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General Systems Theory:
by Kirby Urner
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.
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.
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 Fullers 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
Synergetics on the Web