General Systems Theory:
Proposed New Low Level Associations
for the ‘System’ Concept

by Kirby Urner
Version 1.2
Last modified: 1 October, 1996


Dictionary definitions frequently enlighten us with their etymologies as much as through their pithy, enumerated entries. The formal definitions point in circular fashion to other entries, likewise defined against the standard of present day usage, with the occasional historical gloss. But the etymologies tend to free us altogether from touring within today’s meanings, flinging us back to some mythical time of ‘phonemic roots,’ a period when the many forces of nature were gathered under a more unified set of runes, of ideograms, a time when the multiplication of meanings had done less to efface the primitive beginnings of human thought amidst the archetypes.

To passively partake of the hidden wisdom in etymologies, or in other primitive sign systems disclosed to us through archeology, anthropology or archival cullings, is to treat our cultural heritage as ‘read only memory,’ an attitude which, coupled with veneration of the past, may lead to over indulging in backward-looking scholarship, while shirking of our responsibilities to downstream generations. Instead, what we require are strategies to reinvest our contemporary, living languages with some of their ancient resonance, such that we have more than distant mirrors, cracked and dulled with the passage of time, within which to find reflected our present situation.

imageAn engineering approach to language, mixed with appropriate respect for the supremacy of natural designs over human ones, has arisen from the matrix of computers, communications and library science. Even the most fleeting of human texts may now receive the automated services of what not long ago would have taken huge armies of bureaucrats to perform: date and time stamps and routing information is affixed, ensuring the text gets labeled and filed in storage media permitting random seekers, querying by key word, to retrieve this text at another time and place.

A world wide web of hyperlinked documents, newsgroups scrolling to searchable repositories, private messages traded daily within minutes – all of this infrastructure is presaged in earlier patterns of scholarship, in the memory arts, in the practice of footnoting, in the timeless practice of passing messages – often only two or three in a life time if the correspondents were separated by great distances. But the sheer speed and scope of this infrastructure, provided by engineering and automation, has set the stage for a whole new approach to thinking, and to thinking about thinking. Suddenly, with the internet, our metaphysical universe of thought has been endowed with a very palpable geometry, a topology, signified by the arcane symbolry of URLs and IP addresses.

The inventions of topology and network theory in conjunction with the arising of a global infrastructure for channeling, linking and archiving communications, is feeding our new general systems theories with the metaphors we will need to face the challenges of the future. At the same time, we have an opportunity to rewire some of the low level associations in our language, to supply ‘new etymologies’ as it were.

Whereas historically we may not have had geometric or topological meanings in close proximity to our concept of ‘system,’ for example, we now have the opportunity to create such links. The network nodes and connections tying together writers and readers into ‘schools of thought’ so easily meld with the topological definitions of vertex and edge, which, if not dumbed down to simple “flatlander” plots (i.e. “two dimensional” nets) come to life as polyhedral wire frames, or spherical webs, like the partially overlapping maps of city-hub- connecting airline routes around the surface of our globe. And to this metaphoric picture of our school and corporate communities there correspond literal geographic realities: actual web servers interconnecting key players, many of them wired, yet nomadic, their present locations optionally displayed on a Fuller Projection using real time data from satellite-based global positioning systems.

Primitive System

With the conceptual identification of system with wire frame network and simplest system with tetrahedron the topologically simplest frame-divider of volume into internal and external spaces, we come full circle within a new dictionary of primitive ‘etymologies,’ one more suited to our time, one which anticipates the internet and the need to think circumferentially, or ‘in the round’ at every turn. This move to identify system and tetrahedron at a primitive level is spelled out by R. Buckminster Fuller in his 'explorations in the geometry of thinking' or synergetics, which Fuller himself regarded as potentially convergent with Ludwig von Bertalanffy's general systems theory.

By absorbing a primitive geometric signifier within its definitional apparatus, general systems theory is in a position to recast its cybernetic feedback simulations into spherical webs of nodes linked by data feeds, while tapping in to some of the primitive integer-based mathematics of volumetric accounting. The topologically most primitive system, the tetrahedron, is also the most stable, being all triangles, and, if assigned the role of volumetric unity, defines a strong conceptual beginning for enumeration in conjunction the most with primitive shapes, such as the cube, octahedron and more.

Concentric Hierarchy Polyhedron Volume
Concentric Hierarchy Tetrahedron 1
Cube 3
Octahedron 4
Rhombic Dodecahedron 6
Cuboctahedron 20

The archetypal resonance of pure number, coupled with pure conceptuality in the form of primitive polytopes, brings new rationality and streamlining simplicity to our language. By anchoring ‘system’ in a matrix containing a wealth of simple whole number relationships connecting systems thinking with topology and geometry, we work ‘with the grain’ of the curriculum as a whole. The geodesic sphere becomes a picture of ‘conceptual system’ even as our conceptual system finds a new place for archetypal geometry at its core.

Our ‘system’ concept loses nothing by its identification with primitive geometry, and gains much by way of association. Of course we need our systems to engage in import/export transactions with their environments, which includes other systems, to work internally along dissipative or integrative trajectories, waxing or waning in their powers to cohere. We need to separate their parts into functional aspects of the whole.

All of these capabilities are retained with our identification of ‘primitive system’ with a geometric concept, plus we gain the ability to represent our systems behaviors with structures, using virtual reality markup language (VRML) for example, to signify a corporation-system as an inventory-containing entity with a surface topography of communications circuits interconnecting the job-position nodes, both to one another, and to the inventory (e.g. archived proprietary software assets) saved within.

Papers on general systems theory with embedded VRML views, themselves potentially hot wired with URLs and Java functionality, will make a lot more sense if, in the background, we have an ‘etymological’ (i.e. low-level associational) identification of primitive systems with primitive shapes in the first place. Any four nodes on the surface define the six links of interconnection of a primitive subsystem within the complex network under discussion. The superimposition of systems is a more complicated system.

VRMLSYS.gif - 7.6 K

Click for VRML view

In sum, a forward-looking approach to systems theory that is nonetheless respectful of the values added by ancient wisdom to our thought, in the form of low level associations that often escape simple dictionary definitions, is to work towards a new associational apparatus that is likewise ‘with the grain’ of thought, yet promoting of integrative rationality commensurate with the challenges now facing us. To this end, identification of ‘system’ with ‘tetrahedron,’ as per R. Buckminster Fuller’s Synergetics is consistent with our need to think about schools of thought embedded within the internet context, as well as with the confluence of topology and computer science which the internet represents. More primitively, Synergetics is attuned to simple conceptual relationships obtaining among integers, shapes and concepts (such as ‘system’) which will serve to bolster our visualizations and metaphorics around general systems theory, while perhaps tapping into a new source of rationality that is more inherently contemporary vis-a-vis the curriculum as a whole.

For Further Reading

VRML 3-frequency geosphere generated by Rick Bono's DOME freeware (version 4.6)
Tetrahedron and embedded graphic in Table of Concentric Hierarchy Volumes courtesy of Richard Hawkins

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