Enhancing communication patterns in virtual conferences with zome architecture

From Zoom Organization to Zome Configuration and Dynamics (Part #8)

This argument has developed the implications of a form of "psychosocial phyllotaxis" as a means of enhancing insight capture in conferences, then to be understood as a form of "psychosocial photosynthesis" (Possibility of "psychosocial photosynthesis"?; Optimization of psychosocial "light capture"). The argument was inspired by the widespread use of Zoom technology as a result of pandemic lockdown, and the unusual degree of dependence of the United Nations General Assembly on such technology.

It is remarkable to note that the uptake of virtual conferencing has not been matched by new insights into how the communication patterns might be more fruitfully organized -- especially in assemblies involving hundreds of participants. It would appear that procedures for conventional gatherings have simply been adapted to the virtual environment with no effort to derive advantage of the potential flexibility of that context and the necessarily enhanced role of computer technology, and that expected from artificial intelligence.

As noted, the argument with respect to enhancing light capture through phyllotaxis in nature has been variously explored (Takuya Okabe, Biophysical optimality of the golden angle in phyllotaxis Scientific Reports, 5, 2015, 15358; SÃören Strauss, et al, Phyllotaxis: is the golden angle optimal for light capture? New Phytologist, 225, 2019, 1). The question is how some analogue might be orchestrated in virtual conferencing to enhance "insight capture" as suggested by the spiral patterns in zome configurations. As emphasized, the focus is on communication patterns among a virtual configuration of participants, whether in terms of intervention, dissemination of messages to sub-groups, or thematic organization -- all potentially evolving during the course of the conference, rather than being predefined as is otherwise the conventional practice.

The possibilities have long been envisaged and variously explored through proprietary groupware packages (available under licence), although their relevance to assemblies of international institutions and parliaments is less evident (The Challenge of Cyber-Parliaments and Statutory Virtual Assemblies, 1998). The matter could be deemed increasingly urgent given the degree to which parliamentary assemblies are simply cancelled in the face of pandemic threats, or the results of "national debates" are far from being what is claimed (Multi-option Technical Facilitation of Public Debate: eliciting consensus nationally and internationally, 2019).

Rather than articulate the possibilities verbally, the following images are presented as an indication of communication templates which merit further exploration. In interpreting their potential value in mapping conference-related dynamics, the following possibilities could be considered:

complexification of the zonohedron (beyond the 9-fold example above), perhaps in terms of Fibonacci numbers (13, 21, 34, 55, 89, 144...), according to the number of distinctions to be recognized, whether in terms of participants or topics. Of obvious interest is its potential use for mapping debates relating to the UN's (16+1) Sustainable Development Goals
combination with other series with which phyllotaxis is associated (as noted above), such as the Lucas numbers (7, 11, 18, 29, 47, 76...)
use of zones, edges and vertices to map participants, themes or their groupings -- or communication pathways
switching degrees of complexification and patterns of colouring as indication of distinctive possible dynamics
combination of two zonohedra (possibly of distinct complexity), one in wireframe mode moving over the coloured zones of the other
changing the scale of the central axis (as illustrated below)
transformation of zonohedron into related forms by various morphing techniques (as illustrated below)

21-freqeuency Zome -- a zonohedrified 21-gonal antiprism (side and polar views) (420 faces of 10 types; 840 edges of 21 types; 422 vertices of 11 types)
Zones coloured	Wireframe variant


Images made using Stella Polyhedron Navigator

Animations of transformation of 21-fold zome to related forms by morphing
By sizing	By truncation	By augmentation	By expansion

By tilting quadrilaterals	By tilting triangles	By tilting to compound	By tilting to rectify

Animations made with Stella Polyhedron Navigator

Examples of modification of scaling along polar axis of 21-fold zome

Images made using Stella Polyhedron Navigator and X3D-Edit

It is somewhat ironic to note that the zome configurations shown could be recognized as variously approximating both the pineapple model (on which emphasis has been placed) and the sunflower pattern in relation to which it has been elaborated. There is a further irony that, in developing the argument from floral phyllotaxis, the zome configurations are consistent with distinctive aspects of the work of Keith Critchlow (The Hidden Geometry of Flowers: living rhythms, form and numbers, 2011; Islamic Patterns: an analytical and cosmological approach, 1976).

