One Thousand and One Conjectures

Greenland's ice sheet and Roman monetary history are usually studied by different disciplines, yet the first quietly records the second: lead deposition in Greenland ice cores derives largely from the atmospheric fallout of Roman smelting, and because silver was refined from lead-rich…

Coin hoards and the VIX volatility index are the two well-known things joined here: hoard deposition is antiquity's fear gauge. People bury treasure when they are frightened, and — crucially — they bury on rumor, before armies actually arrive, just as modern…

Circulation velocity — how fast money changes hands, a quantity economists struggle to measure even today — is here read off the physical surfaces of the coins themselves. Every transaction abrades a coin slightly, so cumulative wear divided by time in circulation…

Gibrat's law — the modern finding that firm growth rates are independent of firm size, which generates the Pareto (power-law) distribution of firm sizes seen in every industrial economy — is here tested two thousand years early. Roman brickyards (figlinae) stamped their…

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…

Among the ostraka cast against Themistocles, a famous deposit of 190 sherds turned out to have been inscribed by just a few hands — prepared ballots, evidently readied for distribution to voters. The conjecture generalizes this find into a testable model of…

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…

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 —…

Iron Age hillforts were often built within sight of one another, and lines of sight are functional links: signals, warnings, and social monitoring all flow along intervisibility. Computed from digital elevation models, the intervisibility graph of a hillfort landscape can therefore be…

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 military camps — the most standardized settlements of antiquity — to the physics of crystal lattices. A Roman camp is laid out on a grid as regular as an atomic lattice, and like a lattice it can carry defects:…

This joins Wright's law — the industrial learning curve, under which performance improves as a power law of cumulative production — to the humblest of ancient mass products, amphorae and lamps. Wright's law is usually treated as a discovery of twentieth-century aircraft…

This joins Roman economic history to archaeometric chemistry. Fresh Roman glass was made in a handful of great Levantine furnaces and shipped west as raw chunks; when supply chains ran smoothly, workshops melted fresh glass, and when they faltered, workshops fed broken…

This joins Roman land surveying to archaeoastronomy. When Rome founded a colony, surveyors laid out the centuriation — the great land grid — around a principal axis, and Roman ritual practice tied foundation ceremonies to specific festival dates. The conjecture holds that…

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 Garamantes of the Libyan Fezzan built one of antiquity's great irrigation systems: hundreds of kilometres of foggaras — underground channels of the qanat family — tapping a fossil aquifer left over from a wetter Sahara, water that was being mined, not…

Rome's grain dole served on the order of 200,000 registered citizens each month, administered through the Porticus Minucia Frumentaria, a purpose-built hall whose distributions ran through 45 numbered bays — recipients were assigned a specific bay and day. That is, structurally, a…

The Colosseum moved crowds of tens of thousands through its vomitoria — the numbered entrances and radiating stair-and-corridor system that gave the building its famously fast turnover. Modern stadium safety codes make crowd egress a precise engineering quantity: evacuation-time standards, flow rates…

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…

The two classical ways of casting the I Ching generate hexagrams with different statistics: the older yarrow-stalk procedure is asymmetric — its line-types fall with unequal probabilities, making some changing lines markedly likelier than others — while the later coin method is…

A forecaster facing a high-stakes, high-uncertainty question hedges — wide intervals, conditional phrasing — because a confident miss is fatal to credibility; options markets price the same logic as implied volatility. The oracle at Delphi faced the identical institutional problem for a…

Joins atmospheric physics to colonial sociolinguistics: just as pressure thins exponentially with altitude at a fixed scale height, Greek thinned with river distance up the Nile from Alexandria at a fixed exponential scale length. The mechanism is demand decay: Greek was the…

Joins actuarial insurance pricing to maritime archaeology. A fourth-century BCE Athenian bottomry loan was repaid only if the ship survived the voyage, so the premium over ordinary land-secured interest is a pure risk price: if lenders broke even, the spread directly encodes…

Joins modern campaign geography to Pompeian electoral epigraphy. Political scientists mapping yard signs and canvassing find both decay with distance from the candidate's home, because campaigns run on the candidate's own network of neighbours, clients, and friends, and that network is spatially…

Joins the economics of protection rackets to Han-Xiongnu diplomacy. A racketeer prices extraction to the victim's outside option: what matters is not how hard the racketeer can hit but how badly the victim needs quiet, so payments ratchet up when the victim…

Lanchester's attrition laws distinguish two regimes of combat: aimed fire, where any unit can concentrate on any enemy, yields the square law, in which numerical superiority compounds; frontage-limited melee, where only the front ranks engage, yields the linear law. This conjecture maps…

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…

Service-capacity planning sizes a facility to a fixed fraction of the population it must serve at peak; this conjecture claims Greek cities did the same with their theaters. If theaters were built to seat a set percentile of the citizen body —…

Steppe animal-style motifs crossed gold, openwork bronze, felt, wood, and tattooed skin. What a mobile craftsman memorizes is the armature — which limb crosses which, how the coil closes, how many contact points — while proportions are re-fitted to every object. Topology,…