Demographic anomalies – the puzzle of urban density


I am returning to one particular topic connected my hypothesis, stating that technological change that has been going on in our civilisation at least since 1960 is oriented on increasing urbanization of humanity, and more specifically on effective, rigid partition between urban areas and rural ones. I am returning to a specific metric, namely to the DENSITY OF URBAN POPULATION, which I calculated my myself on the basis of three component datasets from the World Bank, namely: i) percentage of general population living in cities AKA coefficient of urbanization, ii) general headcount of population, and iii) total urban land area. I multiply the coefficient of urbanization by the general headcount of population, and thus I get the total number of people living in cities. In the next step, I divide that headcount of urban population by the total urban land area, and I get the density of urban population, measured as people per 1 km2 of urban land. 

That whole calculation is a bit of a mindfuck, and here is why. According to the World Bank, the total area of urban land, i.e. the two-dimensional total size of cities in the world has remained constant since 1990. Counter-intuitive? Hell, yes, especially that the same numerical standstill is officially recorded not only at the planetary level but also at the level of particular countries. It seems so impossible that my calculations regarding the density of urban population should be meaningless. Yet, the most interesting is to come. That DIY coefficient of mine, the density of urban population is significantly, positively correlated, at least at the level of the whole world, with another one: the coefficient of patent applications per 1 million people, which represents the intensity of occurrence in marketable scientific inventions. The corresponding Pearson correlation is r = 0,93 for resident patent applications (i.e. filed in the same country where the corresponding inventions have been made), and r = 0,97 for non-resident patent applications (i.e. foreign science searching legal protection in a country). You can read the details of those calculations in ‘Correlated coupling between living in cities and developing science’. 

That strong Pearson correlations are almost uncanny. Should it hold to deeper scrutiny, it would be one of the strongest correlations I have ever seen in social sciences. Something that is suspected not to make sense (the assumption of constant urban surface on the planet since 1990) produces a coefficient correlated almost at the 1:1 basis with something that is commonly recognized to make sense. F**k! I love science!

I want to sniff around that one a bit. My first step is to split global data into individual countries. In my native Poland, the coefficient of density in urban population, such as I calculate it on the basis of World Bank data, was 759,48 people per 1 km2, against 124,21 people per 1 km2 of general population density. I confront that metric with official data, published by the Main Statistical Office of Poland ( ), regarding three cities, in 2012: my native and beloved Krakow with 5 481 people per 1 km2 of urban land, and not native at all but just as sentimentally attached to my past Gdansk, yielding 4 761 people per 1 km2. Right, maybe I should try something smaller: Myslenice, near Krakow, sort of a satellite town. It is 3 756 people per 1 km2. If smaller does not quite work, it is worth trying bigger. Poland as a whole, according to the same source, has 2 424 people in its average square kilometre of urban space. All these numbers are one order of magnitude higher than my own calculation.

Now, I take a look at my own country from a different angle. The same site, says that the percentage of urban land in the total surface of the country has been gently growing, from 4,6% in 2003 to 5,4% in 2017. The total surface of Poland is 312 679 km2, and 5,4% makes 16 884,67 km2, against  30 501,34 km2 reported by the World Bank for 2010. All in all, data from the World Bank looks like an overly inflated projection of what urban land in Poland could possibly grow to in the distant future.

I try another European country: France. According to the French website Actu-Environnement: urban areas in France made 119 000 km2 in 2011, and it had apparently grown from the straight 100 000 km2 in 1999. The World Bank reports 86 463,06 km2, thus much less in this case. Similar check for United Kingdom: according to , urban land makes 1,77 million hectares, thus 17 700 km2, against  58 698,75 km2 reported by the World Bank. Once again, a puzzle: where that discrepancy comes from?

