The Death of Distance?

Today, we will examine the hypothesis that remote interaction, such as through telecommunications and easy air travel, cause cities to become less important. The title of this post comes from Cairncross (1997), whose book The Death of Distance: How the Communications Revolution Will Change Our Lives predicts that new technology, and communications technology in particular, will cause physical distance, and thus the physical proximity that is the basis of urban agglomeration economies, to become less important. This hypothesis has not been treated kindly in the last 30 years, but in reality, the evidence for it, on either side, is mixed and patchy.

Today, we will briefly review the history of death of distance reasoning, we will propose a theoretical model of how the death of distance might be compatible with complementarity, and we will examine evidence based on telecommunications and on air travel. We will find that, while there is little evidence to suppose that proximity is becoming less important, there is a bit of evidence, albeit inconclusive, that technology is reducing the importance of proximity. As usual, this article is written under a Living Literature Review grant from Coefficient Giving, though all conclusions are my own. This essay is part of the Scaling in Human Societies project, and the companion piece can be seen here.

Cairncross was, of course, far from the first to speculate about the role of advancing technology on the meaning of distance. As Morus (2000) recounts, Victorian thinkers in the 19th century described the effect of the railroad and telegraph as “the annihilation of space and time”, by which they meant that the instantaneous communication that telegraphs allowed would unify people all over the world, and it furthermore meant that it was no longer necessary to wait for days or weeks to learn of distant news.

The science fiction author H.G. Wells’ (Wells 1901) essay The Probable Diffusion of Great Cities argues, with logic similar to that behind Marchetti’s Constant, that city boundaries were set as an hour commute using the predominant transportation technology of the time. Wells speculated that by 2000, transportation with an average speed of at least 30 miles per hour should be available to the general public, which would lead to cities in which the outer exurbs were at least 30 miles from the city center, a prediction that has proven to be correct. Wells also anticipates job dispersal, writing,

In addition, as we have already intimated, many Londoners in the future may abandon the city office altogether, preferring to do their business in more agreeable surroundings. Such a business as book publishing, for example, has no unbreakable bonds to keep it in the region of high rent and congested streets. The days when the financial fortunes of books depended upon the colloquial support of influential people in a small Society are past …

The vision of a dispersed city, with transportation highly dependent on personal automobiles and with a minimal central business district, was envisioned in Broadacre City, the vision of the designer Frank Lloyd Wright first promulgated in his 1932 work, The Disappearing City (Wright 1932). This vision has largely fallen out of fashion in modern planning and urbanism, but it has been partially realized with increasing suburbanization and the emergence of edge cities.

Cairncross’ thesis traces more directly back to a pair of papers by Melvin Webber (Webber 1963 and Webber 1964). In these works, Webber argues that the concept of “place”, which is central to urban planning, is an increasingly obsolete concept due to advancing transportation and communications technology. Alvin Toffler’s The Third Wave (Toffler 1980) coined the phrase “electronic cottage” to refer to the idea that an increasing share of economically relevant activity would be done at home due to improves telecommunications technology. Work as early as Forester (1988) argued against this hypothesis on the grounds that remote work has been not as easy, cheap, or psychologically fulfilling as Toffler supposed.

Many studies have found complementary relationships between in-person interactions and telecommunications, which to some thinkers poses an open-and-shut case against death of distance reasoning. Modern urbanism is characterized by works such as Ed Glaeser’s Triumph of the City (Glaeser 2011), which characterizes cities as continuing to be the engines of societal progress. We will see today that, while the death of distance has been highly exaggerated, the idea should not be written off so quickly.

Here, I would like to propose a simple model of how it might simultaneously be the case that local and remote interactions are complementary and also that large cities are becoming less relevant to the world economy. Please note at the outset, though, that my model explains how this could be the case, and it does not claim that this is the case.

Some definitions come first. By “local” interactions, I mean those between individuals within the same city. They do not necessarily have to occur in person. “Remote” interactions are between individuals in different cities. As usual, a “city” is loosely defined as a commutershed around a central business district, as suggested by Marchetti’s Constant and H.G. Well above; such a definition does not generally correspond to a city’s political boundaries.

To say that local and remote interactions are “substitutes” means that, as one increases, the other generally decreases. To say that they are “complements” means that, as one increases, the other generally increases as well.

WARNING: For the rest of this section, there is more math than usual for my posts. Don’t worry, it won’t be too bad. If you’d rather, you can skip to the next section, where the math is gone. You’ll miss out on some good stuff, though.

