Theories of Correspondences -- and potential equivalences between them in correlative thinking

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Annex to Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks (2007)

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Introduction

The displacement of one theory of correspondences by another epitomizes the relationship between two contrasting cognitive styles or mindsets. The displacement has been a feature of the Age of Enlightenment, and the Scientific Revolution, in which reason is promoted as the primary basis of authority. The displaced theory was a characteristic of the Renaissance and remains fundamental to many cultural perspectives in which aesthetic qualities are especially valued. Curiously, whereas the implications of the latter theory were, and continue to be, widely comprehended, the authoritative theory is known only to specialists. Neither theory figures as such in online encyclopedias despite the historical role of the displaced theory and the scientific merits of its substitute.

It could be inferred that the algebraic theory of correspondences of science has displaced the symbolist variant, much as some religions are notable for constructing their places of worship on the precise location of the deprecated "pagan" forms performing an "analogous" function in earlier times. Historically the displacement process has also been associated with physical violence done to the proponents of the older theory, notably in the form of witch hunts. More problematic is the psychocultural violence done to society in which a variety of cognitive styles is arguably desirable.

The exploration below is intended to clarify the contrasting implications of such cognitive styles for credible representations of connectivity -- especially in conditions where unsubstantiated conjectures within the dominant mindset are given serious consideration, despite being labelled "moonshine" and being comprehensible (if at all) to only the very few. This is intended to highlight the cognitive challenges implied by the Monster Moonshine Conjecture (Potential Psychosocial Significance of Monstrous Moonshine: an exceptional form of symmetry as a Rosetta stone for cognitive frameworks, 2007) and the extent to which its explorations surreptitiously call upon processes characteristic of the deprecated theory of correspondences.

The consideration given here to a variety of approaches to cognitive connectivity follows from much earlier work of the Integrative Knowledge and Transdisciplinarity Project which resulted from 1976 in some 600 profiles (plus bibliographic resources) on integrative and unitary concepts -- incorporated into successive editions of the Encyclopedia of World Problems and Human Potential.

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