Thursday, August 25, 2011

Self-Similarity: Fractals and People

Last night, I was watching a rerun of a PBS Nova program on fractals entitled, Hunting the Hidden Dimension. I don't think the full episode is online at the moment but you can see the trailer here. (As I look at the preview image below, the full episode may be available via the link below the preview).

Watch the full episode. See more NOVA.

The essence of fractals is the concept of self-similarity - the idea that patterns repeat themselves at ever smaller dimensions. The discoverer of fractals, Benoit Mandelbrot, was initially chastised by his mainstream mathematical colleagues as  a bit of a nut. These patterns weren't real, they said, they were more like an entertaining parlor game. Those days are long gone, of course, and fractals (and their associated concept) Chaos theory are now being used to investigate everything from thunderstorms to heart arrhythmias.  In fact, Mandelbrot's initial insight into the nature of fractals came from his investigation of noise patterns on long distance data transmission lines while at IBM Research Labs.  The patterns are everywhere once you know how to look for them. 

As I was listening to the narrator talk about Mandelbrot's initial rejection by his colleagues, I began to think about the nature of groups and how they come to all conform to certain ideas that make up the status quo. Could it be that groups of people follow some of the same concepts you find in fractals? Let's look at a couple of hypothetical examples.

What if you have two university professors, both highly respected in their fields. One carefully chooses his or her grad students on the basis that they are bright, are seemingly willing to take their direction very closely from the professor, and are relatively conformist in nature. The other professor also wants bright grad students but hires non-conformists and students that have some strong ideas of their own they want to pursue.   

The first lab is going to really churn out productive research that augments the professors views. The ideas will be tight and reinforcing.  The students are self-similar to the professor and so a pattern of conformity emerges.  When they graduate, they go out into the academic world and what do they do? The look for students like themselves and the pattern is replicated again and again. The field begins to develop norms that are much based on self-similar thinking as they are on the underlying science. 

The second professor has a few mavericks in his lab.  Not everyone but a few. These people mix it up and challenge the professor and the other students to look at their way of seeing the problems. The lab is probably a little less successful at churning out papers but every now and then a new idea emerges that comes from the lack of self-similarity. After the mavericks graduate, they go forth in a new academic position and try to hire a few mavericks of their own.  More new ideas emerge.

The reality of the way people are made is that far more of us are conformists than mavericks. It is much easier to get along in the world if you are self-similar than different. Hence, conformist thinking dominates and the Mandelbrot's of the world have to push back hard to be heard. 

The same is true, by the way, in corporations. The pressure to conform to the company's culture can be very high in a large and established corporation.  Certainly, you can see examples where this is not the case in tech startups but in general, once a company has a formula for making money, it likes to keep making money. The business leaders feel they know the formula and don't want to mess with it. Non-conformists are not welcome. 

So the principle of self-similarity that drives fractals may also drive human group dynamics.  Mavericks pay a high price for their independence. But in many cases, like that of Benoit Mandelbrot, the world is far better for it. 

1 comment:

Anonymous said...

I love this! My favorite musician/inventor/person is a bit of a non-conformist nut, himself. :o) It takes awhile, but eventually the new ideas get out there. - Ruthie