Before asking what moved across Eurasia it is worth asking what could move, because the answer can be derived from the biology of a pack animal and a map, without consulting a single document.
The previous lesson argued that the written evidence is thin and unevenly preserved. The argument that follows has the opposite character: it uses almost no documents, it can be checked by anyone with a calculator, and it turns out to predict the contents of the caravans quite well. Where the two kinds of argument agree, the conclusion is about as firm as this subject gets.
How far, in numbers a Han official would recognise
The Hanshu chapter on the Western Regions lists each kingdom with its distance from the capital in li. Shule, which is Kashgar, is given as 9,350 li from Chang'an.
To turn that into kilometres, take the Han li as 300 paces of 6 chi, so 1,800 chi, and the Han chi as about 23.1 cm, a value fixed by surviving bronze and wooden measuring rules. Then one li is m, and the distance is km. That is Chang'an to the far western edge of the Tarim Basin, with the Pamirs, Sogdiana, Persia and the Mediterranean all still ahead. To Antioch is roughly another 5,000 km by any usable line, so the whole span is something over 8,000 km, and more once the detours around mountains and deserts are counted.
A caravan on level ground makes about 4 km/h and walks for seven or eight hours, so 30 km is a normal day and 35 a good one. At 30 km a day, Chang'an to Kashgar is days of travel, or well over four months allowing for rest days, weather and the wait for a pass to clear. Nobody in the ancient world doubted this was a long way. What the arithmetic adds is that it was long in a very specific way: not a voyage but a wage bill, 130 days of paying men and feeding animals before a single item is sold.
The animal
The pack animal of the eastern half of the route is the Bactrian camel, two-humped, wool-coated, and able to work at temperatures from about minus 30 to plus 40 degrees Celsius, which matters because the Tarim Basin does both within a year. West of Persia the one-humped dromedary takes over, and hybrids of the two were bred deliberately in Central Asia because the first cross is larger and stronger than either parent.
A Bactrian carries 150 to 200 kg on a long march, and traditional caravan practice loaded towards the lower figure, since an overloaded camel goes lame and a lame camel is a total loss. This course uses 150 kg throughout as a conservative working payload.
The camel did something more radical than carry loads: it drove the wheel out of large parts of Asia. Richard Bulliet's The Camel and the Wheel (1975) collected the evidence that wheeled transport largely disappeared from the Middle East and North Africa between roughly 300 and 600 CE, and argued that this was an economic choice rather than a decline. A cart needs a road, and a road needs building and maintaining by someone; a pack camel needs neither, crosses ground no cart can, requires one handler for several animals rather than a driver and a team per vehicle, and eats browse that would not feed an ox. Where the state that maintained the roads weakened, the camel simply won on cost. It is a useful corrective to any account in which technology only moves forward: cities in the Islamic world were rebuilt with lanes too narrow for a cart because nobody needed one.
The appetite
Here is the constraint that shapes everything else. A working Bactrian eats roughly 6 kg of dry fodder a day when there is nothing to browse, and drinks heavily when water is available.
Set that against the payload. A camel carrying 150 kg of its own fodder carries days of food. It eats its own maximum load in twenty-five days. Over the 130-day march to Kashgar it would need kg, which is full camel-loads, and those five extra camels each eat 6 kg a day as well, and the camels carrying their fodder eat too. The series does not converge into anything useful. No caravan on this route could ever carry the food for its own journey.
That single fact does more explanatory work than any political history. It means the route cannot exist as a route: it can only exist as a chain of places that sell fodder, water and shelter, spaced a few days apart. It means those places have monopoly power over anyone travelling, since a caravan that cannot buy at the next oasis has no alternative and no reserve. And it means the political history of the Silk Road is mostly a history of who controlled the supply points, which is exactly what the Chinese, Tibetan, Turkic and later Mongol contests over the Tarim were about.
Example. A caravan wants to cross a stretch of eight days with no fodder available at all. Using 6 kg a day and a 150 kg payload, what fraction of each camel's capacity is consumed by its own food, and what does that do to the freight rate over that stretch?
Eight days of fodder is kg, which is per cent of the payload, leaving 102 kg of cargo. The freight rate per kilogram of cargo therefore rises by a factor of , close to a fifty per cent surcharge, for a stretch of only 240 km. Two things follow. Long fodderless stretches are punitively expensive rather than merely difficult, which is why routes bend a long way to stay near supply. And the surcharge rises steeply, not linearly, with the length of the gap: at sixteen days the fodder is 96 kg, the cargo is 54 kg, and the rate has nearly tripled. Beyond about twenty-five days the cargo is zero and the crossing is impossible at any price.
