-- / --
This forms part of a more general discussion, where relevant references are located (Way Round Cognitive Ground Zero and Pointlessness: embodying the geometry of fundamental cognitive dynamics, 2012; see alternative table of contents).
The following anecdotal accounts offer valuable insight into human engagement with reality:
People are readily characterized as "living in a goldfish bowl", a "bubble reality", or a carefully constructed cocoon -- whether made by the inhabitant (even unconsciously) or specially "spun" for them by others. As noted above, living within such a notional sphere, as one's "world", offers a degree of valuable coherence, perhaps to be understood as a "sphere of inluence". The credibility and viability of such experience is enhanced by the increasing capacity to provide a closed electronic boundary to that sphere by viewing the external world primarily (if not solely) through media -- rather than through glass, as in the case of a vivarium.
More intriguing is the sense in which the notional boundary to that world is increasingly a reflective mirror rather than transparent. Whilst extreme, this is suggested by inhabiting a sphere in which all surfaces effectively offer distorting reflections of "oneself" -- if only through the collection of objects in the cocoon, valued as reminders of one's past and aspirations for the future, whether chosen consciously or unconsciously.
The implication of living within a goldfish bowl may indeed be comforting, as implied by the notion of cocooning. It may however be a matter of concern, whether to those who design such vivariums for others or for those who inhabit them. The limitations of inhabiting such a "spherical" world may then evoke a desire for more extensive, even "alternative", experience -- however that might be understood. The second anecdote indicates how the circularity of the spherical reality may be transformed by placing a "rock" at its centre to engender another dynamic. Like the carp, one then "swims" within what is effectively a toroidal form -- a toroidal world.
An extensive mathematical analysis of the possibility of introducing such an "obstacle" within a pattern of communication is offered by Ron Atkin (Combinatorial Connectivities in Social Systems; an application of simplicial complex structures to the study of large organizations, 1977; Multidimensional Man; can man live in 3-dimensional space ? 1981) -- as summarized elsewhere (Social organization determined by incommunicability of insights, 1995). His research focused on communication within academic committes in a university. As in the case of the carp, the key to the toroid-engendering operation of the obstacle within the communication geometry is that it should be such as to be beyond the collective comprehension of those functioning within that world -- in this case the committee engaged in circular communication. A "global" civilization may be understood in such terms, through its essentially "circular" precoccupation with "problems" it is necessarily unable to understand (Web resources on "breaking the cycle", 2002).
Of particular interest is the framing of strategic vision within such a toroidal context. Clearly motivation is then variously engendered by:
Following from the discussion above, a toroidal pathway through time offers a way of framing forms of identity and engagement with reality over time:
As noted above, of particular interest are the possible transformations between these different senses of identity, and the possible pattern of alternation between them according to circumstances. The former may be understood in terms of "shapeshifting" and the latter may offer a sense of "meta-identity" (Secret sharing, Shapeshifting and Embodiment, 2011; En-minding the Extended Body: Enactive engagement in conceptual shapeshifting and deep ecology, 2003).
As summarized in the Wikipedia torus profile, there exist a number of transformations of the torus itself which are suggestive of other ways in which individual and collective identity might be imaginatively framed in engaging with reality
The forms above each suggest a locus for the observer, the invariance of whose identity is sustained through the form. This is more evident when the observer can identity with explicit features of the geometry -- a "point" or a "line" (as used metaphorically). It is less evident when the observer is best understood as at a virtual centre of a "circle of friends", for example. Such virtuality of identity notably occurs in the case of a polyhedron or a sphere -- however much it is "defined" and articulated by the surrounding geometry with which it may partially or momentarily identity. Being implicit, or potentially understood as of a higher order, it may be to a degree unconscious -- or only occasionally a cognitive focus. *** Intimations
The identity of the observer is further "transformed" in relation to the torus. Various forms of identity, of a "lower" geometrical order, are noted above "within" the torus. More intriguing is the sense of identity sustained by the torus "as a whole" (or "as a hole") -- where the principal axis passes through a central "hole" around which the tubular form is configured as a context for the "lower" orders of identity. The identity of the observer is then associated with that virtual "point" or with the axial "line". The distinction between "higher" and "lower" is problematic in that those "lower" forms, potentially travelling through the torus, might in fact include a torus (as with a smoke ring travelling along a tube). This suggests the relevance of a paradoxical perspective in which "higher" and "lower" may be indistinguishable through a form of "self-nesting".
** drilled toroid
As noted above, the geometry obscures the dynamics of which it may be a static approximation (as with a standing wave). In this sense the torus as a whole is a simplistic description of vortical motion (as with a smoke ring). Identity may then be associated with an "upwelling" fountain-like dynamic (or its reverse). The forms of identity within the torus (noted above) necessarily require similar consideration in terms of the dynamics "delineated" by the geometry in each case.
Such considerations give form to the cognitive challenge as to how identity is bounded and to the fundamental question of whether identity, as the locus of observation ("viewpoint"), is "inside" or "outside" the form.
The various geometrical transformations of the torus provide a metaphoric language through which to explore the locus of identity -- and the more subtle possibilities of its non-locality. The paradoxical challenge is well-illsutrated by the Mobius strip. Given the widespread use of "side" to distinguish political identification and adherence, the Mobius strip shows how the asserted distinction between two apparently distinct "sides" may be illusory, if the strip is configured into a circular form -- with a twist.
The argument can be fruitfully extended to the distinction of identity in terms of "insider" and "ousider" -- as might be associated with 3D geometrical forms. As illustrated by the Klein bottle, this has been the focus of the extensive work of Steven Rosen (Topologies of the Flesh: a multidimensional exploration of the lifeworld. 2006; Science, Paradox and the Moebius Principle: the evolution of a "transcultural" approach to wholeness, 1994). Such paradoxical forms are examples of non-orientable surfaces, namely those in which notions of left and right cannot be consistently defined. The Klein bottle offers an example of a form in which the notion of a "centre" offering a "viewpoint" for an observer (and a locus for identity) is effectively lost, potentially implying a "distribution" of identity over the surface. When the Klein bottle is represented and understood dynamically, this is suggestive of a paradoxical cyclic identity.
Topological complexification of the Klein bottle offer interesting challenges to assumptions regarding the invariant nature of the observer and any association of identity with symmetry in a dynamic context. As implied separately (Metaphorical Insights from the Patterns of Academic Disciplines) there is every reason to suspect that it is possible for identity to engage otherwise with reality -- as explored further (Beyond the Standard Model of Universal Awareness, 2010).
*** Kundalini / spin
** bear witness
NB: See separate presentation of relevant bibliographical references.
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