One Thousand and One Conjectures

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…

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 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 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 the economics of protection rackets to Han-Xiongnu diplomacy. A racketeer prices extraction to the victim's outside option: what matters is not how hard the racketeer can hit but how badly the victim needs quiet, so payments ratchet up when the victim…

Newsvendor inventory theory sets stocking policy by a critical fractile — the service level dictated by the ratio of shortage cost to storage cost — and this conjecture finds that optimization solved a millennium before the theory, in the Chinese ever-normal granary.…

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…

The bullwhip effect in supply-chain theory says demand variance amplifies as orders move upstream, because long lead times and order batching drive suppliers to overshoot and then correct. This conjecture finds the bullwhip in Ming tribute logistics: the caoyun system shipped grain…

Joins the two poetic registers of Song China to two enforcement institutions: regulated shi verse was examination technology, rhymed against the frozen categories of the official rhyme books long after speech had moved on, while ci lyrics were written to living melodies…

Sheets and scrolls of stamped Buddhas look like space-filling repetition, but the devotional act was arithmetic: vows specified counts. If the count, not the sheet, was the unit of work, totals should cluster at canonical numbers and their multiples, and completed items…

That Japanese handscroll action tends right-to-left is a specialist commonplace; the unestablished claim is the full mechanism test across cultures. If lateral bias comes from the reading technology — the image must hand the eye onward to the next scene — then…