Perspectives, projections and learning processes in 3D modelling

Global Insight from Crown Chakra Dynamics in 3D? (Part #6)

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Learning processes: As in any creative process, the result viewed, imagined as an objective, distracts from the process by which it was achieved. In the case of 3D models, it is the result which is viewed in a few seconds and found to be interesting or otherwise. The process of achieving that result may take many tedious hours and can be considered to be of little interest. There is little trace of that process, except in the learning involved.

In the case of the models presented here, it might be assumed that they derive from a degree of expertise in 3D geometry and the relevant software applications. Typically this may be far less than is assumed. The creativity may well lie largely in navigating a variety of forms of ignorance. These may relate to use of the application (in this case X3D-Edit, or X3DOM) for which many levels of expertise may exist elsewhere, and relatively inaccessibly. The applications may not function as assumed in engaging with them. Their correct use, and their constraints, have to be discovered progressively. As noted, the applications may be in process of development. Guidance as to their use may be inadequate or out of date.

With respect to the geometry, many of the issues may well be trivial from a mathematical perspective -- if one had access to that and could comprehend it. In thse exercises, any such knowledge has been long forgotten by the author and effortd to apply any remembered principles in the light of guidance in that respect may be experienced as frustrating. Under such circumstances there is a need to adopt a crudely experimental approach of lengthy trial and error -- readily understood to be ridiculous from a professional perspective.

Despite such constraints and inadequacies, trial and error can be recognized as eliciting insight which would not necessarily be available otherwise.It can then be usefully asked how the crown chakra implies an accumulation of learning processes. Of particular interest is the manner in which a learning process may give rise to options -- and models -- whose existence had not been envisaged.

Perspectives: It could be argued that building relatively complex 3D models requires consideration of multiple perspectives. This is the case with the "1,000 petalled lotus". It raises the question as to how many perspectives have to be considered. The simpler concentric models, whatever their dynamics, necessarily call upon a more limited range of perspectives.

As the complexity of the models increases, and especially their dynamics, more perspectives have to be recognized -- progressively. Typically these are not adequately understood when embarking on their construction with software tools -- even though the final result can be imagined or intuited to some degree.

It can then be asked how many perspectives might bre usefully embodied in any model of a "1,000-petalled lotus": why 1,000? Arguably such a model strikes a creative balance between the increasing number of perspectives (with the complexity implied) and the comprehensibility of the model through a sense of its coherence. Clearly this has much to do with symmetry, but not to the point of oversimplification. What forms of complexity are held coherently by speculations of physics regarding super-symmetry? To what degree are they readily comprehensible?

Simplification is a weakness inherent in singular conceptual frameworks -- and any sense of "singularity". References to "love", "unity", "consensus", "wisdom", "insight" or "inspiration" might be considered examples. Given the limited ability (or desire) to articulate these comprehensibly and credibly in practice. as a consequence they tend unfortunately to take the form of slogans in which people are enjoined to believe -- irrespective of any evident constraints on implementation.

The challenge could then be understood as building multiple perspectives -- diversity -- into coherence. A particular opportunity is offered by dynamics rather than relying on static forms of structural symmetry. The question is then what do models of this kind imply for an appropriate balance in comprehensiuon and social organization -- with "organization" then potentially to be understood in its form as a verb, as argued separately (Engaging Playfully with Coronavirus through "Organizing" Global Governance? 2020; Envisaging a Comprehensible Global Brain -- as a Playful Organ, 2019)

Projections: It is intriguing to note the long-standing struggle to represent the planetary globe -- as a form in 3D -- on maps. The latter are characteristically 2D in nature, with a third dimension creatively implied by various means through "projections" -- of which there are many (List of map projections). There are echoes of this challenge in conceptualizing the "shape of the universe" and depicting it on maps of the cosmos -- a matter of concern to astronomers and cosmologists.

Missing is any analogous reflection on the "shape of society" or the "shape of knowledge space". In the case of the former, the focus is on references to "global society", with the implkications that it is somehow speherical, but with little consideration of what this might then imply -- as suggested by the contrasting perceptions of night and day, especially as a consequence of annual variations. In the case of knowledge space, its organization typically takes the form of a nested hierarchy of topics with little effort to consider more complex patterns of order. This is ironically true of the Mathematics Subject Classification whose topics imply a wide variety of subtle approaches to order.

Witbh respect to the structure of knowledge space, for example, a proposal by Thomas E. Portegys (Morphognosis: the shape of knowledge in space and time, 2017) presented to the 28th Modern Artificial Intelligence and Cognitive Science Conference (MAICS 2017) argues that:

Its basic structure is a pyramid of event recordings called a morphognostic. At the apex of the pyramid are the most recent and nearby events. Receding from the apex are less recent and possibly more distant events. A morphognostic can thus be viewed as a structure of progressively larger chunks of space-time knowledge.Â

As a step beyond any nested hierarchy, consideration can be given to the form of a periodic table, as argued separately (Towards a Periodic Table of Ways of Knowing -- in the light of metaphors of mathematics, 2009). Curiously, in the case of the archetypal Periodic Table of Chemical Elements, this too has given rise to an extensive database of alternative modes of organization (The INTERNET Database of Periodic Tables). The relevant mathematics is also a matter of debate (D. H. Rouvray, et al, The Mathematics of the Periodic Table, 2006).

Such considerations can therefore be seen as informing any approach to the organization of the "1,000 petalled lotus" in the light of its implications for higher orders of coherence and comprehensibility -- potentially its requisite variety in cybernetic terms.

One approach explored here is a toroidal form -- which happens to be one of the candidate forms for the "shape of the universe". As a step beyond the "global" form, its possible relevance has been argued separately (Imagining Toroidal Life as a Sustainable Alternative: from Globalization to Toroidization or back to Flatland? 2019). It is somewhat obvious that people do not inhabit a static globe, since it is subject to daily and annual movements -- if nothing else. Less obvious is that the latter traces out a torus -- if not a helix -- with which people have a degree of familiarity, in the absence of much reference to how people live on it.

The particular relevance of the torus is seen as a central to the current design and construction of a nuclear fusion reactor -- promoted as the hope for sustainable energy in the future. An analogue can be speculatively discussed (Enactivating a Cognitive Fusion Reactor: Imaginal Transformation of Energy Resourcing (ITER-8), 2006). Also of relevance are the designs promoted for outer space habitats and vessels to other planets -- both of which have long featured in science fiction.

The models presented here take the argument further through imagining the interlocking, or coupling, of two toruses. (***).

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