Saturday, 20 August 2016

Don't Fear The Clusters, They Are Part Of The Natural Process Of Experimentation


There is a lot of talk in our country about how London is so markedly different from every other city in England that it's almost like a little country by itself. Because of which, politicians are always going on about trying to build up other cities to a similar status.

What they may not know is that there is a mathematical power law that explains why this phenomenon is to be expected - it's called Zipf's law, and it states that given a large sample of data, the frequency of any element of that data is at a certain size inversely proportional to its rank in a table that measures frequency, size or some similar measure.

Consider the usage of words in the English language. Zipf's law states that the most frequent word (the word 'the') will occur approximately twice as often as the second most frequent word (the word 'of'), three times as often as the third most frequent word (the word 'and'), and so on. This is called the rank vs. frequency rule.

The same rule also holds for the distribution in rankings of cities by population - meaning if you compare the biggest city with the second biggest, city 2 is half as big as city 1, city 3 has 2/3 the population of city 2, city 50 has 49/50ths the population of city 49, and so on. We find that while it's not an exact law, by a very close approximation it holds pretty much everywhere you look - be it word frequency, city sizes, income distributions or sizes of corporations.

Compared to smaller cities, large cities show an abnormal distribution of sizes, largely because people tend to flock to big cities to improve opportunities, and for a bunch of other reasons I blogged about here.

These power laws are social laws that resemble natural laws (rather like how Kleiber's law of animals' metabolic rate proportional to their size very closely resembles a power law about how cities use resources as populations increase) - and there's no reason to be perturbed by them.

The key thing that people are gradually starting to learn is that things are generally not designed by a central planner, they evolve over time, and although they look spectacularly like they are too sophisticated to have emerged by a long process of trial and error with no end goal in sight, it is not the case.

The primary vehicle for progression is very much trial and error and experimentation, and these clusters - be they city sizes, income gaps, business growth models, or numerous other things that seem to worry the masses - should not elicit contempt or discomfiture in us; they are what occur when people make choices and when those results are measured mathematically.

Once you understand the mathematics that underwrites all those societal choices and complex interactions, you have the tools for understanding pretty much anything in the triune relationship between economics, politics and human behaviour.

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