Now you. The same camel is worked on a stretch where grazing supplies half its needs. Redo the eight-day calculation and say what kind of country that describes.
Answer
At half rations carried, the camel needs kg, which is 16 per cent of the payload, leaving 126 kg and a freight surcharge of , under twenty per cent instead of nearly fifty. That is the steppe, and it explains why the northern grassland corridor was attractive despite being colder, longer and politically more dangerous than the desert rim. Grass that grows by itself is free transport fuel, and a route across it carries a third more cargo per animal. It also explains something about the people: on the steppe the animals feed themselves and the herds move, so the natural social form is mobile pastoralism rather than the oasis town, and the traffic there depended on coming to terms with nomads instead of paying oasis market dues.
The thirst
Water sets the geometry. A Bactrian camel in cool weather can work five days or more without drinking, and rather less in summer heat. At 30 km a day, five days is about 150 km, and that is the maximum spacing between watering points that a caravan can survive.
Now look at the Taklamakan. It is roughly 1,000 km east to west and 400 km north to south, some 337,000 km² of shifting sand, with no permanent water in the interior. A direct crossing along the long axis is 1,000 km, which is over thirty days, which is six times the camel's dry range. The desert cannot be crossed. It can only be skirted, and the water to skirt it comes from the same place at every point: meltwater streams running off the Kunlun range to the south and the Tian Shan to the north, which sink into the sand a short distance out.
So the route splits, not by choice but by hydrology, into a northern rim through Turfan, Kucha and Aksu and a southern rim through Miran, Niya and Khotan, meeting again at Kashgar before the passes. Draw the streams and you have drawn the map. Every well-known Silk Road town in the Tarim sits where a mountain stream reaches the sand, and the two lessons of the last section apply to all of them: they are the only fodder for hundreds of kilometres, and they know it.
What a cargo has to be worth
Put the pieces together and you can derive, roughly but honestly, which goods could cross.
Measure everything in days of unskilled labour, which travels across centuries and currencies better than any coin. Suppose a camel with its share of a driver, its fodder, its market dues and the caravan's protection costs runs at about two labour-days per camel-day. That is a guess, but it is a guess with a floor, since a driver managing three or four camels has to eat, and the fodder alone is a real cost.
Over 130 days one camel-load costs labour-days, and it carries 150 kg, so the freight is labour-days per kilogram delivered.
Now compare commodities. If a labourer earns about 6 kg of grain a day, grain is worth labour-days per kilogram, so carrying it the length of the route costs about ten times what it is worth. Grain cannot cross, at any price, in any century, under any emperor. Silk is the opposite case: a bolt weighing around 0.35 kg represents perhaps fifteen labour-days of sericulture, reeling and weaving, so silk is worth about labour-days per kilogram, and the freight is , about four per cent of the value. Silk can cross the whole of Asia and arrive having absorbed a transport cost smaller than a single merchant's margin.
The threshold is around 2 labour-days per kilogram, and the goods actually attested in the long-distance traffic sit far above it: silk, precious stones, gold and silver work, musk, aromatics, high-grade paper, coral, glass vessels, medicines. Nothing bulky, nothing cheap, nothing perishable.
Example. Pliny gives the Roman price of black pepper as 4 denarii a Roman pound. Taking a Roman pound as 327 g, a denarius as 4 sesterces and a soldier's pay as 900 sesterces for about 300 working days, could pepper have crossed Asia overland?
Four denarii is 16 sesterces per Roman pound, so the price is sesterces per kilogram. At 3 sesterces a day, that is labour-days per kilogram, comfortably above the threshold of about 2. Overland freight of 1.73 labour-days per kilogram would consume per cent of the Roman retail value, which is survivable. So the answer is yes in principle, and pepper is the interesting borderline case: dense enough in value to cross, but at a cost that eats a tenth of the price before any merchant's margin, in a trade where the sea alternative cost a fortieth as much per unit distance. That is exactly why pepper went by sea and silk could afford to go either way, and it is a good illustration of what the threshold does. It does not sort goods into possible and impossible so much as it decides which route a good is forced onto.
Now you. A caravan pays a toll of 5 per cent of the cargo's value at each of twelve oases. How much of the cargo's value survives, and what does the answer imply about political fragmentation?
