Statistical Structure

Does this map show any purely statistical patterns that are worth commenting on? If you will look at Figure 2, I will speculate upon a few such possibilities. Here I've used color and arrows to suggest a few plausible neighborhoods, groupings, curves, and functions. Actually in some of these cases my reasoning will be only partly statistical.

The first thing that strikes the eye is that the 33 variables have settled dynamically into the circular, even spiral, pattern that is such a common result of mappings of NMDS data onto 2-D space. As for it being spiral, I've recently concluded that the NMDS maps of many idea spaces are best interpreted chirally; that is, the best way to analyze the logic of their order is by starting at some terminal or peripheral extreme and proceeding in an azimuthal sequence, e.g. counterclockwise, around a ring, disc, or spiral, for 360 degrees, or a bit more or a bit less than that. The sets of ideas seem to unfold in this way, whereas in the reverse direction - say clockwise - they may not develop at all or may only do so in a limited, less natural, seemingly defective, or nonequivalent way.

I haven't been able to decide whether this rotatory handedness is saying something about a merely happenstance direction of thought, intrinsic chirality of the human mind or brain, chirality of the universe itself or of the transcendental world of ideas, a form of logic used without truly being necessary or perhaps generally advantageous, or perhaps, very simply, about otherwise trivial peculiarities of the statistical algorithms employed in the calculation of the NMDS graphs.

But in the present case, the evident peripheral start (or stop) of a right-handed spiral in the southwest extreme of the 2-D Causes-of-Forms map could make a kind of sense, since this asymmetry, and the gap just north of the tail, might be the natural correlate of the seemingly unique, unipolar {b,T,X} region, where, conceptually, the morphological causation at play has a somewhat ENDLIKE quality.

Note that the variables of the map show signs of running in two westward arrows from the mideast; and of falling into a vertical line in the west:

  1. There MAY be a WEAK tendency for {g - Osc. Rhy. Cyc.}-relatedness to INCREASE with {M - Branching}-relatedness;
  2. OR for the DISPERSION of {g} to increase;
  3. OR for the EXTREMITY of {g} to increase: so that relatedness to {g} bifurcates (dichotomically or antagonistically) as {M} increases.
Wiser minds than mine will have to decide these things.

If there is in fact a general spiral, one might view it, not as being incomplete - say by ending at {D} after turning only ~345 deg, but rather as a closed spiral of 450 deg-495 deg - that at {E} or {f}. This, too, could make conceptual sense, by allowing a first layer of {M - say of Branching-related causation} (or D sub 1) to covary with {g} (or D sub 2); and a second layer, branch, or spiral turn of {M} (or D sub 1) to vary independently of {g} (or D sub 2) - in the far south of the map. 

Simple x-y Plot of Original Weights

Since I felt queasy about using an NMDS algorithm to create Figure 1, I decided to create for purposes of comparison a simple x-y plot of the original 0-8 weights of DIRECTLY PERCEIVED interrelatedness, qua Causes of Form, between the 2 variables {M} and {g} and the larger set of 33. You can see from Figure 4 that my unease was justified, because there is little difference between it and the NMDS map in Figure 1. (The horizontal axis has been reversed, but this is irrelevant - apart from the fact that such flips make visual comparison onerous.)

About the only difference is that in Figure 4 the corners are rounded, presumably owing to the basic assumptions or world model of NMDS. 

Pictorial Countermap

The 130 different causes of form I've listed, and the subset of 33 I've mapped, are inevitably somewhat puzzling. For one thing, the names I've given them are short and ambiguous, and do not define, much less explain, the presumptive concepts. Readers bothered by uncertainty as to what might be meant or implied by these items may be consoled, if not reassured, by the fact that the author is probably no more knowledgable than they are in many cases. By these devices - a list and a map - I've simply made an attempt to inaugurate what can be expected to be a long-term, often agonizing process of naming, classifying, comparing, and investigating forms' causes entirely and thoroughly.

In an effort to gain and instill a little better understanding of Figure 1, I've drawn an overleaf map to this original map of the space of the interrelatedness of the general causes of forms. On this new, pictorial map I've sketched about 150 iconic pictures of different generic shapes AND/OR of physical or abstract situations apt to cause or influence the development of those shapes. The indicated forms represent the result of a laborious effort to imagine the characteristic kinds of shapes that each of the 33 causes of form are most apt to originate or to contribute or relate to. So on this second map there appears, at the site of each Cause-of-Form on the first map, a family of illustrated shapes and, if you will, morphogenetic principles. (Let me stress that some of the sketches are to be treated metaphorically rather than literally. In a few cases, simply because they are so badly drawn.)

The effect of this countermap should be to render the primary map much more interesting, meaningful, and useful.
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