Transportation as a Constraint

by johnswentworth6 min read6th Apr 202023 comments

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World Modeling
Curated

Imagine it’s late autumn of 332 BC. You’re Alexander the Great, and your armies are marching toward Egypt from Gaza. There’s just one little problem: you need to cross the Sinai peninsula - 150 miles of hot, barren desert. How will you carry food and water for the troops?

Green triangle on the left is the Nile river delta in Egypt; green chunk in the upper right is Israel. The big desert peninsula between them is the Sinai.

Option 1: carry it

A physically-active human needs about 3 lbs of food per day. (Modern hikers can probably find lighter calorie-dense foodstuffs, but we’re talking ancient history here.) Water requirements vary; 5 lbs is a minimum, but the US Army Quartermaster Corps recommends 20 lbs/day when marching through a hot desert. Alexander’s army crossed the desert in 7 days. Food might be reasonable, but to carry the water would mean 7*20 = 140 lbs per person, plus 50+ lbs of armor, weapons, etc.

When I go hiking, I aim for a 20-30 lb pack. US marines are apparently expected to be able to carry 150 lbs for 9 miles - quite a bit less than the 20+ miles/day Alexander’s army managed, and with no comment on how long the marine in question might need to rest afterwards. (Also, I’m not sure I trust that source - 150 lbs for 9 miles sounds unrealistic to me, and if it’s true then I’m very impressed by marines.)

Suffice to say that carrying that much water across that much desert is not a realistic option, even if we drink it along the way.

Option 2: horses

A horse consumes 20 lbs of food (half of which may be forage) and 80 lbs of water per day. In exchange, it can carry about 200 lbs (surprisingly, my source claims that horses can carry more than they can pull). Of course, that 200 lbs has to include the horse’s own food and water, plus whatever useful load it’s carrying. So, marching through a desert, a horse can only transport (200 lbs)/(80+20 lbs/day) = 2 days of supplies for itself, and that’s before whatever useful things actually need to be transported.

In other words, there’s a hard upper limit on how far goods can be transported by horse without refilling supplies along the way. That limit is around 2 days travel time without any refill, 10 days if there’s plenty of fresh water along the route, or 20 days if there’s both water and forage. At 20 miles/day, that’s 40, 200, or 400 miles. Realistically, if we want the number of horses to be reasonable, the limit is more like half that much - 20 miles, 100 miles, or 200 miles, respectively.

So horses also won’t work.

Option 2.5: camels or other pack animals

Contrary to popular image, camels actually need more water than horses. They can go a couple days without, but then need to fill up all at once. They can also carry a bit more weight, but they eat more food. At the end of the day, the numbers end up quite similar.

Mules also end up with similar numbers, and cattle are generally worse.

Option 3: ships

Assuming the army marches along the coast, a supply fleet can sail alongside. At the time, a single large merchant ship could carry 400 tons - in other words, as much as about 4000 horses. Presumably the ship would cost a lot less than the horses, too.

Well then, there’s our answer. Ships are clearly a vastly superior way to move goods. Range is a non-issue, capacity is far larger, and they’re far cheaper. They’re perfect for crossing the Sinai, which runs right along the coast anyway.

Fast forward a few years to 327 BC, and Alexander is marching his armies back from India. He plans to cross the Gedrosian desert, along the coast of modern-day Pakistan and Iran. The plan is much like the Sinai: a supply fleet will sail alongside the army. Unfortunately, neither Alexander nor his commanders knows about the monsoons: across most of south Asia, the wind blows consistently southwest for half the year, and consistently northeast for the other half. There is nothing like it in the Mediterranean. And so, Alexander marches out expecting the fleet to catch up as soon as the winds turn - not realizing that the winds will not turn for months. Three quarters of his soldiers die in the desert.

Thus end the campaigns of Alexander.

Generalization

The above numbers are drawn from Donald Engels’ book Alexander the Great and the Logistics of Macedonian Army. But it tells us a lot more about the world than just the logistics of one particular ancient army.

First, this highlights the importance of naval dominance in premodern warfare. A fleet was a far superior supply train, capable of moving a high volume of food and water over long distance at relatively low cost. Without a fleet, transport of food became expensive at best, regular resupply became a strategic necessity, and long routes through arid terrain became altogether impassable. Destroying an enemy’s fleet meant starving the army. Likewise, controlling ports wasn’t just for show - without a port, feeding the army became a serious problem.

