Tag: density of population

Social roles and pathogens: our average civilisation

MY EDITORIAL ON YOU TUBE

I am starting this update with a bit of a winddown on my previous excitement, expressed in Demographic anomalies – the puzzle of urban density. I was excited about the apparently mind-blowing, negative correlation of ranks between the relative density of urban population, on the one hand, and the consumption of energy per capita, on the other hand. Apparently, the lower the rank of the {[DU/DG] [Density of urban population / General density of population]} coefficient, the greater the consumption of energy per capita. All in all, it is not as mysterious as I thought. It is visible, that the average value of the [DU/DG] coefficient decreases with the level of socio-economic development. In higher-middle income countries, and in the high-income ones, [DU/DG] stays consistently below 10, whilst in poor countries it can even flirt with values above 100. In other words, relatively greater a national wealth is associated with relatively smaller a social difference between cities and the countryside. Still, that shrinking difference seems to have a ceiling around [DU/DG] = 2,00. In the realm of [DU/DG] < 2,00, we do not really encounter wealthy countries. In this category we have tropical island states, or entities such as West Bank and Gaza, which are demographic anomalies even against the background of cities in general being demographic anomalies. Among really wealthy countries, the lowest values in the [DU/DG] coefficient are to find with Belgium (2,39) and Netherlands (2,30).

I am taking it from the beginning, ‘it’ being the issue of cities and urbanisation. The beginning was my bewilderment when the COVID-19-related lockdowns started in my country, i.e. in Poland. I remember cycling through the post-apocalyptically empty streets of my hometown, Krakow, Poland, I was turning in my mind the news, regarding the adverse economic outcomes of the lockdown, and strange questions were popping up in my consciousness. How many human footsteps per day does a city need to thrive? How many face-to-face interactions between people do we need, to keep that city working?

I had that sudden realization that city life is all about intensity of human interaction.  I reminded another realization, which I experienced in November 2017. I was on a plane that had just taken off from the giant Frankfurt airport. It was a short flight, to Lyon, France – almost like a ballistic curve – and this is probably why the plane was gathering altitude very gently. I could see the land beneath, and I marvelled at the slightly pulsating, intricate streaks of light, down there, on the ground. It took me a few minutes to realize that the lights I was admiring were those of vehicles trapped in the gargantuan traffic jams, typical for the whole region of Frankfurt. Massively recurrent, utterly unpleasant, individual happening – being stuck in a traffic jam – was producing outstanding beauty, when contemplated from far above. 

As I rummaged a bit through literature, cities seem to have been invented, back in the day, as social contrivances allowing, on the one hand, relatively peaceful coexistence of many different ethnic groups in fertile lowlands, and, on the other hand, a clear focusing of demographic growth in limited areas, whilst leaving the majority of arable land to the production of food. With time, the unusually high density of population in cities started generating secondary and tertiary effects. Greater a density of population favours accelerated emergence of new social roles, which, in turn, stimulates technological change and the development of markets. Thus, initially, cities tend to differentiate sharply from the surrounding countryside. By doing so, they create a powerful creative power regarding aggregate income of the social group. When this income-generating force concurs, hopefully, with acceptably favourable natural conditions and with political stability, the whole place (i.e. country or region) starts getting posh, and, as it does so, the relative disparity between cities and the countryside starts to diminish down to some kind of no-go-further threshold, where urban populations are a little bit twice as dense as the general average of the country. In other words, cities are a demographic anomaly which alleviates social tensions, and allows social change through personal individuation and technological change, and this anomaly starts dissolving itself as soon as those secondary and tertiary outcomes really kick in.

In the presence of that multi-layer cognitive dissonance, I am doing what I frequently do, i.e. in a squid-like manner I produce a cloud of ink. Well, metaphorically: it is more of a digital ink. As I start making myself comfortable inside that cloud, axes of coordinates emerged. One of them is human coordination in cities, and a relatively young, interesting avenue of research labelled ‘social neuroscience’. As digital imaging of neural processes has been making itself some space, as empirical method of investigation, interesting openings emerge. I am undertaking a short review of literature in the field of social neuroscience, in order to understand better the link between us, humans, being socially dense, and us doing other interesting things, e.g. inventing quantum physics or publishing the ‘Vogue’ magazine.

I am comparing literature from 2010 with the most recent one, like 2018 and 2019. I snatched almost the entire volume 65 of the ‘Neuron’ journal from March 25, 2010, and I passed in review articles pertinent to social neuroscience. Pascal Belin and Marie-Helene Grosbras (2010[1]) discuss the implications of research on voice cognition in infants. Neurologically, the capacity to recognize voice, i.e. to identify people by their voices, emerges long before the capacity to process verbal communication. Apparently, the period stretching from the 3rd month of life through the 7th month is critical for the development of voice cognition in infants. During that time, babies learn to be sharper observers of voices than other ambient sounds. Cerebral processing of voice seems to be largely subcortical and connected to our perception of time. In other words, when we use to say, jokingly, that city people cannot distinguish the voices of birds but can overhear gossip in a social situation, it is fundamentally true. From the standpoint of my research it means that dense social interaction in cities has a deep neurological impact on people already in their infancy. I assume that the denser a population is, the more different human voices a baby is likely to hear, and learn to discriminate, during that 3rd ÷ 7th month phase of learning voice cognition. The greater the density of population, the greater the data input for the development of this specific function in our brain. The greater the difference between the city and the countryside, social-density-wise, the greater the developmental difference between infant brains as regards voice cognition.

