Enumerate the distinct occupations practised in a settlement and plot the number against the settlement's population, and the points approximate a line on logarithmic paper. Double the population and the number of occupations increases by a fixed proportion, and it does so across a range extending from villages of a few hundred to cities of several million, in economies that share no institutions and no history. The regularity is sufficiently old to be discernible in tax rolls and sufficiently consistent that a town well off the line is worth investigating.
The tempting explanation is planning: somebody determined that a settlement of this size needed a farrier and a notary. Nothing of the sort will account for the pattern. The regularity holds in places nobody planned, and it holds at scales where no planner could have had the information. Nor is it a matter of demand alone. Demand explains the capacity of a larger town to support a specialist that a smaller one cannot, but it does not explain why the relationship should take the same mathematical form in the twelfth century and the twenty-first.
The account that has survived scrutiny commences with interaction. A specialist can exist only where sufficient people can reach him frequently enough to keep him in employment. What determines that is not the number of people but the number of encounters, which increases faster than population does because each additional person can encounter all the others. A settlement is, on this account, a mechanism for elevating the encounter rate, and everything that follows from being larger -- more occupations, more inventions per head, higher wages, and also more congestion and higher rents -- follows from the same source.
The account justifies itself by predicting the exceptions. Settlements whose internal circulation is obstructed -- by a river with one crossing, by a ridge, by a regulation that keeps quarters separate -- should behave like smaller places than their population suggests, and they do. Settlements distributed along a route instead of gathered around a centre should do the same, and they do. In each case the population is unchanged and the encounter rate is not, and it is the encounter rate that the occupation count tracks.
What the account does not do is instruct anyone what to build. A regularity of this kind describes what happens when a considerable number of people arrange themselves without coordination. A planner who tries to hit the line directly is undertaking something different from what produced it. The line constitutes a summary of a process, and the process is the thing that has to be present. That is not a counsel of despair, since the encounter rate is something a town can act on -- by constructing a second bridge across the river, by permitting uses to sit next to one another, by not zoning the quarters apart. It is a counsel about which quantity to aim at.