Another interesting insight into premodern warfare: away from friendly seas and rivers, the only way to keep an army fed was to either seize grain from enemies, or buy it from allies, either of whom needed to already be nearby. In Alexander’s case, deals were often struck to establish supply caches along the army’s intended route.

An interesting exercise: to what extent was transportation a binding constraint on the size of premodern towns/cities? (One number you may want: Braudel (pg 121) estimates that 5000 square meters of land growing wheat would provide one person-year of food, not accounting for crop rotation.) Leave a comment if you try a calculation here; I'm curious to see how other peoples' models compare to my own.

Modern Day

Today we have trains and trucks and roads, so the transportation constraint has relaxed somewhat. But here’s an interesting comparison: a modern 18-wheeler in the US is legally limited to haul 40 tons, while a panamax ship could carry about 50k tons through the canal (prior to the opening of the new locks in 2016). That’s a ratio of a bit over 1000 - surprisingly similar to the ship/horse ratio of antiquity, especially considering the much larger new-panamax and super-panamax ships also in use today.

Can we get a quick-and-dirty feel for tautness of the transportation constraint today? Here are a few very different angles:

  • This USDA study shows rates on produce transport, typically about 7-20 cents per pound (see figure 6). The Smart & Final grocery store near me sells the cheaper produce items looked at in that study (bell peppers, cantaloupes, tomatoes, oranges) for 70-100 cents per pound, so transport alone is roughly 10-20% of the cost-to-consumer.
  • What about transporting humans? Average commute in the US is ~30 minutes each way; driving is usually in the 20-30 minute range, while public transit is usually 30-50. Assuming 8 hr workdays, that means commutes are typically ~10-20% of our work-hours.
  • The bureau of transportation estimates transport at 5.6% of the US economy for a very narrow measure, or 8.9% with a broader measure (though this still excludes non-market transport costs like e.g. commute time).

My interpretation: the transportation constraint becomes taut when it accounts for 10-20% of cost. If it’s less than that, it usually doesn’t limit production - we see plenty of goods which aren’t transportation-dependent or which are higher-value-per-weight, and the transportation constraint is generally slack for those. But once transportation hits about 10-20%, people start looking for alternatives, i.e. producing the goods somewhere else or using alternative goods. Obviously this is not based on very much data, but I find it intuitively plausible.

Compared to ancient times, transportation constraints have obviously relaxed quite a lot. Yet qualitatively, the world today still does not look like a world of fully slack transportation constraints. To wrap up, let’s discuss what that would look like.

Extreme Slackness

In Material Goods as an Abundant Resource, we discussed the world of the duplicator - a device capable of copying any item placed on it. In such a world, material scarcity is removed as an economic constraint - all material constraints are completely slack.

What would be a corresponding sci-fi device for transportation constraints, and what would that world look like?

I suggest portals: imagine we can create pairs of devices capable of transporting things from one device to the other, across any distance, at the speed of light. (We could instead imagine teleporters, removing the need for a pre-installed device at either end, but then the entire discussion would be about security.) What does the world of the portal look like?

First, there’s complete geographical decoupling of production from consumption. People have no need to live near where they work; companies can put offices and factories wherever real estate is cheap. We can enjoy miles of wilderness on the back porch and a downtown district on the front porch; a swimming pool can open right into the ocean. Buying direct from the farm or factory is standard for most material goods.

What are now tourist destinations would become options for an evening activity. Disneyworld would sell a park-hopper ticket that includes Disneyland California, Paris, and Shanghai, but the price of that ticket would be high enough to prevent the parks from becoming unpleasantly crowded - probably quite a bit more expensive than today, though possibly cheaper than today’s flights to Orlando.

Obviously roads would cease to exist. Huge amounts of land would revert from asphalt to wilderness, but buildings would also be much more spread out. Buildings would be built close together more for show than for function - e.g. to provide the ambiance of a downtown or a community to those who want it. Physical life, in general, would look more like the structure of the internet rather than the structure of geography; “cities” would be clusters very spread out in space but very tightly connected via the portal network. Filter bubbles would be a much more physically tangible phenomenon.

