Necessary tuning of any periodic representation (original) (raw)

Eightfold Configuration of Nested Cycles of Cognitive Transformations (Part #9)

The concern here has not been to clarify attributions of cognitive transformations within any cluster but rather to consider how the various clusters might be related as a framework within which such attributions could be more fruitfully considered. This is usefully understood as a process of "tuning" relying on a sense of harmony as separately discussed (Tuning a Periodic Table of Religions, Epistemologies and Spirituality -- including the sciences and other belief systems, 2007). Any harmony may also be visual in terms of the mnemonic qualities of the symmetry in the columns and rows of the images above.

Of particular interest to the tuning process are the insights offered by the Chinese eightfold Ba Gua system. This is valuable both through the linear encoding used, through the categories associated to it, through the transformations recognized between them, and through the metaphors by which they are variously rendered comprehensible. The eight are traditionally organized as distinct "houses" -- of relevance to the further articulation echoed in the eightfold pattern of periods in the table (cf. Organization of I Ching hexagrams in terms of traditional "houses", 1995). The distinctions may be notably explored through music (cf. D. C. Harvey, The I Ching Hexagrams Directly Translated Into Music, Math, Geometry and the Zodiac Calendar).

The cognitive approach to tuning is further clarified by the widespread enthusiasm for solving the puzzles exemplified by sudoku and Rubik's Cube, and their more complex variants. This clarifies the sense in which the columns and rows of a table may be shifted in relation to one another in the tuning process. An analogous process could be envisaged in relation to attributions within the pattern of circles. With respect to tuning, it is also of interest how a form of table organization is evident in the fret of a stringed instrument -- a tabular constraint which is transcended through the skills of the player. This interpretation helps to make the point that there are a variety of choices possible in tuning systems -- suggesting that attributions may well be made in different ways according to preferences. There are many techniques for theoretical comparison of tunings, utilizing mathematical tools such as those of linear algebra, topology and group theory.

There is a sense, worthy of some suspicion, that the number pattern of the periodic table is (unconsciously) "played with" in the derivation of coherence of psychosocial significance:

26 (namely 3x8+2) as the number of letters considered necessary for the Latin alphabet
9 (as 18/2 or 8+1) as promoted in the enneagram of personality types
16 (as 2x8 or 18-2) as promoted in the Myers-Briggs Type Indicator
12 (as 10+2) as favoured in a variety of systems of organization (cf. Checklist of 12-fold principles, plans, symbols and concepts, 2011)
6 (as 8-2)
10 (as 18-8 or 8+2)

An interesting tuning challenge derives from the combination of considerations of the 8-fold Ba Gua pattern, with those suggested above in relation to electronic components/functions, and with those deriving from cybernetic insights. The work on the Chinese articulation, from a cybernetic perspective, by Maurice Yolles and colleagues is of particular relevance (Toward a formal theory of socioculture: a yin-yang information-based theory of social change, Kybernetes, 2008). Especially intriguing is the relation between the 8-fold Ba Gua pattern and the 5-fold Wu Xing pattern. The comparison of the latter with that of the 5-fold Pythagorean pattern of Hygiea is of particular interest in relation to understandings of health and systemic viability, by extension (cf. Cycles of enstoning forming mnemonic pentagrams: Hygiea and Wu Xing, 2012; Potentially health developmental integrity from 5-fold symmetry, 2012).

The musical metaphor is helpful in reframing the contrast between the horizontal and vertical axes -- given the distinction made between "technicality" and "musicality" in assessing musical performance in competitions. This offers an understanding of preoccupations with respect to the horizontal axis as appreciation of the tangibles of convention, most notably in the form of consumerism. Those of the vertical axis then relate to the imaginal dimension fundamental to a sense of fulfilment and meaningful quality of life.