From "on the square" through "in the box"

Fibonacci Spiral in 3D Framing Psychosocial Phyllotaxis (Part #11)

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On the square: Given the widely documented role of Freemasonry in relation to governance (irrespective of the suspicions of conspiracy theorists), it is intriguing how the key symbolism of that world view specifically emphasizes the square and the compasses, often embedded within a circle. Considerable emphasis is placed on the implications of the phrase being "on the square" -- a phrase variously adopted outside that context with an indication of morality.

The process of construction of an approximation to the Fibonacci spiral in 2D could be understood as exemplifying use of the symbolic instruments of Freemasonry. However the distinction meriting exploration is between such design and construction, understood as explaining subtle insight, and the experiential embodiment of that insight.

The former is a matter of description, whereas the latter has cognitive implications. As description, the emphasis is on "isness" -- even reification, or a reflection of subtlety into a form of cognitive "flatland". A Flat Earth perspective is variously deprecated as the epitome of misunderstanding, although a variety of arguments can be presented in support of Flat Earth theory. Wikipedia notes, for example, that despite the scientific fact of Earth's sphericity, pseudoscientific flat Earth conspiracy theories are espoused by modern flat Earth societies and, increasingly, by unaffiliated individuals using social media. Unusually, Wikipedia includes al page on Why Wikipedia cannot claim the Earth is not flat.

On the other hand, Scientific American includes an argument by Davide Castelvecchi (What Do You Mean, The Universe Is Flat?, Part I, 25 July 2011; Part II, 31 July 2011). This frames the conceptual dilemma through the following seemingly inconsistent statements which are associated with scientific theories:

As discussed by Davide Castelvecchi, a key issue is the meaning to be associated with "exist" and "existence". How does a person exist in a flattened condition? This is a matter explored from fictional mathematical perspectives (Edwin Abbott Abbott, Flatland: a romance of many dimensions, 1884; Ian Stewart, Flatterland, 2001; Dionys Burger, Sphereland: a fantasy about curved spaces and an expanding universe, 1965; A. K. Dewdney, The Planiverse, 1984).

Many of the cognitive challenges are evident in the follow-up to Alice in Wonderland (1865) in which the Looking-glass world is set out like a giant chess board (Lewis Carroll, Through the Looking-Glass, and What Alice Found There, 1871). The characters represent chess pieces; Alice starts out as a pawn, and the action in the story emulates the moves of a real chess game.

Given the challenge framed by "getting into orbit" around the globe, how does a person achieve the psychological equivalent? Discussion of existence is notably reframed by the suggestion from physics that reality calls for explanation in terms of quantum mechanics, with implications for international relations as ably argued by Alexander Wendt (Quantum Mind and Social Science: unifying physical and social ontology, 2015). The cognitive flatland, into which people are increasingly dumbed down, might then be understood as a form of frozen reality -- a kind of cognitive standing wave.

Such a perspective frames globality in a totally radical manner, as explored separately (Encountering Otherness as a Waveform -- in the light of a wave theory of being, 2013;  Being a Waveform of Potential as an Experiential Choice: emergent dynamic qualities of identity and integrity, 2013). From a "toroidal perspective", it might then be provocatively asked whether a "global life" worth living? (Imagining Toroidal Life as a Sustainable Alternative: from globalization to toroidization or back to flatland? 2019).

In the box: Use of the square metaphor, with its only too evident boundaries, offers one understanding of being trapped. The 3D analogue of a cube offers one sense of perspective on life "on the square" -- experienced as flatland. However the cube as a metaphor also offers the sense of being "boxed in", with a corresponding sense of claustrophobia. Both square and cube frame the aspiration to freedom, however that is to be understood in terms of escape or flight. The challenge is partially recognized through widespread reference to the requirement for "out-of-the-box thinking".

The cognitive argument can be taken further by reference to the knight's move in chess -- and the keima in the Japanese equivalent to chess (shogi), or the ma in the Chinese equivalents of  xiangqi and janggi. In each case a move passes through two squares in one direction across the board, followed by a shift to an orthogonal square. The move implies a degree of shift out of the plane of the square, offering a degree of overview. Ironically the sense in which this implies valuable "oversight" (as implemented in institutions) is curiously undermined by the alternative interpretation of negligence (regrettably evident in official capacities).

The movement of the knight has long been associated with creativity and strategic surprise (Knight's move thinking: appreciated or deprecated, 2012). Curiously, but most appropriate to this argument, "knight's move thinking" is defined by the medical profession as a thought disorder denoting a lack of connection between ideas, namely a loosening of associations.

Considered to be similar to derailment of thought, it is characterized by odd, tangential associations between ideas that lead to disruptions in the smooth continuity of speech. The association between ideas is interpreted to be illogical, notably wandering between various trains of thought. The Knight's move is then a metaphor for the unexpected, and illogical, connections between ideas. The illogicality of the loosening of associations, which is found in schizophrenia, is contrasted with the flight of ideas which characterises hypomania. "Knight's move thinking" therefore features in the early diagnosis of schizophrenia.

The knight is however part of the emblem for the US Psyops as a traditional symbol of "special operations" -- signifying the ability to influence all types of warfare. It featured as the name of a German military operation (Operation Rösselsprung) to kill or capture Josip Broz Tito at Drvar during World War II. With respect to business strategy, Richard Pech and Greg Stamboulidis make the point that:

Utilizing a chess metaphor, they each deployed a knight's-move strategy, leaping forward and sideways in a manner that has caught, and continues to catch their linear-thinking competitors by surprise. (How strategies of deception facilitate business growth, Journal of Business Strategy,  31, 2010, 6)

In a discussion of the current disruptive dynamics of global governance, termed "monkeying" for the purpose, a case was made for Reframing "monkeying" in terms of Knight's move patterns (2011). Both the creative and problematic implications of the argument are developed and illustrated separately (Swastika as Dynamic Pattern Underlying Psychosocial Power Processes: implicate order of Knight's move game-playing sustaining creativity, exploitation and impunity, 2012).

It is however the ancient Chinese game of Go Weiqi, otherwise known as Encirclement Chess, is suggestive of further clues to be derived from the geometry of the construction of the 2D Fibonacci spiral approximation. The successive squares in that construction, distinctively proportioned according to the golden ratio, embody an encircling process consistent with a 3-step pattern like that of the knight's move. Whether understood as achieving a kill (capturing some form of otherness), or achieving an insight ("capturing light"), it is the successful engagement with otherness (even closing a deal) which is highlighted.

The subtlety of the encircling process of go, in contrast to that of chess, is usefully highlighted by the analysis of the Vietnam War by Scott Boorman (The Protracted Game: a wei-ch'i interpretation of Maoist revolutionary strategy, 1971). Of relevance is the study by Li Ma (Xiangqi vs Chess: the cultural differences reflected in Chinese and Western games, Open Journal of Social Science, 9 March 2020).

Given the contrast between the 2D square and the 3D cube, the argument can be taken further in the light of the variants of three-dimensional chess. In that case any encircling engagement is understood in terms of:

• a rook moves through the six faces of a cube in any rank, file, or column.
• a bishop moves through the twelve edges of a cube.
• a knight makes a leap in 3D, comparable to one step as a rook followed by one step as a bishop, thereby enabling it to control 24 different cells from the centre of the game board.

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