Re-membering the Globe from a Flatland Perspective
TRANSCEND MEMBERS, 10 Aug 2020
Reconciling in 3D the Vitruvian Archetype with Sports Ball Curves
Vitruvian Man by Leonardo da Vinci
[click for larger version from Wikipedia]
10 Aug 2020 – This speculative exploration follows from an earlier argument regarding the challenge of mapping the opposing forces of good and evil — in anticipation of any prophesied final battle (Mapping options for 144 distinctive features of a dynamic global system, 2020). . This was followed by a second speculative exercise in exploring the cognitive constraints imposed by adoption of the baseball cap (Baseball Cap Implications in the Quest for Global Hegemony, 2020). This endeavoured to clarify the relationship between sports visors and the form of the curve in 3D which is so fundamental to the manufacture of a baseball and a tennis ball from flat materials.
People are necessarily far more familiar with the form of such balls — even if only unconsciously recognizing the seams defined by those curves in 3D. To that extent it could be claimed that any sense of “global” is understood in an especially constrained manner. This is particularly true given the “treatment” accorded to such balls in games such baseball and tennis. A related argument can be made for the common association football, given the neglected significance of its polyhedral stitching pattern.
A puzzle for the future is how the engagement with “global dynamics” is most commonly recognized through hitting (or kicking) forcefully and skillfully the balls in various games — in order to score against an opponent, thereby defeated, if not triumphantly crushed. The earlier speculations considered the understanding to be derived from the balls used in such games (Game ball design as holding insight of relevance to global governance? 2020).
Those arguments noted how the manufacture of balls used in sports poses the problem of how to curve materials in 2D in order to create a viable ball in 3D. As discussed, of particular importance in this respect is the seam of the tennis ball, which is the feature of the tennis-ball theorem of mathematics. This is of the same form as that of the baseball curve of 108 double stitches (Seam Curve on Sports Balls, Wolfram Demonstration Project). Such construction can be understood as a shift in modality from “flatland” to “sphereland”.
A form of “flatland” perspective featured in the prize winning work by Thomas Friedman (The World Is Flat, 2005; Hot, Flat and Crowded, 2009), as subsequently reviewed (Irresponsible Dependence on a Flat Earth Mentality — in response to global governance challenges, 2008). Irrespective of its relevance to meaningful globalization, a contrasting perspective has long been a speculative focus of mathematicians (Edwin Abbott Abbott, Flatland: A Romance of Many Dimensions, 1884. Ian Stewart, The Annotated Flatland: A Romance of Many Dimensions, 2008; Dionys Burger, Sphereland: A Fantasy About Curved Spaces and an Expanding Universe, 1965).
The speculation here is that the long-admired (and much-reproduced) Vitruvian Man, as famously depicted by Leonardo da Vinci in 1490, could be seen as apparently reinforcing a two-dimensional worldview — even though it is interpreted as implying and exemplifying what could be considered as a vital perspective on proportions in their more integrative global sense. The question here is whether an adaptation of that 2D depiction into 3D offers a higher degree of accessible insight into global engagement — when reconciled with the curve so fundamental to the design of familiar balls.
Understood otherwise, is there a sense in which the 2D depiction of Leonardo da Vinci has been embodied in modern culture in a manner different from the higher-dimensional globality which his image implied and to which it effectively pointed and symbolized? By contrast, the very familiarity with balls in games could then be understood as encouraging and reinforcing a form of “sub-understanding”, as argued by Magoroh Maruyama (Peripheral Vision: Polyocular Vision or Subunderstanding? Organization Studies, 25, 2004, 3). More problematic, could the conventional 2D depiction — frequently highlighted as a key symbol of Western civilization — be caricatured as effectively a paper “cut-out”, namely “all front and no back”? Might this well be asked of many Western-inspired institutions, despite vigorous claims to the contrary?
Is the much deplored fragmentation of society to be recognized as engendered by such misplaced concreteness (Joan Conger, The Fallacy of Misplaced Concreteness Distorts Modern Leadership Study and Practice: four principles of process proposed by Alfred North Whitehead reform four modernist abstractions, 2016). This can be variously explored through visually associating smaller variants of the global form with a version of the Vitruvian image rendered into 3D.
Given the much-cited significance of the Vitruvian depiction to Western civilization and its “architecture”, why has no equivalent cognitive symbol been imagined for the architecture of knowledge in a global system? Are the insights of other traditions of relevance, as argued by Susantha Goonatilake (Toward a Global Science: mining civilizational knowledge, , 1999)?
In a period of intense preoccupation with the sexist implications of gender biased language, there are also visual equivalents (Images in science are still biased towards white men, new research reveals, ResponseSource, 9 July 2020). Any reframing of the historical depiction of a Vitruvian “Man” is therefore highly problematic. It raises questions as to how any new representation might be appropriately named and designed in 3D. Many remarkable efforts have indeed been made to design complementary images of a “Vitruvian Woman” in 2D — readily available via the web, some with considerable aesthetic merit. This site also features an earlier animation in 2D (reproduced below) which addressed the related issue of the degree of racism necessarily reinforced by the original depiction.
As with the Vitruvian Man, the following argument is primarily visual — of necessity. The images and animations are proposed as templates by which complementary narratives and “stories” could be evoked and developed. Variants of those indicated could be readily proposed — potentially of much higher quality and with greater attention to aesthetics. The animations here in 3D could in future respond to these challenges of insensitive representation by embodying variation in skin colour, if not in morphology.
This exploration was only made possible by advances in 3D technology, and notably its use by PLM Technology to design a Vitruvian Man in 3D — made freely accessible via the GrabCAD Community (Vitruvian Man, 31 May 2019).
Given the celebration in what follows of a particular curve in mathematics, it is appropriate to note that — unlike many other such curves — it does not have a name. The reference to it is as the “seam line of a tennis ball: or the “baseball curve” are but widely recognizable instances. It is therefore perhaps appropriate to recall the fundamental argument of the Tao Te Ching: The name that can be named is not the eternal name. The nameless is the beginning of heaven and earth.
Tags: Leonardo da Vinci, Sports, Vitruvian Man
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