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1st October 2010 | Draft

Quest for a "universal constant" of globalization?

questionable insights for the future from physics

-- / --

"Globality" in relation to a "Cosmic" number?
Neglected "external" dimensions
Harmonics of "globalization": a universal constant?
Correspondence between blastosphere and spheroidal I Ching?
Number games and speculations

Annex C of Engendering Invagination and Gastrulation of Globalization (2010)


This annex is a speculative development of arguments in the main paper (where references are listed). As noted there it is based on assumptions regarding isomorphism associated with general systems research. More specifically it is based on an assumption regarding pattern recognition, stated there as:

... with respect to any one domain of human preoccupation, the capacity and requirement for relatively complex pattern recognition (and the associated degree of abstraction) may well correspond to that which is required and applicable in another domain. Rather than imply a controversial direct relation between the two domains, this highlights the determining role of human cognitive capacity with respect to emergence and use of abstract patterns as adaptable tools. It also suggests that failure to apply subtler emergent cognitive tools, in other domains faced with challenging dynamics, may signal dysfunctional development between domains.

This assumption does not deny the further possibility that there may be a more fundamental relationship between cognition and any reality treated as external, following the arguments detailed below.

"Globality" in relation to a "Cosmic" number?

The arguments of the main paper merit reconsideration within the context of long-standing challenges. These are highlighted by the improbable collaboration between psychoanalyst Carl Jung and physicist Wolfgang Pauli in co-authoring (The Interpretation of Nature and the Psyche, 1955 -- including Synchronicity: an acausal connecting principle by Carl Jung, and The influence of archetypal ideas on the scientific ideas of Kepler by Wolfgang Pauli). This preoccupation is consonant with the later arguments of biologist Gregory Bateson (Mind and Nature: a necessary unity, 1979).

In an account of that collaboration, physicist Arthur I. Miller (137: Jung, Pauli, and the Pursuit of a Scientific Obsession, 2009, and Deciphering the Cosmic Number: the strange friendship of Wolfgang Pauli and Carl Jung, 2009) notes Pauli's extraordinary conclusion, as one of the most eminent physicists of the century, that:

[How enlightening it would be to experience an encounter between No Bull Laureate Alan Sokal and Nobel Laureate Wolfgang Pauli. Would each accuse the other of being not even wrong?]

Miller introduces his study with a quote from Jung:

The no-man's land between Physics and the Psychology of the Unconscious [is] the most fascinating yet the darkest hunting ground of our times

Miller's account presents the context for the extraordinary continuing exploration by physicists (and especially Pauli) of the fundamental significance of the dimensionless fine-structure constant (1/137) -- typically called "137" -- namely the coupling constant characterizing the strength of electromagnetic interaction (and usually denoted by α). Might there be a "coupling constant" characterizing the strength of psychodynamic interaction with an "other"?

As the "cosmic number", the fine-structure constant "137" is recognized as fundamental to the organization of the physical universe -- to the extent that its integrity is comprehensible to the human mind. It is appropriate to ask whether there is an analogous dimensionless constant which is fundamental to the organization of any psychosocial form characterized by "globality" -- to the extent that its integrity is comprehensible to the human mind.

It has been argued that stable matter, and therefore life and intelligent beings, could not exist if the constant were much different. For instance, were α to change by 4%, stellar fusion would not produce carbon, so that carbon-based life would be impossible. What "constant" would disenable any analogous psychodynamic coherence?

Another account of the "archetypal" relationship between Jung and Pauli is provided by David Lindorff (Pauli and Jung: the meeting of two great minds, 2004).

Neglected "external" dimensions

Given the shared preoccupations of Jung and Pauli, what is extraordinary is that there is very little trace of five dimensions which might be considered appropriate to their quest, especially in the light of the preoccupations of deconstructionists:

In Pauli's case, as a physicist, it might be said that the degree of his "re-cognition" of such neglected dimensions is evident in his statement (quoted by Miller) to the effect that:

What is decisive for me is that I dream about physics as Mr. Jung (and other non-physicists) think about physics. Every time I have talked to Mr. Jung (about the "synchronistic" phenomena and such), a certain spiritual fertilization takes place.

