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…

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…

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…

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…

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…

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…

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…

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…

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…

The cutting-stock problem of operations research — how to cut standard stock into pieces with minimal waste — meets codicology. This conjecture holds that parchment page sizes were not aesthetic free choices but near-optimal cuts of animal skins: a skin is a…

Packet-switched content distribution splits a file into chunks that travel independently and reassemble at the destination; the medieval university book trade did the same with texts. Under the pecia system, stationers chunked an exemplar into pieces rented out separately, so a single…

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:…

Connects the disputatio's argumentative architecture to the material sources of quotation: the objections a scholastic author stages are the tradition's stock counter-texts, harvested from commonplace collections and classroom memory, whereas the constructive respondeo forces the author back to the authority's actual wording…

Connects the classroom habitus of glossing to stemmatic topology: a schooltext lived its life open beside other copies, its margins stuffed with variants and explanations that the next copyist promoted into the text, while a rarely read historian was copied once a…

Joins the cataloguer's oldest headache — incipit drift — to prosody as an error-correcting code operating exactly where texts are most vulnerable: openings, which suffer lost first leaves, added prologues, and scribal throat-clearing. A verse work's first lines are locked by rhyme…

Connects the world's longest translation chain — Kalila and Dimna from Sanskrit through Middle Persian and Arabic into Syriac, Greek, Hebrew, Latin, and Castilian — to a two-speed model of what a book is to its transmitters: chapters are detachable assets that…

Connects frame-tale morphology to accretion dynamics: some frames advertise a number — seven sages telling set tales, ten narrators times ten days — and some advertise only survival-by-storytelling, an open valve. A counted frame makes every insertion a visible breach of contract…

the Hebrew translations of Judeo-Arabic philosophy were not diffusion but evacuation across a script frontier. As Arabic competence died out among the Jews of Christian Europe, translation was the only way the tradition could survive there at all, so the two versions'…

writing a line-by-line commentary on an authority permanently converts a scholastic's citation channel to that authority from mediated to direct across his whole subsequent output. The commentary forces desk-level engagement with a complete exemplar; afterwards the master quotes from his own annotated…

the Paris condemnation of 1277 did not suppress the condemned theses, it anonymized them. Discussing a censured position under its author's name risked complicity, but the disputational machine could not run without its hardest objections, so masters kept the content and severed…

on the medieval Talmud, the density of the Tosafist layer on a tractate is a live readout of the same yeshiva demand that drove codex production, so glossing intensity and manuscript survival should be tightly rank-correlated at tractate level. Neither halakhic importance…

the Sentences-commentary genre drifted from pastoral coverage to speculative concentration on a measurable schedule. Disputational prestige, not curricular duty, set the incentives, and prestige lived in Book I's frontier problems — divine knowledge, future contingents, intension of forms — so between 1250…

Bestiary images descend copy by copy, but the copyist's eye corrects toward nature only where nature is available: a fox or hedgehog is re-anchored by daily perception, while a crocodile, whale, or bonnacon is pure graphic descent with no external referent. Iconographic…

Pattern sheets travelled as outline drawings with colour given verbally — the Göttingen Model Book literally writes out its recipes — while copying from a finished exemplar transmits paint by eye but forces a freehand redraw. Two transmission channels, opposite bandwidths: model-book…

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…

Chrysography and gold-leaf image grounds drew on the same budget line, the same material stock, and the same specialist hours, and they address different audiences — the reader and the beholder. The naive luxury model says richer books have more of both;…

Insular interlace obeys strict under-over alternation, and its rare violations are treated as random lapses. The conjecture: the slips are structural — they concentrate where the drawing process broke off, at panel joins, pigment-field boundaries, and day-work seams — so error positions…

Romanesque corbel tables read as carnivalesque miscellany, but carving proceeded bay by bay from scaffolds, one carver working consecutive blocks with whatever type he was fluent in that week. Subject types should therefore show strong serial autocorrelation around the eaves — runs…

Gothic Passion diptychs were serial products of Parisian workshops. If scene selection were devotionally bespoke, observed combinations would spread across the combinatorial space of available scenes; if workshop-standardized, they collapse into a few fixed menus, and menu identity should track workshop groups…

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…

The deluxe illuminated copy and the textually best copy of a work are systematically different books: illumination routes production through commercial ateliers optimizing appearance, schedule, and a lay patron's ear — smoothing hard readings as they go — while plain copies made…

Bas-de-page drolleries look like free invention scattered at whim, but the planner's and patron's attention concentrated at the liturgical divisions, where the opening had to perform. If marginal invention is budgeted attention rather than a programme, drollery density and inventiveness should decay…

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…