From specific I pass to the general, and to a review article by Ralph Adolphs (2010[2]). One of the most interesting takeaways from this article is a strongly corroborated thesis that social neurophysiology (i.e. the way that our brain works in different social contexts) goes two ways: our neuro-wiring predisposes us to some specific patterns of social behaviour, and yet specific social contexts can make us switch between neurophysiological patterns. That could mean that every mentally healthy human is neurologically wired for being both a city slicker and a rural being. Depending on the context we are in, the corresponding neurophysiological protocol kicks in. Long-lasting urbanization privileges social learning around ‘urban’ neurophysiological patterns, and therefore cities can have triggered a specific evolutionary direction in our species.

I found an interesting, slightly older paper on risk-taking behaviour in adolescents (Steinberg 2008[3]). It is interesting because it shows connections between developmental changes in the brain, and the appetite for risk. Risk-taking behaviour is like a fast lane of learning. We take risks when and to the extent that we can tolerate both high uncertainty and high emotional tension in a specific context. Adolescents take risks in order to boost their position in social hierarchy and that seems to be a truly adolescent behaviour from the neurophysiological point of view. Neurophysiological adults, thus, roughly speaking, people over the age of 25, seem to develop increasing preference for strategies of social advancement based on long-term, planned action with clearly delayed rewards. Apparently, there are two distinct, neurophysiological protocols – the adolescent one and the adult one – as regards the quest for individual social role, and the learning which that role requires.

Cities allow more interactions between adolescents than countryside does. More interactions between adolescents stronger a reinforcement for social-role-building strategies based on short-term reward acquired at the price of high risk. That might be the reason why in the modern society, which, fault of a better term, we call ‘consumer society’, there is such a push towards quick professional careers. The fascinating part is that in a social environment rich in adolescent social interaction, the adolescent pattern of social learning, based on risk taking for quick reward, finds itself prolongated deep into people’s 40ies or even 50ies.

We probably all know those situations, when we look for something valuable in a place where we can reasonably expect to find valuable things, yet the search is not really successful. Then, all of a sudden, just next door to that well-reputed location, we find true jewels of value. I experienced it with books, and with people as well. So is the case here, with social neuroscience. As long as I was typing ‘social neuroscience’ in the search interfaces of scientific repositories, more or less the same essential content kept coming to the surface. As my internal curious ape was getting bored, it started dropping side-keywords into the search, like ‘serotonin’ and ‘oxytocin’, thus the names of hormonal neurotransmitters in us, humans, which are reputed to be abundantly entangled with our social life. The keyword ‘Serotonin’ led me to a series of articles on the possibilities of treating and curing neurodevelopmental deficits in adults. Not obviously linked to cities and urban life? Look again, carefully. Cities allow the making of science. Science allows treating neurodevelopmental deficits in adults. Logically, developing the type of social structure called ‘cities’ allows our species to regulate our own neurophysiological development beyond the blueprint of our DNA, and the early engram of infant development (see, for example: Ehninger et al. 2008[4]; Bavelier at al. 2010[5]).

When I searched under ‘oxytocin’, I found a few papers focused on the fascinating subject of epigenetics. This is a novel trend in biology in general, based on the discovery that our DNA has many alternative ways of expressing itself, depending on environmental stimulation. In other words, the same genotype can produce many alternative phenotypes, through different expressions of coding genes, and the phenotype produced depends on environmental factors (see, e.g. Day & Sweatt 2011[6]; Sweatt 2013[7]). It is a fascinating question: to what extent urban environment can trigger a specific phenotypical expression of our human genotype?

A tentative synthesis regarding the social neuroscience of urban life leads me to develop on the following thread: we, humans, have a repertoire of alternative behavioural algorithms pre-programmed in our central nervous system, and, apparently, at some biologically very primal level, a repertoire of different phenotypical expressions to our genotype. Urban environments are likely to trigger some of those alternative patterns. Appetite for risk, combined with quick learning of social competences, in an adolescent-like mode, seems to be one of such orientations, socially reinforced in cities.   

