Wednesday, July 15, 2020

The Beauty of Fractals - Images of Complex Dynamical Systems

... I realised that the straight line leads to the downfall of mankind. But the straight line has become an absolute tyranny. The straight line is something cowardly drawn with a rule, without though or feeling; it is the line which does not exist in nature. And that line is the rotten foundation of our doomed civilisation. Even if there are places where it is recognised that this line is rapidly leading to perdition, its course continues to be plotted... Any design undertaken with the straight line will be stillborn. Today we are witnessing the triumph of rationalistic knowledge and yet, at the same time, we find ourselves confronted with emptiness. An aesthetic void, desert of uniformity, criminal sterility, loss of creative power. Even creativity is prefabricated. We have become impotent. We are no longer able to create. That is real sterility.
Friedensreich Hundertwasser 

As Galileo Galilei so powerfully stated the credo in 1623:
Philosophy is written in this grand book -- I mean the Universe -- which stands continuously open to our gaze, but it cannot be understood unless one first learns to comprehend the language in which it is written...
This statement is at the basis of much of the spiritual exploration of humanity. In Judaism we have the Torah, which is the Word of God - and Hebrew which represents the primordial alphabet. Each deep exploration into the complex environment in which we are born follows a similar path. Just as our lives being knowing nothing, and we have to explore our own (and others') grand narratives through the world around us.

He continues to make a definitive statement, and this statement has become an axiom of belief, one of the basic tenets of the what I would term the modern religion: science.
It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures, without which it is humanly impossible to understand a single word of it; without these one is wandering about in a dark labyrinth.
The three pillars of that world view - Euclidean geometry, Galilean mathematics, and Newtonian physics. They formed a mighty edifice and it stood for over 300 years, eventually ruling over us with a might that has never been seen before. As we stand on the precipice of a new age.

However, that is not where our story ends. For some 350 years later, Benoit Mandlebrot, in 1984, asked - just as Galileo questioned the geocentricity of the solar system:
Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line... ...Nature exhibits not simply a higher degree but an altogether different level of complexity. The number of distinct scales of length of patterns is for all purposes infinite.

 He continues, and I think that in this is a recipe for our future:
The existence of these patterns challenges us to study these forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we see or feel.
And this is where I will leave this for today.

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