Sunday, May 24, 2009

As Above So Below, An Introduction To Fractal Evolution

"A decade after Mandelbrot published his physiological speculations, some theoretical biologists began to find fractal organization controlling structures all through the body. The standard 'exponential' description of a bronchial branching proved to be quite wrong; a fractal description turned out to fit the data...." --James Gleick. In the view of the Darwinists, the endlessly exquisite designs of nature are the result of an interplay of two factors--random genetic mutation and Natural Selection. Genetic mutation proposes, Natural Selection disposes.

The question of "design" in nature was one that troubled Charles Darwin all his professional life. In the year following the publication of the Origin, he writes to Asa Gray: "I am conscious that I am in an utterly hopeless muddle. I cannot think that the world, as we see it, is the result of chance; and yet I cannot look at each separate thing as the result of design." Darwinist Ernst Mayr, for one, is well aware of the design dilemma. "No consequence of Darwin's theory of natural selection was a source of greater dismay to his opponents than the elimination of design from nature. Those who studied the countless superb adaptations of animals and plants had been most gratified by the explanation that such perfection was clearly the result of design by the maker of this world." In fact, Darwin did not eliminate design from nature, as he himself indicates in his letter to Gray. Darwin and his followers succeeded only in challenging the traditional idea that the source of all design is God.

Today, any graduate student asked to develop a paper on the subject of design in nature would invariably wind up looking into fractal geometry and mathematics. Fractal geometry, as its name implies, is a geometry focusing on the description of geometrical structures, and structuring, in fract[ion]al space

Until 1975, we didn't have a fractal geometry. Our only geometry was the familiar Euclidean geometry, which goes back over two thousand years. The Elements of Euclid (circa 300 B.C.) summarized in thirteen volumes the mathematical knowledge of ancient Greece. Up into our own century, Euclid's books of geometry were taken as the final, authoritative word on the subject. Euclidean geometry deals with whole rather than fractional realities. Plane geometry concerns planar (one- and two-dimensional) structures, and solid geometry describes volumetric (three-dimensional) structures.

"New geometry's always begin," writes James Gleick, "when someone changes a fundamental rule." Fundamental supposition would be a better term than rule. Gleick continues: "Suppose space can be curved instead of flat, a geometer says, and the result is a weird curved parody of Euclid that provides precisely the right framework for the general theory of relativity. Suppose space can have four dimensions, or five, or six. Suppose the number expressing dimension can be a fraction.... suppose shapes are defined, not by solving an equation once, but by iterating it [repeating it] in a feedback loop,....... Suppose that fractals are the secret to your answers."

As Above So Below, An Introduction To Fractal Evolution Part 1

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