All that neuroscience thing leads me to taking once again a behavioural an angle of approach to my hypothesis on the connection between the development of cities, and technological change, all that dipped in the sauce of ‘What is going to happen due to COVID-19?’. Reminder for those readers, who just start to follow this thread: I hypothesise that, as COVID-19 hits mostly in densely populated urban areas, we will probably change our way of life in cities. I want to understand how exactly it can possibly happen. When the pandemic became sort of official, I had a crazy idea: what if I represented all social change as a case of interacting epidemics? I noticed that SARS-Cov-2 gives a real boost to some technologies and behaviours, whilst others are being pushed aside. Certain types of medical equipment, ethylic alcohol (as disinfectant!), online communication, express delivery services – all that stuff just boomed. There were even local speculative bubbles in the stock market, around the stock of medical companies. In my own investment portfolio, I earnt 190% in two weeks, on the stock of a few Polish biotechs, and it could have been 400%, had I played it better.

Another pattern of collective behaviour that SARS-Cov-2 has clearly developed is acceptance of authoritarian governance. Well, yes, folks. Those special ‘epidemic’ regimes most of us live under, right now, are totalitarian governance by instalments, in the presence of a pathogen, which, statistically, is less dangerous than driving one’s own car. There is quite convincing scientific evidence that prevalence of pathogens makes people much more favourable to authoritarian policies in their governments (see for example: Cashdan & Steele 2013[8]; Murray, Schaller & Suedfeld 2013[9]).    

On the other hand, there are social activities and technologies, which SARS-Cov-2 is adverse to: restaurants, hotels, air travel, everything connected to mass events and live performative arts. The retail industry is largely taken down by this pandemic, too: see the reports by IDC, PwC, and Deloitte. As for behavioural patterns, the adolescent-like pattern of quick social learning with a lot of risk taking, which I described a few paragraphs earlier, is likely to be severely limited in a pandemic-threatened environment.

Anyway, I am taking that crazy intellectual stance where everything that makes our civilisation is the outcome of epidemic spread in technologies and behavioural patterns, which can be disrupted by the epidemic spread of some real s**t, such as a virus. I had a look at what people smarter than me have written on the topic (Méndez, Campos & Horsthemke 2012[10]; Otunuga 2019[11]), and a mathematical model starts emerging.

I define a set SR = {sr1, sr2, …, srm} of ‘m’ social roles, defined as combinations of technologies and behavioural patterns. On the other hand, there is a set of ‘k’ pathogens PT = {pt1, pt2, …, ptk}. Social roles are essentially idiosyncratic and individual, yet they are prone to imperfect imitation from person to person, consistently with what I wrote in ‘City slickers, or the illusion of standardized social roles’. Types of social roles spread epidemically through civilization just as a pathogen would. Now, an important methodological note is due: epidemic spread means diffusion by contact. Anything spreads epidemically when some form of contact from human to human is necessary for that thing to jump. We are talking about a broad spectrum of interactions. We can pass a virus by touching each other or by using the same enclosed space. We can contaminate another person with a social role by hanging out with them or by sharing the same online platform.

Any epidemic spread – would it be a social role sri in the set SR or a pathogen ptj – happens in a population composed of three subsets of individuals: subset I of infected people, the S subset of people susceptible to infection, and subset R of the immune ones. In the initial phase of epidemic spread, at the moment t0, everyone is potentially susceptible to catch whatever there is to catch, i.e. subset S is equal to the overall headcount of population N, whilst I and R are completely or virtually non-existent. I write it mathematically as I(t0) = 0, R(t0) = 0, S(t0) = N(t0).

The processes of infection, recovery, and acquisition of immune resistance are characterized by 5 essential parameters: a) the rate β of transmission from person to person b) the recruitment rate Λ from general population N to the susceptible subset S c) the rate μ of natural death, d) the rate γ of temporary recovery, and e) ψ the rate of manifestation in immune resistance. The rates γ and ψ can be correlated, although they don’t have to. Immune resistance can be the outcome of recovery or can be attributable to exogenous factors.

Over a timeline made of z temporal checkpoints (periods), some people get infected, i.e. they contract the new virus in fashion, or they buy into being an online influencer. This is the flow from S to I. Some people manifest immunity to infection: they pass from S to R. Both immune resistance and infection can have various outcomes. Infected people can heal and develop immunity, they can die, or they can return to being susceptible. Changes in S, I, and R over time – thus, respectively, dS/dt, dI/dt, and dR/dt, can be described with the following equations:  

Equation [I] [Development of susceptibility]dS/dt = Λ – βSI – μS + γI

Equation [II] [Infection]dI/dt = βSI – (μ + γ)I

Equation [III] [Development of immune resistance] dR/dt = ψS(t0) = ψN

We remember that equations [I], [II], and [III] can apply both to pathogens and new social roles. Therefore, we can have a social role sri spreading at dS(sri)/dt, dI(sri)/dt, and dR(sri)/dt, whilst some micro-beast ptj is minding its own business at dS(ptj)/dt, dI(ptj)/dt, and dR(ptj)/dt.

