One Thousand and One Conjectures

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 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…

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…

Joins transport-cost linear programming to the Codex Mendoza, the pictorial register of what each Aztec province owed Tenochtitlan. The empire had no draft animals and no wheels: every tribute load moved on a porter's back, so the true cost of a good…

Early-warning theory of critical transitions says complex systems approaching a tipping point betray themselves in advance — variance and autocorrelation rise as the system loses resilience. This conjecture applies those signals to Maya epigraphy. The Classic Maya katun-ending dedication network was a…

Joins Maya vase literacy to the sociology of workshop imitation: the Primary Standard Sequence — the dedication formula rimming elite drinking vessels — was ordered, slotted, and rhythmic, and patrons wanted its look even from painters who could not read. If pseudo-glyph…

Connects Nahuatl verbal art's signature device — the difrasismo, a fixed semantic couplet such as in atl in tepetl for city — to the differential survivability of oral genres under alphabetic transcription: formal oratory (huehuetlahtolli) was memorized performance in which coupling was…

Maya polychrome cylinders pose a closed-loop composition problem, and workshop painters solved it the way a tailor does: by giving the garment a seam and placing it at the back. Because these vessels were presented and used along a principal viewing axis…

The Primary Standard Sequence on Maya vases is a fixed dedicatory formula fitted onto rims of very different circumferences; if the band was planned like piecework lettering against available length, abbreviation should be hierarchical rather than ad hoc, dropping the same expendable…

Mixtec screenfold painters worked along red guide-lined boustrophedon registers laid out before painting. If composition ran on a short planning horizon, spacing should compress as the painter approaches each register turn — the same crowding-at-the-end signature papyrologists read in line justification —…

Whether Maya codex production divided glyphic and pictorial labour is unresolved. The conjecture: it did not — each glyphically identified scribal hand painted its own deity images, so a hand's iconographic micro-habits (the drawing of God B's eye, ear-ornament forms, foot rendering)…

Ecologists estimate how many species they have never seen by comparing two independent samples of a population, and the Maya sign inventory can be treated exactly the same way: the four surviving codices are one sample of the script, and the stone-monument…

Species-richness estimators of the Chao family infer how many species were never observed from the ratio of once-seen to twice-seen types, and the surviving Maya codices permit exactly this move: treat each self-contained almanac or table unit as a type, and each…

The three long-known Maya codices — Dresden, Madrid, Paris — all reached Europe through colonial-era hands, which means they passed a selection filter run by sixteenth-century collectors and shippers; the fourth (the Codice Maya de Mexico, long contested and now broadly accepted…

The four surviving Maya books are all divinatory-astronomical, while thousands of surviving stone texts are overwhelmingly dynastic-historical; the standard picture files this as two genres and moves on. The sharper structural claim is that the survival filter's narrowness can be measured: the…

The Paris Codex carries a sequence of pages organized by the katun, the twenty-year period that also structures history-telling in the colonial Yucatec Books of Chilam Balam; the usual observation connects those two and stops. The structural conjecture goes further: the Paris…

The physical Maya codices are Postclassic objects, but astronomical tables must anchor themselves to absolute dates, and anchors fossilize: a copied table drags its original entry dates along with it, patched by correction increments rather than recomputed from scratch. So the distribution…

An eclipse-warning table of the sophistication preserved in the Dresden Codex cannot be built from one generation of skywatching: fixing long lunar cycle constants to the precision the table embodies structurally requires observational records spanning centuries. That requirement is an existence proof…

The Madrid Codex is known to carry the work of multiple scribal hands, and the structural conjecture is about where those hands change: hand transitions should align with almanac boundaries, revealing a book assembled from self-contained page-unit modules by a workshop —…

Maya stelae state their dates redundantly — an absolute Long Count position plus chained Distance Numbers linking event to event — and sometimes the arithmetic visibly fails to check. The conjecture is that these failures are transcription errors from paper drafts rather…

If Maya monumental texts were composed on screenfold paper and then transferred to stone, the paper's page module should leave a metrical fossil in the stone: text lengths, counted in glyph blocks, should cluster at multiples of a standard layout unit instead…

Maya monuments routinely record events that happened long before the stone was dedicated, and the distribution of that retrospection gap is a probe of what sculptors' patrons could actually consult. Oral memory has a well-documented horizon of roughly two to three generations;…

Classic Maya artists sometimes signed their work — signature phrases occur on carved monuments and painted vessels — and a signing culture accidentally runs a census of its own workforce: capture-recapture on named artists across signed objects estimates the population of scribes…

The Maya syllabic grid — the consonant-vowel table that epigraphers have been filling in for decades — still has empty cells, and the standing question is whether those cells were empty in the script or are empty only in the surviving sample.…

Maya monuments name other sites — captures, overlordships, royal visits — which yields a political network; independently, glyphs show site-level formal variants, which yields a paleographic similarity network. The conjecture is that these are the same network: subordinate courts write like their…

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…

The surviving Maya codices are laid out as tabular instruments — grids, columns, captioned pictures inside almanac frames — while Maya monumental texts run as continuous double-column discourse. Layout is genre made visible, so the near-total absence of continuous-discourse layout in the…

The Mixtec screenfold codices are unusual among surviving pre-contact American books: several of them narrate overlapping dynastic genealogies, giving the only measurable case of the same content transmitted through parallel manuscript lines in the pre-print Americas. Treating the shared genealogical spans across…

Maya codices carry a phonetic-logographic script packed into block grids; Mixtec codices carry pictographic narrative on open, red-ruled pages read along a winding path. These are two engineering solutions to the same problem — putting court knowledge onto bark and hide —…

The Andean khipu — knotted cords encoding by knot type, knot position, cord color, and ply — and the Maya glyph block are the Americas' two great non-alphabetic information carriers, and they can be compared on equal terms with the plainest of…

Capture-recapture is the ecologist's trick for counting fish you cannot see: mark some, resample, and the overlap tells you the population; book historians use the same mathematics to estimate lost medieval literature from overlapping survivals. The Maya screenfold codices suffered the most…

Medieval computus — the Easter-reckoning literature — offers historians a rare gift: tables whose internal arithmetic can be checked, yielding measured scribal error rates per copied operation. Classic Maya monuments offer the same gift in stone: a Long Count date, its Calendar…