Geographically-defined governments would likely be replaced by some other form of government - governments based around access to portal hubs/networks are one natural possibility. Security would be a priority, early on - carrying an unauthorized portal into an area would earn a facefull of high explosives. On the other hand, it would be hard to prevent a high degree of mobility between areas controlled by different governments; the implications for government behavior are conceptually similar to seasteading.

The structure of space near portal networks would be different in a big-O sense; the amount of space at a distance of about would increase exponentially, rather than like . A nuclear warhead could go off five hundred feet away and you’d feel a breeze through a fast-branching portal network. On the other hand, viruses could spread much more rapidly.

Anyway, at this point we’re getting into specifics of portals, so I’ll cut off the speculation. The point is: if transportation continues to get cheaper and more efficient over time, then we will converge to the world of the portal, or at least something like it. The details do matter - portals are different from teleportation or whatever might actually happen - but any method of fully relaxing transportation constraints will have qualitatively similar results, to a large extent.

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If you found this interesting, you would probably also be interested in "Anthropological invariants in travel behavior", Marchetti 1994.

This is an awesome document. Thanks

That's awesome. How did you run across it?

http://orbis.stanford.edu/ is an amazing customizable map showing transportation costs across the empire and for routes you choose in particular. You can set travel mechanisms, season, transfer costs, etc.

The Terra Ignota sci-fi series by Ada Palmer depicts a future world which is also driven by "slack transportation". The mechanism, rather than portals, is a super-cheap global network of autonomous flying cars (I think they're supposed to run on nuclear engines? The technical details are not really developed). It's a pretty interesting series, although it doesn't explore the practical implications so much as the political/sociological ones (and this is hardly the only thing driving the differences between the present world and the depicted future)

I have another data point that supports your modern day transportation constraint of 10-20%: skyscrapers. Engineers can build skyscrapers that are more than a mile high, much taller than our current skyscrapers. However, the taller a skyscraper gets, the more of its footprint is devoted to elevators and and associated equipment. At a certain point, your skyscraper just becomes a useless bundle of elevators. Right now, developers stop adding floors to a skyscraper when elevators are 30-40% of its footprint and 2-10% of its energy costs. The true transportation costs are probably slightly higher because they also include the costs of elevator installation and maintenance, and are probably roughly in line with your transportation constraint.

This makes me imagine a city-skyscraper, where an inhabitant can do all their work, living, and shopping within the skyscraper, across a limited range of floors. If they only rarely ever need to go to ground level, then that can cut down on how much of the building is dominated by elevators

This post is really cool, I've curated it. It abstracted some massive constraints in history into the key numbers (how much people, horses and ships could carry + how much resources an army needs) and helped me understand history much better. The generalisation of 10-20% is interesting. More stuff like this please! (...I mean I guess there's your whole sequence on this stuff :D)

Btw, your section on extreme slackness reminds me of Hanson's Age of Em, which is related, mapping out the future of civilization if we're all ems. Here are related quotes from his summary on the website:

...a kilo-em runs at 1000 times human speed, while a milli-em runs at one-thousandth... The cost to run an em is proportional to speed probably within at least a factor of one million above and below human speed... Ems can meet well in virtual reality when signal delays are less than reaction times; kilo-ems need to be within 15 kilometers...

Like us, ems gain by clumping together into cities. Unlike us, ems slower than kilo-ems can interact fully across cities without moving brains via virtual reality. This greatly reduces travel congestion, allows bigger cities, and puts most ems in a few big city-states. Iconic city locations are less about travel. City centers host faster ems and those doing interconnected tasks, although the very fastest are often in peripheries. City combinatorial auctions can substitute for centralized zoning and utility allocation, allowing em cities to deal with interdependencies quickly and flexibly. Working ems are faster than milli-ems, kilo-ems is the typical speed, and leisure usually runs faster than work. Em speeds clump, with a ratio between clumps near eight, and so cities may separate into regions for different speeds. Physical transport across a city seems very slow to kilo-ems, encouraging very local production, and hugely discouraging space travel.

It makes me think that as you approach movement at the speed of light, this results in an equilibrium noticeably different than if you approach infinite speed (like your portals), and that might be a more applicable ideal to think about. 

https://en.m.wikipedia.org/wiki/Flash_Crowd

This and the other 4 stories from a mathematician turned sci-fi author have aged well. Hope you enjoy them as much as I did when I read them.