Any given civilization – ours, for example – experiments with the prevalence of different social roles sri in the presence of known pathogens ptj. Experimentation occurs in the form of producing many alternative, local instances of civilization, each based on a general structure. The general structure assumes that a given pace of infection with social roles dI(sri)/dt coexists with a given pace of infection with pathogens dI(ptj)/dt.

I further assume that ε stands for the relative prevalence of anything (i.e. the empirically observed frequency of happening), social role or pathogen. A desired outcome O is being collectively pursued, and e represents the gap between that desired outcome and reality. Our average civilization can be represented as:

Equation [IV] [things that happen]h = {dI(sr1)/dt}* ε(sr1) + {dI(sr2)/dt}* ε(sr2) + … + {dI(srn)/dt}* ε(srn) + {dI(ptj)/dt}* ε(ptj)

Equation [V] [evaluation of the things that happen] e = O – [(e2h – 1)/(e2h + 1)]*{1 – [(e2h – 1)/(e2h + 1)]}2

In equation [V] I used a neural activation function, the hyperbolic tangent, which you can find discussed more in depth, in the context of collective intelligence, in my article on energy efficiency. Essentially, the more social roles are there in the game, in equation [IV], the broader will the amplitude of error in equation [V], when error is produced with hyperbolic tangent. In other words, the more complex is our civilization, the more it can freak out in the presence of a new risk factor, such as a pathogen. It is possible, at least in theory, to reach a level of complexity where the introduction of a new pathogen, such as SARS-Covid-19, makes the error explode into such high a register that social learning either takes a crash trajectory and aims at revolution, or slows down dramatically.

The basic idea of our civilization experimenting with itself is that each actual state of things according to equation [IV] produces some error in equation [V], and we can produce social change by utilizing this error and learning how to minimize it.

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[1] Belin, P., & Grosbras, M. H. (2010). Before speech: cerebral voice processing in infants. Neuron, 65(6), 733-735. https://doi.org/10.1016/j.neuron.2010.03.018

[2] Adolphs, R. (2010). Conceptual challenges and directions for social neuroscience. Neuron, 65(6), 752-767. https://doi.org/10.1016/j.neuron.2010.03.006

[3] Steinberg, L. (2008). A social neuroscience perspective on adolescent risk-taking. Developmental review, 28(1), 78-106. https://dx.doi.org/10.1016%2Fj.dr.2007.08.002

[4] Ehninger, D., Li, W., Fox, K., Stryker, M. P., & Silva, A. J. (2008). Reversing neurodevelopmental disorders in adults. Neuron, 60(6), 950-960. https://doi.org/10.1016/j.neuron.2008.12.007

[5] Bavelier, D., Levi, D. M., Li, R. W., Dan, Y., & Hensch, T. K. (2010). Removing brakes on adult brain plasticity: from molecular to behavioral interventions. Journal of Neuroscience, 30(45), 14964-14971. https://www.jneurosci.org/content/jneuro/30/45/14964.full.pdf

[6] Day, J. J., & Sweatt, J. D. (2011). Epigenetic mechanisms in cognition. Neuron, 70(5), 813-829. https://doi.org/10.1016/j.neuron.2011.05.019

[7] Sweatt, J. D. (2013). The emerging field of neuroepigenetics. Neuron, 80(3), 624-632. https://doi.org/10.1016/j.neuron.2013.10.023

[8] Cashdan, E., & Steele, M. (2013). Pathogen prevalence, group bias, and collectivism in the standard cross-cultural sample. Human Nature, 24(1), 59-75. https://doi.org/10.1007/s12110-012-9159-3

[9] Murray DR, Schaller M, Suedfeld P (2013) Pathogens and Politics: Further Evidence That Parasite Prevalence Predicts Authoritarianism. PLoS ONE 8(5): e62275. https://doi.org/10.1371/journal.pone.0062275

[10] Méndez, V., Campos, D., & Horsthemke, W. (2012). Stochastic fluctuations of the transmission rate in the susceptible-infected-susceptible epidemic model. Physical Review E, 86(1), 011919. http://dx.doi.org/10.1103/PhysRevE.86.011919

[11] Otunuga, O. M. (2019). Closed-form probability distribution of number of infections at a given time in a stochastic SIS epidemic model. Heliyon, 5(9), e02499. https://doi.org/10.1016/j.heliyon.2019.e02499

Demographic anomalies – the puzzle of urban density

MY EDITORIAL ON YOU TUBE

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 (www.stat.gov.pl ), 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, www.stat.gov.pl 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 https://www.ons.gov.uk , 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 https://data.worldbank.org/ , 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: https://www.insee.fr/fr/statistiques/fichier/2571258/imet129-b-chapitre1.pdf . 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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Countries never behave as they should

