumptions, generalizations, or even pictures of images that influence how we understand the world and how we take action."
Part 3: The Patterns Diverge "Building shared vision - a practice of unearthing shared pictures of the future that foster genuine commitment and enrollment rather than compliance."
Part 4: Conquest of Nature "Team learning starts with 'dialogue', the capacity of members of a team to suspend assumptions and enter into genuine 'thinking together'."
Part 5: The Web of Meaning? "Systems thinking - The Fifth Discipline that integrates the other four."

Tracing complex feedback loops

In addition to its emphasis on tracing feedback loops, the book emphasizes the insights to be derived from "complex systems" and "self-organization" (both indexed).

With respect to the N-foldness through which cognitive history might be understood, of particular relevance is the articulation of complex systems in the light of higher orders of cybernetics -- and issues relating to self-reflexivity. A separate discussion of the cybernetics of cybernetics: complex adaptive systems? (In: Consciously Self-reflexive Global Initiatives: Renaissance zones, complex adaptive systems, and third order organizations, 2007, developing that in Interrelating Metaphors -- to enable a cycle of transformation between epistemological modes, 2007) highlighted the following distinctions currently made:

This is a more intrinsic (embodied) methodology and shows the ongoing convergence of all the various systemic disciplines, as part of the general world paradigm shift noticed recently towards more integrated approaches to science and life. In 21st Century systematics, boundaries between systems are only partial and this implies that we must evolve with our systems and cannot remain static outsiders. Thus our mental beliefs echo our systemic behaviours, we co-create our realities and therefore internal and external realities become one. Understanding this mutual control, exhibited by us on our world and our world on us, takes us into the metaview outlined here, where we can see ourselves as being part of the system under examination.

Central to this effort is the application of a unique, critical theory inspired by the works of Anthony Giddens (1971, 1990; see discussion on modernity and reflexivity) and John Francois Lyotard (1979; see discussion on postmodernity) to the cybernetic theoretical framework. The epistemological orientation of the theory proposed here is that of multiple realities shaped by social, cultural, economic, ethnic, gender and disability values, which centralize on the asymmetric power relations in society

Fourth order cybernetics is thus understood as concerned with how multiple realities are shaped by, and impinge upon, power relationships within society.

These considerations of orders of cybernetics are further clarified by Maurice Yolles and Gerhard Fink (A General Theory of Generic Modelling and Paradigm Shifts (part 2): cybernetic orders. Kybernetes, 2015). The self-referential nature of any model or meta-model can be explored otherwise through the work of Douglas Hofstadter (GÖdel, Escher, Bach: an Eternal Golden Braid, 1979; I Am a Strange Loop, 2007; Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, 2013).

A 5-fold interpretation of such distinctions is provided in the discussion of Cadell Last (Towards a Big Historical Understanding of the Symbolic-Imaginary, 2017), as noted in Phases in the "re-cognition" of "bull" according to Zen? (2017):

Some of the confusion in relation to the above distinctions is helpfully clarified by Chris Lucas (personal communication, 2007):

I'm rather amazed that third-order cybernetics seems not to have 'taken-off' as it were, few people seem to mention it now.... It is interesting to note how much this unwillingness to recognise the 'outside influence' on self is based upon current scientific dogma, this is well illustrated by a foreword from Bruce Lipton [to Louise LeBrun, Phoenix Rising! The Freeing of Human Potential].

Yet the actual idea of co-evolution between system and its environment is very much to the fore today. I think perhaps the term 'cybernetics' has itself a poor, mechanical, feel to many people, so the term used in complexity theory for perhaps the same idea is 'Complex Adaptive Systems' (CAS). This is frequently now used in organizational contexts (e.g. see my review of the book Open Boundaries: creating business innovation through complexity by Howard Sherman and Ron Schultz)

When I write on these themes nowadays I tend to use other terms, for example my 2006 essay " Complex Living Tensegrities" (2006) used "Complex Interacting Systems" (of which CAS was 1 of 4). In "Integral Intersubjectivity" (2006) I contrasted the third person (objective) view (1st order), with the first person (subjective) view (2nd order), to generate a middle way (intersubjective) which is close to 3rd order. Finally in... "Qualitative Living and Thinking" (2006) I brought in three forms of knowing, 'knowing how' (1st order), 'knowing that' (2nd order) and 'knowing from' (3rd order).

Whilst the terms aren't common perhaps the understanding is getting more so, the environmental crisis highlights the coevolution of people and planet in a way perhaps never before part of the public mind... I tend to stress recently the need to take three levels into account, these aren't the three cybernetic levels as such, but as Stan Salthe notes, our focus on one level cannot ignore the level below (N-1) which gives rise to level N, nor the level above (N+1) which constrains its behaviour. In human cultural terms the biosphere sustaining planet is N+1, the organizational greed is N and the genetically fear driven human is N-1. A potent mix !

To the extent that The Patterning Instinct traces how humanity has learned, these systemic perspectives merit consideration in terms of double-loop learning, namely the modification of goals or decision-making rules in the light of experience. What feedback loops will the future consider to have been ignored?

Requisite fifth-order thinking?

For the purpose of this review, it could be argued that a mysterious "fifth order of cybernetics" and self-reflexivity is the cognitive challenge posed by Part 5 of The Patterning Instinct.

Cognitive development: This argument can be explored in the light of the cognitive focus of The Patterning Instinct -- necessarily on cognitive development as collectively understood. How indeed might the cognitive development of humanity be related to the "patterns of meaning" recognized through the sequence of stages in the first four parts of the book? There have been numerous attempts to identify such stages in individual cognitive development. It could be argued that the book has effectively attempted to apply such thinking to humanity as a whole -- especially since some authors offer that implication.

In any quest for the nature of fifth-order thinking, there is therefore a case for examining the "patterns of meaning" held to characterize individual cognitive development. There are many cognitive development theories, developmental stage theories, and many related understandings of group development. As noted in Wikipedia, stage theories are based on the idea that elements in systems move through a pattern of distinct stages over time and that these stages can be described based on their distinguishing characteristics. Specifically, stages in individual cognitive development have a constant order of succession, later stages integrate the achievements of earlier stages, and each is characterized by a particular type of structure of mental processes which is specific to it. This understanding of stage theory would seem to describe the sequence of patterns of meaning recognized collectively in The Patterning Instinct.

The insights of Robert Kegan are especially relevant in this respect (In Over Our Heads: the mental demands of modern life, 1994), usefully summarized by Bernie Neville (Out of Our Depth and Treading Water: reflections on consciousness, culture and new learning technologies, 1998), by J. Berger, et al, (How consciousness develops adequate complexity to deal with a complex world: the subject-object theory of Robert Kegan. 2007), and by C. J. Cameron Johnson (Kegan's 5 Stages of Development, Prezi, 2014). The latter is remarkably indicative of the kind of visualization which would have rendered The Patterning Instinct more widely comprehensible.

For Neville, Kegan's approach is:

... the most coherent attempt to extend developmental theory into a consideration of adult experience. His theory is of particular interest because he is concerned not only with individual cognitive development but with the interaction between individual and culture. Kegan defines the stages of cognitive development in terms of increasingly complex subject-object differentiations.

From this perspective there are five distinct stages -- or orders of mind -- through which people may develop based on an understanding of "transformation" to qualitatively different stages of meaning making involving qualitatively different ways of constructing reality (none being inherently better than the other):

Especially valuable is the systematic summary offered in the Wikipedia entry on Kegan is the comparison with other development stage theories, identified as "analogous". Those compared are Jean Piaget, Lawrence Kohlberg, Jane Loevinger, Abraham Maslow, David McClelland, and Erik Erikson. Curiously, and seemingly without question, these also identify five such stages (possibly with an additional stage zero).

A similar phenomenon is evident in the distinctive comparison made with respect to the integral theory of Ken Wilber. The theories usefully compared are those of: Aurobindo, Jean Gebser, Jean Piaget, James Fowler. In that case the number distinguished is seemingly related to the constraint long noted by George Miller (The Magical Number Seven, Plus or Minus Two: some limits on our capacity for processing information, Psychological Review. 63, 1956, 2). This is recognized as the most cited paper in psychology.

