The Once and Future Wallace

A Theory of Spatial Systems: Final Remarks.

I have long since come to see that no one deserves either praise or blame for the ideas that come to him, but only for the actions resulting therefrom. Ideas and beliefs are certainly not voluntary acts. They come to us--we hardly know how or whence, and once they have got possession of us we can not reject or change them at will.

(Alfred Russel Wallace)

     Like Mr. Wallace, one of my favorite people, I feel only so responsible for the "begatting" of such ideas as come to me. Once they're here, however, I often find it difficult to just let them go. I suppose that is my only defense for spending the three or four full years it took to develop the analyses described in this section. But the results just seemed to keep supporting the conclusion that the general model might actually hold water.

     I still acknowledge that I have not satisfactorily proven that it does--but perhaps, not being in satisfactory circumstances to pursue this further myself at the moment, it is time to turn over the reins. I suggest the following actions at this point.

     First, there is the practical matter of how to equitably measure correlated spatial patterns. Spatial autocorrelation measurement is already at an advanced stage as a study; still, it would be nice to have an authoritative verdict on the preferred use of a specific formulation.

     Beyond this, one needs merely to dig in and approach in the general way suggested those studies that seem to present the clearest relations between pattern and process. State-of-the-art treatments of the kinds of patterns associated with stream basins and the earth's internal compositional structure (especially, over time) would seemingly draw attention to the model, regardless of anyone's possible initial misgivings. Beyond these (and the other ones I dealt with more briefly), the following contexts seem to present some potentially interesting challenges for investigation:

     (1) DNA (and molecules in general) modeling. The DNA molecule is most fundamentally distinguished by a structure in which two pairs of structures interact with one another--as is exactly the case in the general spatial model I have been suggesting (recall that a graphic representation of symmetric z scores is as two pairs of points that are symmetrically opposed to one another in three dimensions). At the level of atomic interrelationships, of course, pattern per se is unlikely to be a biassed surrogate for interaction--our concept of space being based largely on the results of the interaction rather than the other way around--so measures of actual flows/attractions between/among/as constituent particles would probably be the focus.

     (2) Unified Field Theory. The last I heard, it was thought that four basic kinds of forces give rise to all material structure: strong and weak nuclear forces, electromagnetic force, and gravitational force. This, and the fact that they are progressively weaker in the order named, seems possibly suggestive in the context of the discussion here.

     (3) Worldwide meteorological patterns. While at present it is possible to correlate only some of the most obvious patterns of worldwide climatology with the onset of certain conditions (such as El Niño), such correlations are being worked out under much more lenient assumptions about system organization than those posed here. Inasmuch as the model presented here would likely identify many posed "unconstrained" patterns of pressure, temperature, etc. as being impossible, a priori, it could aid in the construction of more precise forecasting tools.

     (4) Meso-scale storm modeling. It is tempting to look at the various representations of individual storm cells (as seen on television severe weather reports, for example) as systems whose internal variations might be modeled along the lines described here (for example, in analogy with the spatial variations inherent in stream basin topography, but in this case dealing with wind speed, etc.).

     (5) Funnel-cloud modeling. A tornado represents a system of forces whose geometric arrangement is not so unlike the arrangement of the potential energy forces in a stream basin, wrapped into a funnel-like shape. Otherwise put, the exact spatial arrangement of varying pressure or wind velocity within the funnel might well be broken down into four classes of intensity, "mapped" in three dimensions, spatially autocorrelated, matricized, and subjected to double standardization. Seemingly, "funneling" would only take place within a range of matrix representations leading to symmetric double-standardized scores.

     Enough of this for now. I hope the reader has found this exploration amusing, at whatever level. There remains only one last point to be made.

     As to whether the particular system I have introduced here can be worked with further, we shall see. However, it can hardly be denied, even if it proves flawed in whole or in part, that it represents a view of natural organization based on an enaction of final causes. To this extent I believe it falls truly within the spirit of Wallacean thinking, and even if shown to be incorrect should provide fodder for discussion among those who currently believe--assume--that the universe evolves in a way that is largely free from such influences.

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