The data reported on , as regards the extent of urban land apparently comes from one place: the Center for International Earth Science Information Network (CIESIN), at the Columbia University, and CIESIN declares to base their estimation on satellite photos. The French statistical institution, INSEE, reports a similar methodological take in their studies, in a  paper available at: . Apparently, urban land seen from the orbit of Earth is not exactly the same as urban land seen from the window of an office. The latter is strictly delineated by administrative borders of towns and cities, whilst the former has shades and tones, e.g. are 50 warehouse, office and hotel buildings, standing next to each other in an otherwise rural place, an urban space? That’s a tricky question. We return here to the deep thought by Fernand Braudel, in his ‘Civilisation and Capitalism’, Volume 1, Section 8:‘Towns and Cities’: The town, an unusual concentration of people, of houses close together, often joined wall to all, is a demographic anomaly.  

Yes, that seems definitely the path to follow in order to understand those strange, counterintuitive results which I got, regarding the size and human density of urban spaces across the planet: the town is a demographic anomaly. The methodology used by CIESIN, and reproduced by the World Bank, looks for demographic anomalies of urban persuasion, observable on satellite photos. The total surface of those anomalies can be very different from officially reported surface of administrative urban entities within particular countries and seems remaining constant for the moment.

Good. I can return to my hypothesis: technological change that has been going on in our civilisation at least since 1960 is oriented on increasing urbanization of humanity, and more specifically on effective, rigid partition between urban areas and rural ones. The discourse about defining what urban space actually is, and the assumption that it is a demographic anomaly, leads me into investigating how much of an anomaly is it across the planet. In other words: are urban structures anomalous in the same way everywhere, across all the countries on the planet? In order to discuss this specific question, I will be referring to a small database I made, out of data downloaded from the World Bank, and which you can view or download, in Excel format, from this link: Urban Density Database. In my calculations, I assumed that demographic anomaly in urban settlements is observable quantitatively, among others, as abnormal density of population. Official demographic databases yield average, national densities of population, whilst I calculate densities of urban populations, and I can denominate the latter in units of the former. For each country separately, I calculate the following coefficient: [Density of urban population] / [Density of general population]. Both densities are given in the same units, i.e. in people per 1 km2. With the same unit in both the nominator and the denominator of my coefficient, I can ask politely that unit to go and have a break, so as to leave me with what I like: bare numbers.

Those bare numbers, estimated for 2010, tell me a few interesting stories. First of all, there is a bunch of small states where my coefficient is below 1, i.e. the apparent density of urban populations in those places is lower than their general density. They are: San Marino (0,99), Guam (0,98), Puerto Rico (0,98), Tonga (0,93), Grenada (0,72), Mauritius (0,66), Micronesia Fed. Sts. (0,64), Aruba (0,45), Antigua and Barbuda (0,43), St. Kitts and Nevis (0,35), Barbados (0,33), St. Lucia (0,32). These places look like the dream of social distancing: in cities, the density of population is lower than what is observable in the countryside. Numbers in parentheses are precisely the fractions [Density of urban population / Density of general population]. If I keep assuming that urban settlements are a demographic anomaly, those cases yield an anomalous form of an anomaly. These are mostly small island states. The paradox in their case is that officially, their populations mostly urban: more than 90% of their respective populations are technically city dwellers.

I am going once again through the methodology, in order to understand the logic of those local anomalies in the distribution of a general anomaly. Administrative data yields the number of people living in cities. Satellite-based data from the Center for International Earth Science Information Network (CIESIN), at the Columbia University, yields the total surface of settlements qualifiable as urban. The exact method used for that qualification is described as follows: ‘The Global Rural-Urban Mapping Project, Version 1 (GRUMPv1) urban extent grid distinguishes urban and rural areas based on a combination of population counts (persons), settlement points, and the presence of Night-time Lights. Areas are defined as urban where contiguous lighted cells from the Night-time Lights or approximated urban extents based on buffered settlement points for which the total population is greater than 5,000 persons’.  

Night-time lights manifest a fairly high use of electricity, and this is supposed to combine with the presence of specific settlement points. I assume (it is not straightforwardly phrased out in the official methodology) that settlement points mean residential buildings. I guess that a given intensity of agglomeration in such structures allows guessing a potentially urban area. A working hypothesis is being phrased out: ‘This place is a city’. The next step consists in measuring the occurrence of Night-time Lights, and those researchers from CIESIN probably have some scale of that occurrence, with a threshold on it. When the given place, running up for being a city, passes that threshold, then it is definitely deemed a city.

