Monday, March 18, 2019

Time Out

We are temporarily withdrawing the writings from the public domain. We may or may not return, depending upon various and sundry things or this or that.

Thursday, January 24, 2019

Lost Art

A baby can't draw. A child draws the human form using four straight lines and a circle. An adult art student draws the human form using an assemblage of overlapping circles or ovals; three large ovals describe the torso, four ovals describe a leg, one describes the head, and so forth. Both renditions work as approximations, but always, upon closer inspection, the renditions fail to describe what is seen. The common human head is not a circle, at least at pressures found below 40,000 feet. Besides, the drawings are two dimensional and humans are historically three dimensional and in recent years, it has been argued that we have expanded so greatly that we need to find a fourth dimension to contain us.
Canals in sugar cane fields, former sawgrass marsh
Belle Glade, FL (GoogleEarth)
Irrigation circles in former mixed-grass prairie
Kearney, NE (GoogleEarth)
Subdivision in former high desert
Las Vegas, NV (GoogleEarth)

It's a fact, humans have an affinity for simple geometric shapes. Lines, triangles, squares, cubes, spheres. It begins in childhood, with shiny silver balls, stick figures, and alphabet blocks. It continues into adulthood, the same simple shapes defining cityscapes, architecture, gardening, interior decorating, sports, prints, storage, cooking, infrastructure, spatial reference systems, raster images, packaging, modern art, it's everywhere you look. The only exception to this seems to be gerrymandered districts, which, despite origins in human geographic design and idealized political thought, exhibit a strikingly random, organic, almost serpentine shape. Of course, this was not the predicted outcome.
Spatial reference systems project grids on the surface of the earth, subdividing it into zones. In 1796, the United States passed an act that ordered the subdivision of the land surface into grids called townships, six miles on each side, containing 36 one-square-mile (640 acres) sections. This is known as the Public Land Survey System (PLSS). This was strictly geometric. It was superimposed on the natural landscape. The organic structure of the environment was ignored, the shapes of floodplains, streams, watersheds, divides, fire perimeters, animal herds, blowdowns, old growth, peatlands, sand barrens, savannas, badlands, and the likes, all seemingly random, irregular polygons. 
This comprehension of undeveloped land became a template for city planning, railways, agriculture, waterways, forestry, roads, and even parklands. Human geometry multiplied, like salt crystals in evaporation ponds, superimposed upon the natural environment. This has been romanticized as the taming of nature, the quaint "patchwork quilt" of agriculture, but the consequences are well known: loss of migration corridors, genetic isolation, wetland destruction, channelization, increase of edge species, invasive corridors, loss of interior species, increased blowdown, and you name it.
Henry V. Hubbard, Professor of Landscape Architecture at Harvard University stated it this way: "The mature man who has dealt all his life with straight lines, simple surfaces, rigid materials to which he can give permanently almost any form, is likely to attempt something unfitting when dealing with undulating topography, flowing water, and growing plants" (Hubbard 1941).
Detail of anytown, USA. 
Life, July 24, 1970, photo by Michael Rougier.
Pie Goes on to Infinity
The PLSS surveyors eventually realized that land on the Mississippi Delta is different from land in the Sawtooth Mountains. If you were to purchase a section of land in the delta, it would measure about 640 acres. The topography is geographically flat. That land in the Sawtooths, it's montane, with an undulating surface. Flattening out the entire surface in the Sawtooths would result in far more than 640 acres - especially if that section of land was perfectly vertical. That's a lot of grass to mow, but it gets easier once you escape gravity and you find that your head really is a perfect sphere. It also depends upon what scale the flattening would occur. In theory, the scale descends infinitely, so the parcel could contain an infinite acreage, in which case, you have become the greatest feudal lord in the universe. Of course, the same is true for all of the earth's surface, so all landlords are suddenly superior to each other.
The same is true with pie. When it is time for dessert, children fight over the larger piece of the pie. Invariably, one slice is larger than the other, resulting in a bitter dispute. This daily inequality in family food distribution instills a compounding sense of outrage in the children. One parent solved this by having one child cut the slices for the other child. This led to a meticulous, time-consuming effort by the child to make certain the slices were equal in size. It worked. Family peace returned. 
Ah, but this is all a cynical ruse. 
Parents well know that most children are not physicists. A magnifying glass would reveal minute differences in size which would lead to more disputes, whereby the pie would cool and harden, losing its appeal. Use of a light microscope would reveal even more differences in size, resulting in more disputes and what may appear to be the spontaneous production of fruit flies. Use of an electron microscope would lead to yet more protracted disputes and shocking mold growth. And, in theory, since scale goes on to infinity, an inspection at the smallest possible level would result in starvation and death. So too, with feudal lords. If they had known about the infinite scale of detail, perhaps feudalism would have disappeared sooner than 1867.
The hungry children suffer at the hands of what are called Fractals. These are a class of non-differentiable functions that are iterated; there is no derivative; it is not possible to determine the rate at which the function is changing at any given point. Fractal Dimensions refer to an index or measure of the complexity of patterns. This is expressed as a ratio that compares the change in detail in the pattern as the scale at which it is measured changes. The slice of apple pie, for example. As one descends in detail, the irregularities in the border continue to appear. As Mandelbrot (1967) stated, "As even finer features are taken into account, the total measured length increases." The end result: The pie has an infinite outer edge.
The reason is, fractals exhibit self-similarity, that is, the whole has the same shape as the parts, into infinite detail. It is also called expanding symmetry or unfolding symmetry. This can be compared to Russian nesting dolls, a hall of mirrors, or big fish eating medium fish eating small fish. Thus, no indivisible shape exists from which a derivation can be made. 

