The Fractured-Land Hypothesis
Jared Diamond held that “fractured land” was responsible for China's tendency toward political unification and Europe's protracted polycentrism. A dynamic model of state formation, built on granular topography and the location of productive agricultural land, gauges the claim quantitatively: topography alone is sufficient — but not necessary. A single core region of high land productivity in northern China delivers the same result on its own.
A famous claim, and an awkward fact
Europe's polycentrism is standard equipment in explanations of the Great Divergence: many states, competing, unable to shut each other's ideas down. But why was Europe polycentric in the first place?
Diamond's answer was fractured land. Europe is cut up by mountains, dense forest and an indented coastline; China is not, so China unified and stayed unified. The claim has an obvious problem, pressed hardest by Philip Hoffman: on the raw numbers, China is the more mountainous of the two. Over 37% of modern China counts as mountainous against barely 10% of Europe. Restrict attention to China proper — south of the Great Wall, east of the Tibetan plateau — and more than 33% sits above 1,000 metres, against roughly 6% of Europe.
That distinction — total ruggedness versus the placement of ruggedness — is exactly the kind of thing a verbal argument cannot settle. How rough does terrain have to be before it stops an army? Was Qin's success structure or luck? Our move is to stop arguing and start simulating.
The world as sixty-five thousand hexagons
Every landmass on Earth except Antarctica is tiled with hexagonal cells of 28 km radius — about one day's march on flat ground, and roughly the territory a Bronze Age polity could watch and defend. Each cell contains real data: terrain ruggedness from CGIAR-CSI elevation, mid-Holocene maximum and minimum temperatures from WorldClim, attainable caloric yield from pre-Columbian cereals in GAEZ v4, and alluvial soil share from the FAO soil map.
At t = 0 every cell is its own polity. The clock runs from 1000 BCE to 1500 CE in 500 periods of five years — from the fragmented aftermath of the Late Bronze Age collapse to the eve of the Age of Exploration. Three things can then happen to a cell.
- Conflict. A cell picks a fight with probability proportional to its own productivity, and picks its opponent in proportion to the neighbour's productivity. Rich land is worth taking, and worth taking from.
- Conquest. The winner annexes one cell — not the whole enemy polity. Wars trade borderlands; they rarely swallow kingdoms whole.
- Secession. Border cells break away with a probability rising in their own ruggedness and in the length of the parent polity's frontier. Long, ragged borders are expensive to hold.
Water resists. Sea invasions are calibrated at a tenth the rate of land conflicts, reach no further than six cells (~330 km), and a polity split across water can bring only a third of its overseas resources to a fight. That is the "stopping power of water," and it is why an indented coastline is a genuine obstacle rather than a curiosity.
Seven parameters, most of them pinned to something outside the model
| Parameter | Value | Where it comes from |
|---|---|---|
| α — conflict hazard | 1 / ymax | Normalises so the richest cell fights with probability 1 per period |
| αsea — sea conflict rate | 0.10 | ≈10% of recorded historical battles were fought at sea |
| σ — overseas resource reach | 0.33 | Dupuy's combat-power weights, used to calibrate staff-college war games |
| θrugged | Θ·x = 2 at p90 | Defence roughly doubles in strength on bad terrain (Dupuy; Lanchester estimates from Iwo Jima and the U.S. Civil War) |
| θhot, θcold | Θ·x = 2 at p90 | Heat-stress and cold thresholds from military and pharmacopoeial standards |
| β — secession rate | 1 × 10-5 | Set deliberately low, so secession cannot be what fragments Europe |
The last row matters more than it looks. Europe's long coastline makes its simulated states straggly, and a generous β would fragment Europe by construction. We tie our own hands.
Who wins a war
The model can be summarized in one equation. Polity i wins in proportion to its share of the two sides' combined resources — total resources, not per capita; Estonia in 1939 was richer per head than the USSR and it changed nothing — divided by a terrain penalty that lets the war end in stalemate instead. Move the sliders.
m = max{ Θ·xk , Θ·xk̄ }
Stalemate probability is m/(1+m) — it depends only on the ground, never on who is fighting. On flat, warm, workable land the frontier always moves. That asymmetry is the engine of everything that follows.
China consolidates. Europe does not.
The model is run 30 times and bootstrapped 10,000 times, because the point is not to reproduce any particular border but to ask what the distribution of histories looks like. Political concentration is measured by a Herfindahl index over the cells of a region: 1 means one polity holds everything, 0 means universal fragmentation.
