Global Psychosocial Implication in the Pentagramma Mirificum


Anthony Judge – TRANSCEND Media Service

Clues from Spherical Geometry to “Getting Around” and Circumnavigating Imaginatively

Annex 5 of Correlating a Requisite Diversity of Metaphorical Patterns: entuning the dynamic of cognitive eases and diseases (2015)


The challenge of how to get around the globe now appears to be trivial. With global positioning satellite (GPS) technology accessible in one form or another, the challenge of navigating around a sphere is no longer of active concern. The assumption can even be made that the Earth is flat, as has been emphasized by Thomas L. Friedman (The World Is Flat, 2005; The World Is Flat; the globalized world in the twenty-first century, 2006; Hot, Flat, and Crowded: Why We Need a Green Revolution – and How It Can Renew America, 2009). The first was given the first Financial Times and Goldman Sachs Business Book of the Year Award. The award recognizes one business book that provides “the most compelling and enjoyable insight into modern business issues, including management, finance and economics”. Although readily assumed the “flatness” of the Earth can be explored as inappropriate to the times (Irresponsible Dependence on a Flat Earth Mentality — in response to global governance challenges, 2008).

It is indeed curious that in a global civilization, readily portrayed symbolically as a sphere, what globality may imply is elusive if not mysterious. Whilst the earliest explorers are upheld for their capacity to circumnavigate the globe, the skills which they required to do so are far from being common knowledge. Might this be the case with respect to a “global” civilization? How do people “get around” — other than by assuming the Earth is somehow “flat”?

At the same time there is no lack of information to the effect that satellites somehow get “around” the Earth, providing information services and extracting surveillance information. Many are aware of the capacity of missiles to strike anywhere, having followed trajectories “around” the globe. However, at the same time, the skills for getting “around” society and the “global” nature of its issues seem to be lacking in some fundamental way. Things are not getting better and many have a sense of being lost with nowhere to go.

The question here is whether there are clues to be found from the insights which have enabled spherical navigation over recent centuries. To what extent do those insights reflect understandings of relevance to getting “around” a global information-based society? Is there more to that forgotten art than is implied by a recent study (Glen Van Brummelen. Heavenly Mathematics: the forgotten art of spherical trigonometry, 2013)?

As noted in the main paper, a key contributor into understanding of navigation around the globe was the mathematician John Napier. He derived what continue to be cited as Napier’s rules for right spherical triangles. These were associated with a simple 5-fold structure later termed the Pentagramma Mirificum by the mathematician Carl Friedrich Gauss. Their work continues to inspire more complex forms of mathematics whose potential significance for global understanding calls for exploration. As in the main paper, the concern here is not with that mathematics but with what such a structure may suggest for unrecognized possibilities of imaginative “navigation” in a complex world — for “getting around”.

As argued there, a case can be made for recognizing that the 10 Napier’s Rules for navigation in spherical geometry are indicative of the distinctive forms of metaphor required for the navigation of globality (Napier’s Nifty Rules, ThatsMaths, 12 August 2012). Ironically these are associated with what are termed Napier’s Analogies (What is the analogy in Napier’s Analogy? Quora).

As the name of that form implies, the 5-fold structure is indeed a form of pentagram — but an unusual one. Attaching new significance to a pentagram may seem somewhat irrelevant in the world of today. However there is little need to stress the key role played by The Pentagon in this period — with whatever organization of knowledge and strategy a pentagonal structure may imply. The importance of 5-pointed stars is evident in the manner in which these figure in the iconography of national symbols of many nations, most notably those of Islamic faith. Exactly what determining force this may exert on such cultures remains unclear — whether in terms of consciousness or by whatever may be signified by collective unconsciousness. The potential relevance of the latter at this time is indicated by studies by John Ralston Saul (The Unconscious Civilization, 1995; The Collapse of Globalism and the Reinvention of the World, 2006).

Major intercultural conflicts at this time might even be described as “star wars”, as separately explored (Middle East Peace Potential through Dynamics in Spherical Geometry: engendering connectivity from incommensurable 5-fold and 6-fold conceptual frameworks, 2012). If there is any possible relevance to such arguments, then there is a strong case for exploring how the geometry of “stars” may frame thinking in some poorly recognized way — potentially to be informed by neglected insights concerning the mathematics of globality. The main paper drew attention to the curious parallel with respect to health and healing between the pentagonal Wu Xing pattern, as a fundamental Chinese concept, and the Pythagorean symbol of the Hygiea, also compared separately (Cycles of enstoning forming mnemonic pentagrams: Hygiea and Wu Xing, 2012; Potentially health developmental integrity from 5-fold symmetry, 2012). That there is a degree of sensitivity to such pentagonal symbols is evident from the concern which can be aroused in the media by their inversion and association with questionable rituals.

It is this context which justifies renewed exploration of the Pentagramma Mirificum and the possibilities of visualization of its subtleties using virtual reality techniques which have not been available in the past.

Continue reading the paper in the Original –


This article originally appeared on Transcend Media Service (TMS) on 8 Jun 2015.

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