Saturday, November 6, 2010

In memory of Benoit Mandelbrot

The king of "roughness" departed the physical world on the 14th October, 2010, but our memory of him lives on in the name of a spectacular example of self-similarity at every scale, the Mandelbrot set.

The Mandelbrot set which honors his work (which can be expressed as z² + c, where Z is a complex number e.g. the square root of -1) exhibits patterns of dazzling complexity at ever greater magnifications, all the way to infinity.

Benoit Mandelbroit discovered order in the apparent messiness of life. He shows how a cauliflower is both simple and complex all at the same time. When you cut off one of the floreats, you find it is composed of many more smaller floreats, that are essentially the same design. And if you cut off one of those floreats, and look closer, you discover many smaller floreats, again similar to the larger floreat.

Self-similarity or fractal order is a field of mathematics which Mandelbrot helped develop and popularize. Simple rules describe natural features or artefacts of great complexity. The ruggedness of mountains. The branching of arteries. The growth of neurons. The shapes of rivers. The leaves of ferns.

He discovered that self-similarity, where simple patterns are repeated infinitely,  can explain complex data sets such as stock prices and non-smooth objects such as clouds and coastlines. His work grew out of a field of mathematics - Julia sets - which was once regarded a mere curiosity with little practical use.

So what if you were able to apply fractals to psychology and sociology.

Here is a workshop to think "fractally" to discover the simple rules in the complex, and develop the complex from the simple:

1. Brainstorm a list of all the artefacts, natural features, processes, etc. you can think of that are self-similar at every scale, e.g. like cauliflower floreats
2. Choose one artefact, natural feature, process or method from your list and describe how it is fractal, self-similar at every scale and how the generation of smaller or larger versions follow the same simple rules.
3. Fractals in discourse - Choose a problem to be solved. Write down three solutions. Discuss with a pair, and combine your two sets of ideas, into a single set of three ideas. Meet with two other people and combine your six ideas into three. Repeat the entire group has generated just three fantastic ideas.
4. Create a new fractal decision/learning game. Create a new set of discussion rules similar to the Fractals in discourse
5. Fractal leadership. Craft a set of three rules for how you will expect to be led by others to maximise your support and engagement.
6. Connecting with others. Craft a set of 2-5 simple rules for successfully engaging with others so they feel a close connection. Describe how the rule applies in relation to a wife/husband/partner, sister/brother, friend/enemy, family group, work team, community, organization, nation.
7. Finding the fractals in new relationships. Look back over your life and think about the people, groups, organizations and communities you know or have known or joined with. What are the rules for maintaining long term relationships? What are the rules for losing connections?
8. New concepts. You have been given the task of creating a wisdom age ecology of new products and services. Looking back over the Hunter-Gatherer, Agricultural, Industrial, Information and Knowledge eras, what are the simple rules for generating whole/integrated ecologies of products/services/jobs at each scale?

1 comment:

  1. Check this out for a very colorful rendering of the Mandelbrot set