One Thousand and One Conjectures

The Yule process — the preferential-attachment mathematics behind power laws in citations, city sizes, and web links — is here applied to the medieval book world. A text gets copied because copies of it exist to be found and read: every extant…

Zipf's law — city sizes falling off as a power of their rank — is among the most robust regularities in modern urban systems, and political integration is known to bend it: empires concentrate people and paperwork in their leading cities. Mesopotamia…

In critical phenomena, systems that differ microscopically collapse onto a single curve after rescaling — the signature of a shared universality class. This conjecture claims textual survival has exactly one such class. Greek works at large, catalogued in Pinakes' 21,500 works, and…

Heaps' law — the corpus-linguistics regularity that a collection's vocabulary grows as a sublinear power of its size — is here applied to the oldest writing system on earth. Cuneiform's inventory of distinct signs should grow with corpus size along a Heaps…

Island biogeography famously finds that the number of species an island supports scales with its area as a power law, S = cA^z, with a characteristically shallow exponent. The claim ports this law to writing: a region is an “island” for scripts,…

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…

Gibrat's law — the modern finding that firm growth rates are independent of firm size, which generates the Pareto (power-law) distribution of firm sizes seen in every industrial economy — is here tested two thousand years early. Roman brickyards (figlinae) stamped their…

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 —…

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…

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…

Taylor's law — fluctuation scaling from statistical physics and ecology — says that across populations, variance grows as a power of the mean: exponent 1 for independent Poisson noise, 2 for perfectly synchronized fluctuation. This conjecture applies it to the geography of…

Sublinear scaling laws — the urban-economics finding that infrastructure grows more slowly than city size — meet museum acquisition history. This conjecture claims the dispersal of a cuneiform site's tablets across the world's collections scales sublinearly with the size of the find.…

Priority queueing theory has a textbook pathology: give one class of customers near-absolute priority and their waiting times stay compact while low-priority waits blow up into a heavy tail. This conjecture finds that pathology in the Heian court's promotion ladder as recorded…

What survives of the Andean khipu record survived overwhelmingly through graves — cords bundled with the dead in the dry coastal desert — while the state's central cord archives at administrative centers were destroyed, dispersed, or rotted in wetter highlands. Grave goods…

Monumental writing among the Maya was a court technology, and the number of inscribed monuments per site is wildly unequal — a fact usually reported, not modeled. The conjecture: the inequality is the fingerprint of contagious adoption plus cumulative advantage — sites…

Geniza book-lists let us count how many books individual medieval households actually owned — a number usually guessed from anecdote. Modern collections and wealth alike tend toward heavy-tailed distributions: many small holders, a few enormous ones. The conjecture is that medieval Jewish…

This conjecture imports burstiness statistics — the tools used to describe irregular human communication patterns — into the study of itinerant medieval kingship. An itinerant chancery issued documents where and when the king was available: acta came in bursts at assemblies, sieges,…

Excavated tablet groups run from a dozen tablets in a jar to tens of thousands in a palace wing, and the sizes are usually treated as accidents of preservation. Economics knows that firm sizes form structured distributions, with small owner-operated firms and…

Survival analysis distinguishes institutions by the shape of their exit curves: fixed terms produce peaked tenure distributions, seniority protection produces falling hazards, and service at pleasure — where dismissal strikes like lightning — produces the memoryless exponential. Ur III prosopography supplies thousands…

Zipf's law — a few signs used constantly, most rarely — is usually taken as a fact about languages. Cuneiform ran a natural experiment no other script can offer: the same sign inventory served Sumerian, then Akkadian, then a heavily logographic late…

Assyriology, sitting on hundreds of thousands of digitized tablets, learned to treat administrative writing as a statistical population: text types and formulae in the Ur III archives follow heavy-tailed frequency distributions with stable shape parameters. Medieval English charters, digitized in the DEEDS…

Byzantinists can rank ancient Greek works by popularity because Pinakes counts surviving copies: a few texts survive in hundreds of manuscripts while most survive in one, and the shape of that concentration is a signature of the copying economy. The manuscript libraries…