The Hindu Business Line : Quakes, markets and power play

Suppose you study the distribution of wealth in a city. You find that the number of people whose wealth is Rs 100 crore is twice as much as those who have Rs 200 crore, which is twice as much as those who have Rs 400 crore.

You have just written a power law distribution. It is essentially a system where smaller versions of the phenomenon you are studying are more frequent than the larger versions.

What is power-law relationship for earthquakes? A study shows that an earthquake with a magnitude of two is ten times stronger than that with a magnitude of one. Similarly, earthquake with a magnitude of three is ten times stronger than one with a magnitude of two. This power law is called the Gutenberg-Richter Law.

Another study found a similar power-law relationship between the magnitude of the earthquake and the frequency of its occurrence. That is, the higher the magnitude, rarer is its occurrence.

Financial markets follow power law too. One study found that the number of mutual funds with, say, Rs 1,000 crore is twice the number of funds with Rs 2,000 crore. Similarly, the number of funds with Rs 2,000 crore is twice that of funds with Rs 4,000 crore. This pattern is called the Zipf's law, named after George Kingsley Zipf who found that the frequency of use of words in any language follows a similar power law.

Power laws are typically observed in systems that scientists research in the area of complexity theory. This theory centres on the phenomenon called self-organised criticality. It essentially means that things do not happen gradually but abruptly in avalanches. Now you can picture why high-magnitude quakes occur and stock markets crash.

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