Mapping the Space

Afterwards I made a first effort to MAP THE NATURAL SPACE of the causes of forms I had named. In effect I was asking, "What is the simplest abstract space in which the brain conceives of fundamental relationships among this set of causes?"

Mind you, I was not in this particular effort concerned with what I could have been instead, had I wished to acquaint myself with that space - cousin to the former - by which our mind entertains simple similarities among the things which cause or influence the origin of shape. Mapping the former is harder, but more important.

The result of this preliminary mapping of Causes of Forms Space was the two-dimensional map in Figure 1. Note that only 33, or 24%, of the 135 listed causes are included in this map. Moreover, the NMDS (nonmetric multidimensional scaling) cartography is enormously oversimplified through having been generated by the expedient of an indirect statistical method, which relied on the estimated relatedness, on a 9-point scale, of just 2 causes ("Branching" and "Oscillations, Rhythms, Cycles") to the larger set of 33. Despite its limitations, this early glimpse of an important ideonomic space is of considerable interest.

As the product of only two variables, the projection is surprisingly good, which hints that the two Causes of Forms may naturally possess an orthogonal relationship that strikes close to the heart of the space in question. The possibility is underscored by the fact that in the map these two variables - which by good fortune are themselves mapped, as {M} and {g} - turn out to define the western and northern extremes of orthogonal Dimension 1 and Dimension 2.

And in fact it is intuitively obvious that "Branching" and "Oscillation, Rhythms, Cycles" - which might be construed either literally or metaphorically - DO have this coessential status and stature, for if one thinks in terms of dyadic branching oscillations, cyclic branching, etc, it becomes much easier to understand the otherwise problematic origin of a large part of both pure and physical morphology. Thus the archetypal shape Tree can be thought of as a phenomenon arising from cyclic branching (or cycles of branching), just as Foam might be described as being the result of the inverse etiological process of branched cycling (or branching cycles). Similarly it is possible to think of the origin of Knots (with their displaced loops), flexible Chains, Networks, Lattices, the cyclic and branched irregularities of Blobs, regular and irregular Clusters, Polyhedra - even (virtually) Polygons, and many other generic forms, and species thereof, in this way.

Moreover, much of the morphology that is on display in the two fields of nonlinear dynamics and cellular automata is explicable by reference to the various logical combinations of those two variables that are possible. Indeed, in this manner the logic of all of the four types of cellular automata (I, II, III, and IV) could be rather elegantly accounted for.

In any case, if one juxtaposes the map of Forms' Causes with an NMDS map of Generic Forms (e.g. Figure 3), the power of the former to illuminate the latter - or the existence, taxonomy, behavior, and natural interactions of the diapason of shapes - is a revelation. Yet one can only wonder how much more pertinent might be an improved and complete version of the same.
Back to the Homepage