The timing is right too. China was first unified in 221 BCE, but the far south — Fujian, Guangdong, Guangxi, Guizhou, Yunnan — stayed outside real bureaucratic control for centuries; Yunnan was only incorporated in 1276, near the end of the simulation window. The model reproduces that slow southward fill rather than an instant empire. From Qin to the Republic, China was unified for 1,142 of 2,132 years.
Sufficient, but not necessary
Fractured land has two readings: the narrow one about mountains and coastlines, and a broader one about where the productive farmland sits. Switch each off in turn and see which one was carrying the result.
The non-linearity is the finding. Neither channel is individually decisive, and switching off both at once is what finally makes Europe and China consolidate at a comparable pace. Any test that treats "ruggedness" as a single regressor and asks whether it is significant will miss this entirely.
Everything starts on the Central Plain
The simulations do not just get China unified; they get it unified from the right place. Flooding by the silty Yellow River kept North China fertile under primitive tools, the terrain is flat enough to campaign across, and it sits next to three more flat cores — the Guanzhong Plain, the Jianghan Plain, the Yangtze Delta. Once one state holds that block, no rival region can match it.
In 1943 the geographer Sha Xuejun called North China and its adjoining plains "the hub of China," paraphrasing Mackinder: to control China, first control its heartland; to control the heartland, first control the hub. The simulation rediscovers the hub without being told it exists.
Europe gets middle-sized states, not a scatter of tiny ones
This is the part that matters for the Great Divergence literature. The interesting European configuration is not fragmentation as such — Southeast Asia is more fragmented than Europe in these simulations — but several comparably-sized powers, none able to dominate. Mokyr's competitive market for ideas needs states big enough to be worth fleeing to.
Things that do not change the answer
The result survives an unusually long list of attacks, and several of them make China unify faster, not slower.
- Different productivity data. Ramankutty's cropland suitability index; KK10 land-cover in 1000 BCE in place of alluvial soil; HYDE 3.1 population; the FAO Harmonized World Soil Database; 1960s temperatures instead of mid-Holocene.
- Different reasons to fight. Attack the neighbour offering the highest expected gain; attack any neighbour with equal probability; add the cost of moving resources to the front.
- Adding realism. Navigable rivers, the loess plateau, the steppe as a grass highway, steppe pastoralism, and tropical/cold productivity discounts — separately and jointly. The joint version is our preferred specification, and it looks like the parsimonious baseline.
- Giving Europe the advantage. Start the clock in 250 CE with Rome intact and Han China split into three kingdoms, and Europe's concentration still falls while China's climbs past it. Start with a Carolingian-sized empire in Europe and a China broken into seven macroregions — same crossover. If the simulated Rome collapses it is never rebuilt; every Chinese collapse is followed by reunification.
- Rome itself. Better Mediterranean climate alone does not produce a Roman Empire. A Roman military edge alone does not either. Only both together generate a Mediterranean empire, and it still rarely crosses the Alps — which reads as support for the historians who call Rome contingent and unrepeatable.
The honest misses are stated too: the baseline never produces anything resembling the Mongol Empire or the Golden Horde. Recovering those requires the steppe extensions in the appendix.
Where the model breaks — and what that buys
Run the same machinery on Africa and the Americas and it fails, twice, in informative ways. We use the failures as measurement: what has to be added to close the gap tells you what the simplest version of the hypothesis was missing.
What is deliberately left out
There are no alliances, no dynastic marriages, no investment in state capacity, no military innovation, no strategic path of conquest. That omission is a computational necessity, and we argue it works against us rather than for us.
- Balance of power. Coalitions form against would-be hegemons — the Greek leagues, the Italian city-states, the alliances against the Habsburgs and then the Bourbons. Europe's several nuclei are precisely what makes balancing feasible, so adding strategy should widen the gap, not close it.
- Bandwagoning. In China the opposite equilibrium takes hold. Wu and Shu could stall Wei only while Wei was weak; once the northern plain's resources were mobilised, resistance stopped paying.
- Feedback from growth. Venice and the Dutch Republic punched far above their weight because polycentrism made them rich. That channel also reinforces the mechanism.
- Military technological change. Hoffman's tournament — competition breeding better guns — is absent. Our claim is not that it did not happen, only that you do not need it to get the comparative outcome.
The model is explicitly offered as a platform: religion, language, genetic diversity, migration, irrigation, transport, imagined community. Each is a cell attribute or a modifier to one equation away.