Aid on the Edge of Chaos: Rethinking International Cooperation in a Complex World by Ben Ramalingam

Author:Ben Ramalingam [Ramalingam, Ben]
Language: eng
Format: epub, mobi
Publisher: Oxford University Press
Published: 2013-09-27T14:00:00+00:00

The Mathematics of ‘The New Normal’

Per Bak started his investigation into self-organized criticality to try and explain the common recurrence of power laws in a range of natural phenomena. These statistical regularities, which I touched on previously in the context of networks, are a key signature of complex dynamic systems. Although power laws are now firmly embedded in the toolkit of statistical physics, the first identified power law was in an economic context.

Intrigued as to why so much of the land in his native Italy was concentrated in the hands of so few, nineteenth-century engineer-turned-economist Wilfred Pareto set out to map wealth distribution more generally.33 Looking at a large variety of datasets, from Swiss tax records to Parisian rental income and personal income from the UK, Prussia, Italy, and Ireland, he found a series of long tails, today known widely as Pareto distributions. Instead of being normally distributed, as he had expected, wealth was concentrated in the hands of a few. This clearly depressed Pareto, who saw it as evidence of a harsh social Darwinism. The notion of democracy was a lie: human nature was base and selfish.

Rather less portentously, Pareto found similar trends in a range of other phenomena, including in the yields of his home-grown broad beans. A lot of research has been done following Pareto’s discovery to understand the nature and cause of inequality, and the same long tail has been found in many other countries. But the mathematics of the curve eluded Pareto. The question he and his contemporaries didn’t ask, as far as we know, is why this pattern occurs.34

That said, a few notable thinkers do seem to have grasped its potential, among them Schumpeter, who wrote in the 1940s, ‘Nobody seems to have realized that the hunt for, and the interpretation of, invariants of this type might lay the foundations for an entirely novel type of theory’ (emphasis added).35

The ‘novel type of theory’ that would eventually emerge from Pareto’s foundation ended up transcending economics and the social sciences. Researchers working in different fields discovered similar long tails in other contexts. At Harvard in the 1940s, George Zipf found power law distribution when analysing word frequencies in different languages and texts, and also in city sizes.36 Lewis Fry Richardson found a power law in war casualties.37 Richter and Gutenberg in the 1950s, in their study of earthquakes, discovered what is perhaps the most famous power law to date, used in the Richter scale.38 Such diverse examples were drawn together when—surprise, surprise—Herb Simon looked at power laws in a number of contexts in 1955.39 Simon noted that long tails were so frequent, and so widespread, that they could only signify some common underlying pattern of probability. He explored a number of assumptions against each case and showed that, in all the cases, correlations between events of different kinds played a central role in the creation of the long tail. Simon’s analysis is formal and detailed, but is useful because of its focus on assumptions made about the distribution of events in complex systems.

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