Varieties of connectivity

Theories of Correspondences -- and potential equivalences between them in correlative thinking (Part #10)

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The various forms of correspondence, and the vigorous views regarding their merit in the organization of any collectivity, may usefully focus attention on the varieties of connectivity as highlighted by the following examples and contexts:

• academic disciplines
  • natural sciences, exemplified by the standards promoted through the Skeptical Inquirer by the Committee for Skeptical Inquiry
  • social sciences, typically scorned as "unscientific" by the natural sciences, and exemplified by the issues raised in the Sokkal Affair
  • other "disciplines", as deliberately recognized by Paul Feyerabend (Against Method: Outline of an Anarchistic Theory of Knowledge, 1975)
• commerce, exemplified by the adage "the client is king", irrespective of any judgements about the client's sense of connectivity
• aesthetics: exemplified by the variety of aesthetic preferences in designed relationships, irrespective of judgements about taste
• elective affinities and affective relationships: exemplified by romance, irrespective of judgements regarding the viability of such relationships
• faith and belief: exemplified by religious belief, irrespective of judgements as to their foundation -- especially highlighted by faith-based science (creationism, intelligent design, etc)
• ecophilosophy/ecopsychology: exemplified by a profound experiential relationship with nature (Gregory Bateson, Mind and Nature: a necessary unity, 1980; David Abram, The Spell of the Sensuous: perception and language in a more-than-human world, 1996; Alan Drengson, Ecophilosophy, Ecosophy and the Deep Ecology Movement: An Overview)

Especially interesting, again illustrated by the Sokkal hoax, are issues of:

• deliberate misconnectivity: as practiced by Sokkal and in any commercial transaction dependent on bluff -- or more generally in any game, including the strategic bluff that is fundamental in warfare, and the camouflage techniques employed by predator and prey in nature
• inadvertent ignorance: as exemplified by the pronouncements of scientists -- subsequently discredited by the advancement of knowledge; especially interesting are cases of groupthink, notably those within the intelligence community (cf Groupthink: the Search for Archaeoraptor as a Metaphoric Tale: missing the link between "freedom fighters" and "terrorists", 2002)
• dependence on authority and accredited expertise: as exemplified in the case of mathematical proofs requiring many years of education to comprhend, and hundreds of pages to elaborate
• superstition as explanation: as exemplified by the criticism of the Skeptical Inquirer, which has nevertheless been unable to stem the widespread belief in what it rates as superstition (astrology, UFOs, etc) -- where others are satisfied by the quality of connectivity they see as evidence
• placebo explanation: as exemplified in medication, where what is believed to offer a remedy does indeed offer therapeutic benefit, or is felt to do so; the placebo effect has been applied metaphorically to a variety of situations
• pre-logical axes of bias: as exemplified by supposedly "rational" debates between "schools of thought" within academic disciplines, even the natural sciences (cf W T Jones, The Romantic Syndrome: toward a new method in cultural anthropology and the history of ideas, 1961) -- possibly to be substantiated by genetic disposition in favour of particular styles of explanation

Metaphorically extreme forms of connectivity might be illustrated by contrasting an elephant and a migrating bird (or flying squirrel). The connectivity considered viable for an elephant in travelling from A to B, is quite distinct from that considered viable by a migrating bird. The former, like the "monstrous" komodo dragon, is unable to travel between continents. How subtle may be the pattern of connectivity that enables meaningful travel within a collectivity? (cf Walking Elven Pathways: enactivating the pattern that connects, 2006)

A trap is a function of the nature of the trapped (Geoffrey Vickers. Freedom in a Rocking Boat : Changing values in an unstable society, 1972)

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Moonshine Anecdotes

Those involved in the Atlas project, which was central to the process through which the Monster sporadic group was detected, were notably fond of word and number games -- to the point of seeing patterns in the names of the participants in the project. It is therefore intriguing to look at the name chosen by two of their members for the key paper announcing the outrageous conjectured implications of the Monster (John Conway and Simon Norton, Monstrous Moonshine, Bull. London Math. Soc., 1979). Given the 26 exceptional sporadic groups, and the 26 dimensional bosonic string theory through which the truth of the Monstrous Moonshine Conjecture was finally demonstrated in 1998, it is curious that: the letters of Monstrous + Moonshine total to 18, which equals the number of countably infinite families of finite simple groups (to which the Monster and 25 other sporadic groups are exceptions) the initials of Monstrous and Moonshine, the thirteenth letter of the alphabet, total to 26 the letters of Monster + Moonshine + Conjecture total to 26 the closest packing of spheres (12) around a central sphere, with a second such pattern, totals 26

Given the uncontroversial, Apollonic, beauty of symmetry, it might be expected that psychocultural dynamics would engender a Dionysian counter-part onto which negativity could be comfortably projected. To a large extent this role has been well-performed by the proponents and practitioners of the symbolist theory for the benefit of the fundamentalists of convention, whether rationalist or religious. There is therefore a curious symmetry to the facts: that a culmination of a mathematical quest into the fundamentals of symmetry, exemplifying the algebraic theory of correspondences, should have given rise to what has long been termed a Monster by its discoverers (and contrasted with a Baby Monster) that, almost from the origins of the mathematical quest, there emerged a prime exemplar of Dyonisian symbolism at the centre of of one of its most influential "laboratories" -- the Hermetic Order of the Golden Dawn -- made famous by such as W B Yeats. The irony is that the individual was variously dubbed the "Great Beast" and the "Monster", but produced and maintained one of the major tabular classifications of the symbolist theory of correspondences. From the perspective of archetypal psychology, critical thinking and cognitive hygiene, there is however a real challenge to distinguish and assess the various qualities and processes in play for any meaningful understanding -- especially given the appreciation widely accorded to mnemonic devices embodying those insights.

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