Requirement for emirps and enantiodromia in navigating songlines

Memetic Analogue to the 20 Amino Acids as vital to psychosocial life? (Part #9)

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Emirps as indicative of "through the looking glass": The relationship between key primes in the pattern above is strikingly apparent, through their reversal into another prime -- namely as an emirp ("prime" reversed). This calls for particular comment with regard to the quest for psychosocial "route maps", and the challenge of navigating the cognitive transformations for which such "songlines" of the noosphere may call (From Information Highways to Songlines of the Noosphere: global configuration of hypertext pathways as a prerequisite for meaningful collective transformation, 1996; Noonautics: four modes of travelling and navigating the knowledge "universe"? 2006).

This paradoxical relationship -- a questionable mathematical curiosity in its own right -- derives significance from reversal of a number.What might that imply -- perhaps as might be suggested by research on the experience of doing mathematics (Philip J. Davis and Reuben Hersh, The Mathematical Experience, 1981). It recalls the extensive mythology associated with mirroring in a variety of forms -- including the need to "walk backwards" under certain conditions, recalling the ambiguity associated with the appreciation and deprecation of Knight's move thinking (Predictability and pattern-breaking: the Knight's move, 2011). Cognitive significance attached to such reversal includes that associated with the so-called mirror test of self-recognition.

As noted in the main paper, this may be understood in terms of a "cognitive twist". Its nature has been variously framed by the titles of the famed tales of Lewis Carrol (Alice's Adventures in Wonderland, 1865; Through the Looking-Glass, and What Alice Found There, 1871). These obscure recognition that his primary occupation was as a mathematician and logician. Such use of "looking glass" contrasts fundamentally with conventional strategic use of optical metaphors -- vision, image, focus, and the like -- implying a fundamental form of cognitive inversion, as separately discussed (Stepping into, or through, the Mirror: embodying alternative scenario patterns, 2008).

Reversal and cognitive twist: A route marked by emirps is therefore an indication that it cannot be effectively used without inversion. It requires a form of creative "cognitive magic" beyond what is now appreciated as lateral thinking. It is curious that issues of reversal are well understood in optics and the use of mirrors -- even though this understanding does not extend to their metaphorical use in strategy development. The reversal of digits is readily perceived as nonsensical in conventional mathematics, irrespective of any cultivation of that interest by mathematicians. Its meaning is much more readily associated with reversal of financial patterns, in retrograde music, and where there is any emphasis on reciprocation. Visually evoked pattern reversal is of significance in some human pathologies.

Encompassing such reversal, the wider implications of the theory of harmony, as modelled and widely understood through music, remain to be explored (Paradigm-shifting through Transposition of Key: a metaphoric illustration of unexplored possibilities for the future, 1999). Douglas Hofstadter points to this in his reference to the 30 Goldberg Variations in the music of Bach (Gödel, Escher, Bach: An Eternal Golden Braid, 1979). As he argues:

Every aspect of thinking, can be viewed as a high-level description of a system which, on a low level is governed by simple, even formal, rules...The image is that of a formal system underlying an 'informal system' - a system which can make puns, discover number patterns, forget names, make awful blunders in chess and so forth.

The paradoxical nature of the twist can be variously discussed and illustrated (Sphere eversion as guide to the cognitive twist of global introversion? 2013; Requisite cognitive inversion: higher orders of twistedness, 2014). Of particular interest is the account of a video produced by Jos Leys (Colin Marshall, The Genius of J.S. Bach's "Crab Canon" Visualized on a Möbius Strip in Music, Open Culture, 11 February 2013). As Marshall indicates:

You can follow the score, note for note, and then watch as the piece reverses itself, running back across the staff in the other direction. So far, so easy, but another layer appears: Bach wrote the piece to then be played simultaneously backwards as well as forwards. But prepare yourself for the mind-blowingcoup de grâce when Leys shows us at a stroke just what the impossible shape of the Möbius striphas to do with the form of this "crab canon," meaning a canon made of two complementary, reversed musical lines. Hofstadter had a great deal of fun with that term inGödel, Escher, Bach, but then, he has one of those brains -- you'll notice many Bach enthusiasts do -- that explodes with connections, transpositions, and permutations, even in its unaltered state.

As discussed separately (Cognitive "twist", 2007), of particular interest is the possibility of understanding the "cognitive twist" in terms of the adaptive cycle of complex systems -- especially with respect to how it might be navigated. Many helpful images of this are available on the web in two and three dimensions.

Familiarity with use of mirrors enabling a sense of self recognition, suggests that "route maps" of psychosocial life could well be experienced as having an analogous function. As designed above, they have a degree of resemblance to mandalas, with all that is implied in their construction and use. Of some relevance to global organization is the past use of the mandala as a political model indicative of patterns of distribution of diffuse power -- in contrast to current preoccupation with unified political power.

Netherworld: Lewis Carrol's phrase "down the rabbit hole" has recently been used in a widely distributed multimedia presentation to frame the recognition of an emerging reality based on a spiritual connection between quantum physics and consciousness (What the Bleep! Down the Rabbit Hole, 2006). The cognitive nature of going "down the rabbit hole" can be usefully explored in terms of the inversion characteristic of optical systems in representing and focusing an image.