My editorial

After having started, yesterday, an overview of articles concerning renewable energies (see ‘Deux théories, deux environnements’), I continue on this path and I am reading through a paper by Peter D. Lund, entitled ‘Effects of energy policies on industry expansion in renewable energy’ (Lund 2009[1]). Peter D. Lund comes to the conclusion that policies of pure growth, like pumping money in R&D or favouring the development of exports, bring substantial results regarding the development of renewable energies. Moreover, substantial technological change in industries upstream of renewable energies can have a pushing effect on the latter, and the role of public policies, in this case, is to make or facilitate the connection between them. As for details, Peter D. Lund covers the following cases: Denmark, Germany, Finland, Austria, USA, Brazil, Japan, Estonia, Sweden, China, and Canada. The really strong claim of that article is that the size of exports from a given country, in renewable energy properly spoken or in technologies upstream of energy production, is more important for the development of renewable energies in the given country than its domestic market. In general, the capacity to expand into the global market, either with energy as such or with technologies serving to generate it, seems to be crucial for the transition to green energies inside the country.

As usually, I want to confront the claim with my own empirical data. First of all, I took a handful of countries, and I compared the size of their respective, domestic markets in renewable energy, to the share of renewable energies in their primary output of electricity, in 2014. The percentage of variables in electricity output comes straight from the World Bank (see: https://data.worldbank.org/indicator/EG.ELC.RNEW.ZS ). As for the size of domestic markets in renewable, this is my own calculation, mostly on the grounds of World Bank data. First, I took the indicator of final energy consumption per capita, in kilograms of oil equivalent (https://data.worldbank.org/indicator/EG.USE.PCAP.KG.OE ), and I multiplied it by the population of each country reported. That gave me the total size of domestic markets in energy, which I put against another indicator, namely the percentage of renewables in the final consumption of energy (https://data.worldbank.org/indicator/EG.FEC.RNEW.ZS ). Anyway, you can see the results of that little rummaging in Table 1, below. As I am looking at this form of data, the coin starts dropping: it does not look like a strong correlation between market size in renewables and their share in the output of electricity. I am minting that coin (the one which has just dropped in my mind, I mean) with the royal stamp of Pearson correlation of moments, and it looks respectable: r = -0,075205406. I mean, this is a lousy correlation, it just has the name of correlation, but not the guts it takes to correlate significantly, and still it shows a part of a point: there is no correlation between market size and the share of renewables in the output of electricity. Peter D. Lund, you were at least partly right.

   Table 1

country Renewable electricity output as % of total electricity output, 2014  Renewable energies consumption, in tons of oil equivalent, 2014
Australia 14,9%  12 305 298,40
Austria 81,1%  11 441 257,56
Belgium 17,0%  4 880 723,09
Canada 62,8%  58 225 979,12
Chile 41,2%  10 259 815,33
Czech Republic 10,8%  5 304 306,22
Denmark 55,9%  4 955 203,30
Estonia 11,2%  1 528 618,08
Finland 38,6%  14 145 185,02
France 16,4%  31 607 372,84
Germany 26,1%  40 451 222,42
Greece 24,2%  3 647 766,79
Hungary 10,7%  2 348 769,99
Iceland 100,0%  4 398 469,36
Ireland 24,5%  1 095 777,67
Israel 1,5%  2 113 663,77
Italy 43,4%  24 579 456,45
Japan 14,0%  24 318 733,45
Luxembourg 20,9%  264 125,74
Mexico 17,5%  18 553 983,66
Netherlands 11,3%  4 101 339,30
New Zealand 79,1%  6 181 040,15
Norway 97,7%  17 204 238,06
Poland 12,5%  11 130 427,59
Portugal 60,7%  6 434 268,18
Republic of Korea 1,6%  7 478 135,80
Slovakia 22,9%  1 874 348,18
Slovenia 38,5%  1 533 076,92
Spain 40,1%  19 664 012,75
Sweden 55,8%  23 125 017,52
Switzerland 58,0%  5 921 322,49
Turkey 20,9%  13 827 194,22
United Kingdom 19,4%  12 912 006,53
United States 13,0%  196 963 466,86

Source: World Bank, Penn Tables 9.0

Now, my internal happy bulldog, that cute beast who has just enough brains to rummage in raw empirical data, has gathered momentum. We made a table, so why couldn’t we make an equation? And when we will have made that equation, why not running just some linear regression and test it? Good, let’s waltz. Science can be fun, after all, and so I am unfolding an equation. I take my percentage of renewables in the production of electricity, or ‘%RenEl’, and I put it on the left side of my equation, as explained variable. That gives me ‘ln(%RenEl) = ?’. I follow up with a makeshift right side. There has to be that market size in renewables, which I endow with the symbol ‘RenQ’, and this leads me to saying ‘ln(%RenEl) = a1*ln(RenQ) + ?’. Now, I need something connected to exports. The closest match I can find with the intuitions by Peter G. Lund is the share of exports in the GDP, or ‘X/Q’. Good, so now, I can proudly state that ‘ln(%RenEl) = a1*ln(RenQ) + a2*ln(X/Q) + ?’. Smells interestingly. I drop another size factor, namely population (Pop), into the kettle, and as I keep stirring with my right hand, I use the left one, temporarily left free by having pegged the left side of the equation, to add other logarithm-ized things of life: GDP per capita (Q/Pop), and my dear supply of money as % of GDP (M/Q). The recipe seems to be ready, and it looks like:

ln(%RenEl) = a1*ln(RenQ) + a2*ln(X/Q) + a3*ln(Pop) + a4*ln(Q/Pop) + a5*ln(M/Q) + residual constant

