One Thousand and One Conjectures

Fracture physics and Viking economics meet in the hack-silver hoard. When brittle materials are broken repeatedly and more or less at random, the resulting fragment masses follow a universal power-law distribution — a robust result from fragmentation physics that holds for shattered…

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…

Nominal wage rigidity — the Keynesian observation that wages resist adjustment even when prices move — is here pushed back four thousand years to the ration lists of Ur III Mesopotamia. Ur III institutions paid workers standardized rations of beer and barley,…

Mesopotamian kings periodically proclaimed debt-cancellation edicts — the acts remembered in the biblical Jubilee — and cuneiform loan contracts were physical objects, clay tablets whose destruction voided the debt. Join the two and the conjecture follows: royal debt cancellations should have left…

The Polya urn — the classic mathematical model of path dependence, in which each ball drawn adds another of its color so that early luck compounds forever — is here applied to the medieval pilgrimage market. Pilgrims bought cheap metal badges at…

The lender of last resort — Bagehot's celebrated principle that a central bank should lend freely when private credit dries up — is here sought in the Old Babylonian credit market, more than three millennia before the Bank of England. Babylonian lending…

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…

In the 13th century, English law adopted a rule for how far apart markets must be — the spacing derived in the classic legal reckoning from a day's return journey on foot, about 6.6 miles. The conjecture joins this statute to the…

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…

Herodotus reports distances for places he never saw, relayed to him through chains of informants stretching away from the Aegean. Each retelling plausibly multiplies an estimate by some random factor — a merchant rounds up, a guide exaggerates, a translator garbles —…

Caravanserais — the fortified roadside inns of the Silk Road and the Islamic world — existed to break overland journeys into daily stages, so their spacing was governed by a physical constant: how far a loaded camel walks in a day. The…

Pre-modern coastal seafaring was rhythmic: ships coasted through daylight and sought harbor by nightfall, which makes a day's sail — roughly 35 nautical miles for typical Mediterranean craft — the natural spacing unit of maritime infrastructure. The conjecture is that this rhythm…

Around the Bronze Age tells of northern Mesopotamia, millennia of feet and hooves wore the landscape into 'hollow ways' — sunken route networks still visible in Cold War CORONA satellite imagery. The slime mold Physarum polycephalum famously grows near-optimal transport networks between…

Obsidian is archaeology's ideal tracer: every piece can be chemically fingerprinted to its volcanic source, so its spread maps prehistoric exchange with unusual precision. Falloff with distance from source is conventionally summarized by a single distance-decay exponent — steep when goods move…

Baltic amber moved from its northern shores to the Mediterranean through hand-to-hand exchange, and FTIR spectroscopy can certify which finds are genuinely Baltic, giving a clean tracer of prehistoric long-range flow. Physics offers a ready model for such flow: the advection–diffusion equation,…

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 —…

The Cistercian order expanded by filiation — mother abbeys founding daughter houses — under statutes and economic pressures that discouraged crowding, since each abbey lived off its own granges and lands. That is the setup of competitive exclusion in ecology, where territorial…

The medieval Champagne fairs ran as a fixed annual cycle of six fairs in four towns, and the merchants of Flanders and Italy worked the whole circuit. Seen with modern eyes, scheduling that cycle is a traveling-merchant optimization: fair dates and durations…

The Shapley value, cooperative game theory's canonical answer to fair division, pays each member of a coalition its average marginal contribution to the coalition's worth. The Hanseatic League was such a coalition: member cities jointly controlled Baltic and North Sea trade routes,…

The Byzantine empire ran a fire-signal chain that could relay news of Arab raids from the Cilician frontier to Constantinople within hours — a communication channel in the exact information-theoretic sense, and one operating under noise, since fog and haze could blind…

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…

As chess spread from India across Eurasia, both its objects and its rules mutated regionally: the piece carved as an elephant in the Islamic world became the bishop in Europe, and the moves themselves varied between documented regional rule sets. Linguistics maps…

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…

Gothic churches were built in successive campaigns over decades, and masons could watch how earlier bays and earlier buildings cracked, leaned, or stood. Modern limit analysis can compute, for any buttress geometry, how far it sits from the thrust-line optimum — the…