This had applications beyond the chalkboard. Mandelbrot found that while the irregular shapes in the natural world could not be described in terms of classic Euclidian geometry - our beloved lines, triangles, squares, circles - they could be described in terms of fractal dimensions, or fractals, particularly when randomness was inserted into the function. Thus, fractal functions have been discovered that describe coastlines, clouds, mountain ranges, smoke, trees, ferns, seashells, noise, turbulence, galaxy clustering, vascular systems, river systems, the very things we bury beneath monuments to Euclidean geometry.
Middle of Nowhere.
A computer-generated fractal landscape.
A determinist view of the math behind nature would reject the notion of randomness, but at our level of cognition, unable to track all particles, motion, and force at all scales of existence, this is the best we have. That butterfly in Brazil may well cause a tornado in Texas, but we will never know.
Art Is                         
The probability of finding an adult who draws stick figures is increasing over time. This may be due to the loss of our fractal environment. This is akin to the child who is forced to watch television from birth and, as an adult, has no depth perception. We mention this because we are approaching the point where we confuse stick figures and actual, three-dimensional human beings. The stick-figure drawing will hang in the Louvre, in the spot where Michelangelo's Dying Slave used to stand.  
Beauty is a debate. Scientists have tried to define the nature of beauty, and, as one might expect, the theories focus on utility, especially as an indicator of health, advantageous genes, and fitness despite the burden of ornamentation. Others say that beauty is a product of sensory bias, that the beauty characteristics fit within the range of what the opposite sex is able to sense - light, sound, smell, taste. Others say it is a product of environmental and physiological constraints. Still others say that it is entirely accidental, that the pairing of preferences and ornamentation are arbitrary and the traits are not necessarily advantageous. This is not something you would say on a date.
Other than philosophical mutterings and the works of Shakespeare, the randomness of fractals that resulted in shapes that mimic those found in the natural environment may be one of the closest things we have to a definition of beauty.
Early in the past century, the National Park Service (NPS) developed a philosophy of landscape architecture, principles that would govern the development of parks for public access and enjoyment. Their objective was "the one dominant purpose of preserving essential esthetic qualities of their scenery unimpaired as a heritage" to generations to come, "substantially unimpaired by the intrusion of other functions" (Olmsted 1973), the "preeminence of a landscape preservation ethic in the development of natural areas of outstanding value" (McLelland 1998). Hubbard wrote, "The good landscape designer must think in terms of natural beauty and natural expression" and that roads, bridges, and houses "are not there for their own sake, and usually the less they are noticed the better...The National Park designer cannot, of course, design the mountains. But if he is from long and humble study an interpreter of natural beauty, he can present the mountains to the observer effectively." He warned, "The architect often regretfully stops his thinking with the outside of his building because he cannot govern what happens nearby." (Hubbard 1941) Principles took precedence, not prototypes. 
Floor Plan, Museum Building, Madison Junction
Yellowstone National Park

Thus, applying these principles to buildings, roads, bridges, villages, guardrails, culverts, curbs, campgrounds, signs, and trails, the NPS used native materials, plants, shapes, and colors. The structures and landscaping harmonized with the natural surroundings, matching, blending, appearing as if they grew out of the setting, as if they had been there all along. 
Now, this is art. 
An outcome of such an approach is the reduced visual impression of straight lines, triangles, squares, and circles, the dismissal of Euclid, and an increase in the impression of randomness. A closer inspection of the edge of the buildings, roads, bridges, and culverts may reveal a stochastic edge, wandering aimlessly along the line of sight, an edge that, at the moment, we could describe as a fractal, and certainly something that we may define as beautiful.
We might not know much about art, but we know what we like. 
Clearcuts up to the boundary of
Redwoods State and National Parks, CA
Limits to Human Growth
Yet, around the world, National Parks are being surrounded by human activity and development. In many places, the borders of the park are clearly defined by the contrast between development and unspoiled wilderness. The development is often visible from within the park, a visual pollution, degrading the visual resources, the viewshed. In many other places, the parks are being encroached by poachers, squatters, miners, humans seeking to convert the value of beauty into economic value. Elsewhere, the park status is rescinded, deliberately opening it to development, no longer managing for beauty, but for profit. This is a pandemic, an illness of humans sweeping the globe, one that appears when they are or believe they are threatened by economic failure. This is to say, parklands express a belief in economic security. This is not a stable relationship.
So, we return to kindergarten, drawing stick figures all over the place with grease pencils, mesmerized by silver balls, randomly stacking up alphabet blocks into senseless strings of babble. We are fighting over a piece of pie, but this one will not go on forever, despite the geometry, and any more fighting and the whole pie will rot and nobody gets to eat.

Hubbard, Henry V. 1941. The Designer in National Parks. National Park Service, 1941 Yearbook: Park and Recreation Progress.
Mandelbrot, Benoit. 1967. How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension. Science  05 May 1967: Vol. 156, Issue 3775, pp. 636-638 
McLelland, Linda Flint. 1998. Building the National Parks: Historic Landscape Design and Construction. The John Hopkins University Press, Baltimore, MD.Olmstead, Frederick Law. 1973. Forty years of landscape architecture: Central Park. Reprint, MIT Press, Cambridge, MA.