Testing time. I take my database, namely Penn Tables 9.0 (Feenstra et al. 2015[2]), now embroidered with loads of other data from the World Bank, and I am about to test my equation, and this is the moment when my internal curious ape becomes vocal and says: ‘Oooogh’, which means ‘Look, Krzysztof, why not to repeat that trick with density of population as control variable. It worked once, it might work more times, as well. So?’ (meaningful frown). Fine. If could have indulged to the wants of a bulldog, I can cooperate with the ape. Will not kill me, after all. So I slice my database into sextiles of density in population, and I am going to perform, and to delight you, my readers, with the results of seven tests: one general and six specific. I start with the general one: n = 1 913 valid observations yield R2 = 0,427 in terms of explanatory power. The table of coefficients shows an interesting landscape, which, for the moment, contradicts the findings by Peter G. Lund. Everything on the right side of the equation, with the exception of market size in renewable energies, has a negative sign, and the share of exports in GDP does not make exception.

Table 2

variable coefficient std. error t-statistic p-value
ln(Pop) -0,764 0,036 -20,968 0,000
ln(M/Q) -0,251 0,059 -4,286 0,000
ln(Q/Pop) -0,311 0,033 -9,348 0,000
ln(RenQ) 0,756 0,029 25,871 0,000
ln(X/Q) -0,277 0,03 -9,143 0,000
constant -8,316 0,62 -13,41 0,000

Right, now I am ploughing through sextiles (regarding the density of population). First sextile, between 0,632 and 11,713 people per square kilometre: n = 111 observations, coefficient of determination R2 = 0,493. Coefficients in Table 3, below. Small and quite robust, I could say, save for the share of exports in the GDP, which, with a p-value of 0,527 is basically on vacation. Money starts counting, by the way, as I am controlling for that density of population.

Table 3

variable coefficient std. error t-statistic p-value
ln(Pop) -0,332 0,166 -1,998 0,048
ln(M/Q) 1,281 0,491 2,61 0,010
ln(Q/Pop) -1,075 0,238 -4,508 0,000
ln(RenQ) 0,835 0,113 7,416 0,000
ln(X/Q) -0,274 0,431 -0,635 0,527
constant -10,2 3,542 -2,88 0,005

Second sextile, from 11,713 to 29,352 people per square kilometre. It has n = 366 valid observations to present, and they yield quite a crunch into explanatory power, with R2 = 0,720. Table 4, below, shows that all coefficients get back to discipline, in their p-values, and still money becomes negative again. The domestic market size in renewable energies seems rock-solid in this model: it keeps the same sign, same magnitude, and a robust p – value, across all those sampling tricks I have made so far.

 Table 4

variable coefficient std. error t-statistic p-value
ln(Pop) -0,852 0,073 -11,693 0,000
ln(M/Q) -0,102 0,043 -2,39 0,017
ln(Q/Pop) -0,317 0,05 -6,37 0,000
ln(RenQ) 0,895 0,075 11,886 0,000
ln(X/Q) -0,434 0,091 -4,751 0,000
constant -11,513 1,561 -7,376 0,000

Good. Third class of density in population, between 29,352 and 56,922 people per km2. Here, it becomes lax, somehow: n = 362 observations yield just R2 = 0,410 in terms of explanatory power. The coefficients of regression (Table 5) suggest that the story changes as people cluster on that square kilometre. Money is even more deeply negative, and the size of domestic market in renewables becomes negative, as well. I noticed it already with another model, a few updates ago, which I controlled for the density of population. There are some classes of density, which look just like kind of transitory states between more solid equilibriums. That could be the case here.

Table 5

variable coefficient std. error t-statistic p-value
ln(Pop) 0,146 0,092 1,587 0,113
ln(M/Q) -1,36 0,175 -7,784 0,000
ln(Q/Pop) 0,08 0,118 0,68 0,497
ln(RenQ) -0,181 0,09 -2,02 0,044
ln(X/Q) -0,635 0,113 -5,633 0,000
constant 9,478 1,766 5,366 0,000

