Classification of "projections" versus Classification of "conjections"?

Envisaging NATO Otherwise -- in 3D and 4D? (Part #11)

Projections in cartography: Many sources enadeavour to clarify the types of projection in cartography. A fundamental projection classification is based on the type of projection surface onto which the globe is conceptually projected. The projections are described in terms of placing a gigantic surface in contact with the earth, followed by an implied scaling operation. These surfaces are:

cylindrical (e.g. Mercator): these map regularly-spaced meridians to equally spaced vertical lines, and parallels to horizontal lines.,
conic (e.g., Albers): these map meridians as straight lines, and parallels as arcs of circles.
azimuthal (projections onto a plane, e.g. stereographic): these map meridians as straight lines and parallels as complete, concentric circles. They are radially symmetrical. In any presentation (or aspect), they preserve directions from the center point. This means great circles through the central point are represented by straight lines on the map..

Many mathematical projections, however, do not neatly fit into any of these three conceptual projection methods. Hence other categories have been described in the literature, such as:

pseudocylindrical: these map the central meridian and parallels as straight lines. Other meridians are curves (or possibly straight from pole to equator), regularly spaced along parallels.
pseudoconical: these represent the central meridian as a straight line, other meridians as complex curves, and parallels as circular arcs.
polyhedral maps: these maps can be folded up into a polyhedral approximation to the sphere, using particular projection to map each face with low distortion.
retroazimuthal: these emphasize the shortest route between locations
pseudoazimuthal: these map the equator and central meridian to perpendicular, intersecting straight lines. They map parallels to complex curves bowing away from the equator, and meridians to complex curves bowing in toward the central meridian. Listed here after pseudocylindrical as generally similar to them in shape and purpose.
other: these are typically calculated from formula, and are not based on a particular projection

Properties and implied distortions distinguished include:

conformal (orthomorphic): Preserves angles locally, implying that local shapes are not distorted.
equal area (equiareal, equivalent or authalic): Areas are conserved.
compromise: Neither conformal nor equal-area, but a balance intended to reduce overall distortion.
equidistant: All distances from one (or two) points are correct; a trait possible only between one or two points and every other point.
azimuthal (or zenithal), a trait possible only from one or two points to every other point
gnomonic: All great circles are straight lines; preserving shortest route

Projections in psychology: As noted above, psychological projection is recognized as a process whereby humans defend themselves against their own unconscious impulses or qualities (both positive and negative) by denying their existence in themselves while attributing them to others. Different schools of psychology and psychoanalysis tend to define projection in distinctive ways. A limited number of examples are offered but it is seemingly not the case that there is any classification of modes of projection in any way analogous to projection in cartography (John M. Grohol, 15 Common Defense Mechanisms, PsychCentral, 17 May 2016). With respect to NATO, it is interesting to note the shared emphasis on defence.

Ironically, given the clear distinctions made in cartography, there is a case for exploring the distortions in cartographical projections as a means of distinguishing and "mapping" the distortions in psychological projection. Any such exploration could necessarily be informed by the more systematic approach to cognitive biases and their classification (see List of cognitive biases). The Wikipedia description includes a remarkable Cognitive Bias Codex as reproduced below. This clusters some 180 biases into 20 subcategories clustered into four main categories:

Cognitive Bias Codex
(link to larger original version)

Categorized by Buster Benson using an algorithmic design by John Manogian III derived from Wikipedia data

Such a document is necessarily of value with respect to exploring collective cognitive bias, as might be evident in the case of NATO and its opponents (Robert Cordray III and Marc J. Romanych, Mapping the Information Environment, Joint Information Operations Center, 2005; Eric R. Mandel, Cognitive bias and UNSC Resolution 2334, Jerusalem Post, 3 January 2017; J. T. Byford, Conspiratorial explanations of the Nato bombing of Yugoslavia: cognitive bias or an ideological tradition. In: International Society for Political Psychology, Annual Meeting, Berlin, July 2002).

However, whilst the design of the above document necessarily emphasizes the "entropic" tendency towards some form of bias (at any point on the circumference), it offers no clues as to the nature of the reverse "negentropic" process -- framed in the argument above as "conjection". Ironically the form of the diagram echoes that of many traditional mandalas -- which have that preoccupation but call for other considerations. In the light of the cartographic approaches to projection, it is intriguing that the above design uses an "algorithmic" approach.

Forms of transdisiplinarity as indicative of the "conjection" process: Reference was made above to the various flavours of interdisciplinarity as a conventional surrogate for "conjection". It might therefore be asked how integrative cognitive procsses could be fruitfully clustered and classified. One early exercise identified some 600 such "understandings" but explicitly avoided any classification (Integrative Knowledge and Transdisciplinarity Project: overview).

A recent exercise collected 43 methods from a number of transdisciplinary research projects dealing with a variety of research topics (Matthias Bergmann, T. Jahn, T. Knobloch, W. Krohn, C. Pohl, and E. Schramm, Methods for Transdisciplinary Research: a primer for practice, 2012). These were then grouped into seven classes following an epistemological hierarchy -- starting with methods in the narrower sense, progressing to integration instruments:

Integration through conceptual clarification and theoretical framing
Integration through research questions and hypothesis formulation
Screening, using, refining, and further developing effective integrative scientific methods
Integrative assessment procedures
Integration through development and application of models
Integration through artifacts, services and products as boundary objects
Integrative procedures and instruments of research organizations

Missing from such an approach is any sense of the nature of transdisciplinary insight. What is the "transdisciplinary experience", given use of an analogous expression with respect to mathematics (Philip J. Davis and Reuben Hersh, The Mathematical Experience, 1981, with a chapter on the Varieties of Mathematical Experience; Douglas R. Hofstadter, Metamagical Themas: questing for the essence of mind and pattern, 1985; Wolff-Michael Roth, Phenomenology and Mathematical Experience, Linguistics and Education). How is this to be related to the argument of George Lakoff and Rafael Nunez (Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2001).

The latter argument reinforces the implication that "conjection" may be more intimately related to a sense of integrative comprehension otherwise understood. This was the original preoccupation in collecting some 4,400 such approaches, again explicitly avoiding any classification (Human Potential and Development Project). Such classification, through the AQAL pattern, has been a notable preoccupation of the integral theory articulated by Ken Wilber (The Spectrum of Consciousness, 1977).

Despite the extensive literature cited above, missing would appear to be any meaningful classification of "conjections". Do the classifications with respect to cartography offer indications as to how this might be explored? In terms of the polyocular argument of Maruyama (2004), this would help to clarify the variety of ways in which NATO might be understood -- and might understand itelf in relation to its opponents.