This joins medieval craft practice to modern acoustics. An organ builder must decide how pipe diameter should vary with pipe length across a rank — too narrow and the trebles turn thin and stringy, too wide and the basses go dull —…

This joins Viking shipbuilding to modern fracture mechanics. A clinker hull is a shell of overlapping oak planks, and its worst enemy is a running split: a crack that starts at a fastening and propagates along the grain. Fracture mechanics says such…

This joins political history to the humble measuring rod: it treats measurement variance as a government-strength index. Enforcing standards is one of the costliest, least glamorous things a state does — inspectors must travel, deviant rods must be seized, workshops must be…

This joins the Dresden Codex — the finest surviving Maya astronomical manuscript — to the mathematics of best rational approximation. The codex's Venus table tracks the planet with a canonical 584-day period, but the true synodic period is close to 583.92 days,…

This joins calendrics to political economy. Before the 19-year cycle fossilized Babylonian practice, Mesopotamian leap months were declared ad hoc, by royal or priestly decision, ostensibly to keep the lunar calendar aligned with the seasons. But an extra month is also an…

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.…

This joins the three great survivals of ancient gearing — the Antikythera mechanism of Hellenistic Greece, the Byzantine geared sundial-calendar, and the Islamic geared astrolabes — into a single line of craft descent. The tooth module, the characteristic size of a gear…

This joins the Classic Maya collapse to the physics of percolation — the mathematics of systems that fail not gradually but when a critical threshold is crossed. Lowland Maya cities rode out the dry season on constructed reservoirs, so each city's resilience…

This joins the vast water network of medieval Angkor to the theory of self-organized criticality — the sandpile physics in which a slowly loaded system tunes itself to a critical state where avalanches of every size occur, their sizes following a power…

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…

The Bass diffusion model, the workhorse of new-technology adoption studies, splits uptake into two forces: an innovation coefficient p (adopters persuaded by external influence) and an imitation coefficient q (adopters copying their neighbours). Medieval Europe's watermill boom is a textbook diffusion process,…

The Wadi al-Jarf papyri preserve the logbook of Merer, a boat-crew overseer under Khufu, recording day by day his gang's deliveries of Tura limestone to the Giza works — effectively a shipping ledger for the Great Pyramid. Independent arrivals at a facility,…

The Inca road system, the Qhapaq Ñan, was punctuated by tambos — state way-stations providing lodging and stores — whose spacing has usually been described loosely as a day's walk apart. But a day's walk in the Andes is not a distance:…

Medieval masons cut personal marks into the blocks they dressed — piece-work signatures for the paymaster — and a cathedral wall therefore carries, frozen in stone, a record of who cut what. Work organisation leaves statistical fingerprints: if masons produced blocks in…

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 Shang kings at Anyang divined by heating cattle scapulae and turtle plastrons until they cracked, reading the cracks as answers — and the inscriptions often record the sequence in which the questions were put. Crack formation, driven by micro-structural accidents of…

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…

Lapita pottery — the dentate-stamped ware that tracks the first colonisation of Remote Oceania — carries a formal decorative system: a repertoire of standardised motifs whose consistency across thousands of kilometres testifies to a connected early exchange network. Information theory offers a…

Joins the bunching estimators of modern public finance — the kink analysis that detects tax brackets as piles of taxpayers stacked exactly at the threshold — to the Chinese examination system. If jinshi degrees simply tracked the geography of talent and schooling,…

Joins index-number theory — the chained construction behind the modern consumer price index — to Tamil temple epigraphy. Thousands of dated Chola-era endowment inscriptions record in stone the rates of paddy, ghee, and oil required to keep a temple lamp burning in…

Joins stream-power hydrology to the great fiscal cadastre of 1086: the Domesday survey, in recording what each water-mill rendered to its lord, unwittingly logged a physics meter across England. A mill's earning power was set by the hydraulic power of its site…

Joins the economics of luxury counterfeiting to Japanese sword connoisseurship. Counterfeiters allocate effort where brand equity is highest — today's fakes concentrate in the top handbag brands, not the mid-market — because the payoff to a forged label scales with the premium…