One Thousand and One Conjectures

Bronze needs tin, and Late Bronze Age tin moved through a long-distance exchange network linking a handful of distant sources to every workshop in the eastern Mediterranean. In network terms, some cities were mere consumers while others were high-betweenness brokers — nodes…

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…

A qanat taps groundwater through a 'mother well' sunk into an aquifer, and every producing well draws down the water table around it in a cone whose radius is set by measurable aquifer physics — transmissivity, storativity, discharge rate. Two qanats sunk…

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…

Joins transport-cost linear programming to the Codex Mendoza, the pictorial register of what each Aztec province owed Tenochtitlan. The empire had no draft animals and no wheels: every tribute load moved on a porter's back, so the true cost of a good…

Joins web-graph topology to hadith science: when Broder and colleagues mapped the early web, they found a bowtie — a small strongly-connected core through which most hyperlink paths route. This conjecture claims the isnad network of the canonical hadith collections has the…

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,…

Vertical-monopoly pricing from industrial organization shows that a chain of independent monopolists along one route charges more in total than a single owner would, because each ignores the damage its markup does to the others' traffic. This conjecture reads the toll castles…