A Bad Analogy using Fractals

February 29th, 2012
in Op Ed

by ECB Watch

GEI encourages rebuttals and here's one of Social fractals and corruption of America.  FYI, I recently wrote two reviews exposing flawed analysis, this one, and this one.

fractal-fernSMALLThe analogy under consideration, here, is that between fractals and social behavior. But even more basic aspects come under criticism. The header: "Social fractals and social control myths help explain the complete corruption of America." contains an exaggerated premise. The claim: "Correspondent Kathy K. recently elucidated a powerful concept: social fractals." fails to mention who Kathy K. is, what she is a correspondent of, and what her authority on the topic is. Already, the author has lost my trust Click on graphic for large image of fractal fern.

Follow up:

Here's the author's description of a fractal:
"We typically think of fractals--structures that are scale-invariant--as features of Nature or finance. For example, a coastline has the same characteristically ragged appearance from 100 feet, 1,000 feet and 10,000 feet in altitude. It is scale-invariant, i.e. its characteristics remain constant whether it is viewed on a small, medium or large scale."

How are we to talk about a topic (social behavior) in terms of another (fractals), if the latter is so poorly described? Conversely, if it is assumed that the reader knows enough about fractals, why not jump to the more interesting aspects about fractals?

The British Isles have a fractal dimension of 1.25 = 5/4, a fraction measuring the raggedness of the coastline. Establishing the fractal-fraction correspondence is the obvious first thing to do. Walking the reader through this example, and explaining why the dimension must fall between 1 and 2, seems like the minimum requirement. It takes some skill to understand it, and yet more talent to faithfully convey it to a diverse audience. If it can't be done properly, then talking about fractals is sheer pedantry.

The more interesting aspects include the relation to chaos theory (sensitivity to initial conditions) and the purpose they serve in nature, starting with things that are familiar such as the lining of the intestine, because it's likely to get readers attention. One would assume that these or other interesting aspects translate to social fractals. If not, there is no point in bringing up this mathematical object.

It turns out, unfortunately, that if the author's description of fractals was so poor, that's because social fractals only seem to fit that description, maybe not even that:

"The concept of social fractals can be illustrated with a simple example. If the individuals in a family unit are all healthy, thrifty, honest, caring and responsible, then how could that family be dysfunctional, spendthrift, venal and dishonest? It is not possible to aggregate individuals into a family unit and not have that family manifest the self-same characteristics of the individuals. This is the essence of fractals."

The essence of fractals, really?! Why not show us a plot then, so we can all appreciate its raggedness, and tell us what the fractal dimension is? Either social fractals don't exist (deception), or this article missed its target completely.

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