Complexity as such is uninteresting. Yet it poses a threat to our existence. Imagine being placed in a complex maze when you desperately search for the way out otherwise you might starve to death. In order to save yourself you have to simplify and look for a pattern which points the way out.
Our interest in complexity is driven by the urge (need) to simplify it. One way to grasp it is by creating complex systems in order to simplify them. The more difficult the simplification, the more interesting is the system. The ease of simplification may thus serve as a measure of the system complexity.
Let's start with the complexity of the class-4 in Wolfram’s book (p. 231) which is easily simplified. You generate a CA set which displays calss-4 complexity and apply the following transformation. For every state, sum up its elements and you will get a number. In this way you may simplify any evolving CA in Wolfram’s book into a series of numbers.
The Mandelbrot set is somewhat more complex. It has two simplifying features. It is self similar, and has a fractal geometry.
What about noise which generates unpredicatable patterns? In a previous section it was mentioned that whenever noise is multiplied by itself it does not become more complex. Thus noise cannot generate complexity. In addition noise does not exist as such in nature and therefore does not pose a threat to our existence.
Life cannot be simplified at
all. Any attempt to simplify it generates inconsistencies.
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