Tuesday, April 01, 2008

Note on fractals

Yesterday I mentioned fractals in comparison to the increasing complexities of life. Creation has built in uncertainty so while every instantiation of the real contains within itself all that went before it also embraces new elements. This is why it is true that while nothing changes in reality it is also true that at the same time the real is forever new. Look closely at your breathing, for instance. Every breath is somewhat like all that went before yet if you look closely you will see that every breath is also unique. This pattern repeats itself endlessly. To know something in this environment is impossible just because of the uncertainty that seeds the new. Therefore only heuristic learning is effective learning. As we approach an understanding we see that final knowledge escapes our precision and minor flaws emerge in our calculations. On these "mistakes" we ground ourselves anew and the self learning, self teaching, continues.

For a fractal galery go here. More from MathWorld here.

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