Awesome! Thanks for the link.

A physically-active human needs about 3 lbs of food per day. (Modern hikers can probably find lighter calorie-dense foodstuffs, but we’re talking ancient history here.)

2 lbs of beef give you 2500 calories which is enough to survive. Cheese is even higher density. It turns out that for both you need a lot of salt which in turn makes salt very important militarily.

For the sake of comparison. I am from Estonia and Estonia still has conscript army. 9 month training (was 12 months in my time) ends with a 31 mile hike over 2 days, night is spent in the wilderness. Every soldier has to carry 31 kg or 71 lbs, some units at 90 lbs. It was hard, but doable.

If, as far as he knew, winds are random, shouldn't he still have turned around after half his supplies were gone, in case the winds randomly decide to starve him?

In Alexander's experience, the winds randomly changed direction from day to day. Over the course of a week or two, one was very likely to encounter a favorable wind. It's not one random variable, it's more like one independent random variable per day.

Also, although I didn't discuss it in the OP, the book argues that a large premodern army sitting in one place would quickly exhaust nearby food stores. That was probably also a large factor in Alexander's decision to leave India; turning back would likely have left them in a tough spot within a couple months.

An additional thought occurs in this regard. When talking about a transportation constraint we are likely talking about multiple margins - time, volume, mass, cost in energy (both to move and to keep the goods good). As we start shifting the constrain for one the others start coming into force.

It might be interesting to know if all are currently well balanced or if we have several that are nonbinding.

Another solution to the portal, and perhaps a different way of envisioning that innovation might be 3D printing from downloadable plans. I would think we will figure out how to create some type of generalized printer or see advances in materials.

The more I've considered it I am coming to the conclusion that we won't be able to make a good estimate on city size in terms of transportation costs. First, cultural aspects (e.g., language) and preferences (mountain versus beach) will have a large impact. Second, relaxing the transportation constraint supports both a highly urbanized outcome and a highly dispersed outcome. Perhaps rather than impacting city size, relaxing a transportation constraint might impact suburbs rather than the true urban settings.

Good Post!

Here is another point. The population of a city is constrained by the agricultural area accessible in less than 3-4 days, which is the time corresponding to the storage time of vegetables and fruits. During antiquity, Paris was the biggest town in France and was inhabited by 10,000 inhabitants, which corresponds to the population fed by a circle of arable land within a 3-day radius of oxcarts. If in the future transport becomes more constrained (oil shortage?), we should then expect to see the size of the cities greatly reduced.

If you speak French you can look at Jean-Marc Jancovici's lecture https://www.youtube.com/watch?v=Ci_cz18A2F8

Regarding your premodern city size question---I don't see a real constraint emerging from transportation speed. Here's my reasoning using your figures: a city with N people needs N * 5000 sq. meters of land to supply it with food (assume the land can sustain production indefinitely). If this land is a disk around the city the furthest the food has to come is sqrt(N) * 40 meters. If the food is carried at 10 miles a day, the longest supply lines require transporting food for only ~2-3 days for a city of a million, or ~25 days for a city of a 100 million.

Of course this does not a lead to a clean limit because it seems to me there is no very simple limit on how long the food could travel before it is eaten... But especially the first of these (2-3 days) seems reasonable.

Now, as you note it is transportation cost that is key, not just speed. But this requires estimating many more numbers. What did your calculation / model look like?

Not an answer to your city size question but one might use your question in part of the explanation of why cities and towns all seem to have emerged as market and trade centers historically. Of course there is some endogeneity present there

Buildings would still be built close together in order to share infrastructure (power, clean water, sewer, etc). Living outside of the city would certainly be more convenient with a portal system, but economies of scale mean it would still be far more expensive than living in the city.

If transportation isn't a problem then transporting water/sewer/energy over long distances would presumably also be cheap, so buildings could share infrastructure without being colocated, right?

True. I guess it depends on exactly how cheap/ubiquitous/miniaturized this portal technology is; I was imagining fridge-sized one-per-home, not pipe-sized dozens-per-home. It also matters what it's capable of transporting (water and sewage are just physical matter, but electricity is a different thing entirely).

Even in remote locations in the US power/clean water/sewer aren't expensive enough to get people to want to leave those locations.

The lower cost of lands makes up for it.