Although excluded from the Wikipedia comparison with integral theory, the latter has been closely related to the spiral dynamics model of human development of Don Beck and Chris Cowan (Spiral Dynamics: mastering values, leadership, and change, 1996). This distinguishes a first tier of 6 memes coded by colour: Beige, Purple, Red, Blue, Orange, Green. Followed by a second spiral tier coded: Yellow and Turquoise. Again it might be asked whether such distinctions are constrained by "plus or minus seven".

Recognizing the need for transition: From a cultural perspective, of particular interest is the "cognitive failure" implied in the four earlier "patterns of meaning" of The Patterning Instinct -- a failure occasioning the transition to a subsequent pattern. That failure is the inability within any pattern to envisage or account for the desirability of such a transition.

Why the disaffection in the prelude to collapse of the older order? Why the compensating "shifting baseline syndrome", to which reference is variously made in the book (p. 414, 419-420, 431, 539) and elsewhere (Masashi Soga and Kevin J Gaston, Shifting Baseline Syndrome: causes, consequences, and implications, Frontiers in Ecology and the Environment, 16, 2018, 4)? Valuable in the latter respect are the insights of Karen Cerulo (Never Saw It Coming: cultural challenges to envisioning the worst. 2006). Much is made in the book of possible parallels to the collapse of the Roman Empire, a theme of Thomas Homer-Dixon (The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization. 2006).

From a systemic learning perspective, four insights could be considered of particular relevance to any effort to "re-member" a pattern of coherence:

Beyond the 2-dimensional: It could be argued that the predilection for linear presentations -- of which the text of The Patterning Instinct is an example -- obscures the degree to which the requisite cognitive engagement with the future requires 3-dimensional thinking -- if not 4-dimensional or 5-dimensional -- whatever these may be held to imply. The popular enthusiasm for special effects in media has yet to be informed by its cognitive implications for governance -- which is seemingly happy to ignore such implications.

Notably in the light of the spiral dynamics model, the point can be made otherwise in the light of proposals for a "quintuple helix model", beyond the current focus on a Triple Helix model of innovation (Elias G Carayannis, Thorsten D Barth and David FJ Campbell, The Quintuple Helix Innovation Model: global warming as a challenge and driver for innovation, Journal of Innovation and Entrepreneurship: a systems view across time and space, 1, 2012, 2). *** other helix ***

Of potential relevance from the perspective of so-called kinetic intelligence, is the manner in which the quintuple jump is highlighted as an elusive goal of figure skating (Will figure skating ever see a quintuple jump? NBC News, 23 February 2018; Is It Possible for Figure Skaters to Complete a Quintuple Jump? Olympic Channel)

Comprehending the challenge to comprehension: The challenge of integration beyond any binary clash is admirably clarified using the mathematics of q-analysis, as developed by Ron Atkin (Multidimensional Man; can man live in 3-dimensional space?, 1981), as separately summarized (Comprehension: Social organization determined by incommunicability of insights). Atkin illustrates the challenge of comprehension in relation to experience from "within" the geometry of a triangle -- especially with regard to the perspective necessary to comprehend the geometry of the triangle as a whole when travelling from point to point.

The perceptual significance of this approach is well-illustrated by visual sensitivity to colours resulting from the three primary hues (red, green and blue). These may be represented on a simple triangle (below left). Here the vertices (O-simplexes) represent the primary hues, the sides are twofold combinations (1-simplexes), and the combination of the three hues makes the central white (2-simplex). A suggested equivalent of Atkin's triangle in terms of a pentagram is presented here (below right), using the colours of spiral dynamics with the suggestion that it is the final colour in that pattern whose recognition is the current challenge.

Indication of comprehension of the whole from within the geometry
Triangular variant Codification of relative orders Pentagonal variant
Comprehension challenge  through a triangular model

0-dimension:
Red, Green or Blue

1-dimension:
Yellow (=Red/Green)
Purple (=Red/Blue); or
Turquoise (=Blue/Green)

2-dimension:
White (=Red/Green/Blue)

Comprehension challenge  through a pentagonal model

One merit of such arguments from geometry is the emphasis it gives to the constrained role of linear thinking in traversing the geometry of the pattern as a whole, and the difficulty of comprehending that pattern from within such "tunnel vision". Useful also is the abrupt transition from one linear orientation to another in order to "circumscribe" the whole and imply comprehension of a higher order.

Trajectories to our future -- and their recursive implication?

The focus of this review, Part 5 of the book, is entitled: The Web of Meaning?. It is composed of a single chapter entitled Trajectories to Our Future. In order to identify these trajectories, the chapter is divided into a number of sections. It is unfortunately less evident from their titles (or the content of those sections) how these are necessarily to be considered as framing "trajectories" -- and the linearity that that metaphor implies.

Scenarios: As noted earlier, approaches to futures studies have tended to identify a number of scenarios which merit reconciliation with the book's Trajectories for Our Future. Of relevance to a typically unstated constraint is the comment that:

A good set of scenarios will contain two to five different narratives. More than five scenarios tend to get confused with one another. Three scenarios run the danger that people will try to pick the most moderate or most apparently plausible and forget about the other two. Four is a good number -- neither too many nor too few. (Scenario Planning and Strategic Forecasting, Forbes, 8 January 2015)

Examples of four scenarios include:

Examples of five scenarios include

Worldviews: What is being framed in such cases, effectively as "patterns of meaning" comparable to those in The Patterning Instinct, are worldviews. As summarized by Wikipedia:

A worldview is the fundamental cognitive orientation of an individual or society encompassing the whole of the individual's or society's knowledge and point of view.... Worldview remains a confused and confusing concept... Worldviews are often taken to operate at a conscious level, directly accessible to articulation and discussion, as opposed to existing at a deeper, pre-conscious level, such as the idea of "ground" in Gestalt psychology and media analysis. However, core worldview beliefs are often deeply rooted, and so are only rarely reflected on by individuals, and are brought to the surface only in moments of crises of faith.

Of relevance to this argument are the similarly restricted number of worldviews in various comparisons:

Of current relevance to the challenges of governance, the Wikipedia entry notes a clustering of American political worldviews into five categories: Green Malthusianism, Libertarian Isolationism, Neoliberal Globalism, Populist Nationalism, Social Democracy. (Michael Lind, The five worldviews that define American politics, Salon Magazine. 12 January 2011).

Trajectories? The possibility with respect to the systemic organization of The Patterning Instinct is that the "patterns of meaning" of the first four parts function recursively in the organization of Part 5. This has the further implication that the modalities they represent are effectively coexistent as much as sequential. This could be tentatively presented as follows, raising questions about the implications of the requisite 5th-order thinking for the systemic part.

Clustering strategic trajectories
Trajectories to Our Future
(sections constituting Part 5)
Appropriately clustered?
(given a degree of conflation in the arguments)
Fractal equivalence as patterns of core meaning
(reflecting the pattern of the book)
1. Limits to Growth 1. Global collapse: Resilience in accordance with the adaptive cycle? Part 1: Everything is Connected
2. Scenarios for Our Future
3. Dinosaurs, Forest Fires, and Resilience
4. How Societies Collapse
5. Will Our Society Collapse Like Rome?
6. Technology as Savior? 2. Techo-optimism -- "fix it" instrumentalism Part 2: Hierarchy of the Gods
7. Engineering Our Planet
9. Toward the Singularity?
8. Transcending Our Humanity 3. Cognitive adaptation and bifurcation Part 3: The Patterns Diverge
10. Pure Intelligence?
11. Human Superorganism?
12. Toward a Bifurcation of Humanity?
13. What It Means to be Human
14. The Great Transformation 4. Global dominance cognitively reframed Part 4: Conquest of Nature
15. The Movement for a Shared Humanity
16. Choosing Our Future 5. Engaging creatively with "otherness" Part 5: The Web of Meaning?

How then to configure those trajectories in order to enable any choice? How to engage with that configuration as a form of psychoactive mandala?

Mapping? One approach is simply to map the five trajectories onto the lines of a pentagram in order to be able to visualize the pattern of the whole -- effectively the pattern of The Patterning Instinct as a whole. The image on the left below could then be used -- whether the variant with lines crossing, or the dashed-line version in which they do not. An alternation between the two could even offer a helpful indication of the manner in which the two perspectives are confused in reality.