As with the long-secret alchemical priorities of Isaac Newton, seemingly these dimensions are assumed to be "external" to any conventional consideration of the "universal" when, particularly in the case of "globalization", they may well be fundamental, especially if "externalities have to be cognitively embodied in some way, as separately discussed (Existential Embodiment of Externalities: radical cognitive engagement with environmental categories and disciplines, 2009). Curiously consideration of such "externality" may be evident to a degree in the respective contributions of Jung and Pauli to their co-authored publication (The Interpretation of Nature and the Psyche, 1955) and in the light of their shared acknowledgement of the well-documented, and highly problematic, "Pauli effect".

Is an adequate "Theory of Everything" an integrative form of "globality" and associated "globalization"? Is it really held to be possible to envisage a "global" knowledge society -- comprehensively ordered by some "Theory of Everything" -- in which the educational challenges of comprehension, self-reference, imagination, ignorance and incompleteness are somehow "external" -- as with those of "copyright", discussed above?

Fundamental physics, as practiced, is seemingly totally irrelevant to the challenges of globalization (and "proud" of it), except through the provision of more energy to sustain more-of-the-same expansion of the "blastosphere", hopefully to new "islands of stability" (as argued in the main paper).

Harmonics of "globalization": a universal constant?

There is a long tradition across cultures of interest in the music of the spheres (musica universalis). Whilst is not usually thought to be literally audible, it has been understood as a harmonic and/or mathematical and/or religious concept (Jamie James, The Music of the Spheres: music, science and the natural order of the universe, 1993). This was a preoccupation of Kepler (David Plant, Kepler and the Music of the Spheres). As noted above, its archetypal nature provided a focus for the study of Wolfgang Pauli (The influence of archetypal ideas on the scientific ideas of Kepler, 1955).

Of interest is the extent to which any insight into "globality", engagement with it, or enactivation of it, is usefully understood through harmony. This is potentially crucial given the widespread accessibility of music and appreciation of it -- its comprehensibility in contrast to the often alienating representations of "globality" through text, mathematics or geometry.

The possibility can notably be explored in the light of the work of Ernest McClain (The Myth of Invariance: the origins of the gods, mathematics and music from the Rg Veda to Plato, 1976; The Pythagorean Plato, 1978; Meditations through the Quran, 1981). He stresses the role of invariant ratios defining pitches and tones and their significance for ancient cosmology (Musical Theory and Ancient Cosmology, 1994). With respect to the argument here, McClain has produced a valuable summary (The Harmonic Series as Universal Scientific Constant, 2010). He indicates:

Modern education emphasizes the harmonic series as establishing the natural foundation of quantification (numbered partials function as divisors of monochord string length), and so it is presented first as a common reference. Everything that follows concerns its colorful mythologizing in narrative allegory....What we hear as a 'musical' tone turns out to be, on physical analysis, a 'manifold' of partials with varying proportions of the total energy, so that hearing is always influenced by invisible and normally inaudible forces, a 'magic' beyond our control except as, in performance, we become the magicians. Thus sound functions as the greatest clue to psychic 'interiority' without ever fully disclosing its secrets.

The argument for exploring harmonic relations, as a means of rendering comprehensible (and engaging) complex global strategies, has been developed separately (A Singable Earth Charter, EU Constitution or Global Ethic? 2006). In a period when over one trillion dollars has been expended fruitlessly in a "battle for hearts and minds" in Afghanistan, the development of the drone offers a totally appropriate musical caricature of the inspirational value of the "martial music" deployed in that arena (Poetic Engagement with Afghanistan, Caucasus and Iran: an unexplored strategic opportunity? 2009; Strategic Jousting through Poetic Wrestling, 2009). Exploiting the caricature, it might be said that in the quest for "harmony", the capacity to allocate resources to eliciting insights from music has proven to be totally absent. Aside from an unprecedented demonstration of arrogant military incompetence, the future may see the focus on "drone" deployment as a demonstration of ignorance of rhythm and tone by a civilization that is effectively "tone deaf". NATO might be further caricatured as "No Adequate Tonal Operacy". This has become more curious when such insights might have been relevant to an elegant exist strategy.

Correspondence between blastosphere and spheroidal I Ching?

The main paper notes recognition that during embryogenesis the blastosphere numbers some 128 cells, namely 27-- following the initial cell division process. Such cells, especially following invagination, are recognized as having a "fate" in terms of their future differentiation and the forms to which they will variously contribute. Cell fate determination is a current preoccupation of developmental biology -- especially given the possibilities of stem cell research.

