Ancient population estimates

Why can excavating an ancient city more thoroughly still leave its population uncertain?

There is an assumption buried in the phrase "we don't know how many people lived there yet": that the number is in the ground, and enough digging will bring it up. But look at what happens. Sites excavated for a century, with plans of thousands of rooms, still carry published figures that differ between careful scholars by a factor of two, three or more — and newer figures are not converging on older ones so much as re-arguing them. If more evidence is not closing the gap, the uncertainty is probably not the kind evidence closes. So what kind is it?

Start from the fact that nobody has ever counted an ancient population. The number is always computed, and always a product: settled area multiplied by people per unit area, or roofed floor space multiplied by people per unit of floor. Either way at least two quantities are multiplied, and in careful work there are four.

Take the first term, the one digging genuinely improves. What is the settled area? Not the area inside the wall — walls enclose gardens, stock pens, dumps, precincts and ground held empty for refuge. Not the area with sherds on the surface, since manuring scatters domestic rubbish across fields. Excavation and survey really do narrow this, which is why the effort feels as though it should work.

Now the second term, persons per hectare. Where does it come from? Not from the site. It is imported — from ethnographic observation of living settlements, from historically documented towns, or from a comparable excavated site whose own figure was derived the same way. Nothing you dig changes it. You can uncover every house in the city and the coefficient you multiply by is exactly what it was before you started. That is the crux: excavation improves one factor and leaves another untouched.

The third term bites hardest. A site's visible plan is a palimpsest; its houses were not all standing at once but accumulated over centuries as buildings were abandoned, robbed and rebuilt. To know how many stood together you need dating fine enough to separate them, and ceramic phasing typically resolves to something like a century — wider than a lifetime and far wider than the question. Excavating more of the same phase adds houses without saying how many were occupied in any one year.

And a fourth, quieter one: how many people occupied a house. The classic move — a fixed floor area per person, Naroll's roughly ten square metres of roofed space (recalled, and disputed almost from publication) — is again a coefficient from elsewhere, and later comparative work found no universal constant to import.

Do the arithmetic on that structure, because the structure is the answer. Suppose each of three factors is known only to within a factor of one and a half either way — an optimistic assumption. One and a half cubed is about 3.4, so the low combination sits 3.4 below the middle and the high one 3.4 above, and the full range spans roughly elevenfold. Errors that multiply do not average out; they compound, and they compound in factors rather than percentages.

Three clarifications, one of them a warning against my own tidiness.

First, this is a different problem from a census undercount. A census is a count that came out wrong, and it has a true value that better fieldwork approaches. An ancient population figure is not a count at all; it is the output of a model whose inputs are mostly borrowed, and better fieldwork improves one input.

Second, the uncertainty is not a caveat attached to a number — it is the subject. The honest answer is a range with the reasoning for its ends, and where an author gives a single figure the useful question is which coefficient they chose and why. Two scholars can agree on every excavated wall and still differ threefold, entirely on the coefficient and the contemporaneity assumption.

Third, against myself: the multiplicative story sounds worse than the situation is, because the factors cannot roam independently. They are bounded by things that are not archaeological at all — a city cannot exceed what its catchment feeds at known yields and transport costs, or what its water supply delivers. Those bounds are themselves uncertain, but they cut off the extremes, which is why serious estimates cluster rather than spanning the full elevenfold spread the arithmetic permits.

What would refute the account? It predicts that disagreement should track the choice of coefficient rather than the amount excavated — so if published figures for a site narrowed steadily as more of it was dug while analysts went on using different coefficients, the diagnosis would be wrong. And I will not hand you figures for named cities. For every well-known ancient city I can think of, the published range spans a factor rather than a margin, and quoting the midpoint would present a modelling choice as a fact.

• How catchment and water-supply ceilings are computed, and how much they really narrow an estimate.
• Why the same multiplicative structure governs estimates of ancient mortality from cemetery populations.

Every term the collection defines is gathered in the glossary.