And so I swing my intellectual weight towards the fourth class of density in population, 56.922 ÷ 97.881 people per square kilometre. I have n = 336 observations here, and they echo to me with a R2 = 0,510 coefficient of determination. It looks like my house when my wife decides to do what she calls ‘put order in all that’. The result is a strange mix of scalpel-sharp order in some places with bloody mess in other places. Here, as you can see in Table 6, this is something akin. The size of domestic market in renewables comes back to the throne, and good for it. Still, the velocity of money goes completely unhinged, with the probability of null hypothesis towering over 90%. Another transitory state? Maybe.Table 6

variable coefficient std. error t-statistic p-value
ln(Pop) -0,487 0,054 -8,956 0,000
ln(M/Q) 0,008 0,066 0,114 0,909
ln(Q/Pop) -0,362 0,047 -7,673 0,000
ln(RenQ) 0,795 0,054 14,834 0,000
ln(X/Q) -0,04 0,045 -0,889 0,375
constant -10,109 1,335 -7,571 0,000

And so I climb the ladder of density, and I come to the fifth sextile, which hosts between 97,881 and 202,36 people on my average square kilometre. I mean, not just mine, yours as well. I have n = 419 observations, and I have a bit of disappointment in my R2, as my R2 makes R2 = 0,342 this time, and I have the coefficients shown in Table 7. Those coefficients look nice, and robust in their p-values, but on the whole, they are not really blockbusters in terms of R2. What do you want, there are those situations in life, when being nice and predictable does not necessarily give you power.

Table 7

variable coefficient std. error t-statistic p-value
ln(Pop) -1,104 0,12 -9,233 0,000
ln(M/Q) 0,502 0,088 5,703 0,000
ln(Q/Pop) -0,39 0,061 -6,443 0,000
ln(RenQ) 0,817 0,111 7,378 0,000
ln(X/Q) -0,628 0,082 -7,65 0,000
constant -11,583 2,39 -4,846 0,000

And so comes the top dog, namely the sixth and highest sextile of density in population: 202,36 ÷ 21 595,35 people per km2. I have n = 299 valid observations in this category, and they allow to determine 56%, or R2 = 0,560, of the overall variance in the percentage of electricity coming from renewable sources. Table 8 gives details regarding the coefficients of my equation. This highest class of population density seems to be the only one that yields a result fully coherent with the findings by Peter G. Lund: both the size of the domestic market in renewable energies, and the share of exports in the GDP have positive signs, respectable magnitudes, and robust correlations. Interestingly, my pampered factor, namely the velocity of money, goes feral again. There must be something about social structures, as measured by the density of their populations, which sometimes just creates an opening for money to play a significant role. Interesting. Worth going deeper. Bulldog! Come over, please. Here, dig.

Table 8

variable coefficient std. error t-statistic p-value
ln(Pop) -0,214 0,186 -1,149 0,251
ln(M/Q) 0,073 0,125 0,584 0,559
ln(Q/Pop) -0,92 0,102 -9,042 0,000
ln(RenQ) 0,784 0,073 10,73 0,000
ln(X/Q) 0,976 0,213 4,571 0,000
constant -5,162 1,871 -2,758 0,006

Now, some general discussion about those results. In general, my research partly contradicted the findings by Peter G. Lund. Cross-sectional analysis (Table 1) shows no correlation between the size of domestic market in renewable energies, and their share in the output of electricity. More elaborate an investigation, with hypotheses-testing in a time-space sample of observations, shows a major role to be played by domestic markets. Still, in the highest class of population density, the pattern found by Peter G. Lund seems to hold. I can categorize the countries studied by Peter G. Lund into those classes of density in population I have defined. It looks like (numbers in brackets are densities of population in 2014):

1st sextile: Canada (3,909 people per km2)

2nd sextile: Brazil (24,656), Finland (17,972), Sweden (23,805),

3rd sextile: USA (34,863), Estonia (31,011),

5th sextile: Austria (103,505), Denmark (133,535), China (145,317),

6th sextile: Germany (232,108), Japan (348,727),

Unfortunately, I cannot really test my equation at the level of countries. When all the variables have been accounted for, I have like 17 – 24 observations per country, which is just not enough for quantitative tests, and the correlations I get are not robust regarding their p – values. I cannot say, thus, if those countries behave as they should, regarding their density of population. But you know what? Countries never behave as they should.

[1] Lund, P.D., 2009, Effects of energy policies on industry expansion in renewable energy, Renewable Energy 34, pp. 53–64

[2] Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), “The Next Generation of the Penn World Table” American Economic Review, 105(10), 3150-3182, available for download at http://www.ggdc.net/pwt

The difference jumps to my eye, but what does it mean?

My editorial

I hope I am on the right track with that idea that the maturing of markets can be represented as incremental change in the density of population. This is what I came up with yesterday, in my research update in French (see ‘Le mûrissement progressif du marché, ça promet’). I am still trying to sort it out, intellectually. This is one of those things, which just seem to work but you don’t exactly know how they do it. I think I need some time and some writing in order to develop a nice, well-rounded, intellectual crystallization of that concept. It all started, I think, as I multiplied tests on different quantitative models to explain incremental changes in the value of those two variables I am currently interested in: the percentage of renewable energy in the primary production of electricity (https://data.worldbank.org/indicator/EG.ELC.RNEW.ZS ), and the percentage of renewables in the final consumption of energy (https://data.worldbank.org/indicator/EG.FEC.RNEW.ZS ).

