If Darwin was under assault, the twentieth century was nonetheless a time of real progress for the ecological point of view. For one thing, the familiar mechanisms of classical physics were themselves being challenged. Early on, Albert Einstein coupled space and time, then went on to show that mass and energy are just different manifestations of the same thing. With this, he shifted things still further from the narrow verities of machine age thinking.

Three others who contributed to that shift were the physicist Henri Bénard, the mathematician Jules-Henri Poincaré, and the naturalist D’Arcy Thompson. At this time, the 2nd Law of Thermodynamics—which rules that energy always dilutes and structures always degrade—still challenged any notion that the natural world could have evolved to higher states. Bénard’s work was the first to suggest an answer to that challenge. He was studying heat transfer in thin layers of liquid. When he applied heat slowly and evenly from below, the warmth behaved as would be expected, simply moving from bottom to top. As he gradually increased the temperature, though, a ghostly pattern emerged. Evanescent hexagonal cells like those in a honeycomb formed in his liquid. Further study revealed that the cell walls were carrying cool liquid down as heat upwelled through their centers. The formerly chaotic molecules had self-organized into efficient structural patterns.

At around the same time, Poincaré developed a new school of mathematics called topology. Sometimes referred to as “rubber sheet geometry,” topology demonstrates how different shapes that can be stretched into one another are equivalent. For instance, in theory a square can be stretched to form a rectangle or triangle, even a circle. More complex shapes can be equivalents, too. A coffee cup can’t become a pancake but it can become a doughnut, with the hole in its handle becoming the doughnut hole.

Those two discoveries opened the way for Thompson. In his classic book, On Growth and Form, he described patterns that connected Bénard’s hexagonal cells to the way energy and materials flow through living systems. Those self-organizing hexagons, he said, recalled the microscopic cell structure of rapidly growing tissue. In a later chapter on related forms he also built on the rubbery patterns of Poincaré, bringing the principles of topology to living creatures. For instance, after drawing a rabbit’s skull on a grid, he then stretched and deformed the grid to show a relationship between the rabbit’s skull and that of a horse. In a series of these brilliant “transformations,” he established like similarities between other species, in groups ranging from crustaceans to primates.

The work of those three reached not only toward the future but back in time. After more than a century, Kant’s “self-organization,” along with Goethe’s “moving order” and his belief that every living thing “is but a patterned gradation of one harmonious whole,” was once again becoming current.

Tags: DArcy Thompson, Darwin, evolution, Henri Benard, Jules Henri Poincare, self organization, topology

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Posted on April 18th, 2006 @ 3:00 pm