One Thousand and One Conjectures

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…

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…