Eliciting Memorable Spheres and Polyhedra from Hyperspace
TRANSCEND MEMBERS, 3 Aug 2015
Integrative Connectivity of Problems, Strategies, Themes, Groups or People
Much is made of the recognition that everything is now connected to everything, especially as reflected in patterns of links in cyberspace (Albert-Laszlo Barabasi, Linked: how everything is connected to everything else and what it means for business, science, and everyday life, 2014; David Easley and Jon Kleinberg, Networks, Crowds, and Markets: reasoning about a highly connected world, 2010).
This insight has notably been explored through small-world network graph theory and through understandings of “six degrees of separation“, popularized by the parlour game Six Degrees of Kevin Bacon (Duncan J. Watts, Six Degrees: the science of a connected age, 2004). Various efforts at offering an idea of the complexity of this connectivity have been made based on internet traffic, web links, and the like.
Systematic efforts to document the connectivity of problems, strategies and international organizations as networks have been made in developing the online databases associated with the Encyclopedia of World Problems and Human Potential and the Yearbook of International Organizations. Extensive efforts have been made to analyze these networks and to find fruitful ways of visualizing them to render them more meaningful as a basis for new modes of action appropriate to the challenges of the times (Visualizing Relationship Networks: international, interdisciplinary, inter-sectorial, 1992; Visualizing Latent Significance in Patterns of Relationships: a case study in relative incompetence, 2012).
Considerable progress in this respect has been recently made in this respect by Tomáš Fülöpp and Jacques de Mévius (Loop mining in the Encyclopedia of world problems, 2015), as reported at the conference on Futures Studies Tackling Wicked Problems (Turku, 2015). In the light of these efforts, the concern here is with the issue of how to render memorable and communicable the connectivity which emerges from such analysis. The concern is partially highlighted by possible responses to information overload (Optimizing Web Surfing Pathways for the Overloaded: polyhedral insights from the travelling salesman problem of operations research, 2015).
Web users have an increasing concern with how best to manage their web surfing experience given the constraints of time and information overload. The question explored here is a possible means of moving beyond a browser checklist of links (“favourites”) and bookmarks, whether or not these are carefully nested within menus and organized by theme. This followed from earlier concern with the challenge of organizing relationships between websites in terms of the conversation threading of internet exchanges (Interweaving Thematic Threads and Learning Pathways: noonautics, magic carpets and wizdomes, 2010).
The complexity of some efforts at such network visualization has been deprecated through resulting in so-called “hairballs” (Graphs Beyond the Hairball; Lynn Cherny, Visualizing Graphs: beyond the “hairball“, 2012; Martin Krzywinski, Hive Plots: Rational Network Visualization — Farewell to hairballs; Arlind Nocaj, et al, Untangling Hairballs, 2014; Stephen Few, From Giant Hairballs to Clear Patterns in Networks, Visual Business Intelligence, 2013; Hive plots and hairballs, Seeing Complexity: visualizing complex data, 2011; Hans-Jörg Schulz and Christophe Hurter, Grooming the Hairball: how to tidy up network visualizations? 2013; Jeff Johnston, Embracing the Hairball, Exapative, 2015). Special software applications, such as sigma,js, have been developed to address the current challenge of graph drawing (Sigma.js Cleans up Hairball Network Visualizations). Hairballs are inherently unmemorable.
The particular focus here is on using analytical data on triangles of relationships in such a way as to construct memorable networks of these triangles based on any shared edges. This effectively weaves together those triangles detected into a “flat” 2-dimensional “carpet”. The further possibility then derives from detecting “folding” of that carpet into the form of a 3-dimensional “bowl”, as a consequence of connectivity at its outer edges forcing a degree of closure. As a result there is a “curling up” of the edges of the carpet with the possibility of detecting some such patterns which close completely to form a sphere. Approximations to such spherical closure, based on triangles, could take the form of polyhedra, whether simple or more complex — based on loops of more than three relationships (squares, pentagons, hexagons, etc).
Through their characteristic symmetry, this approach offers a means of detecting and communicating visually memorable forms of order within very complex networks — however they need to be labelled or colour coded. A particular feature of the approach is the use of force-directed graph drawing, charactetistic of Data-Driven Documents (d3.js), to elicit self-organizing convex polyhedra — without the conventional prerequisite for vertex coordinates.
This article originally appeared on Transcend Media Service (TMS) on 3 Aug 2015.
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