One Thousand and One Conjectures

Joins the chronology of Thomas Aquinas's writing career to the arrival curve of the new Greek-Latin Aristotle: early on, Aquinas met much of Aristotle through florilegia, commentary lemmata, and older versions, quoting at second hand; as William of Moerbeke's literal translations and…

in the scholastic classroom the objection-side authorities functioned as a memorized bank of classic difficulties — an objection had to be recognizable to master and audience to carry disputational force, so the same hard sayings of Augustine, Aristotle, and Jerome were recycled…

A scholastic article has a fixed anatomy: objections against the thesis, a short 'sed contra' authority for it, and the master's resolution. The conjecture is that this structure sorts authorities by age like a centrifuge: the sed contra, which must be unimpeachable,…

An abecedarium — a written-out sequence of an alphabet in its canonical order — is copied and taught from teacher to pupil down the generations, and each retransmission risks small changes to the order: a transposition, an inserted letter, a dropped one.…

When binders needed stiffening material they cannibalised old manuscripts, cutting them into the waste fragments now recovered from bindings. The naive model treats this as physical wear-out — books used until they fell apart — which would produce a smooth aging hazard.…

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…

Guido of Arezzo's staff notation — the 11th-century invention that fixed pitches on lines rather than leaving them to memory-jogging squiggles — is here treated as an error-correcting code, and its effect on transmission is claimed to be discontinuous rather than gradual.…

Radiocarbon dating works because decay happens at a constant rate; the conjecture is that manuscript copying does too. Scribes make errors, and within a single scriptorium — same training, same exemplars, same working conditions — the rate of new errors introduced per…

Stemmatics — reconstructing the family tree of manuscripts from shared copying errors — is here fused with computational astronomy. A dated horoscope is a calculation: the astrologer looked up planetary positions in one specific physical copy of a set of astronomical tables…

Information theory meets Homer: the stock formulas of oral epic — the swift-footed heroes and wine-dark seas — are here interpreted as redundancy bits, the padding a noisy channel needs to protect its payload. In transmission over fallible human memory, the hard-to-recover…

Two transmission technologies for Sanskrit ran side by side for centuries: the mnemonic machinery of Vedic recitation — interlocking recitation modes and error-checking permutations built to preserve the Rigveda syllable-perfect — and ordinary manuscript copying, which carried texts like the Mahābhārata. Philologists…

Chinese court astronomers recorded celestial omens for two millennia, but they worked for a state in which comets and eclipses bore directly on the Mandate of Heaven — so the record was politically sensitive by construction. Korean, Japanese, and Arabic astronomers watched…

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 —…

The Tabula Peutingeriana, the famous medieval copy of a Roman route map, was almost certainly compiled from multiple earlier itineraries rather than drawn from any single survey. Each source itinerary would carry its own error habits — its own units, rounding conventions,…

Rongorongo, the undeciphered glyph system of Easter Island, does not have to be read to be classified: its sequence statistics can be compared against the signatures of known genres. Recitation genealogies and chants — well attested in Polynesian tradition — have a…

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 medieval fiscal instruments to information theory. An Exchequer tally was a wooden stick notched with a debt's value and then split lengthwise, creditor and debtor each keeping half; the split's matching grain already authenticated the pair. The conjecture claims the…

This joins Mesopotamian glyptic art to the economics of security. A cylinder seal was its holder's signature, and like any signature it invited forgery; the defence was engraving complexity, since an intricate scene costs a forger far more to copy than a…

This joins the world's oldest accounting technology to modern medical imaging. Before writing, Mesopotamian administrators sealed counting tokens inside clay envelope-bullae and impressed matching marks on the outside: the surface advertised the contents, and breaking the envelope audited the claim. Envelopes that…

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…