Potentially more interesting is a 3D form of the image on the left -- with each line (in the image on the left) considered as "hiding" the circularity of one trajectory. That would then give rise to the 3D image on the right.

Indicative transformation of a 2D pentagram of linear trajectories to form a 3D configuration of 5 circular trajectories
2D Pentagram   2D Pentagram lines as circles in 3D
Pentagram circumscribed

Each line in the standard 2D depiction of
a pentagram on the left can be assumed to be a circle (seen edge on).

The image on the right depicts those circles as they might then be configured in 3D
(from a particular external perspective)

The circle on the left then takes the form of a sphere on the right

Trajectories around the 3D configuration are suggested by the movement of small spheres along each of the 5 circles

5-fold spherical configuration of circular trajectories
 

As a 3D form, the configuration on the right above can be rotated in virtual reality, offering the alternative perspectives below. The model could be enhanced by colouring each circle differently (and the moving spheres, in addition to changing the rates at which they move).

Alternative views of the 5-fold configuration of circular trajectories
(simple rotation of the animation above right)
5-fold spherical configuration of circular trajectories 5-fold spherical configuration of circular trajectories 5-fold spherical configuration of circular trajectories 5-fold spherical configuration of circular trajectories
  x3d    

Implication of the observer? Missing from such depiction is consideration of the place of the observer, supposedly implicated in experiencing the possibility of each trajectory (in terms of 5th-order thinking), and confronted by the challenge of choosing between them -- whether as an individual or collectively. As is only too evident at this time, the confusion of the complex of trajectories, and the uncertainty with regard to the transition to the future, are a challenge to any neat mapping -- whether in 2D or 3D. Any such "neatness" distracts from the highly problematic nature of such a challenge, especially given the conflicting investments in each of them,

Use of a virtual reality browser offers the possibility of shifting the locus of the observer to the origin of the 3D sphere -- from which the circular trajectories can be variously experienced with a degree of confusion far more appropriate to comprehending the challenge of choice in the present time.

Catastrophic harmony? Greater complexity is however implied by the further work of Christopher Alexander on The Nature of Order (Harmony-Seeking Computations: a science of non-classical dynamics based on the progressive evolution of the larger whole, International Journal for Unconventional Computing (IJUC), 5, 2009). Therein he detects 15 "transformations", as described separately (Harmony-Comprehension and Wholeness-Engendering: eliciting psychosocial transformational principles from design, 2010).

Are these transformations to be understood as subsumed in some way by the 5-fold cognitive pattern? From a mapping perspective, it is interesting to note that the spherical geometry of the model above is such that the 2 sets of 5 pentagons on the surface, one on each side of the sphere, could have their points linked across the sphere by parallel lines -- together forming 15 lines with which Alexander's transformations could potentially be associated (Comprehending Alexander's transformation principles within the psychosocial realm, 2010).

A further consideration in this regard is the manner in which that mapping facility might be of relevance to the 15 Global Challenges distinguished by the Millennium Project, as discussed separately (From poster sessions to stellar futures via aesthetic visualizations, 2015) with respect to their polyhedral mapping..

As discussed below, however, how do these relate to the seven elementary catastrophes of RenÉ Thom ( Structural Stability and Morphogenesis: an outline of a general theory of models, 1972). Is harmony to be "quintessentially" associated with 5-foldness -- and the mythical fifth element?

Clues to systemic implications of 5-fold cognitive organization?

If the prevailing cognitive modality artfully embodies a process of avoidance in failing to recognize a fifth order of thinking -- or to comprehend its self-reflexive nature -- there is a case for provocative speculation towards such thinking. This could be understood as requiring a degree of engagement with what is variously rejected as reprehensible and inappropriate. Seemingly inherently incommensurable, each rejecting the other (and considered irrelevant for one reason or another), these might be configured as a pentagon of contrasting modes of thinking:

The 5-phase Wu Xing pattern is discussed further below. Potentially the least controversial pattern is that of the Pentagramma Mirificum, whose depiction in 3D helps to indicate the challenge to comprehension, even though it is fundamental to navigation around the globe. The mathematical form was discovered by John Napier, and named by Carl Friedrich Gauss.

Screen shots of the complementary variants of Pentagramma Mirificum on opposite sides of a sphere
(one pattern with 5 white balls, the other pattern with 5 black balls; 5 circles link both patterns together)
[options for viewing interactive 3D animations: classic browser-based WRL format; or via standalone FreeWRL viewer]

White pattern in front(vertical);
black pattern (inverted)
seen through sphere
  Side view of linkage between variants
showing great circle continuity
around sphere
  Black pattern in front (inverted);
white pattern (vertical)
seen through sphere
Pentagramma Mirificum Pentagramma Mirificum Pentagramma Mirificum

Further (requisite) provocation regarding 5-fold thinking is offered by the following images, variously echoing the single pentagonal pattern discussed earlier. Each could be said to challenge the adequacy and convenience of a 2D representation.

Challenging insights into 5-foldness
Discordian mandala 5 Interleaved pentagons Vitruvian Animation -- man/woman
(multi-coloured variant)
Pentacle
Discordian mandala 5 Interleaved pentagons Vitruvian man/woman animation Pentacle
Images variously reproduced from Wikipedia, or adapted from therefore

Cognitive glass ceilings impeding integrative comprehension

The Patterning Instinct offers a cognitive history of 4 patterns of meaning -- widely appreciated as noted. However it effectively shifts phase in raising the question as to the future, framed as a 5th pattern of meaning. The argument above is that comprehension of 5th-order thinking is necessarily a particular challenge with which humanity is confronted in the present. Arguably there are particular features to this challenge which could be usefully compared to confrontation with a puzzle or a riddle (Global Governance as a Riddle: but is a solution the answer to the question? 2018).

Understood metaphorically as the Gordian Knot faced by Alexander the Great, this continues to be cited with respect to the current issues of governance (Mapping grossness: Gordian knot of governance as a Discordian mandala? 2016). Commenting on a session of the World Economic Forum, John Jullens argues that: It's as if the global economy is being strangled by a gigantic Gordian knot from which it cannot untangle itself (The Gordian Knot of Global Economic Growth, Strategy-Business, 15 October 2013). "Cutting it" may not however be consistent with the ingenuity otherwise associated with solving riddles.

4-fold cognitive closure: There is a sense in which the ease of describing the four previous historical phases in The Patterning Instinct can be seen in terms of a form of (premature) cognitive closure in a mode of explanation which is unchallenged by the dilemmas of the present with regard to the future. This is only too obvious in the governance of major countries at this time, to say nothing about global governance. There is perhaps a case for recognizing a form of "cognitive glass ceiling" with which conventional thinking is faced.

Any intuitive recognition of the coherence of a 4-fold patterning merits consideration in the light of the work of Marie-Louise von Franz (Number and Time: reflections leading toward a unification of depth psychology and physics, 1974) a focus she inherited from Carl Jung. A chapter in that study is entitled: The Number Four as the One-Continuum's Model of Wholeness in all Relatively Closed Structures of Human Consciousness and in the Body. Therein it is noted that:

The number four thus signifies (as Menninger points out) a peculiar border number [Zahlwort und Ziffer: Eine Kulturgeschichte der Zahl: Zählreihe und Zahlsprache. Zahlschrift und Rechnen, 1957]. This boundary aspect of the number four is reflected in many figures of speech. Many languages, for instance, possess a trial and quaternal case beyond the dual, but never more. Also, in all languages the numerals up to four are etymologically formed as adjectives, but never higher ones... Only beginning with number five do we find, as Menninger states, genuine "empty" numbers, detached from their objects.... Since Jung devoted practically the whole of his life's work to demonstrating the vast psychological significance of the number four, I must refer the reader to his writings in this connection.... The fact that mankind's repeated attempts to establish an orientation toward wholeness possess a quaternary structure appears to correspond to an archetypal psychic structural disposition in man (pp. 114-115).

Further examples cited include:

Further insights are offered from a philosophical perspective by Antonio de Nicolas (Four-dimensional Man: meditations through the Rg Veda, 1978). In recognizing the limitations of a single language as offering a pattern of meaning, this focuses on the use of four complementary languages in the Rg Veda, as summarized separately (Epistemological challenges: Language, Global Strategies Project).

