One Thousand and One Conjectures

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 two of the medieval world's best data series: the Nilometer readings of the Nile's annual flood, kept for centuries at Cairo, and the grain prices preserved in the Cairo Geniza's merchant letters. Egypt's harvest was the flood: a low Nile…

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…

Markowitz's portfolio theory says diversification pays exactly when the assets you spread across are weakly correlated — variance falls fastest where covariance is low. The medieval open-field system's scattered strips, a puzzle ever since they were read as peasant insurance, are a…

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,…

Airborne LiDAR has stripped the canopy from the Maya lowlands and revealed settlement in the tens of thousands of structures, making true regional settlement hierarchies measurable for the first time; settlement-scaling theory, meanwhile, holds that integrated urban systems produce Zipfian rank-size distributions…

The Swahili stone towns of the East African coast — Kilwa above all — were built of coral rag set in lime mortar, and construction there was governed by the monsoon: the rains halt building and lime-burning, so work proceeds in an…

RT60 — the time a sound takes to decay by sixty decibels — is the basic figure of architectural acoustics, and a great stone nave can hold a note for many seconds; a fast syllabic melody blurs into mud in such a…

The Norse thing — the open-air assembly at which law was recited, cases were pled and decisions proclaimed — was above all an exercise in unamplified speech before a crowd, and sites like Thingvellir have long invited the suspicion that their cliffs…

Muqarnas — the honeycomb vaulting of Islamic architecture, thousands of small stepped niches filling domes and squinches — is usually read as pure geometry made ornament. But a surface of many differently sized and angled cells is exactly what a modern acoustician…

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 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…

Spanish chroniclers report that Inca accounting was run by paired officials who kept independent records of the same stocks so that each could check the other — and the surviving corpus does contain matching khipus, cord records whose numerical content substantially overlaps.…

Bachet's classic weight problem asks for the smallest set of standard weights that can weigh out every required quantity on a balance — a combinatorial optimisation whose solutions depend on whether weights may sit in one pan or both. The Indus Valley…

The Polynesian settlement of the Pacific is the greatest search problem ever solved by a preindustrial society, and optimal search theory says how a rational searcher orders targets: not by raw distance, but by how easy each target is to find. An…

Oceanic navigators built two great families of direction-finding system: star compasses, like the Carolinian sidereal compass, which hang the frame of reference on the fixed rising and setting points of stars; and wind compasses, which name directions by the winds themselves. 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…

The deep blue of medieval stained glass comes from cobalt, and medieval Europe mined very little of it: the colorant travelled along long-distance routes whose ultimate sources lay far to the east. Every ore body carries a trace-element fingerprint — the ratios…

Joins autocatalytic reaction kinetics to the sociolinguistics of conquest: in Egypt's dated documentary papyri, the replacement of Greek and Coptic by Arabic behaved like a chemical substitution running with a nearly universal rate constant. The mechanism is autocatalytic — every office and…

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 capture-recapture ecology to Greek philology: ecologists estimate how many species they have never seen from the ratio of species observed exactly once to species observed exactly twice, and the same arithmetic applies to books. Each surviving witness to a Greek work…

Joins neutral models of cultural evolution to Byzantine book epigrams — the short verses scribes copied into margins and colophons, catalogued by type in the DBBE. Under the standard rich-get-richer model of cultural copying, an epigram type spreads because scribes copy what…

Joins the statistics of radioactive decay and modern firm-survival analysis to monastic geography: manuscript-producing places, the claim runs, went extinct at a constant hazard, like unstable isotopes. The mechanism is that the deaths of scriptoria were dominated by external shocks — raids,…

Joins statistical seismology to archival formation processes: an administrative archive, the claim runs, forms like an earthquake sequence. A main shock — a reform, a new institution, a royal accession — sets off a burst of documentation, and what follows obeys the…

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 crime — Gary Becker's principle that offenses rise when their returns rise and legitimate wages fall — to the Deir el-Medina archives of the royal tomb-builders. The workmen were paid in grain, and the ostraca record their ration…

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 statistical process control — the control charts and capability indices of modern manufacturing — to Andean ceramics. Inca state pottery, above all the standard aryballos storage jar, was the output of an administered production system, so the tightness of its dimensional…

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 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…

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 process-engineering labor accounting to Viking naval history. Tally the person-hours in a longship and the surprise is that the hull is the cheap part: replication labor budgets show a large woolen sail — the wool sorted, spun thread by thread, woven,…

Joins the cognitive psychology of recall to the stemmatics of oral law. The serial-position curve is among psychology's oldest findings: in reproducing a fixed sequence, people hold the beginning and end best and blur the middle. Iceland's law was exactly such a…

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,…

Joins the concentration indices of industrial organization — the tools economists use to tell competitive markets from managed ones — to Indus glyptic. Stamp seals were the emblems of whoever ran Indus commerce, and if their animal motifs were the competing badges…