Answer
Each stop leaves 95 per cent, so twelve stops leave , and 46 per cent of the value has been taken in tolls alone, before transport costs, losses or profit. At 10 per cent a stop the figure is , so nearly three quarters is gone. Two things follow. Tolls, not freight, were probably the largest single cost on the overland route, and they are the one cost that the previous section's model cannot predict, because they depend on how many independent authorities lie between the ends and what each thinks it can extract. And fragmentation is quantifiably expensive: halving the number of toll-taking polities is worth more to a merchant than any improvement in camels. That is the arithmetic behind the value of a single large empire spanning the route, which is why the Mongol century is treated later as the natural experiment of the subject, and it is also why every ruler on the road had an incentive to conquer his neighbour and then, having done so, to advertise how safe the road had become.
The model can be checked against an independent source. Diocletian's Price Edict of 301 CE fixes maximum prices for goods and for freight, and the classic result drawn from it, by A. H. M. Jones and Richard Duncan-Jones, is that carrying wheat about 300 Roman miles by land roughly doubled its price. Three hundred Roman miles is km, or 15 days at caravan pace. Run that through the model above: 15 days at two labour-days is 30, divided by 150 kg is 0.20 labour-days per kilogram, against a grain value of 0.17. The transport adds about 118 per cent to the price, which is to say it slightly more than doubles it. A crude model built from a camel's appetite lands on the same answer as a Roman price schedule, which is the sort of agreement that should raise your confidence in both.
Example. Lapis lazuli from Badakhshan, in the mountains of northeastern Afghanistan, reached Egypt from at least the third millennium BCE, well before any of the states in this course existed. Does the freight model explain that?
Yes, and cleanly. Lapis is a stone of no practical use whatever, valued entirely for its colour, and the good grade is scarce, which puts its value per kilogram in the same class as silk or above it. A commodity like that pays a freight of two labour-days per kilogram out of small change, so distance is nearly irrelevant to whether it moves; what limits it is demand at the far end, not carriage. This is why the earliest long-distance trade in every region is in gems, metals and aromatics rather than in anything useful, and it is a warning against reading the antiquity of a trade as evidence of a developed route. Lapis crossing 4,000 km in 2500 BCE tells you only that a chain of short exchanges existed, which is a much weaker claim than the one it is usually recruited for.
Now you. Chinese paper, when it began moving west, was expensive and light. Cotton cloth from India was cheap and light. Iron tools were cheap and heavy. Predict which crossed the whole route, which crossed part of it, and which did not.
Answer
Paper crosses the whole route, and did: the Sogdian letters of 313 found near Dunhuang are on paper, a Chinese product already thousands of kilometres from home. Its value per kilogram is high while its production is confined to one region, and that is exactly the condition for long-distance movement, which is also why paper stops travelling as a commodity once it is manufactured locally. Indian cotton crosses part of it, moving freely over hundreds of kilometres and into regions with no cotton of their own, but a cheap textile cannot absorb 1.73 labour-days per kilogram, so it does not go the whole way overland; it goes the whole way by sea, later, once freight costs collapse. Iron tools do not cross at all as trade goods, being both heavy and cheap, though the technique of making them travels perfectly well, which is the distinction a later lesson is built on. The general rule is that low value per weight goods move locally in every period, and their absence from the long-distance record is arithmetic rather than an absence of demand.
The limits of the model
This is a model, and it is worth naming what it leaves out before the next lesson uses it.
It ignores everything but freight. Tolls, protection payments and outright robbery could easily exceed transport costs, and they varied wildly with who held the passes, which is a political variable no camel arithmetic can predict. It assumes camels, when the Pamir crossings used yaks and porters, the steppe used horses and ox wagons, and rivers were used wherever they ran the right way. It assumes a merchant pays cash costs, when much of the actual traffic moved as tribute, gift, salary or plunder, and none of those respect a freight rate. And it is calibrated on assumptions, the two labour-days most of all, that are defensible rather than measured.
What it does reliably is separate the impossible from the possible. Nothing in the historical record contradicts it, and where a document seems to show a bulk good crossing a great distance overland, the explanation has always turned out to be that the state was paying, which is the subject two lessons ahead.
The next lesson takes the strongest consequence of the model, that no caravan can feed itself, and follows it to the institution it implies. If the trade depends absolutely on places that sell fodder and water, then those places are not stops on the route. They are the route, and understanding how an oasis worked, how it got its water and what happened when the water failed, explains more about the rise and fall of the traffic than any account of emperors.