zipf’s law – well, it’s not really a law.  it’s an observation, that many naturally occurring phenomena follow the same mathematical distribution.  these are things with seemingly no order to them – say, the words we use when we use language.  zipf’s (first described by harvard linguist george kingsley zipf) holds that in ANY given body of utterances – this post, shakespeare’s corpus, or the lifetime conversations of dick cheney – the frequency of any word is inversely proportional to its frequency rank.  in other words, the second most-used word occurs 1/2 times – or 50% as much – as the most-used.  weird, but okay – there may be some systemic, grammatic explanation for this, something about the use of articles vs. prepositions, and the maximum number of articles the human mind has a need to invent – something.

but it doesn’t just happen for language.  say you ranked the richest people in the world?  incredibly enough, you see the same distribution there too (though with some multiplier factored in, and obvious outliers discounted).  population of world cities?  roughly the same.  commonality of earthquakes?  yep, that too.  a 2002 atlantic article observes that these are ‘complex systems whose next perturbation is unpredictable but whose behavior, viewed on a large scale and over time, follows certain patterns—patterns, moreover, that the individual actors in the system … are quite unaware of generating.’  though it may be the furthest thing from our minds, as we are moving into and away from cities, we are doing so in a volume that fulfills a fairly specific mathematical pattern.

over and over, reality proves that it arranges itself according to startlingly simple patterns.