I will again refer to a foundational work in urban economics and scaling theory, Bettencourt (2013), and my early write-up on that subject. That paper shows how socioeconomic quantities, such as gross domestic product, tend to grow with the 7/6 power of the population N of the city. For this post, I would rather express quantities in per capita terms, and so GDP per capita tends to grow with the 1/6 power of N. The paper’s model shows how the number of interactions that each person engages in also tends to grow as N^(1/6), and it argues that GDP is proportional to the number of interactions.

However, one shortcoming of Bettencourt’s (2013) model is that it treats all interactions as local. Clearly, this is a simplification that keeps the model tractable and clear, and obviously there are some economically valuable remote interactions. Let’s suppose that GDP is proportional to the sum of all interactions, local and remote:

Here, y(N) is GDP in terms of the population size N. The local interaction term aN^(1/6) is as before. To that I added a remote interaction term r(N). The symbol ∝ means “proportional to”.

Now, let us suppose that r(N) is proportional to the 1/12 power of population. To emphasize, I have no empirical evidence that this is the case; this choice is made for illustrative purposes only. We have,

The reader might object that a remote interaction is less valuable than an in-person interaction. That may be the case, and this devaluation could be regarded as being incorporated into the term b.

Now suppose that we measure the scaling exponent by taking the derivative of ln(y(N)) with respect to ln(N), as this parameter is normally estimated. Using a dark art known as calculus, we find that the measured exponent β is as follows:

Note several features of this model. First, the case of the isolated city of Bettencourt (2013) is realized with r(N) = 0. To say that local and remote interactions are substitutes means than r(N) is a decreasing function in N, while if they are complements, then r(N) is increasing in N. If b is large relative to a, i.e. remote interactions dominate, then the measured exponent β is close to 1/12. If the exponent of the remote interaction term is greater than 1/6—as we will see may be the case with air travel—then remote interaction would actually strengthen urban scaling.

A testable prediction of this model is that the scaling exponent should be smaller for small cities and larger for large cities. Whether that holds might be a good future topic.

In a post on the pace of life earlier this year, I discussed Sapienza et al. (2023), which finds that cell phone usage tends to be about 5% higher in urban areas than in rural areas after accounting for demographics. Their results are robust to a check for self-selection, i.e. that people who use their phones more tend to prefer living in cities, as opposed to cities causing people to use their phones more. And way back in the 7/6 rule post, I referred to Schläpfer et al. (2014), which finds that cell phone call volume tends to grow with about the 1.10 power of population in Portugal and in the UK.

Superlinear scaling has been found by other researchers. Bokányi, Kondor, and Vattay (2019) examine a dataset of Twitter (now X) corpora and find that the number of Tweets per user grows with the 0.02 power of city size. The number of words tweeted also tends to grow with the 0.02 power, negating the possibility that users in large cities are decreasing the size of tweets to compensate for volume. They also examine the prevalence of individual words and find that some grow superlinearly with city size and some grow sublinearly. The confidence interval of Bokányi, Kondor, and Vattay (2019) contains 0, and so they cannot rule out that there is a no relationship between city size and per capita Twitter activity. In a similar vein, Arthur and Williams (2019) examine the relationship between the number of Tweets from a region and the region’s population density. Excluding some types of Tweets, such as from bots and weather stations, they find much stronger relationship: the number of Tweets from a region grows in an exponent of the population density as high as 0.7, depending on the spatial resolution at which density is measured.

There are several methodological differences between Bokányi, Kondor, and Vattay (2019) and Arthur and Williams (2019) that makes the results not directly comparable. The geographic scopes differ; the former spans the United States, while the latter is based in the South-West region of the United Kingdom. The former study regresses against city sizes, while the latter study regresses against population density. To further illustrate the sensitivity of the results to the geographic unit of analysis, Arthur and Williams (2019) find a scaling exponent of about 0.7 for a spatial resolution of around 30×30 kilometers to 80×80 kilometers; the exponent drops to around 0.3 to 0.4 for resolutions less than 20×20 kilometers, and it also shrinks for higher resolutions. Arthur and Williams (2019) also consider geo-tagged Tweets, which remove the majority of Tweets that are generated by bots, weather stations, and third party services, while the other study does not make such a modification. A moral of the story is that some scaling results, such as those related to social media usage, are not robust to methodological choices and should not be extrapolated far beyond the context in which the result was measured.