Now, I am returning to those strange outliers with urban populations being apparently less dense than general populations. In my mind, I can see three maps of the same territory. The first map is that of actual human settlements, i.e. the map of humans staying in one place, over the whole territory of the country. The second map is that of official, administratively defined urban entities: towns and cities. Officially, those first two maps overlap in more than 90%: more than 90% of the population lives in places officially deemed as urban settlements. A third map comes to the fore, that of urban settlements defined according to the concentration of residential structures and Night-Time Lights. Apparently, that third map diverges a lot from the second one (administratively defined cities), and a large part of the population lives in places which administratively are urban, but, according to the CIESIN methodology, they are rural, not urban. 

Generally, the distribution of coefficient [Density of urban population] / [Density of general population], which, for the sake of convenience, I will further designate as [DU/DG], is far from the normal bell curve. I have just discussed outliers to be found at the bottom of the scale, and yet there are outliers on its opposite end as well. The most striking is Greenland, with [DU/DG] = 10 385.81, which is not that weird if one thinks about their physical geography. Mauritania and Somalia come with [DU/DG] equal to, respectively, 622.32 and 618.50. Adverse natural conditions apparently make towns and cities a true demographic anomaly, with their populations being several hundred times denser than the general population of their host countries.

The more I study the geographical distribution of the [DU/DG] coefficient, the more I agree with the claim that towns are a demographic anomaly. The coefficient [DU/DG] looks like a measure of civilizational difference between the city and the countryside. Table 1, below, introduces the average values of that coefficient across categories of countries, defined according to income per capita. An interesting pattern emerges. The wealthier a given country is, the smaller the difference between the city and the countryside, in terms of population density. Most of the global population seems to be living in neighbourhoods where that difference is around 20, i.e. where city slickers live in a twentyish times more dense populations than the national average.

I have been focusing a lot on cities as cradles to hone new social roles for new people coming to active social life, and as solutions for peacefully managing the possible conflicts of interests, between social groups, as regards the exploitation of fertile lowland areas on the planet. The abnormally high density of urban population is both an opportunity for creating new social roles, and a possible threshold of marginal gains. The more people there are per 1 km2, the more social interactions between those people, and the greater the likelihood for some of those interactions turning into recurrent patterns, i.e. into social roles. On the other hand, abundant, richly textured social structure, with a big capacity to engender new social roles – in other words, the social structure of wealthy countries – seems to be developing on the back of an undertow of diminishing difference between the city and the countryside.          

Table 1 – Average values of coefficient [Density of urban population] / [Density of general population] across categories of countries regarding wealth and economic development

Category of countriesDensity of urban population denominated over general density of population, 2010Population, 2010
Fragile and conflict affected situations91,98 618 029 522
Heavily indebted poor countries (HIPC)84,96 624 219 326
Low income74,24577 274 011
Upper middle income26,422 499 410 493
Low & middle income22,885 765 121 055
Middle income20,875 187 847 044
Lower middle income15,392 688 436 551
High Income15,811 157 826 206
Central Europe and the Baltics9,63104 421 447
United States9,21309 321 666
European Union5,65441 532 412
Euro area5,16336 151 479

Table 2 represents a different take on the implications of density in urban population. Something old and something new: the already known coefficient of patent applications per 1 million people, and a new one, of fundamental importance, namely the mean consumption of energy per capita, in kilograms of oil equivalent. One kilogram of oil equivalent stands for approximately 11,63 kilowatt hours.  Those two variables are averaged across sextiles (i.e. sets representing 1/6th of the total sample n = 221 countries), in 2010. Consumption of energy presents maybe the clearest pattern: its mean value decreases consistently across sextiles 1 ÷ 5, just to grow slightly in the sixth one. That sixth sextile groups countries with exceptionally tough natural conditions for human settlement, whence an understandable need for extra energy to consume. Save for those outliers, one of the most puzzling connections I have ever seen in social sciences emerges: the less difference between the city and the countryside, in terms of population density, the more energy is being consumed per capita. In other words: the less of a demographic anomaly cities are, in a given country (i.e. the less they diverge from rural neighbourhoods), the more energy people consume. I am trying to wrap my mind around it, just as I try to convey this partial observation graphically, in Graph 2, further below Table 2.

