Zipf’s Law
I’d heard of Zipf’s Law before, but was still astonished when a friend sent me this New York Times article about some of the things it applies to. The parts of it that really got me:
[T]he largest city is always about twice as big as the second largest, and three times as big as the third largest, and so on. In other words, the population of a city is, to a good approximation, inversely proportional to its rank. Why this should be true, no one knows.
—“Guest Column: Math and the City”, Steven Strogatz, The New York Times, 19 May 2009
Whether you measure miles of roadway or length of electrical cables, you find that all of these also decrease, per person, as city size increases. And all show an exponent between 0.7 and 0.9.
—“Guest Column: Math and the City”, Steven Strogatz, The New York Times, 19 May 2009
The same law is true for living things. That is, if you mentally replace cities by organisms and city size by body weight, the mathematical pattern remains the same.
—“Guest Column: Math and the City”, Steven Strogatz, The New York Times, 19 May 2009
I don’t know what it “means”, but it strikes me as completely fascinating.