Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks

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Introduction

Given the beauty of symmetry as an attractive indicator of truth (cf Ian Stewart, Why Beauty Is Truth: the history of symmetry, 2007), and given the "monstrous" complexity of the highest forms of symmetry (cf Mark Ronan, Symmetry and the Monster: one of the greatest quests of mathematics, 2006), is it possible that the governance challenges of "globalization" call for a form of marriage between "beauty" and such a "monster" -- but of a quite unexpected order of complexity? Why is it assumed that the knowledge required is not of such an order of complexity?

Mathematicians exploring forms of symmetry now accept that any proof of a theorem relating to them may be hundreds of pages in length. That for the so-called "enormous theorem" is some 15,000 pages in length -- and far beyond the capacity of any single individual, however specialized. Unforeseen, "outrageous" implications of work have been specifically labelled "moonshine" by mathematicians challenged to explain them. This evolution in knowledge creation and substantiation, in domains potentially fundamental to the future management of complexity, raises questions about how knowledge emerging from such a process is to be rendered credible to more than a a small group of experts -- themselves challenged in that respect. Specifically how is that unforeseen connectivity, possibly vital to issues of governance, to be comprehended?

If the proof of mathematical conjectures, potentially vital to global governance of complexity, is recognized as acquiring such characteristics, what if proof of an essential insight were in future to take years to read and understand -- possibly a lifetime -- and how would the correctness of the proof be confirmed? How could it be credibly communicated? The length and complexity of the following argument is but a trivial example of the challenge !

The current psychosocial context is characterized by a multiplicity of belief systems, disciplines and cognitive frameworks. It is conjectured here -- in the light of the fundamental nature of the symmetries of the newly discovered Monster of symmetry -- that such conceptual systems are each coherent cuts or slices through the multidimensional complexity of such symmetry, effectively functioning as a Rosetta stone. Furthermore, it is argued that their complexity can best be communicated through symbols and metaphors with mnemonic characteristics. One thread in what follows is how such different cognitive styles interweave to create knowledge and ensure its comprehension and credibility -- despite its complexity.

This exploration arose from the "outrageous" possibility that the formulation of the special theory of relativity was to some degree influenced by patent office procedures and mindsets (Einstein's Implicit Theory of Relativity -- of Cognitive Property? Unexamined influence of patenting procedures, 2007). To what extent can "frames of reference" be considered as finite simple groups fundamental to higher orders of symmetry?

Whilst symmetry is intimately associated with truth, its beauty and elegance can also be fruitfully understood dynamically as a form of strange attractor for all human endeavour -- not only that of mathematicians ! High degrees of symmetry are therefore very powerful attractors and may be fruitfully associated with the drivers constituted by the highest human values (Human Values as Strange Attractors: coevolution of classes of governance principles, 1993). However, whilst Ian Stewart relates the beauty of symmetry to truth, elsewhere (Fearful Symmetry: is God a geometer? 1992) he emphasizes symmetry breaking as necessary to create structure -- with a completely symmetrical system having no structure, and arguably therefore no "truth". If the world is as complex as it appears, then lack of symmetry offers an alternative understanding of "truth" -- as with the beauty associated with the "harmony of imperfections", so valued by the Japanese.

Could the generation of value through socio-economic "development" be associated with some new understanding of the "velocity" of a frame of reference relative to other frames, with "acceleration" indicative of "development" plus "knowledge creation" (R&D)? Rather than appropriate policy as a typical form of cognitive property for which claims are made and upheld, should a degree of emphasis be shifted to the dynamics of the art of policy-making as a creative process (cf Poetry-Making and Policy-making: arranging a marriage between Beauty and the Beast, 1993)?

Inspired by the mathematical quest for the Monster of symmetry, this exploration is fundamentally about the relationship between connectivity (and coherence), conjecture, comprehension, credibility and communication -- namely to what degree a conjecture "holds" and for whom. This would appear to go to the root of current challenges of governance -- whether evidence-based or faith-based -- and in what it is then appropriate for people to express belief, as a "credo". It highlights the challenging relationship between "conjecture" and "projecture" in determining the nature of reality -- in a context in which much is conditioned by simplistic "projection". The length of this document also highlights related challenges of concision in explicating complexity.

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