It is therefore intriguing that a fundamental representation of the patterns of change and distinction, namely the Chinese I Ching binary coding system, should be based on 64 hexagrams, namely 26. Although the hexagrams can be represented for convenience in circular form, of greater potential significance in relation to any correspondence with the blastosphere is the spheroidal representation of József Drasny, as shown below -- and previously reproduced separately (Designing Global Self-governance for the Future: patterns of dynamic integration of the netherworld, 2010). The relationships are at least suggestive of the psychodynamic tensions which might correspond to the biomechanical tensions basic to the development of the blastosphere.

Selected images of the Yi-globe of József Drasny
reproduced with permission from The Image of the Cosmos in the I Ching: the Yi-globe (2007)

Yi-globe of József Drasny Yi-globe of József Drasny
Yi-globe of József Drasny Yi-globe of József Drasny
These images point to the possibility of a correspondence between the spherical organization of conditions of change
and the more familiar understanding of how the Earth, as a globe, is exposed to light and darkness

Number games and speculations

The question of how sets of holons are configured (to form other, more general, holons) is summarized elsewhere with examples (Representation, Comprehension and Communication of Sets: the role of number, 1978; Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation, 1980).

The following table endeavours to "confront" various ways of approaching the spheroidal coherence of a psychodynamic analogue to the biomechanical pattern constraints in the blastosphere. The early prime number combinations are potentially significant in relation to harmonics and the capacity to hear such distinctions (as emphasized in the work of Ernest McClain mentioned above). They are also relevant in relation to the structure of regular polyhedra -- and the capacity to recognize the patterns associated with them. Both might however ensure that many rows in the table were "dropped" as basically irrelevant. The columns relating to data on social network size, notably in online communities, are necessarily approximate. Viable sizes, as noted in the discussion of the Dunbar  number in Annex B, may be highly dependent on the investment in "grooming" -- or its equivalent in intellectual discourse.

Any numerical constraint may be a matter of probability, with some "numbers" being more probable -- as suggested by the "magic numbers" of the perioidic table. Jean-Claude Perez has proposed a simple numerical formula computing the number of elements within every period, modelling the entire structure of the periodic system (Mendeleiev Periodic Table Prediction Equation, 1997-2008; Codex Biogenesis; les 13 codes de l'ADN, 2009). This could be interpreted as an approach to predicting patterns of "globality".

The column relating to polyhedra is associated with previous exploration of "polyhedral governance" (Towards Polyhedral Global Governance: complexifying oversimplistic strategic metaphors, 2008; Polyhedral Pattern Language: software facilitation of emergence, representation and transformation of psycho-social organization, 2008)

Juxtaposition of constraining patterns of potential relevance to "global" organization
(purely indicative and tentative)
Prime number factors Social network
(Dunbar, 2003)
Ultima Online
guild size freq.
(Allen, 2004)
Regular polyhedra
features (total:
Periodic table
of elements
"magic numbers":
nucleons (electrons)
2 3 5 7 Total
2 - - - 2 2%
(ca. 2)
2 (2)
- 3 - - 3
2x2 - - - 4
- - 5 - 5
2 3 - - 6
- - - 7 7
2x2x2 - - - 8 8
- 3x3 - - 9
2 - 5 - 10 (10)
2x2 3 - - 12
2 - - 7 14
- 3 5 - 15
2x2x2x2 - - - 16
2 3x3 - - 18 (18)
2x2 - 5 - 20 20
- 3 - 7 21
- - 5x5 - 25 4.6%
- 3x3x3 - - 27
2x2 - - 7 28 28
2 3 5 - 30
2x2x2x2x2 - - - 32
- - 5 7 35 37
(ca. 45)
2x2 3x3 - - 36 (36)
2x2x2 - 5 - 40
2 3 - 7 42
- 3x3 5 - 45
2x2x2x2 3 - - 48
- - - 7x7 49
2 - 5x5 - 50 9.3%
2 3x3x3 - - 54 (54)
2x2x2 - - 7 56 61
(ca 68)
2x2x2x2x2x2 - - - 64
2 - 5 7 70
2x2x2 3x3 - - 72
- 3 5x5 - 75 9.3%
(tuncated octahedron and cube)
2x2x2x2 - 5 - 80
- 3x3x3x3 - - 81 82
2x2 3 - 7 84 85
(ca. 44)
2 3x3 5 - 90
2 - - 7x7 98 98
(small rhombi-cuboctahedron)
2x2 - 5x5 - 100 20.9%
- 3 5 7 105
2x2 3x3x3 - - 108 109
(ca. 44)
2x2x2x2 - - 7 112
- - 5x5x5 - 125 122
2x2x2x2x2x2x2 - - - 128 11.6%
(ca. 30)
2x2 - 5 7 140 142
(small rhombicosi-
2 3 5x5 - 150 7.0%
(great rhombi-cuboctahedron)
2x2x2x2x2 - 5 - 160 157
(ca. 10)
2 3x3x3x3 - - 162 162
(great rhombi-cosidodecahedron)
2x2x2 3 - 7 168
2x2 3x3 5 - 180 9.3%
(ca. 7)
2x2 - - 7x7 196
(< 5)

