SHAPES OF THINGS TO SUM

I suppose it seems self-evident to me: I recall that in my western travels I saw how mountains, desert, shores and rivers were formed: by time, by event; and it simply looked obvious to me that the geodesics (elegant logistics, parsimony in energy transfer) elucidated by Fuller was right there to be seen, writ large upon the landscape. (And I think Bucky's magnum opus could be elegantly titled The Ergonomicon.)

So: what do we mean by interface? In the case at hand, I am referring to the boundary domain where intermeshing, metalevel recursive systems come in contact. A useful model, I feel, is the increasingly interwoven complexity which forms the domain of criticality mapped by the Mandelbrot (and subordinate Julia) Set(s). Hence, Interface can be seen not only as a Hilbert Space domain but also, and significantly, as an algorithmic process. So, consider Interface in terms of water at its phase-space shifts; crystal to liquid to vapor to plasma. (I find it instructive to map human evolutionary/intellectual/cultural/technological phases of development along a similar continuum.) Put simply, what we're dealing with here is a model of ergonomic transactions occurring in four (or more) dimensions.

Thus, for instance, water vapor condenses into clouds with fractal forms, (a Maxwellian heat-exchange phase-shift); crystallizes into fractal snowflakes (formed by recursively iterated temperature/altitude inversions--a second phase-shift); thaws into liquid water, (a third phase-shift); and proceeds, under the influence of gravity, to run downhill (seek its own level), whereupon, since it then interfaces with the fractal shapes of geological forms, it must necessarily delineate the fractal boundaries (interfaces) of streambanks and coastlines.

Meanwhile, fractal tree roots take up water from the soil, transport it through internal geodesic structures, and lift it high above the ground, where fractal branch/leaf systems transpire water vapor (and gases such as oxygen) to release back into the air. And so on. (Needless to say, other ergonomic regimes, from seas, lakes, mountains, etc, are occurring at the same time). Likewise the interface at which photons of certain wavelengths, from the sun, are interacting with chlorophyll in the leaves of plants, which are themselves fractally arrayed. Similarly evolved interfaces (oxygen/hemoglobin, blood/brain, synapse/dendrite, etc.) take fractal (process) form.

So what we see at work is a global pattern in Nature of using various least-means algorithms to structure maximal Interface as Process while investing minimal logistical overhead. Just as geodesic structures are the least-means algorithm for maximal space-enclosing systems with minimal structure. Both cases (fractals as well as geodesics) are algorithms of logistical elegance, Processes unfolding in spacetime, and as such are organically intermeshed at complexly recursive metalevels of form and function. And what I find most beautiful about all this is the way these algorithms recursively define the involute/evolute apects of function in systems; like yin and yang taken to immeasurable orders of magnitude--and all with absolutely stunning simplicity and elegance! I wouldn't have missed it for the world...bdm