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…

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 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…

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,…

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,…

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…

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…

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,…

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…

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…

Common-value auction theory predicts the winner's curse — the highest bidder is the one who most overestimated the shared value — and that experienced bidders learn to shade their bids downward. This conjecture finds the earliest documented correction in Venetian state finance:…

Medieval painters had almost no access to antique painting or free-standing portrait sculpture, but Roman coins passed through their world by the thousand. If coinage was the operative model medium for picturing antiquity, ancient rulers should be drawn in strict numismatic profile…

Ornament in stained glass — border types, diaper grounds, grisaille foliage — is studied inside glass scholarship, but glaziers stocked their cartoon chests from painters' books. Ornament families should therefore appear in dated manuscripts before dated glass of the same region, with…

Donor portraiture is one genre under two theologies of presence. Latin donation imagery kept renegotiating scale as lay patronage broadened and purgatorial accounting personalized the stakes; the Byzantine proskynesis format was liturgically frozen. The handbook impression that donors get bigger is not…

That Japanese handscroll action tends right-to-left is a specialist commonplace; the unestablished claim is the full mechanism test across cultures. If lateral bias comes from the reading technology — the image must hand the eye onward to the next scene — then…