Chaos & Complexity

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—–  “how it all fits together”  —–

Early in the 1980’s there was a lot of enthusiasm about the emerging science of “Chaos Theory”.  Chaos appeared to be answering questions no one had ever previously thought to ask.

Many thought that Chaos Theory might be “The Next Big Thing”; if Relativity Theory and Quantum Theory were the sciences of the 20th century, then Chaos Theory and its cousin Complexity Theory were to be the sciences of the 21st century.

Some thirty years on however, and this enthusiasm has waned somewhat; and while Chaos may have provided some interesting insights into many different and diverse scientific disciplines, it most definitely has failed to live up to, or even come close to, its initial high expectations!

One of my favorite quote is “If I had more time I would have written a shorter letter!”  The beauty of this famous quote is in its self-referential brevity and simplicity.  The point is very clear; brevity and simplicity are very hard to do!…

Writing a shorter letter is, of course, what’s difficult about science.  Good science is essentially about simplifying complexity.  It is about showing that each bit of seemingly unrelated complexity is in fact just a unique realization of some more general underlying simplicity.  This however has proved difficult for both Chaos Theory and Complexity Theory. Much of the reason for this difficulty can be attributed to the fact that despite all that has been written on these subjects (and many related areas) there has never materialized, from all of this work, a clear and simple unifying theme.

My goal is to provide that unifying theme.  My aim is to reveal how, Chaos & Complexity are different manifestations of the same unifying underlying behavior: a behavior that could be best described as Coarse Damping.

If the book of the universe is indeed written in the language of mathematics, as Galileo suggested; then mathematical chaos would seem to imply that everything in the universe (including space and time) is actually “non-continuous”, “atomistic” and Coarse Granular. 

Coarse damping occurs with the “clustering of  granular structures”; and consequently, coarse damping has a tendency to resist the natural mathematical pull of a finely-tuned, highly symmetric, but fundamentally bland and featureless equilibrium.

In the latter part of the 20th century, the computer revolution brought with it a computational microscope that allows us to see the recursive power of Coarse Mathematics  –  and that it alone is actually all that is necessary for “rich diversity to spontaneously emerge from bland uniformity”.

Quantum Physics, Emergent Chemistry, Evolutionary biology, and even an Complex Adaptive Economy, all are driven by the same Coarse Mathematics that universally drives all Chaos and Complexity…

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Albert Einstein once said “If you can’t explain it simply, you don’t understanding it well enough”.  Chaos and Complexity and Coarse Mathematics are undeniably complicated but I believe I understand them all well enough to write:

A short letter on:  What is Chaos Theory?

A short letter on:  What is Complexity Theory?

A short letter on:  What is Euler’s Secret Identity?