Appropriate to the central role of time in Part 5 of The Patterning Instinct -- in referring to the future -- is the manner in which this transcends the 4-fold quaternary pattern. With respect to the complex relation to the fivefold, von Franz notes:

In China the number five possesses the same significance as four does with us, because it is taken to represent the centered four... This concept is also found in the West, in the alchemical idea of the quinta essentia. The quinta essentia is not additively joined onto the first four as a fifth clement. but represents the most refined, spiritually imaginable unity of the four elements. It is either initially present in and extracted from them or produced by the circulation of these elements among one another. (pp. 120-121)

There is however a challenge to comprehension of the 4-fold, especially evident in the continuing controversy associated with the various versions of the Swastika, as discussed separately (Swastika as Dynamic Pattern Underlying Psychosocial Power Processes: implicate order of Knight's move game-playing sustaining creativity, exploitation and impunity, 2012).

Cognitive "dilemmas": Potentially relevant, it is appropriate to note the understanding of currently recognized "dilemmas", and how these might relate to the pattern phases in the book.

no dilemma Part 1: Everything is Connected consensus; no conflict?
dilemma Part 2: Hierarchy of the Gods conflict between two requirements
trilemma Part 3: The Patterns Diverge conflict between three requirements
tetralemma / quadrilemma Part 4: Conquest of Nature conflict between four requirements
pentalemma Part 5: The Web of Meaning? conflict between five requirements

Whilst there is great familiarity with dilemmas and contradictions, there is far less recognition of a trilemma and a tetralemma. The latter is more commonly recognized in Eastern traditions and is notably featured in the work of Kinhide Mushakoji (Global Issues and Interparadigmatic Dialogue: essays on multipolar politics, 1988). The following examples, and the relations between the lemmas, are discussed separately (Intuited complementarity: environmental cycles and learning cycles? 2018).

Comparison of lemmas
Trilemma (for example, as indicated by Wikipedia): Quadrilemma (for example):

Pentalemma: Appropriate to this argument is the rarity of a pentalemma, understood as implying a conflict between 5 separately undesirable alternatives. Cited indications of the implied challenge are offered by:

More substantive indications include:

These are discussed separately (Decision-making capacity versus Distinction-making capacity: embodying whether as weather, 2015) with respect to enhancing strategic discourse systematically using climate metaphors (Five-fold ordering of strategic engagement with time; Five-fold cognitive dynamics of relevance to governance?). That discussion mentions the even rarer use of hexalemma and heptalemma, although an octalemma is seemingly recognized by Edward Andersonto (Problem of Time in Quantum Gravity, 2012). The Euthyphro "dilemma" is restated as an octalemma by Richard Goode (Nothing Is Permitted: an argument for moral eliminativism). Consideration could therefore be given to Strategic Octalemmas (2009).

Beyond the 4-fold cognitive modality: integrating the 5-fold, 6-fold and 7-fold?

Just as the binary "dilemma" is a major constraint in any form of psychosocial organization and governance, it could be argued that any form of pentalemma is indicative of a constraint beyond the tetralemma. This suggests the distinctive challenges of articulating and comprehending Part 5 of The Patterning Instinct. It does not lend itself to the "comfortable" explanatory modality of the 4-fold historical articulation of patterns of meaning in the preceding parts. It necessarily constitutes a major paradigm shift, notably through the requirement to engage through choice with an uncertain future -- rather than simply to explain the pattern breaking of past transitions as a historical observer.

The systemic perspective requiring 5th-order thinking calls for the implication of the observer in a manner foreign to conventional systems thinking of a lower order -- for which the dissociation of the observer is a natural characteristic of any explanation. Such considerations are evident in the case made for recognition of the insights of quantum mechanics -- most remarkably by Alexander Wendt (Quantum Mind and Social Science: unifying physical and social ontology, 2015). Discussion of quantum mind is now variously considered (Arnold Mindell, Quantum Mind: the edge between physics and psychology, 2000).

There is therefore an argument for reviewing 4-fold sets of scenarios, patterns or worldviews in contrast with 5-fold or N-fold variants -- especially in terms of their comprehensibility, credibility and how such patterns "work" in systemic terms. Obviously this cannot preclude the sets with higher numbers of patterns, but it does suggest that they may have a distinctive cognitive role. Also to be recognized is the potential degree of conflation and confusion where the challenge of coherence and comprehensibility of the set as a systemic whole is avoided.

Of potential relevance is the argument of David R. Gibson (Marking the Turn: obligation, engagement, and alienation in group discussions, Social Psychology Quarterly, 72. 201, 2). This concludes that those who contributed somewhat less recently remain engaged but have more latitude to take discordant positions; and those who have been quiet for longer periods are susceptible to "alienation from topic", as a result of which reentry is often accompanied by an attempt to change the topic.

Comprehension and ignorance of the whole: As stated with respect to quantum reality, and sometimes attributed to Richard Feynman: If you think you understand quantum mechanics, you don't understand quantum mechanics. This cautionary note would seem to be especially relevant to imagining the systemic characteristics of the Trajectories to Our Future of Part 5 of The Patterning Instinct.

Just as there is a case for explicit consideration of comprehension, and the relative lack thereof in comprehending any system, so there is a case for associating this with an explicit recognition of ignorance. This is notably suggested by the triangular example of Ron Atkin (presented above). In that case comprehension (of "white") is usefully placed at the centre, with the implication that ignorance of the whole could be similarly located (as the alternative condition). It follows that the emptiness of the centre is therefore (elusively) significant in any pentagonal configuration of the whole.

With respect to ignorance, of considerable value are the arguments of Nicholas Rescher (Ignorance: on the wider implications of deficient knowledge, 2009; The Strife of Systems: an essay on the grounds and implications of philosophical diversity, 1985), or others (Stuart Firestein, Ignorance: How It Drives Science, 2012; Joseph Acquisto, Poetry's Knowing Ignorance, 2019). Some relevance is evident from more speculative explorations (University of Ignorance: engaging with nothing, the unknown, the incomprehensible, and the unsaid, 2013).

Another consideration is that any fruitfully meaningful philosophical language needs to encompass "something missing", as suggested by the arguments Terrence Deacon (What's Missing from Theories of Information? 2010). As discussed separately (Necessary incompleteness, 2014; Cognitive mystery of holes, lacunae and incompleteness, 2014), for Deacon:

The problem is this: Such concepts as information, function, purpose, meaning, intention, significance, consciousness, and value are intrinsically defined by their fundamental incompleteness. They exist only in relation to something they are not.... The "something" that each of these is not is precisely what matters most. But notice the paradox in this English turn of phrase. To "matter" is to be substantial, to resist modification, to be beyond creation or destruction -- and yet what maters about an idea or purpose is dependent on something that is not substantial in any obvious sense. So what is shared in common between all these phenomena? In a word, nothing -- or rather, something not present. (Incomplete Nature: how mind emerged from matter, 2011p. 23, emphasis in original)

A case for the relevance in this period of discourse of another kind is suggested by a traditional Daoist tale from Zhuangzi, as quoted by Ellen M. Chen (In Praise of Nothing: an exploration of Daoist fundamental ontology. 2010, p. 114). They are psychodynamic tensions of dilemmas, experienced from within (or participated in). Chuang Tzu, in another Chinese classic, makes the point that:

The wise man therefore... sees that on both sides of every argument there is both right and wrong. He also sees that in the end they are reducible to the same thing, once they are related to the pivot of Tao. When the wise man grasps this pivot, he is the canter of the circle, and there he stands while "Yes" and "No" pursue each other around the circumference (The Way of Chuang Tzu, interpreted by Thomas Merton, 1970)

6-fold, 7-fold, 8-fold, 9-fold? The existence of a succession of "glass-ceilings" can be considered in the light of sets of greater than 5 patterns of meaning:

Such distinctions are notably explored through systematics, namely as articulated by J. G. Bennett (The Dramatic Universe, 1956). Some may indeed be distinguished as stages explicitly associated with cognitive breakthroughs and reframings (Varieties of Rebirth: distinguishing ways of being "born again", 2004):

The transition beyond the 4-fold articulation of the earlier patterns of meaning in The Patterning Instinct, could be explored through associating the 7 "elementary" distinctions of catastrophe theory with the classical 7 "WH questions" (Conformality of 7 WH-questions to 7 Elementary Catastrophes: an exploration of potential psychosocial implications, 2006; WH-Questions as derivative psychosocial constructs, 2010).

