Transportation as a Constraint

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

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.

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

You wrote this, and I just saw it, so I took up your request:

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.

My general model is that a town or city cannot at all function as a cohesive urban entity if it takes longer than a day to traverse. If a journey from an edge home to a central production facility (and back) consumes each day, then the person in that home can't actually work in the facility. 

If cars go 80 miles per hour, a city with a diameter of >160 miles is probably geo-economically "taut" as you put it, and close to its limits. (These will tend to have to be on an ocean or navigable river to give them access to global food markets.)

I checked with Google Maps just now. From Cuautitlán Izcalli to San Pedro Mártir via public transit through the center of Mexico City takes ~3 hours. From Santa Clarita to San Juan Capistrano through LA by car takes ~2 hours. These are probably modern functional "town sizes" for people who greatly value "an exurban home", and engage in "moderately productive centralized labor coordinating with a huge labor pool to achieve extreme specialization" on most work days.

The same basic idea, interacting with agricultural productivity as a constraint, doesn't limit "the city based on food", but changes what specific agricultural uses are optimal in surrounding rings around a market center (where prices will typically be most accurate, such as to allow arbitrage opportunities to be noticed back before telegraph) when planting strategies are optimized based on the transport cost characteristics of the foodstuffs.

In the idealized case you get circles around the market.

In practice (with rivers, roads, and mountains) you get "isoclines" of cost or time or time-as-part-of-cost. The importance of locating cities at the mouth of a navigable river falls our of this from first principles <3

This thinking framework was famously started by Von Thunen (who wanted to optimize agricultural practices on a german hacienda, basically) who is arguably the "founding father" of a field called economic geography.

Chisholm's Rural Settlement and Land Use is maybe a bit dry, but it aptly applies the tools of the field to include relatively modern updates (like the effects of current global prices being known around the planet and cheap transcontinental shipment) and generates resulting maps showing a good match between theory and practice, with vast areas of the globe acting like food production basins for major global population centers.

(Learning about economic geography was a big part of how I realized that "zoning laws" are not even really necessary to get "zones of similar production". All you need is cheap switching costs on land use, and local sanity, and it should mostly just "all coase out" in the end.)

I think modern knowledge work might be turning the internet and its various online language communities into "one big virtual city", where the barriers to making such a thing truly work probably occur in "communication travel time" or some such... perhaps related to psychologies of trust, intellectual coordination, shared languages, the latency and publicness of important broadcasts, maybe percolation theory applied to gossip networks, and maybe also some Dunbar issues?

Presumably the Sage of Omaha noticed this and noticed that he wanted to live where he was born, and could do so, maybe treating his home location as an input into his emotional and intellectual stability? This only could work for him after having learned value investing via physical co-presence on the east coast from Benjamin Graham, and then heading back to Nebraska to systematically apply his brain to information according to certain algorithms without the "distractions of NYC"? 

But I think it is not an accident that he went to a huge central place, then filtered like crazy to find a good teacher, then learned the algorithms early in life that he could apply from anywhere, then went off to a non-central city to make money simply by very precisely "knowing things about how to turn precise knowledge into money".

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.

This post was well written, interesting, had multiple useful examples, and generally filled in models of the world. I haven't explicitly fact-checked it but it accords with things I've read and verified elsewhere.

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.

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 [? · GW] :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. 

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

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.

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?

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.

Really interesting stuff.

If you (or others) are interested the excellent science fiction books "Hyperion" and "Fall of Hyperion" have a very similar portal setup in the background (its not the focus). It mentions people who chose to place their house's living room on a different planet than the kitchen to get a range of views. 

Re: your speculation regarding future transportation costs, I vaguely recall something by an economist a couple of years ago (maybe on the Krugman blog), stating that economic reasons by themselves were enough to ensure that transportation couldn't get arbitrarily cheap. But I can't recall the specifics.

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.