Ceramic seriation

How can a pile of undated potsherds be put in chronological order without a single absolute date?

Here are forty boxes of broken pottery, each the contents of one grave or one floor. No inscriptions, no coins, nothing to send for radiocarbon, no record of which deposit lay above which. An archaeologist will nonetheless put them in order, and can be shown to be right.

Stated that way it sounds like getting information out of nowhere. So be careful about what is claimed — the first move is noticing the claim is smaller than it sounds.

We are not asking how old anything is. Age needs a clock, and there is no clock in a crate of sherds. We are asking only which came before which — an ordinal question, not a measured one, and its cheapness is the whole trick.

So what regularity in the material could carry an order?

Think about any style at all — a rim profile, a handle shape, a way of painting a band round a pot. Somebody makes the first; a few copy it; it spreads, becomes ordinary, and then something newer arrives and it dwindles. Rise, peak, fall. Nothing forces that; it follows from styles spreading by imitation among people whose taste keeps moving. Call it the single-peak assumption, and mark it as an empirical regularity about fashion rather than a law, because everything below rests on it.

Now the step that turns an observation into a method. Each box gives the proportions of the types it contains, so any arrangement of the boxes in a line assigns every type a sequence of percentages across that line. Ask: for how many arrangements is every type's sequence single-peaked?

Shuffle the boxes at random and a type that really did rise and fall shows up as a jagged mess — common, rare, common again. Now notice how demanding the constraint becomes when many types are present at once: each imposes its own condition on the same arrangement, and all must hold together. The true chronological arrangement satisfies them by construction, because that is how the types behaved; almost nothing else does. So the order is recovered by searching for the arrangement that makes all the curves behave — and out comes the calendar you did not have.

Draw the result and you get the picture that named the method. Plot each type's percentage as a horizontal bar, one per box, stacked down the page in the recovered order, and its history is narrow at top and bottom and broad in the middle: a battleship curve.

Two things this does not deliver. Direction: reverse the entire order and every curve is still single-peaked, so the method yields a sequence with no arrow on it. One external fact settles that — a deposit lying beneath another, a datable import, a radiocarbon result — and one is enough, which is why seriation and absolute dating are complements, not rivals. And spacing: adjacent positions are not equal intervals of time, because the method knows nothing about rates. A seriation is a ranking, not a ruler.

Two historical forms, both attributions recalled: presence-and-absence seriation, as in Petrie's sequence dating of predynastic Egyptian graves, and the proportional form associated with Ford. Modern practice searches by correspondence analysis, whose characteristic arch is itself the signature of the structure we assumed.

ice-core-records.md and how-tree-rings-record-the-past.md share the proxy-evidence tag, and the fixed point of difference is that both rest on a physical process laying down one increment per year. The archive has a clock inside it, so it can be counted and yields calendar dates and durations. Seriation contains no physical process whatever: it exploits a regularity in human taste, and its output is ordinal. Which is why the pairing is not seriation or radiocarbon — seriation orders finely where radiocarbon's uncertainty ranges overlap, and radiocarbon supplies the anchor and arrow that seriation structurally cannot.

age-heaping.md is the closer methodological cousin, both reading a pattern rather than measuring a quantity — but opposite things. There, a distortion in how people reported becomes evidence about the reporters; here, a regularity in fashion becomes evidence about order.

One misconception to retire: that this is typology plus intuition. It is a combinatorial constraint problem with a checkable answer, which is why it can be handed to a computer.

The honest caveats are the ways the single-peak assumption fails. An heirloom buried late puts an early type in a late box. A deliberate revival gives a type two humps. Pooling deposits from two valleys makes regional variation masquerade as change over time. Mixing a kitchen midden with a shrine deposit compares assemblages differing by use rather than date. And a small box gives percentages that are mostly noise. Each yields an ordering that looks perfectly respectable.

Which is why the test matters: the recovered order predicts things beyond the data used to find it. Every type's curve should be single-peaked, including types brought in afterwards that played no part in fixing the order; and wherever independent evidence exists — a stratigraphic section, an import of known date, a radiocarbon result — it should agree.

The refuting observations are correspondingly sharp. A well-sampled type that is common, vanishes, and returns is a two-peaked curve the method cannot accommodate. A section in which the layer placed later lies beneath the one placed earlier refutes the ordering outright. And if two very different arrangements satisfy the constraint equally well, the data do not determine an answer, and the honest output is a set of possible orders.

• How correspondence analysis turns the search for an ordering into a geometry, and why the resulting arch is itself evidence the assumption held.

Every term the collection defines is gathered in the glossary.