The argument would be that there are four simpler types of strategic question to be associated with the four simpler types of catastrophe which are recognized. There are a further three styles of question then to be associated with the three more complex styles of catastrophe, notably related to observer implication. Are the latter then effectively conflated and confused as trajectories within Part 5 of The Patterning Instinct -- if only as challenging questions for governance?

Whilst this is helpful in marking the boundary between 4 and 5, it raises the question as to the nature of the cognitive boundary between 7-fold and 8-fold patterns, and potentially the boundary implied by 12-fold and 20-fold articulations, as indicated above:

When 5-foldness is organized in three dimensions, it is fundamental to the integrity of the 12-fold organization of the dodecahedron with its pentagonal sides, as noted separately (Time for Provocative Mnemonic Aids to Systemic Connectivity? Possibilities of reconciling the "headless hearts" to the "heartless heads", 2018). Is that 5-foldness somehow significant to the concluding Part 5 of the book, and its organization, themed as The Web of Meaning?

Eliciting systemic answers from a 5-fold web of meaning?

Beyond a web perspective? As the concluding part of The Patterning Instinct, Part 5 is entitled The Web of Meaning? -- appropriately framed by an interrogation mark. The implication is that there is a confluence of insights into patterning from which can be discerned a pattern of meaning for engaging with the future. Any such pattern is perhaps necessarily elusive, especially given the manner in which detection of that pattern implicates the collectivity in its recognition.

Unfortunately the condition of global civilization at this time is so unstable that there are few clues as to how any systemic insights are to be detected. The crisis of crises is only too evident:

The response in Europe to this complex of crises further exemplifies the challenge of eliciting insights into how to govern the emerging pattern. Poisonously divisive debates in the UK, Germany and France are indicative of the limited capacity for systemic thinking -- of a 5th order in the cybernetic terms (as indicated above). France has offered the most remarkable dynamics in the months past through the popular Yellow Vest challenge to conventional authoritarian governance. This has been complemented by a 3-month, country-wide debate, together with a special TV channel offering commentary on the crisis by panels of 4-6 people (France's Great Debate - how it worked, OpenDemocracy, 15 March 2019).

The TV panel discussions are especially remarkable in that the content, articulated from a variety of perspectives and levels of expertise, does not engender a higher level of insight. The volume of recorded discourse merits sophisticated dialogical analysis to detect the pattern of points made -- and the integrative failure. The content of the national debate in every region, and the thousands of written submissions elicited, has also failed to be processed in a manner commensurate with the investment in that process (What will France do with 'National Debate' data? France24, 3 March 2018). The challenge and the failure are discussed separately (Multi-option Technical Facilitation of Public Debate: eliciting consensus nationally and internationally, 2019).

More generally it can be argued that the title of Part 5 -- as The Web of Meaning? -- is a valuable metaphor for the dysfunctional dynamic of elicitation of collective intelligence towards pattern recognition. Ironically there is no lack of expert elicitation initiatives through which authoritative reports are engendered. Clearly the immense riches of the internet enable the "web of meaning" to be explored from multiple perspectives -- but with very little evidence of global coherence. There is large scale indulgence in eliciting meaning but limited capacity and motivation to interrelate the patterns assertively detected from any given perspective.

Ironically the cover illustration of The Patterning Instinct is a modest schematic depiction of a web of meaning inspired by standard depictions of networks. The irony is all the greater in that, in reviewing the earlier systemically focused study by the author of the foreword to that work, a similar point was made (Transcending an Asystemic View of Life: review of The Systems View of Life: a unifying vision, 2014). To a far greater degree than The Patterning Instinct, the cover implied a degree of coherence to life as a system, as reproduced below left. However the contents did not reflect that coherence to any degree, evoking the image on the right in the critical review -- as a systemic perspective.

The Systems View of Life: a unifying vision (2014) by Fritjof Capra with Pier Luigi Luisi
Cover imagery of the book
(detail)
Organization of the contents
(schematic representation by reviewer)
Systems view of life: cover detail Systems view of life: organization of contents
Reproduced from Transcending an Asystemic View of Life: review of The Systems View of Life: a unifying vision (2014)

Coexistence of problematic patterns: The historical succession of patterns of meaning in The Patterning Instinct suggest that humanity has superseded the earlier patterns. As emphasized above, one difficulty in eliciting any systematic perspective is that the "older" patterns coexist with whatever is to be recognized as the emergent pattern of the future -- intimated in Part 5. Especially evident is a high degree of indulgence in:

Problematic 5-fold pattern? Each successive pattern, understood as sequential, is readily framed as problematic from the perspective of the preceding pattern. It is readily demonised. From the unitary perspective of acclaimed by an Abrahamic religion, binary dynamics exemplify the challenge of "evil" to the "good" with which they identify. A 5-fold pattern has long been considered problematic in its own right -- as exemplified by its association (through the pentacle) with witchcraft. Neopagans would however claim a particular association with the 4-fold dynamics of natural magic -- through which they engage via that symbol.

It is therefore useful to look experimentally at the conventionally problematic dimensions of any 5-fold organization -- juxtaposed with a corresponding pentagram of conventionally valued functions. The experiment follows from a previous exploration (Prefix "Re-cognition" as Prelude to Fixing Sustainability -- "Pro" vs "Con" ? Speculative review of missing emphases potentially vital for psychosocial balance, 2017).

Experimental mnemonic aid to reconcile "pro" and "con"
Problematic pentagram (experimental) Pentagram of concord (experimental)
Problematic pentagram experimental - animation Pentagram of concord - animation

Ironically the relevance of the problematic articulation can be illustrated by a work of Peter Senge subsequent to his "fifth discipline" insight informing this review. References indicate that he has outlined the possibility of a "sixth discipline" in The Ecology of Leadership (Leader to Leader, 1996, 2, pp. 18-23). Because of the "paywall" constraint, protecting his intellectual "property", this attractive "pattern recognition" he has promulgated could not be accessed. The knowledge is effectively "incarcerated" -- presumably for the exclusive benefit of leaders. This could be understood as the problematic nature of the fifth discipline which is deprecated to a much higher degree in other contexts, especially when the pentagram is inverted.

It is appropriate to note that most of the references cited here are subject to intellectual property constraints and paywalls. More ironic, as noted below, it that articulations of disciplines may be further subject to trade-marking -- irrespective of the profundity of which they are held to be indicative.

Systemic psychosocial viability: In contrast to the 5-fold Wu Xing cyclic pattern of phases cited above, that of the thermodynamic cycle is understood to be composed of 4 phases. To a tantalizing degree, they might well be understood as referring to similar processes -- or to the capacity of the human mind in comprehending them individually and as a cycle. The question is how a system of pattern phases is to be understood as "working" -- especially that in which humanity is embedded, as discussed separately (Psychosocial Energy from Polarization -- within a cyclic pattern of enantiodromia, 2007; Psychosocial Work Cycle: beyond the plane of Möbius, 2007).

How is the pattern of trajectories in Part 5 of The Patterning Instinct to be understood as "working" systemically? As a characteristic of conventional 4-fold thinking, the thermodynamic cycle depicted below can be understood as missing an implicit dimension, namely the manner in which human intelligence has been able to frame and comprehend its cyclic nature. On the other hand, how are cognitive characteristics of relevance to this argument to be understood as associated with the 5-fold Wu Xing configuration?

Examples of mutually irreconcilable modes of thinking?
Wu Xing Thermodynamic cycle
Wu Xing

Thermodynamic cycle

1?2: Isentropic expansion: Constant entropy (s), Decrease in pressure (P), Increase in volume (v), Decrease in temperature (T)

2?3: Isochoric Cooling: Constant volume(v), Decrease in pressure (P), Decrease in entropy (S), Decrease in temperature (T)

3?4: Isentropic compression: Constant entropy (s), Increase in pressure (P), Decrease in volume (v), Increase in temperature (T)

4?1: Isochoric heating: Constant volume (v), Increase in pressure (P), Increase in entropy (S), Increase in temperature (T)

Reproduced from Wikipedia

With respect to the Wu Xing configuration, in Chinese culture the "elements" in the phase diagram have long had metaphoric interpretations rendering them variously comprehensible and meaningful. Of relevance to this argument, comprehension of the states of matter through metaphors with which they are often associated, lends itself to understanding in terms of the symbolism of the classical four-element Western pattern, with its implication of a fifth. Although this can be readily deprecated, it does however allow for representation in a phase diagram with plasma as a fifth state of matter (Cognitive patterns of environmental significance, 2010). Such distinctions might then correspond to the stages of reification as the quality of knowing in the moment "hardens" into objective reality -- passing through analogues to the states of matter (plasma -- gas -- liquid -- solid).

