Optical systems

In Quest of Mnemonic Catalysts -- for comprehension of complex psychosocial dynamics (Part #16)

---

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

---

If, as implied above, the geometry of the curves of the fundamental catastrophes (hyperbola, ellipse and parabola) is indicative of various perspectives on the complexity and interrelationships of the four attractors (problematique, resolutique, irresolutique and imaginatique), then insights may be gained from comparisons with optical systems for the various (corrective) lenses based on such curves. This possibility suggests several fruitful approaches to any comparison:

• lens design: as required to enable higher resolution of patterns that are:
  • cognitively "distant" or "larger" (by analogy with the telescope). (cf Joël de Rosnay. The Macroscope: a book on the systems approach, 1979)
  • cognitively "closer" or "smaller" than normal (by analogy with the microscope)
• corrective lens design: as required to correct vision (for myopia, presbyopia, astigmatism, etc), extended by analogy to the correction of defective "vision" as articulated in support of strategies, policies and future goals and achievements, notably in the promises so universally made by political and religious leaders as well as by futurists and artists
• optical systems design: as required in more complex variants of the above, in which a series of lens may be used to correct for distortions to achieve the degree of augmented resolution sought

Any such comparative exercise would clearly need to take account of the distinct properties of lenses based on the hyperbola, the ellipse and the parabola, or combinations thereof (see list of lens designs). It is also appropriate to note how, in mathematical terms, these curves are themselves understood as conic sections -- each being formed by intersecting a cone (namely a right circular conical surface) with a plane, but in different ways. The more obvious defining conditions that distinguish them can be combined into one condition that depends on a fixed point F (the focus), a line L (the directrix) not containing F, and a nonnegative real number e (the eccentricity). These suggest ways of distinguishing both distortions of cognitive perspective (posibly associated with "eccentricity") and the corresponding means by which they may be corrected, if appropriate. They also suggest relationships to the Möbius transformations discussed above.

Of particular interest is the role played by mirrors in optical system design, especially with respect to the high tolerances required for the successful manufacture of those required for the largest astronomical telescopes. Such design challenges are indicative of those that may be required in their cognitive analogues -- as well as raising the question of what patterns might be resolved by "cognitive instruments" of such exceptional nature. Curiously the mirror metaphor has been a theme of centuries of dialogue between the "sudden" and the "gradualist" approaches to enlightenment in Chinese thought (Peter N Gregory (Ed) Sudden and Gradual; approaches to enlightenment in Chinese Thought, 1991). This dialogue was notably triggered by two very simple contrasting poems based on a mirror -- by Shen-hsiu (606-706) and Hui-neng (638-713) in the Platform Sutra [texts] and whether it needed "cleaning".

Given the parallels, both mathematically and in design terms, between achieving resolution (and elimination of distortion) in processing information through optical systems with those based on electromagnetic radiation, two further possibilities merit consideration:

• radiotelescope design:
• electron-microscope design:

The technology developed for both very large radiotelescopes, and in order to focus light in very large solar power generators, is very suggestive in terms of the role and design of arrays of panels through which focus is achieved in each case. In the case of such radiotelescopes, this may be done through a single large parabolic array of reflecting panels or through an array of interconnected smaller parabolic arrays (possibly separated by a considerable distance to achieve a longer baseline). In the case of power generation, a very large number of flat mirrors may be arrayed parabolically (and continually moved) to focus sunlight on a central boiler unit.

The strategic challenge faced by humanity in managing the problematique, the resolutique, the imaginatique and the irresolutique may be understood as dependent on the insights of the many "disciplines" that have emerged in response to particular concerns. If this is the case, it may be fruitful to consider how appropriate "interdisciplinarity" or "transdicsiplinarity" could be understood in terms of the appropriate configuration of "cognitive arrays" analogous to those required for radiotelescope or solar power generators. In both cases the challenge is how to bring insights to a common "integrative" focus -- whether to achieve understanding of larger patterns or to mobilize human energy resources. One of the merits of this approach is that it allows for the "linear thinking" natural to many disciplines, cognitive frameworks and modelling preferences -- whilst ensuring that these many "flat" perspectives are appropriately arrayed in response to the non-linear knowledge management requirements of the larger strategic challenge. "Non-linear" would here be contrasted with "flat" in the epistemological shift to self-reference as notably argued by Douglas R. Hofstadter (Gödel, Escher, Bach: an Eternal Golden Braid, 1979).

Such a possibility challenges the adequacy of efforts to configure sets of topics (and their associated disciplines, problems and strategies) as a tabular matrix rather than a nested list (cf Functional Classification in an Integrative Matrix of Human Preoccupations, 1982). These may be essentially inadequate because of the absence of "curvature" required for an integrative focus as argued elsewhere (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006; Spherical configuration of categories to reflect systemic patterns of environmental checks and balances, 1994). Such a need for some form of integrative "curvature" may be of even greater relevance where the "disciplines" are understood as belief systems (cf Tuning a Periodic Table of Religions, Epistemologies and Spirituality -- including the sciences and other belief systems, 2007).

---

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