"Split a pizza?"

A few days ago Steven Strogatz, an applied mathematician at Cornell University, wrote a guest article in the New York Times about scaling laws in nature and human society.

For example, if city A is twice as large as city B, does it have twice as many gas stations? It turns out that it has something like 1.77 times as many. Or, if mammal X is twice as large as mammal Y, does it need twice as many calories to live? It turns out that it needs something like 1.74 times as many. Why is this, and is it a coincidence that these numbers are so close? The answer seems to be that we have some ideas, but no definite answers. Perhaps we should think of a city as one big organism with each person living there as one “cell”?

In any case, it’s an interesting article and, even more interesting, has lots of good comments. Especially those that point out that Zipf’s Law is more like Zipf’s Rule of Thumb.

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A friend emailed this to me and we both tried to find actual examples of places where Zipf’s Law worked — we couldn’t find any.

I think rather than Zipf’s Rule of Thumb it’s more Zipf’s Light Suggestion.

Jason,

A big part of the problem is giving a consistent, meaningful definition of the population of a city. But even given that, it’s a fudge.

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