Coffee Last

Every within-page pair is a small contest: on this card, was the celery printed above the Camembert? Ten million of those contests, fitted the way you would rank chess players, collapse the whole library onto one line.

What comes back is a bill of fare. Not a schematic of one — an actual runnable menu, in the order it would have been served, assembled from thousands of restaurants that never compared notes. The raw bar is at the top, named oyster by oyster. Soup follows. Then fish, then the birds and the game, then the joint and the chop, the vegetables beside them, salad after, then pastry, then ices and fruit, then the cheese — and under all of it, always, coffee.

Which lines are printed here is a choice; where they sit is not. One spelling per dish, and a spread wide enough to cover the whole line rather than two hundred kinds of oyster. The vertical order is the fit's, untouched. The course names in small capitals are mine, read off afterwards, and two of them genuinely overlap: cheese and coffee share the foot of the card.

Because the order comes from counted pairs and not from a theory, you can interrogate it directly. Pick two dishes and the collection answers from the cards that printed both.

Some answers are flat: Blue Points are above coffee on all 457 cards that carry both, without a single exception. Some are perfect coin flips, and those are the interesting ones — they mark the seams where American restaurants never quite agreed. Coffee and tea share 3,680 cards and split them almost exactly down the middle, because they were not competing for a place in the order; they were printed side by side at the end of it.

A ranking can always be fitted. The question is whether it deserves to exist — whether “printed above” behaves like a single queue rather than a tangle of local habits. Three tests, none of which the fit can pass by construction.

Transitivity. Take the pairs the collection decides firmly, at nine to one or better. If A is above B and B above C, is A above C? Across — sampled triples it holds — of the time. Cycles are almost absent, and a relation that acyclic is a line.

One line, many cards. The single fitted order calls the direction of — of well-observed pairs correctly. That is a hard ceiling to approach with one number per dish standing in for every restaurant in the country.

Card by card. The real test is a page the fit has to predict whole. Rank correlation between what a card printed and what the fitted order says it should have printed has a median of — across — pages — against — for the same pages scored against a shuffled order. Only — of cards come out negative, and those are mostly wine lists and breakfast cards, which run to their own grammar.

These are actual pages, drawn at the coordinates the transcribers clicked — the same numbers the order was built from, put back where they came from.

Nothing here is laid out by hand. Each dish sits at its own recorded position, and its ink is coloured by where the global fit puts it: top of the menu through foot of the menu. If the order were an artefact of the fitting, the colours would be noise. Instead every card bleeds cleanly from one end of the scale to the other, top to bottom, because that is what a menu is.

The order is rigid, not frozen. A few dishes walked the length of the card over a century, and one of them walked further than any other.

Grapefruit started as a dessert and ended as the first thing you ate. In 1880–1915 its median place on a card was 0.76 — three-quarters of the way down, in among the fruit and the ices. By 1930–2000 it sits at 0.15, up with the oysters and the cocktails. Even the spelling moved with it: the early cards print grape fruit as two words, the late ones grapefruit, and both spellings make the same journey independently.

Fortified wine went the other way. Sherry ran from 0.24 to 0.58 and port from 0.36 to 0.73 — off the aperitif end of the card and down into the after-dinner position they hold now. Sliced tomatoes slid from 0.21 to 0.56, leaving the relish tray for the salad course. Welsh rarebit stopped being a savoury and became a late snack.

The reason to believe any of this is what did not move. Celery, olives and radishes — the relish trio, and three of the most-printed items in the whole collection — sit at 0.13, 0.13 and 0.14 before 1915 and at 0.11, 0.14 and 0.14 after 1930. If these shifts were an artefact of later cards being shorter, or of the collection drifting toward breakfast, the relishes would drift with them. They do not budge.

The very highest strengths in the whole fit do not belong to a course. They belong to oysters named after the water they were dredged from.

Blue Points, Cotuits, Lynnhavens, Cape Cods, Rockaways, Buzzard Bays, Saddle Rocks, Shrewsburys, Cherrystones, Little Necks. An American diner in 1910 chose shellfish by bed the way a wine list is chosen by vineyard, and those lines are printed above everything else on the card — the single most reliable fact in the dataset.

Then they go. Named beds run at — mentions per hundred dated menus in their best decade and — by the 1980s, reaching zero in the 1990s. Rockaways and Buzzard Bays stop appearing after the 1900s, decades before the rest. The page is not the place to settle why — the collection thins out badly after 1960, and fashion, pollution and the beds' own collapse all point the same way — but the menus stop offering a choice of water, and never start again.

A side effect of transcribing menus is a long price series for things nobody thinks to price.

Two oddities. The demi-tasse cost exactly fifteen cents in every decade from the 1890s to the 1940s — six decades at an unmoved nominal price, through two wars and a depression. And celery cost three times what coffee cost: thirty to thirty-five cents a serving against a dime, more than apple pie, more than ice cream. It is the third most-printed item in the collection and it was priced like a delicacy, which is roughly what it was.