The Social meaning of the power law

By | February 8, 2010

If you count the book sales on Amazon and plot them according to frequency, the curve hugs the vertical and horizontal axes, indicating a few very large numbers (the blockbusters) and many small ones (the ‘long tail’ of books like yours and mine). This is a typical manifestation of something called a ‘power-law’ distribution. This is a relationship between the size and frequency of a variable, where the frequency decreases faster than the size increases. If the data are plotted on a log-log scale, the result is a straight line sloping down from left to right. Thus an earthquake that is twice as strong will occur four times more rarely. If this pattern holds for earthquakes of all sizes, it is said to ‘scale’, meaning that there is no typical size that could be said to be representative of earthquakes as a class of phenomena, as is the case with normal distributions. Power laws are found in a wide range of natural and manmade instances. But research on them has grown rapidly in recent decades. Power laws have been discovered for the frequency of words used in natural language; and the distribution of molecular reactions in cells reveals a few hubs linked to most reactions and many weakly connected molecules.

Keith Hart in the essay goes on to discuss the science of networks, the differences in the ability of people to act as hubs or connectors in networks, and the paradigm shift in ideologies that accept the inevitability of, say, inequality in income distribution.

This whole paradigm shift in scientific and statistical models coincides with the breakdown of the nation-state’s monopoly of society and with it the corporatist premises of twentieth century economy, such as jobs for life and social planning. For three decades neo-conservative liberals subordinated national economy to global markets; and the digital revolution has given us a new emergent model of society in the internet. The norm of this new world market was stark inequality. The egalitarian premises of nation-states, seeking to curb capitalism’s polarizing tendencies, gave way to a world society where the winner takes all. All of this has been thrown into stark relief by the economic crisis of 2008-9. But for now the power-law is king. It’s a different model of statistics, for sure. Perhaps it captures society poised between national and world forms. Or maybe we reverted temporarily to the imbalance between market and state typical of the Gilded Age, before national regulation aspired to curb domestic capitalism. The pressing political question for humanity, now given a new urgency by the collapse of the credit boom, remains whether new forms of association will enable us to harness the polarities of the network economy for common ends.

The whole article.

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