As stated in the foreword by Frijtof Capra (cited above): Cognition is embedded in matter at all levels of life.

Pattern spiralling challenge of biomimetics

Despite their implicit dynamic, arguably such representations might well be recognized as effectively a form of "standing wave". Missing is any sense of the spiral nature often associated with cognitive development. The chambered nautilus is valued as emblematic of desirable forms of growth and development. It is therefore useful to contrast two poems in which spiralling is a concern -- that by Yeats being characteristic of the condition of society a century ago, and a second indicative of potential at this time.

The Second Coming (1919)
by W. B. Yeats
(first verse)
The Chambered Nautilus
by Oliver Wendell Holmes Sr.
(second verse)
Turning and turning in the widening gyre
The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.
Its webs of living gauze no more unfurl;
Wrecked is the ship of pearl!
And every chambered cell,
Where its dim dreaming life was wont to dwell,
As the frail tenant shaped his growing shell,
Before thee lies revealed, --
Its irised ceiling rent, its sunless crypt unsealed!

The question is how to benefit from such a dynamic recognized intuitively, as discussed separately (Enabling Governance through the Dynamics of Nature: exemplified by cognitive implication of vortices and helicoidal flow, 2010). Given the association of The Patterning Instinct with a Systems View of Life through its forward, one key to any such possibility is through the biomimetics which has been so significant to the development of aerodynamics, as discussed separately with respect to Technomimicry as analogous to biomimicry (Engendering a Psychopter through Biomimicry and Technomimicry: insights from the process of helicopter development, 2011). Biomimetics could be recognized as pattern recognition par excellence. In such terms it could be argued that the challenge of Part 5 for humanity is one of "learning how to fly".

In this respect it is perhaps appropriate to discover the recognize importance of the chambered nautilus from a biomimetic perspective:

Spiral forms
Chambered Nautilus shell
(cutaway)
Logarithmic spiral
(with dashed circles to indicate the 3D "cognitive habitat"
of the developing body within)
Nautilus shell (cutaway) Logarithmic spiral
Adapted from image in Wikipedia profile Adapted from image in Wikipedia profile

Relevance to psychosocial patterning? There is considerable knowledge of the marine nautilus / chambered nautilus (W. Bruce Saunders and Neil H. Landman, Nautilus: The Biology and Paleobiology of a Living Fossil, 2010). It is unclear whether insights from the application of its structure and development to the architecture of buildings have been considered with respect to psychosocial development, despite its value as a symbol of educational development and of strategic appropriateness (New Zealand Curriculum Nautilus, Nautilus Institute for Security and Sustainable Development). As has been argued in a journal of that name: Science, too, builds then rebuilds as new evidence is accumulated. Theories are constructed, then subsumed, or even abandoned (Chambered Nautilus: a metaphor for science. Nautilus, 22 April 2013).

With respect to such spiralling, an earlier document discusses the interplay between the Fibonacci sequence, aesthetics and the golden ratio symbolized by phi (Spiralling around "nothingness" and "pointlessness": the implication of phi, 2012). In mathematics, the ratio of sequential elements of the Fibonacci sequence approaches the golden ratio asymptotically. Much appreciated in design, that ratio has been recognized in the spiral phyllotaxis of plants. A Fibonacci spiral, based on that series, closely approximates the golden spiral -- a logarithmic spiral whose growth factor is the golden ratio.

The construction of the Fibonacci can be discussed separately as providing a framework to hold an evolving pattern of distinctions (Construction of Fibonacci spiral as providing an open-ended integrative framework, 2010). The image on the right below lends itself to experimental attribution of the Chinese encoding of patterns of systemic insights,as shown in the image on the left, derived separately (Experimental attribution of binary codes to Fibonacci pattern, 2010). This is as an exploration of the relevance of the pattern to sustainable governance (Fibonacci's magic carpet of games to be played for sustainable global governance, 2010).

Experimental attribution of binary codes
to Fibonacci pattern on right
Construction of Fibonacci spiral
(numbers indicate length of sides of squares,
not the number of "boxes" within each square in the image on the left)
Attribution of binary  codes to Fibonacci spiral pattern Fibonacci spiral pattern

From 4-fold to 5-fold: The image on the right is potentially especially suggestive with respect to the transition from 4-fold thinking to 5-fold thinking. The first four positions (marked 1, 2, 3, 5) complete one turn of the spiral curve. The curve marked 8 starts a new cycle (and is effectively parallel to the first). The next four positions (marked 8, 13, 21, 34) complete a second cycle -- which could be related to 5th-order, 6th-order, 7th-order, and 8th-order thinking.

The Chinese binary coding in the various squares (in the left-hand image) can be understood as a reflection of those different patterns of thinking, ranging from use of a single line (yin or yang notation), through a set of 4 double lines, a set of 8 triple lines, etc.

From a game-playing perspective, the pattern could be considered as corresponding to a 1-person, 2-person... up to an 8-person game. Each square requires that a more complex game be played (Succession of dynamic "game-playing arenas", 2010) .

As noted above, the pathetic dynamics over centuries between the three Abrahamic religions is indicative of the difficulties of a game of "lower order", whereas that of a "higher order" is indicated by the relations between the set of religions identified by Stephen Prothero (God Is Not One: the eight rival religions that run the world -- and why their differences matter, 2010). Such dysfunctional dynamics exemplify the case for mathematical theology (Mathematical Theology: Future Science of Confidence in Belief -- self-reflexive global reframing to enable faith-based governance, 2011).

Each such game can be considered as a form of mirror, as specifically recognized with respect to the so-called "BaGua mirror", presenting the self-reflexive challenge of how to engage with it in the elaboration and embodiment of scenarios (Stepping into, or through, the Mirror: embodying alternative scenario patterns, 2008).

The spiral pattern above can be fruitfully extended into a reverse spiral, variously known as the Euler spiral or clothoid (Design considerations and possible implications, 2010). It is valued as the key to interrelating a linear trajectory with curvature. Given the degree to which The Patterning Instinct traces the linear progress of human history, the manner in which curvature figures in human development is of potential significance (Clothoid as a psychosocial transition curve: from linear to circular, 2012). .

Polyhedral possibilities of interrelating patterns comprehensibly: a "cognitive gearbox"?

It is appropriate to note that patterns of distinctive N-foldness can be related in a memorable manner through the extensively studied sets of spherically symmetrical polyhedra, most notably the 5-fold Platonic polyhedra and the 13 Archimedean polyhedra. These can each be understood as patterns or systems in their own right, especially as articulated by Buckminster Fuller (Synergetics: Explorations in the Geometry of Thinking, 1975; Synergetics 2: Further Explorations in the Geometry of Thinking, 1979). Beyond their use for the purposes of mapping distinctions, the question is how they could be understood as containers or vehicles for the comprehension of the various patterns of meaning in The Patterning Instinct, and especially the challenge of Part 5.

One approach to this possibility is through the complexification of the insight associated with the Triple Helix model of innovation, and the integrative challenges it poses. As discussed separately, this specifically introduces the role of such polyhedra in extending insights to 4-fold, 5-fold, and higher patterns (Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity -- Eppur si muove: Biomimetic embedding of N-tuple helices in spherical polyhedra, 2017).

Specific possibilities. Of relevance to Part 5, these include:

Animation of mapping of 5-fold and 6-fold symbols onto a truncated icosahedron
(generated using Stella Polyhedron Navigator)
Animation of Islamic star and Star of David into icosahedral form

Transformational pathways between patterns of N-foldness: Rather than any necessary focus on transformation between specific patternings of meaning, the challenge of Part 5 can be reframed as that between distinctive patterns of meaning more generally. It is in this sense that the well-studied geometrical transformations between the 18 spherically symmetrical polyhedra (Platonic plus Archimedean) are of interest, especially since they can be variously mapped, with an indication of the variously viable transformations between them. The following schema are discussed separately in Changing Patterns using Transformation Pathways (2015). That on the right derives from the remarkable study by Keith Critchlow (Order in Space, 1969).

