Pottery Seriation

Have someone else invent eight to twelve pottery styles, decide their true order, then write out fifteen "graves", each holding a few styles that were current at that point. Do not look at the true order — you are going to try to recover it.

Make each style appear in several consecutive graves, with new ones entering as old ones leave. If styles never overlap the puzzle is trivial; the overlaps are what carry the information.

Write each grave on its own card: the grave number and the styles it contains. One physical card per assemblage — this is exactly Petrie's method and the physicality matters.

Shuffle thoroughly and lay them in a row in random order. This is the state a real excavation leaves you in.

Draw a grid with graves as rows in their current random order and styles as columns, and mark each cell where that style is present. The pattern will look like noise.

Write the target at the top of the page: every style should occupy one unbroken run of consecutive rows. Every move from here is judged against that one sentence.

Find the style appearing in the fewest graves and move those graves next to each other. Rare styles have short runs and are the easiest constraints to satisfy first.

Slide a single grave card to a new position and redraw its row. Move one thing, check whether the total number of breaks went up or down, keep it or undo it.

Count every place where a style's run is interrupted by a gap. That count is your score, and the whole exercise is driving it to zero. Now you are doing optimisation, not intuition.

Graves sharing no styles with each other must sit far apart; graves sharing several must sit close. Fix the two extremes first, then fill the middle.

When single moves stop helping but breaks remain, swap two distant cards and rework. You are stuck in a local optimum, and this is exactly why seriation was later handed to computers.

Now reveal the answer. Count how many graves are in the right place, and whether your sequence is the true one or its exact reverse.

If you produced the mirror image, you have not failed. Seriation cannot tell early from late — it recovers an order, not a direction. Something external is always needed to orient it.

Have the setter reveal a single dated grave. That one fact flips the whole sequence the right way round. One external date turns a relative order into a chronology.

Now use how many pots of each style each grave holds rather than yes/no, and plot each style's counts down the sequence. Each style should rise, peak and fall — the lens shape called a battleship curve, and the basis of frequency seriation.

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.