Paradox of identity-confidence associated with inversion?

Alternating between Complementary Images of Coronavirus (Part #5)

---

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]

---

The tesseract animation is valuable in challenging the cognitive closure implied by the 2D schematics above. Given the widespread dependence on cubic architecture, both in buildings and knowledge organization, the challenge to comprehension can be further emphasized by the seeming impossibility of the "inversion of the cube". This can be understood as an articulation of the dilemma of outside-inside and inside-outside (Interface challenge of inside-outside, insight-outsight, information-outformation, 2017).

The explorations of the designer Paul Schatz led to discovery of the possibility inverting or everting the cube -- for which he is widely known, as illustrated by a number of videos:

• Charles Gunn:Â Schatz Cube Eversion (Vimeo, 25 April 2017;
• Daniel Wall:Â The Schatz Cube, or inverting cube (YouTube, 8 October 2010;
• Ryser Andreas:Â Invertible Cube (30 March 2013; Invertible cube)
• Dolf Perenti:Â Inverting Cube (YouTube, 13 July 2011).

Flexible card models are also marketed with commentaries (model; model) as with many wireframe models known as Hexyflex. His approach is described by the Paul Schatz Foundation as resulting in the construction of several machines, of which the most famous are the Turbula, the Inversina and the Oloid.

The potential of this approach is consistent with that widely framed in terms of the need for "thinking outside the box", as discussed separately (Time for Provocative Mnemonic Aids to Systemic Connectivity? 2018).

The cubic images above can then be considered as framing the challenge of how to think "outside" them. The argument of Paul Schatz is especially relevant in that so much of psychosocial organization is framed by the static architecture of the cube in 3D -- or through its compression into a square in 2D. This is the favoured modality for most explanatory tables. Through its 12-edges, the cube potentially offers clues to a relationship within any 12-fold pattern, but has not been extensively explored in that respect, although it is a feature of studies of oppositional logic, and a relationship to the 8-fold pattern valued in Chinese thinking (see image below left).

Reference to "inside the box" is considered analogous with the current, and often unnoticed, assumptions about a situation. The associated dynamics are consistent with arguments for fluidity in creative thinking (Douglas Hofstadter, Fluid Concepts and Creative Analogies: computer models of the fundamental mechanisms of thought, 1995). There is a case for recognizing the analogy implied by literal use of "the box" as a widely employed method of punitive solitary confinement, as vividly described by Shruti Ravindran (Twilight in the Box: what does solitary confinement do to the brain? Aeon, 27 February 2014). Widespread conventional dependence on a cuboid framework may well constitute an analogous form of a solitary confinement -- curiously relevant to the lockdown imposed in response to the COVID-19 pandemic.

The question is therefore whether the form that Schatz extracted from the cube -- through the dynamics of its possible eversion -- offers indications of a way of transforming conventional preoccupation with its static form. The following images offer some indication of this, as discussed separately (Eliciting the dynamics of the cube: reframing discourse dynamics, 2018).

Cubical representation of BaGua pattern of I Ching	Rotation of views of a phase in inversion of cube	Animation of selected phases in inversion of cube
Reproduced from Z. D. Sung, The Symbols of Yi King or the Symbols of the Chinese Logic of Changes (1934, p. 12)	Images derived from Charles Gunn (Schatz Cube Eversion, Vimeo, 25 April 2017) with the assistance of the author; interactive vrml version of centre model adapted by Sergey Bederov (Cortona3D)

Explorative 3D animations of the image on the left above are presented separately (Succinct mapping of multidimensional psychosocial dynamics? 2016).

In terms of the argument with respect to features hidden from the observer, this is especially evident in the case of the central image above. In that phase, the 24 sides are visible through the animation. But in the case of the static blue-green perspective or the static red-yellow perspective, only 12 sides are visible. Being hidden, the other 12 can only be inferred unless the structure was rendered transparent. In the reality of sociopolitical discourse opposing sides are never "transparent" to one another -- whatever the claims that are made. Cognitively each could be interpreted as a form of shadow for the other in the Jungian sense. The wireframe image on the right is indicative of the commercial product widely marketed as Hexyflex.

Schatz cube (solid and wireframe screen shot images) prior to inversion
	Sergey Bederov of Cortona3D has produced an interactive vrml version of the complete cycle of the original, with formulae kindly provided by Charles Gunn. Thanks to both. See video of the complete cycle

---

[Parts: First | Prev | Next | Last | All] [Links: To-K | From-K | From-Kx | Refs ]