Map of relationships between spherically symmetrical polyhedra Map of relationships between Archimedean polyhedra
Map of relationships between spherically symmetrical polyhedra Polyhedron of Archimedean Polyhedra

Rather than particular patterns of meaning, and any implied desirability of thinking of a "higher order", this reinforces the sense of the coexistence of distinctive patterns of meaning and the capacity to shift between them. Emerging from the challenge of Part 5, is then not just another pattern of meaning but rather the capacity to shift between a requisite diversity of patterns of meaning -- framing the capacity to encompass the disagreement between them.

Ironically this capacity has effectively been anticipated in the worldwide enthusiasm for transformer toys and the depiction of transforming robots in movies. This familiarity is far greater than that with respect to tentative arguments for international organizations of "variable geometry".

As noted separately, no questions seem to be asked as to why related polyhedra are not of significance -- even when extensively studied by other disciplines, This is especially striking in the case of the rhombic dodecahedron, favoured as a pattern in the study of logical connectivity (Neglected recognition of logical patterns -- especially of opposition, 2017). This polyhedron is a geometric dual of the cuboctahedron whose particular characteristics with respect to transformation between polyhedral forms have been highlighted by Buckminster Fuller.

Pattern transformation through a "cognitive gearbox"? A simpler metaphor is offered by the gearbox enabling the shift between different gears in a vehicle. This suggests the need for insight into the operability of "conceptual gearboxes" or "cognitive gearboxes" (Conceptual gearboxes, 1980; Forms of requisite complexity, 2008; Cognitive dimensions of governance: 2, 3, 4, 5, 6, 7, 8?, 2016; Engaging a new gear to navigate the adaptive cycle, 2010).

Somewhat ironically such a gearbox can be explored in terms of the memorable nesting of polyhedra (Transformation: changing cognitive gear and pattern shape shifting, 2015; Nesting polyhedra to enable comparison of patterns of discourse, 2015; Relative movement of nested Platonic polyhedra: pumping and rotation, 2015). If only for mnemonic purposes, the 5 Platonic polyhedra could be understood as exemplifying the 5 distinctive patterns of meaning identified in The Patterning Instinct. The earlier documents variously explore how they might be nested to enable the dynamic functions of a gearbox or transmission system. This involved 3D representation, using interactive virtual reality applications, with the possible dynamics rendered comprehensible through videos.

The screen shots below variously show how each of the distinctively coloured polyhedral patterns might emerge into prominence ("dominance"?) or collapse. As discussed in those commentaries, the container for this cognitive gearbox is a particular polyhedron with requisite properties -- the rhombic triacontahedron -- the dual of the icosidodecahedron, an Archimedean polyhedron.

Screen shots of a virtual reality rendering of an expansion/contraction ("pumping") dynamic
within a rhombic triacontahedron (green) as a nesting framework
Version as video animation (.mov); access to X3D variant
Rhombic triacontahedron framework

Tetrahedron (mauve) emergent

Icosahedron (red) emergent
Nested Platonic polyhedra: rhombic triacontahedron framework Nested Platonic polyhedra: tetrahedron emergent Nested Platonic polyhedra: icosahedron emergent
Dodecahedron (blue) and Icosahedron (red) Dodecahedron (blue) emergent Emphasis of Cube (grey) and Tetrahedron (mauve)
Dodecahedron and Icosahedron nested within Rhombic triacontahedron Nested Platonic polyhedra: dodecahedron emergent Nested Platonic polyhedra: emphasis of cube and tetrahedron

With the patterns variously perceptible as above, the 5-fold confusion of Part 5 of the The Patterning Instinct is usefully represented when understood in conventional static terms -- given the coexistence of 5 distinctive patterns of meaning. Greater clarity emerges when the operation of the cognitive gearbox is perceived dynamically, although this is obviously difficult to represent in 2D or through the linearity of text (irrespective of any emphasis on feedback loops embedded therein).

Patterning dynamics: animations suggestive of cognitive gearbox operation
(patience may be required to allow time for these large animations to load)
Relative "pumping" dynamic of nested Platonic polyhedra
within Rhombic triacontahedron (green) as a nesting framework
Relative "rotation" dynamic of nested Platonic polyhedra
within Rhombic triacontahedron (green) as a nesting framework
Relative pumping dynamic of nested Platonic polyhedra Relative rotation dynamic of nested Platonic polyhedra
virtual reality: vrml or x3d; video: mp4 virtual reality: vrml or x3d; video: mp4

Speculation regarding a requisite "sixth discipline" and more

Beyond the five patterns of meaning, as identified by Jeremy Lent and associated with the organization of The Patterning Instinct, are there more to be identified -- perhaps from other perspectives? This review has taken advantage of the much-cited systemic "fifth discipline" articulated by Peter Senge (The Fifth Discipline: The Art and Practice of the Learning Organization, 1990). At that time he is reported to have suggested a "sixth discipline" whose nature is such that it could not be grasped at that time. In making that point in The Seventh Discipline: the art and science of integrating multinational organizations, Michael Stankosky argues:

In my thought-piece on the Mosaic of Management, I argued on the need for a framework to integrate all the past theories and practices on management. Evcnts unfolded so rapidly [since 1990] that we need to leapfrog the thinking of an ungraspable 6th, and go to a 7th discipline. We need to come to grips with this if we are to advance in, and deal with, these major paradigm shifts in this 21st century. We cannot be stuck in the dark ages of management, nor the middle ages. We need to be in the age of a renaissance. (21 for 21: Leading the 21st Century Global Enterprise, Emerald Group Publishing, 2018, p. 102)

Nature of discipline: Before considering other disciplines variously understood as required to complement or compensate for the perceived inadequacies of the fifth, it is appropriate to note a reflection on disciplinarity as such by Wolff-Michel Roth (Mathematics in the Everyday World and at Work; prolegomena for rethinking the concept of interdisciplinarity, In: Bharath Sriraman and Viktor Freiman (Eds), Interdisciplinarity for the 21st Century: symposium on mathematics and its connection to arts and sciences, Moncton, 2009, pp. 67-108). Roth argues for the need to the etymological origins of the term in order to recapture the semantic field it now covers. Usage may then be distinguished as:

  1. Denoting instruction imparted in a teaching/learning process
  2. Denoting a branch of instruction or education
  3. Indicative of the sense of formation or training to proper conduct and action
  4. Denoting the orderly conduct and action which result from training, namely a trained condition.
  5. The sense of order maintained and observed among pupils or others, namely a system of maintenance of order
  6. The sense of the system regulating the practice of some institution, notably a church
  7. Denoting penance, especially religious penance.
  8. Denoting treatment for some special purpose, such as a medical regimen.
  9. As used in compound nouns, as in discipline-master indicative of the process through order is kept (p. 104-105)

These overlapping senses help to indicate the prevailing confusion in the distinction between "disciplines", and especially any which may follow the Senge's "fifth" discipline.

Given that focus on "interdisciplinarity", this raises the question of how many "disciplines" (especially in the academic sense) are required to detect the patterns of meaning distinguished in each part of The Patterning Instinct? Here the sense of "discipline" is distinct from that of Senge's "fifth discipline", and any assumption that distinctive disciplines might be associated with the earlier parts of The Patterning Instinct. How many "disciplines" (in the academic sense) are required to detect an emergent pattern?