Comparison of alternative zome configurations: The approach taken to the creation of zomes using the application Stella4D, derived from the advice originally given by Robert Webb who developed that application and its facility for creation of zonohedra. The advice related to the earlier focus on a zome of 9-fold symmetry in the light of the strategic issue of 9 planetary boundaries. Without the advantage of other critical insight into zome mathematics, that procedure has been followed for the creation of the 21-fold pattern above, and in the following exploratory creation of analogous patterns. Zome configurations could well be developed by zonohedrification of other polyhedra and by other methods.

The selection of examples is based on a mix of numbers of N-fold zomes -- zonohedrified N-gonal antiprisms:

5, 8, 13, 21, being the early Fibonacci numbers highlighted in the exploration above. The tests with regard to the later numbers were less successful:
- 34: 4556f (4556); 9112e (9112); 4558v (4558) -- no symmetry
- 55: 2970f (2970s); 5940e (5940); 2972v (2972) -- no symmetry
- 89: 8368f (49); 20468e (116); 1228v (69s)
8, 16, 17, as featured in the 8 UN Millennium Development Goals and the 16(+1) Sustainable Development Goals
12 and 20 as notably favoured in the articulation of strategic initiatives:
- Checklist of 12-fold Principles, Plans, Symbols and Concepts (2011); Eliciting a 12-fold Pattern of Generic Operational Insights: Recognition of memory constraints on collective strategic comprehension (2011)
- Requisite 20-fold Articulation of Operative Insights? Checklist of web resources on 20 strategies, rules, methods and insights (2018).
30, in the light of the set of 30 articles in the Universal Declaration of Human Rights and the 30-edged icosahedron used for mapping that is central to the cybernetic argument of Stafford Beer (Beyond Dispute: the invention of team syntegrity, 1994).
14 and 15 were also tested (although not included). These feature in the:
- 14 Grand Challenges for Engineering in the 21st Century: 756f (14); 1512e (27); 758v (15)
- 15 Global Challenges of the Millennium Project: 210f (7); 420e (15); 212v (8)

This exercise in identifying polyhedra of value to mapping strategic preoccupations, follows from earlier exercises (which did not focus on zonohedra):

With respect to the following images, it is surprising to note with respect to potential memorability (although requiring mathematical clarification), that:

the 13-fold pattern is ordered to a greater degree than the 12-fold (despite strategic preferences for 12-fold organization)
the 17-fold pattern is ordered to a greater degree than the 16-fold (relevant to any commentary on the 17-fold organization of the UN's SDGs)
the 21-fold pattern is ordered to a greater degree than the 20-fold (despite strategic preferences for 20-fold organization)
the 30-fold pattern is not to a degree which might be expected ((despite preferences for 30-fold patterns)

Exploration of zome configurations of potential relevance to governance with numbers of faces, edges and vertices, in each case (number of types of each in parentheses)
5 20f (2); 40e (5); 22v (3)	8 56f (4); 112e (7); 58v (5)	9 72f (4); 144e (9); 74v (5)	12 552f (12); 1104e (23); 554v (13)	13 156f (6); 312e (13); 158v (7)

16 992f (16); 1984e (31); 994v (17)	17 272f (8); 544e (17); 274v (9)	20 (no symmetry)) 1560f (1560); 3120e (3120); 1562v (1562)	21 420f (10); 840e (21); 422v (11)	30 (no symmetry) 3540f (3540); 7080e (7080); 3542v (3542)

Images made using Stella Polyhedron Navigator

As noted earlier with respect to the 9-gonal pattern, the mix of 72 faces with 74 vertices is somewhat ironic given the current global challenge represented by a coronavirus with a number of spikes estimated to be of that order (and widely depicted), as illustrated separately (Cognitive Engagement with Spike Dynamics of a Polyhedral Coronavirus, 2020; Spike-endowed Global Civilization as COVID-19, 2020).

In the quest for the relevance of such patterns to new approaches to knowledge architecture and the organization of communication patterns in virtual conferences, there is clearly an advantage to be able to switch dynamically between distinctive patterns of N-foldness, whether as required by the gathering as a whole or as preferred by individual participants. Of particular relevance to how and why such selections are preferred, the cognitive arguments of George Lakoff and Rafael Nuñez merit consideration (Where Mathematics Comes From: how the embodied mind brings mathematics into being, 2001).

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