One Thousand and One Conjectures

Gresham's law — bad money drives out good — is here joined to the physics of phase transitions. The conjecture is that the driving-out is not gradual: when rulers debase the coinage, users tolerate the slide in silver fineness up to a…

The gravity model of trade — flows decay with distance, and how steeply they decay depends on what the goods are worth relative to what they cost to move — is here tested on sourced ancient artifacts. Provenance science can trace both…

The walls of Pompeii preserve genuine written conversations: graffiti that answer, mock, and extend earlier graffiti on the same surface, recorded in CIL IV. Modern online forums show a robust statistical signature in how such exchanges unfold — the distribution of reply…

The Tabula Peutingeriana, the famous medieval copy of a Roman route map, was almost certainly compiled from multiple earlier itineraries rather than drawn from any single survey. Each source itinerary would carry its own error habits — its own units, rounding conventions,…

Ancient shipwrecks preserve frozen samples of trade: each cargo is a snapshot of what was moving, and from where, at the moment of sinking. The Shannon entropy of cargo composition — how mixed a ship's load is across goods and origins —…

Transport science distinguishes two ideal networks: the Wardrop user equilibrium, in which each traveler selfishly takes the route fastest for himself, and the system optimum, in which a planner routes everyone so as to minimize total travel time. The two diverge precisely…

Roman aqueducts held gradients of centimeters per kilometer over tens of kilometers, and how surveyors achieved this with simple instruments is a genuine puzzle. Statistics offers a diagnostic: if each leg of a survey adds a small independent error, accumulated error grows…

This joins Roman timekeeping to the archaeology of mass production. A sundial only reads true at the latitude it was cut for, and a surprising number of portable Roman dials are misfits — engraved for latitudes far from where they were found.…

The astragalus — the ankle bone of a sheep or goat — was the everyday die of Greek and Roman gaming, and unlike a cube it is honest about its dishonesty: its four usable faces land with very different frequencies, broad faces…

Roman dice are notoriously irregular — surviving cubes are often visibly asymmetric, with face dimensions and pip placement far from the modern standard — and the crookedness has usually been waved off as indifference to fairness. Asymmetry, though, is measurable: 3D scanning…

Joins eigenvector centrality — the recursive logic behind Google's PageRank, in which authority flows to those cited by the authoritative — to Roman jurisprudence. The Law of Citations of 426 CE decreed that courts follow five jurists — Papinian, Ulpian, Paulus, Modestinus,…

Price-ceiling economics predicts that goods capped below market price withdraw from legal, recorded exchange, while goods capped at or above market trade on visibly. This conjecture reads Diocletian's Price Edict of 301 CE through that lens: the Edict's famous failure should be…