Petrie's problem. Excavating predynastic cemeteries in Egypt in the 1890s — Naqada and Ballas in 1894-95, Diospolis Parva in 1898-99 — Flinders Petrie faced hundreds of graves with no stratigraphic relationship to each other and nothing to date them by. He wrote the contents of each grave on a slip of paper and rearranged the slips until he had a sequence he was satisfied with, reasoning that the best order was the one in which each design style was concentrated over the shortest span. He published the resulting sequence dating in 1899 and the chart in 1901. It is now called seriation, and it was a genuine breakthrough for empirical archaeology.

The assumption underneath. Seriation works only if styles behave the way fashions do: introduced, adopted, popular, abandoned — a single continuous span of use. A style that is revived after a gap, or that persists as an heirloom, breaks the assumption. Archaeologists have to argue, not assume, that their material behaves this way.

Order, not date; and not direction. A seriation gives a relative sequence and nothing more. Reversed, it fits the data exactly as well. Dates and direction come from outside — stratigraphy at another site, a datable import, radiocarbon. Petrie's predynastic sequence has since been tied to absolute chronology by radiocarbon work, which is what converted his relative order into calendar time.

Contextual and frequency seriation. Petrie's method used presence and absence. Later workers used proportions instead, plotting how common each style is at each point, which produces the battleship-shaped curves that give frequency seriation its nickname. Same logic, finer resolution.

Why it is done by computer now. The number of possible orderings of n assemblages is n factorial — fifteen graves already gives more than a trillion arrangements. Hand-shuffling finds a good order, not provably the best one, and gets trapped in local optima exactly as you found. Algorithms search that space properly. What they do not do is decide whether the underlying assumption about style holds, which is still the archaeologist's judgement and still where the method actually lives or dies.

Analysis

Blueprints (3)

Pottery Seriation

Flotation for Seeds and Charcoal

Dendrochronology