From Mandelbrot working in the IBM laboratories to Feigenbaum working on the universal nature of chaos to the Germans, Peitgen and Richter trying to make sense of nature the answer was the same: Fractals are universal in the morphology of nature. Their existence means that no phenomenon can ever be satisfactorily explained on the basis of specific local events. It also means that in a sense the Newtonians, intuitively, were right and everything is predetermined: man’s fate is written in the stars; affected by the time of birth. Determinism however operates by the application of limits and within those limits reigns chaos!
Presaging the modern scientific developments at a slightly earlier date Alistair Crowley had said that “man is capable of being, and using, anything which he perceives, for everything that he perceives is in a certain sense part of his being...”.
That much is certainly true for fractals are active even within us: Though the anthropomorphic theory of semen has long since been discarded, DNA cannot specify the vast number of detail that goes in the particular spatial structure of man, animal or plant, but it can specify a repeating process of bifurcation and development that is in nature the same for all!
Mandelbrot in his study of the shapes of nature discovered that whether studying vuscular, pulmonary or botanical trees or the formation of snowflakes there was, waiting to be perceived, an underlying unity. Not a similarity of appearance or characteristics but (as magic has long specified) a similarity of process.
To the eyes of chaos scientists’ discovery a rising column of smoke breaking into wild swirls, a flag flapping in the wind, a dripping faucet, the weather, the flight of a plane, oil flowing in a pipe, cars on the motorway, the spread of galaxies in the solar system, the rise and fall of prices on the stock exchange and the emotions of a populace are all governed by the same invisible but all pervading principle.
The world view that is emerging from the discoveries of Chaos is one of infinite processes contained within finite limits. The mind of man containing the entire process of the Universe. The falling of rain from the sky attributed as much to the prayers of the shaman as to global weather conditions. The death of a king, the birth of a child; as connected to the spatial configuration of the planets as that configuration is linked to the presence of man on Earth.
It is singularly ironic that nearly 200 years after Franz Anton Mesmer’s death and the discrediting of his theory of animal magnetism his fellow countrymen, mathematician Heinz-Otto Peitgen and physicist Peter H. Richter would spend sleepless nights in their laboratory studying the magnetization and demagnetization of materials in order to fathom the workings of nature.
As the computer-generated pictures of the physical processes involved grew and grew in complexity they increased their computer magnification until at last one picture loomed particularly clear: the Mandelbrot set!With a nod to Mesmer and the enlightened thinkers that preceded him they wrote in their laboratory notes “Perhaps we should believe in magic”.
Wednesday, July 25, 2007
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