The concern here is with the cognitive "patterns that work" in psychosocial systems -- corresponding ironically to the widespread quest for "practices that work" and for "strategies that work". It can be fruitfully assumed that they are intimately (if elusively) related to issues described by such terms as conceptual packaging, proximity and least elastic energy. As noted, the nature of the tantalizing quest for an explanation of the fine-structure constant has been well-document by Miller (2009) in relation to Jung and Pauli (and many others). As Miller notes with respect to that "cosmic" constant, speculations have included:

Comprehension challenge of a "cosmic number"?
1 / α = 8π(8π5/15)1/3 = 137.348
1 / α = (8π4/9)(245!/π5)1/4 = 137.036082

Given the above-mentioned remark by Pauli to the effect that "even the most modern physics lends itself to the symbolic representation of psychic processes", and the questions raised above by the many neglected dimensions, one might well speculate on the possibility of a psychosocial analogue, or reinterpretation, of the factors defining "α", notably in the last two cases.

Explored as an indicative pattern of psychosocial factors, what experiential meaning might their combination offer -- if that pattern "held" the otherwise problematic dynamics between psychosocial actors? It is somewhat ironic that the physical terms recur in a psychosocial context -- subject "matter", it does not "matter", and "energy" -- as discussed separately (Reframing Sustainable Sources of Energy for the Future: the vital role of psychosocial variants, 2006).

Factors relevant to a cosmic-global "constant"?
. Physical
e elementary charge minimal "charge" of "otherness" ?
ħ = h/2π reduced Planck constant ?
c speed of light in vacuum speed of comprehension?
ε0 electric constant or permittivity of free space maximal openness / permissiveness?
µ0 magnetic constant or permeability of free space psychosocial permeability?

Coulomb constant


Again, as noted by Miller, 137 can be written as a series of Lucas numbers related to Fibonacci numbers and therefore associated with the spiral) and with the golden ratio. Both Lucas and Fibonacci numbers produce the golden ratio. However, as he indicates:

Because all these numbers are related, any formula for 137 in terms of the Golden Ratio can be rewritten in terms of Fibonacci and Lucas numbers, though whether this is anything more than merely abstruse relationships between certain numbers is not clear. (p. 256) (emphasis added)

On the other hand that it was precisely such "abstruse relationships" -- even termed "moonshine" by mathematicians" -- which resulted in the discovery of the (then totally unexpected) connection between the monster group and modular functions. As discussed separately, the issue is what "correspondences" of this nature are to be considered credible under what conditions (Theories of Correspondences -- and potential equivalences between them in correlative thinking, 2007)? Given the "universal" importance attributed to the discovery of the Monster Group -- appropriately to be considered the most fundamental form of "globality" -- the question for non-mathematicians is its relevance to the challenges faced by a global society (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007).


Physics may indeed be currently a victim of "abstruse relationships" -- with the potential exception of musical harmony -- and largely irrelevant to the challenges of "globalization". However, given Pauli's statement "even the most modern physics lends itself to the symbolic representation of psychic processes", a case can be made for exploring "reinterpretations" of the psychosocial significance of the most challenging current applications of physics:

Crazy enough?

Physicists proudly refer to the much-quoted statement by Niels Bohr in response to Wolfgang Pauli:

"We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough."

To that Freeman Dyson added:

"When a great innovation appears, it will almost certainly be in a muddled, incomplete and confusing form. To the discoverer, himself, it will be only half understood; to everyone else, it will be a mystery. For any speculation which does not at first glance look crazy, there is no hope!" (Innovation in Physics, Scientific American, 199, No. 3, September 1958)

The question with regard to the much-sought "new thinking" with respect to "global govenance", and the "governance of globalization, is whether any theory is "crazy enough" -- as may well be essential.

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