Profound Contributions
In my previous post I wrote,
The major difference between Sunbelt and OAC is, of course, that most of the participants in the former are comfortable using network and other forms of quantitative analysis, in a subfield of social science to which mathematicians and physicists have and continue to make profound contributions.
What did I mean, however, by "profound contributions"? Until the rise of network science (and chaos and complexity defined mathematically), social science analysis was, in my experience, confined to categorical or statistical reasoning. Categorical reasoning employed a deductive logic essentially unchanged since Aristotle's Organon. Societies, groups, statuses, roles—all were conceived categorically, as entitles defined by necessary and sufficient conditions, sharply bounded and uniform. In statistical reasoning, categories are replaced by populations and samples and necessary and sufficient conditions by measures of distribution and inferences based on probabilities. Statisticians might note the usefulness of other distributions (Poisson and T, for example), but the normal distribution became the paradigm assumed by informal debate about probabilities. Linear regression, based on the assumption that effects result from the sum of causes identified by least-squares reduction, became the standard formal model to which quantitative social science aspired.
Network science, together with chaos, complexity, fractals and recursion (of which fractals are one example) profoundly transforms the assumptions on which the standard quantitative (normal distribution and recursion) model of social science is based. Independent cases are replaced by interconnected nodes, which, by definition, do not act independently. Power law distributions, e.g., the Pareto curve, and the hierarchical, hub-and-spoke network topologies they imply have been identified across virtually the whole spectrum of natural and social phenomena, from protein cascades in cell biology to transportation and power grids, the Internet and World Wide Web, and a host of social networks.
In my own data, on winners of a Japanese ad contest, I have already seen how reliable the new mathematics of networks is. Large networks tend to have a single giant component (a component is a subnetwork in which there is at least one path from each node to every other) with a scattering of, relatively speaking, tiny components as outliers. The larger the network the more likely it is that the giant component is also a giant bicomponent, in which there are at least two paths connecting every node to every other (a matter of concern to those who worry about the robustness of networks). The degree distributions in my data (degree being the number of immediate neighbors of a given node) are, indeed, power laws. The fit is uncannily close, far closer than the .05 or .001 significance levels commonly referred to in statistical studies. This is a social physics that works--and works with amazing accuracy, just as mathematical theorems imply that it should.
Are we forced, then, to imagine a world in which human behavior is totally controlled by the mathematical laws that network science reveals? Not at all. I recall a high school physics class in which the teacher remarked that the laws of electromagnetism apply to large numbers of electrons, not to predictions about individual electrons. The fact that, other things being equal, the law of gravity will cause objects to fall from sky to earth does not prevent humans from designing balloons, airplanes and helicopters that fly. The trick is to find and employ countervailing forces.
In a similar spirit, the discovery that, left to themselves, totally free markets will inevitably result in sharp polarizations of wealth and opportunity does not mean that this result is inevitable. Here, too, countervailing forces may be identified and used to ensure different outcomes. Progressive tax schedules and estate taxes may, for example, be used to prevent inequalities in wealth and opportunity from reaching extremes. Ditto for rules governing executive compensation. Working out the specifics may be as difficult as designing or improving the design of an airplane's wings. It is not, however, impossible.
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