One important caveat of these studies, as well as the studies of Sapienza et al. (2023) and Schläpfer et al. (2014), is that they do not distinguish between local and remote interaction. It is thus unclear how much they contribute to the remote r(N) term in our model. Nevertheless, while these studies provide evidence that remote interaction is complementary with local interaction, they shed little light into whether telecommunications are diluting the importance of proximity.

Distant interactions can be mediated by telecommunications, as discussed above, or by intercity transportation such as commercial aviation. Matsumoto (2007) hypothesize that a gravity model explains the volume of air travel, both passenger and cargo, between cities. Modeled from Isaac Newton’s law of gravitation, a gravity model holds that the volume of interaction between two cities should be proportional to the product of the “masses” of the two cities (here, measured both as GDP and as population) and inversely proportional to the square of the distance.

For intercontinental flights in 2000, Matsumoto (2007) finds scaling exponents with respect to population of 0.25 and 0.33 for per capita passenger air travel and per capita cargo transport respectively. These high numbers suggest that aviation increases, rather than diminishes, the importance of size in explaining a city’s prowess. Scaling exponents greater than Bettencourt’s (2013) theoretical 1/6 are found for per capita passenger and cargo air transport for flights within the Americas, within Europe, and within Asia as well. The paper also finds strong scaling with respect to GDP—exponents of 0.31 and 0.32—and similarly high values for the regional flights, with the exception of an exponent of -0.10 for per capita air cargo within the Americas.

O’Connor (2003) argues that the impact that commercial aviation has on cities depends greatly on the particulars of aircraft technology. He finds that prior to 1990, aviation generally favored GDP growth in the largest and wealthiest cities. However, from 1990 to 2000, second tier cities (defined on a four tier scale) gained the greatest number of air passengers, while first tier cities lost the greatest number. Among the top 100 airports by traffic, the top 10 declined from 36.3% to 31.0% of passengers from 1990 to 2000, and those ranked 21-50 increased from 25.2% to 29.4%. He attributes this change to the introduction of mid-sized long haul aircraft—the Boeing 777 and Airbus 340 in particular—the refinement of engine technology to enable 13-15 hour flights, and the introduction of regional jets, though the latter’s impact may be ambiguous by increasing the catchment area of top tier airports. Additional factors include deregulation of the airline industry and congestion at top tier airports. O’Connor and Fuellhart (2013) perform a similar analysis and find that from 2005 to 2010, the 41 Alpha cities saw a 13.0% increase in the number of passengers, while in 40 Beta cities, that increase was 16.4%.

Wong et al. (2019) also perform an analysis similar to that of O’Connor (2003), and they too find that second tier airports gain passengers relative to top tier airports, as well as an increasing phenomenon of hub bypassing. However, their analysis extends to the phenomenon of large cities that host multiple airports. On the airport-city level, they find a slight increase in total concentration.

Oliveira et al. (2020) find ambiguous effects on the concentration of air travel in Brazil. When examining cities by population, they find a decoupling from 1995 to 2012, driven by the technological feasibility of smaller jets and by deregulation. However, when examining cities by GDP, they find an increased concentration over that time, indicating that new routes were concentrated in wealthier cities.

One important distinction between these studies is the cross-sectional analysis versus temporal trends. Matsumoto (2007) finds strong cross-sectional scaling of air travel with city size, while O’Connor (2003) and the follow-up analyses find dispersal over time. Thus the effect of aviation on city concentration depends on which perspective we take. For the “death of distance” hypothesis, the temporal perspective is more relevant, and so we find some modest evidence that aviation technology is in fact making proximity less important.

Today’s post was rather long and technical. The central question is whether advancing technology is bringing about a “death of distance”, meaning that physical distance matters less, or at least if some technologies hold back the increase. We saw that this can be true even if large cities facilitate more distant interactions, but it is unclear whether this is true in the real word.

Obviously, this hypothesis is true in some sense. Cities are physically larger and more dispersed larger due to widespread automobile ownership. Also obviously, the death of distance has not proceeded to the extent that thinkers like Toffler (1980) and Cairncross (1997) imagined. The evidence reviewed today is mixed, patchy, and not very robust, and it generally does not support the hypothesis of the death of distance, though it does weakly suggest that technology may be working against concentration. The relative importance of large, alpha cities may decrease modestly in the foreseeable future, but barring a major technological revolution1, I don’t imagine that the importance will diminish much.

The death of distance is one of these predictions that, like technological unemployment and resource depletion, keeps coming back up because it sounds plausible. It would be wrong to conclude that, because proximity has remained important to the present day, it will remain important forever. But before making the prediction again, one should understand why it hasn’t panned out in the past.