Table 2 – Mean coefficients of energy use per capita, and patent applications per 1 mln people, across sextiles of density in urban population, data for 2010        

Sextiles (Density of urban population denominated over general density of population)Mean [Energy use (kg of oil equivalent per capita)], 2010Mean [Patent applications total per 1 million people], 2010
50,94 ≤ [DU/DG] ≤ 10 385,812 070,5468,35
23,50 ≤ [DU/DG] < 50,941 611,73596,464
12,84 ≤ [DU/DG] < 23,502 184,039218,857
6,00 ≤ [DU/DG] < 12,842 780,263100,097
2,02 ≤ [DU/DG]  < 6,003 288,468284,685
0,00 ≤ [DU/DG] < 2,024 581,108126,734

Final consumption of energy is usually represented as a triad of main uses: production of goods and services, transportation, and the strictly spoken household use (heating, cooking, cooling, electronics etc.). Still, another possible representation comes to my mind: the more different technologies we have stacked up in our civilization, the more energy they all need. I explain. Technological change is frequently modelled as a process when newer generations of technologies supplant the older ones. However, what happens when those generations overlap? If they do, quick technological change makes us stack up technologies, older ones together with the newer ones, and the faster new technologies get invented, the richer the basket of technologies we hold. We could, possibly, strip our state of possessions down, just to one generation of technologies – implicitly it would be the most recent one – and yet we don’t. We keep them all. I look around my house, and around my close neighbourhood. Houses like mine, built in 2001, with the construction technologies of the time, are neighbouring houses built just recently, much more energy-efficient when it comes to heating and thermal insulation. In a theoretically perfect world, when new generation of technologies supplants the older one, my house should be demolished and replaced by a state-of-the-art structure. Yet, I don’t do it. I stick to the old house.

The same applies to cars. My car is an old Honda Civic from 2004. As compared to the really recent cars some of my neighbours bought, my Honda gently drifts in the direction of the nearest museum. Still, I keep it. Across the entire neighbourhood of some 500 households, we have cars stretching from the 1990s up to now. Many generations of technologies coexist. Once again, we technically could shave off the old stuff and stick just to the most recent, yet we don’t. All those technologies need to be powered with at least some energy. The more technologies we have stacked up, the more energy we need.  

I think about that technological explanation because of the second numerical column in Table 2, namely that informative about patent applications per 1 million people. Patentable invention coincides with the creation of new social roles for new people coming with demographic growth. Data in table 2 suggests that some classes of the coefficient [Density of urban population] / [Density of general population] are more prone to such creation than others, i.e. in those specific classes of [DU/DG] the creation of new social roles is particularly intense.

Good. Now comes the strangest mathematical proportion I found in that data about density of urban population and energy. For the interval 1972 ÷ 2014, I could calculate a double-stack coefficient: {[Energy per capita] / [DU/DG]}. The logic behind this fraction is to smooth out the connection between energy per capita and the relative density of urban population, as observed in Table 2 on a discrete scale. As I denominate the density of urban population in units of density in the general population, I want to know how much energy per capita is consumed per each such unit. As it is, that fraction {[Energy per capita] / [DU/DG] is a compound arithmetical construct covering six levels of simple numerical values. After simplification, {[Energy per capita] / [DU/DG] = [Total energy consumed / Population in cities] * [Surface of urban land / Total surface of land]. Simplification goes further. As I look at the numerical values of that complex fraction, computed for the whole world since 1972 through 2014, it keeps oscillating very tightly around 100. More specifically, its average value for that period is AVG{[Energy per capita] / [DU/DG]} = 102.9, with a standard deviation of 3.5, which makes that standard deviation quasi inexistent. As I go across many socio-economic indicators available with the World Bank, none of them follows so flat a trajectory over that many decades. It looks as if there was a global equilibrium between total energy consumed and density of population in cities. What adds pepper to that burrito is the fact that cross-sectionally, i.e. computed for the same year across many countries, the same coefficient {[Energy per capita] / [DU/DG] swings wildly. There are no local patterns, but there is a very strong planetary pattern. WTF?

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