Sixth discipline: Reference to such a discipline has variously inspired a quest for a "sixth discipline" -- here to be understood as the emergence of a new pattern of meaning. It has been described as an integrative discipline, which combines all the domains into an integral theoretical and practical whole. (Peter Senge, The Ecology of Leadership, Leader to Leader, 1996, 2, p. 21)

Examples include:

There is some considerable irony to the fact that the most cited reference to a "sixth discipline" is to a work of science fiction (Carmen Webster Buxton, The Sixth Discipline, Cracked Mirror Press, 2011)

Other sets of disciplines: Following this pattern, examples of reference to a "seventh discipline", and more, include:

Secular disciplines ("outer-oriented")
Ford Motor Company Vladimir Elie Christopher Laszlo
  Eight disciplines problem-solving Disciplines You Must Develop to Achieve Remarkable Results (2018) Sustainable Value: How the World's Leading Companies are Doing Well by Doing Good (Stanford University Press, 2008): The Eight Disciplines Studying of Discipline Larning from the Japanese Nation: Cultural disciplines
1 Plan Setting clear targets Understand current value position Bushido Principle
2 Create a team Taking action. Anticipate future expectations Principle of Samurai Discipline
3 Define and describe the problem Time management Set sustainable value goals Concept of Keishan Culture
4 Contain the problem Finishing what you start Design value creation initiatives Kai Zen Principle
5 Choose corrective actions Sharpening your skills. Develop the business case Positive attitude, morale, loyalty
6 Implement and validate corrective actions Mastering your habits Capture the value Work and time spent in the workplace.
7 Take preventative measures Associating with the right people. Validate results and capture learning Work
8 Congratulate your team Thinking empowering thoughts Develop the mind-set, management capability and skills needed to capture shareholder and stakeholder value Discipline of small problems
9   Keeping your commitment   Work ethic

It is useful to contrast such conventional strategic disciplines with those articulated from a spiritual perspective. This is especially relevant given the increasing influence of religion, notably of a fundamentalist nature, on political processes.

Spiritual disciplines ("inner-oriented")
A. R. Weisser Everett Fritz Warren Ziegler John Ortberg Jack Hayford
  Alaskan Job: the disciplined pursuit of greatness (WestBow Press, 2015) Freedom: Battle Strategies for Conquering Temptation (Ignatius Press, 2016) Disciplines for Battling toward Purity Ways of Enspiriting: transformative practices for the Twenty-First Century (Spiritual Learning, 1995) The Life You've Always Wanted: Spiritual disciplines for ordinary people Living the Spirit-Formed Life: Growing in the 10 Principles of Spirit-Filled Discipleship (Chosen Books, 2017)
1 Walk with God's light Prayer

Deep listening™: the empty vessel way

Joy and celebration Committing to hear God's voice
2 Friendship with God Writing Deep questioning™ Solitude Living in the power of baptism
3 Gather your family Engaging the Holy Spirit in Prayer Deep learning™ Prayer Celebrating the Lord's table
4 Enjoy God's abundance Protecting Your Eyes Deep imaging™ Servanthood Walking in the spirit of gorgiveness
5 Pursue honor Fasting Intentioning Confession Feeding on the word of God
6 Pursue mercy Setting Boundaries Discerning Guidance from the Holy Spirit Maintaining integrity of heart
7 Execute justice Accountability Dialogue Practice of secrecy Abiding in the fullness of the Spirit
8 Ready for rough times     Reflecting on Scripture Living a live of submission
9 Speak wisdom       Practicing solitude
10 Fulfill the covenant       Living as a worshiper
           

Clarification: breadth vs depth? In a period in which appropriate discipline would appear to be necessary in response to emerging patterns of meaning, the confusion as to how many strategic and cognitive disciplines there are, and how they are organized, is clearly of concern. How are those cited to be distinguished in cognitive terms? As indicated above, how many academic disciplines are required to recognize the existence of a new pattern of meaning?

One approach is to argue that some disciplines are more fundamental in cognitive terms. From that perspective, by contrast, various listings of disciplines could be understood more as practices (even thinking habits), and steps (possibly as a form of checklist). The cognitive disciplines characteristic of the classic 12-step program could be explored in this light. As steps in a checklist, they are readily understood as categories somewhat equivalent in nature.

Another approach is to see additional steps as an "extrapolation" of the logic of the 5-fold pattern previously articulated -- even one that is primarily opportunistic. It is profoundly sad to note that the names of some disciplines have even been made subject to trade-mark under intellectual copyright. Is this intended to limit the scope of those who might refer to them or practice them?

Yet another approach, as partially articulated with respect to the 5-fold ordering above, is to understand each additional discipline as more akin to a new dimension of complexification -- even involving compactification (analogous to that understood by physicists). This suggests that each then becomes an ever greater challenge to comprehension. The existence of patterns of higher order may be intuited or suggested but that does not mean that they are readily understood. As noted, Senge considered a sixth discipline to be ungraspable. They then become patterns which ought to be meaningful -- if one could but comprehend them. The point could be emphasized through juggling as a metaphor. Given the limited number of objects the average person can juggle (2, 3, 4?), what is the possibility of juggling 7, 8 or 9 disciplines in practice and collectively (Governance as "juggling" -- Juggling as "governance": Dynamics of braiding incommensurable insights for sustainable governance, 2018)?

This sense of complexification suggests that such disciplines, and the patterns of meaning they recognize, merit recognition in terms of "depth". Clearly spiritual disciplines may indeed be understood in this way. However there is a complementary sense in which a set of disciplines may be more closely associated with "breadth", namely as a variety of perspectives, even to be understood as practices without necessarily implying any particular depth of understanding. Clearly it may be a matter of debate whether a named discipline is primarily associated with depth or breadth.

A breadth perspective is consistent with Team Role Inventories, as with that of Meredith Belbin who distinguishes the following "behavioural traits" valuable to a team (Plant, Resource Investigator, Co-ordinator, Shaper, Monitor Evaluator, Teamworker, Implementer, Completer Finisher, Specialist). Such distinctions are variously distinguished from personality types -- with both implying a form of discipline of whatever cognitive depth.

Missing is the systemic insight which would clarify these matters. In comparing the sets of disciplines in the tables, it would seem that the insights cultivated by the early Society for General Systems Research would be of benefit in exploring the isomorphy of systems -- in this case cognitive systems. The issue is how to compare the functional roles of each discipline independently of the terms in which they are articulated, whilst allowing for issues of conflation and extrapolation.

If patterning of meaning can be fruitfully understood as intuitive, the current confusion raises the question of whether reference should be made to "the" fifth discipline, or any other, rather than to "a" discipline as it is intuitively distinguished according to one'own light

Appreciation of music as a vital clue: Intriguingly it is music that provides a remarkable interface between patterning instinct and patterning intuition -- arguably between "elites" and "populists". Music brings together themes explored above whose connectivity can appear questionable, most notably patterns experienced as of an "inner" cognitive nature and those explicable as "outer". Especially intriguing is the emerging understanding of the cognitive organization of patterns, in the light of topology, the Fibonacci sequence, and the golden ratio. Music could be considered the pattern language par excellence -- especially given its widespread comprehensibility and appeal.

How the future may be apprehended more imaginatively and coherently may depend on such patterning insights. Relevant studies, citing many further references, include:

For Tymoczko, for example, a musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Western music lies at the intersection of two seemingly independent disciplines: harmony and counterpoint. Counterpoint (or voice leading) is the technique of
connecting the individual notes in a series of chords so as to form simultaneous melodies. The circle of fifths depicts efficient voice leadings among the twelve major scales.

With respect to the argument above, how might the organization of The Patterning Instinct be understood in the light of the circle of fifths? The term 'fifth' defines an interval or mathematical ratio which is the closest and most consonant non-octave interval. The circle of fifths is a sequence of pitches or key tonalities, represented as a circle, in which the next pitch (turning clockwise) is found seven semitones higher than the last.

Circle of fifths as interface between instinct and intuition?
Circle of fifths as interface between instinct and intuition?
Reproduced from Wikipedia

Any further exploration of patterns in terms of meaning in the light of such configurations would benefit from consideration of the work of musicologist Ernest McClain (The Myth of Invariance: the origins of the gods, mathematics and music from the Rg Veda to Plato, 1978; Meditations Through the Quran: tonal images in an oral culture, 1981).

Given the current challenge of contrasting "voices" in society, how might "efficient voice leadings among the twelve major scales" then be comprehended? What indeed are the twelve major scales in global society, as speculatively explored (Generic Reframing of the 12 Tribes of "Israel", 2009)? What part might in future be played by sonification of discourse (Sonification for subtle pattern recognition, 2018)? The argument has been development with respect to strategic declarations (A Singable Earth Charter, EU Constitution or Global Ethic? 2006).


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