Given recent discussions and critiques, I thought a decent documentary on fractals would be beneficial. Simply put, the fractal is too complex to demonstrate without computer imagery. These complex forms, based on sets, demonstrate infinities are realities, and not merely a nominalist, “limiting factor” token symbol humans have “invented” or socially constructed. Despite the absurdity of the scientists in the documentary positing “natural selection” as the “creator” of fractals, the obvious truth is that they point directly to telos in nature, and thus God. And not just a content-less, impersonal force, but a Personal God – a divine Mind or Logos. And aside from the absurd discussions of global warming at the end, the totality of this video is a testament to the amazing symmetry, order and underlying logoi structure of the natural world (like cymatics!).
Reorienting your worldview to understand the universe is constructed in this way puts an end to the naturalistic materialist dogmatists and their cult. It opens the mind to new parameters. Just as the scientists and mathematicians prior to Mandelbrot were unable to “see” the order and symmetry (as in how Thomas Kuhn described the structures of scientific revolutions), in like fashion the way we “see” abstract objects like numbers, and how they relate the world, undergoes a change when the mind is opened in this new way. Also included below is a hyper-magnified fractal with some sweet techno. Enjoy the ride!
“Platonic reality of mathematical concepts?
How ’real’ are the objects of the mathematician’s world? From one point of view it seems that there can be nothing real about them at all. Mathematical objects are just concepts; they are the mental idealizations that mathematicians make, often stimulated by the appearance and seeming order of aspects of the world about us, but mental idealizations nevertheless. Can they be other than mere arbitrary constructions of the human mind? At the same time there often does appear to be some profound reality about these mathematical concepts, going quite beyond the mental deliberations of any particular mathematician. It is as though human thought is, instead, being guided towards some eternal external truth — a truth which has a reality of its own, and which is revealed only partially to any one of us.
The Mandelbrot set provides a striking example. Its wonderfully elaborate structure was not the invention of any one person, nor was it the design of a team of mathematicians. Benoit Mandelbrot himself, the Polish-American mathematician (and protagonist of fractal theory) who first studied the set, had no real prior conception of the fantastic elaboration inherent in it, although he knew that he was on the track of something very interesting. Indeed, when his first computer pictures began to emerge, he was under the impression that the fuzzy structures that he was seeing were the result of a computer malfunction (Mandelbrot 1986)! Only later did he become convinced that they were really there in the set itself. Moreover, the complete details of the complication of the structure of Mandelbrot’s set cannot really be fully comprehended by any one of us, nor can it be fully revealed by any computer.
It would seem that this structure is not just part of our minds, but it has a reality of its own. Whichever mathematician or computer buff chooses to examine the set, approximations to the same fundamental mathematical structure will be found. It makes no real difference which computer is used for performing calculations (provided that the computer is in accurate working order), apart from the fact that differences in computer speed and storage, and graphic display capabilities, may lead to differences in the amount of fine detail that will be revealed and in the speed with which that detail is produced. The computer is being used in essentially the same way that the experimental physicist uses a piece of experimental apparatus to explore the structure of the physical world. The Mandelbrot set is not an invention of the human mind: it was a discovery. Like Mount Everest, the Mandelbrot set is just there!” (pgs. 94-5)
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