As a form of "loopery" (discussed in the main paper), the process can be usefully explored through a torus (Now as the Ultimate Cognitive Strange Attractor: a continuing invitation "down the rabbit hole"? 2014). As indicated there, the drilled truncated cube has a toroidal form as one of the toroidal polyhedra.

The phrase is also somewhat reminiscent of the mythology regarding the encounter with Hades as it may be variously framed (Designing Global Self-governance for the Future: patterns of dynamic integration of the netherworld, 2010). Given the nature of the demonisation by "Us" of "Them", as highlighted in the main paper, this process merits attention -- especially increasing recognition of the role of the "black economy", corruption and criminal networks, otherwise readily ignored. Given the manner in which demonisation leads to weaponisation, that argument follows appropriately from an earlier discussion (Tao of Engagement -- Weaponised Interactions and Beyond: Fibonacci's magic carpet of games to be played for sustainable global governance, 2010).

In the light of the method employed to highlight the "routes" -- namely by first excluding the factor 2 -- questions can be asked about its relation as the first prime with enabling and sustaining the polarizing dynamic of "us and them" which has proven to be so problematic in global society. The method used is indicative of a means of transcending such polarization, as may be variously explored (Psychosocial Energy from Polarization within a Cyclic Pattern of Enantiodromia, 2007; Coherent Value Frameworks: pillar-ization, polarization and polyhedral frames of reference, 2008).

Enantiodromia: An emirp associated with a route map may therefore signal the requirement for enantiodromia (or its probability) in order to navigate the pathway in question. This strange process, named by Carl Jung, indicates that the superabundance of any force inevitably produces its opposite. When things get to their extreme, they turn into their opposite. In Jungian terms, however, a thing psychically transmogrifies into its Shadow opposite, in the repression of psychic forces that are thereby cathected into something powerful and threatening. This can be anticipated as well in the principles of traditional Chinese religion -- as in Taoism and yin-yang. This is discussed separately (Psychosocial Energy from Polarization within a Cyclic Pattern of Enantiodromia, 2007; Mirroring of self and other: enjoyment "through" the world, 2011).

Enantiodromia is consistent with a felt need to be able to shift "between worlds". Enantiodromia is therefore highly relevant to extremism and the extreme response it evokes -- the "Us" and "Them" dynamic which is a focus of the main paper. Each of these worlds is potentially associated with the cognitive organization framed by the pattern of categories of a particular polyhedron in the route map (Living as an Imaginal Bridge between Worlds: global implications of "betwixt and between" and liminality, 2011). The facility curiously resembles the familiar process of changing gear in an automobile, or perhaps shifting to a different broadcast channel -- a different wavelength.

Such metaphors highlight the sense in which it not a particular condition which is vital to the integrity of psychosocial living, but rather the capacity to shift between conditions and forms. Understood as "wholth", it is how the dynamic of that pattern is embodied rather than its static representation (Wholth as Sustaining Dynamic of Health and Wealth: cognitive dynamics sustaining the meta-pattern that connects, 2013; En-minding the Extended Body: enactive engagement in conceptual shapeshifting and deep ecology, 2003).

From 37 to 137 ? As noted above, of particular potential interest is the (questionable) relationship between 37 and 137, given the special significance attached to 137 in both mathematics and physics. The friendship of Carl Jung and Wolfgang Pauli, and their search for the meaning of 137 in science, medieval alchemy, dream interpretation, and the I Ching, is described by Arthur I. Miller (Deciphering the Cosmic Number: the strange friendship of Wolfgang Pauli and Carl Jung, 2009; 137: Jung, Pauli, and the Pursuit of a Scientific Obsession, 2010) and by Giorgio Piacenza Cabrera (The Mystery of 137: Calling for a new scientific relationship with interiority? Integral World). Somewhat curiously, given its association with the fine structure constant fundamental to the organization of matter, the hyped appreciation of 137 now corresponds to that for 37 indicated in the introduction (Sam Leith, The Answer to Life, the Universe and Everything, DailyMail Online, 19 June 2009).

Further comments of some relevance to the argument are developed by Peter Collins (The Number 137, Integral Science, 28 October 2009), with respect to the psycho-mathematical connotation as a symbol of integration, .notably:

From one perspective prime numbers can be viewed as the basic building blocks of the natural number system (which we literally view in a linear manner as stretched out on a straight line). However when we take the reciprocal of prime number a fascinating transformation is involved whereby a highly circular numberpattern is involved, with the same sequence of digits continually recurring in a predictable manner.

So for example when we obtain the reciprocal of 7 the six digit sequence 142857 continually recurs. This represents a fine example of a prime number whose reciprocal has a full periodic cycle. A full cycle is measured as one less than the prime number in question which in this case gives a cycle of 7 - 1 = 6. Though many other prime numbers e.g. 17, 61 and 97 exhibit full cycles in the digit sequence of their reciprocals, most prime reciprocals operate with a cycle of digits that is an exact fraction of the original prime number less one.

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