With the software I have, that Wizard for MacOS – and this is really not heavy artillery as statistical software comes – testing models sums up to quick clicking. Setting up and testing a model – or an equation – with that tool is much faster than my writing about it. This is both the blessing and the curse of modern technology: it does things much faster than we can wrap our mind around things. In order to understand fully this idea that I came up with yesterday, I need to reconstruct, more or less, the train of my clicking. That should help me in reconstructing the train of my thinking. So, yesterday, I was trying to develop, once again, on that idea of the Wasun, or virtual currency connected to the market of renewable energies. I assumed that empirical exploration of the question would consist in taking the same equations I have been serving you on my blog for the last few weeks, and inserting the supply of money as one more explanatory variable on the right side in those equations. It kind of worked, but just kind of: adding the supply of money, as a percentage of the GDP, to a model explaining the percentage of renewables in the final consumption of energy, for instance, added some explanatory power to that model, i.e. it pumped the R2 coefficient of determination up. Still, the correlation attached to the supply of money, in that model, did not seem very robust. With a p-value like 0,3 or 0,4 – depending on the exact version of the equation I was testing – it turned out that I have like 30 or 40% of probability that I can have any percentage of renewable energies with a given velocity of money. That p-value is the probability of the null hypothesis, i.e. of no correlation whatsoever between variables.

Interestingly, I had the same problem with a structural variable I was using as well: the density of population. I routinely use the density of population as a quantitative estimator of difference between social structures. I have that deeply rooted intuition that societies displaying noticeable differences in their densities of population are very different in other respects as well. Being around in a certain number in a given territory, and thus having, on average, a given surface of that territory per person, is, for me, a fundamental trait of any society. Fundamental or not, it behaved in those equations of mine in the same way the supply of money did: it added to the coefficient of determination R2, but it refused to establish robust correlations. Just for you, my readers, to understand the position I was in, as a researcher: imagine that you discover some kind of super cool spice, which can radically improve the taste of a sauce. You know it does, but you have one tiny little problem: you don’t know how much of that spice, exactly, you should add to the sauce, and you know that if you add too much or too little, the sauce will taste much worse. Imagined that? Good. Now, imagine you have two such spices, in the same recipe. Bit of a cooking challenge, isn’t it?

What you can do, and what great cooks allegedly do, is to prepare a few alternative sauces, each with the same recipe, but with a different, and precisely defined amount of the spice under investigation. As you taste each of those alternative sauces, you can discover the right amount of spice to add. If you are really good at it, you can even discover the gradient of taste, i.e. the incremental change in taste that has been brought by a given incremental change in the quantity of one particular ingredient. In quantitative research, we call it ‘control variable’: instead of putting a variable right in the equation, we keep it out, we select different subsets of empirical data, each characterized by a different class of value in this particular variable, and we test the equation, without the variable in question, in those different subsets. The mathematical idea behind this approach is that we never know for sure whether our way of counting and measuring things is accurate and adequate to the changes and differences we can observe in those things. Take distance, for example: sometimes it is better to use kilometres, but sometimes even a centimetre it too much. Sometimes, small incremental changes in a measurable phenomenon induce too much complexity for us to crystallize any intelligible thought about it. In statistics, it manifests as a relatively high p-value, or the probability of the null hypothesis. Taking that complexity out of the equation and simplify it into a few big chunks of reality can help our understanding.

Anyway, I had two spices: the density of population, and the supply of money. I had to take one of them out of the equation and treat as control variable. As I am investigating the role of monetary systems in all that business of renewable energies, it seemed just stupid to take it out of the equation. Mind you: it seemed, which does not mean it was. There is a huge difference between seeming to be stupid and being really stupid. Anyway, I decided to keep the supply of money in, whilst taking the density of population out and just controlling for it, i.e. testing the equation in different classes of said density. For a reason that I ignore, when I ask my statistical software to define classes in a control variable, it makes sextiles (spelled jointly!), i.e. it divides the whole sample into six subsets of roughly the same size, 1577 or 1578 observations each in the case of the actual database I am using in that research. Why six? Dunno… Why not, after all?

So I had those sextiles in the density of population, and I had my equation, regarding the percentage of renewable energies in the final consumption of energy, and I had that velocity of money in it, and I tested inside each sextile. Interesting things happened. In the least dense populations, the equation barely had any explanatory power at all. As my equation was climbing the ladder of density in population, it gained explanatory power as well. Still, there is an interval of density, where that explanatory power fell again, just to soar in the densest populations. Those changes in the coefficient of determination R2 were accompanied by visible changes in the sign and the magnitude of the regression coefficient attached to the velocity of money. The same happened in other explanatory variables as well. My equation, as I was trying to wrap my mind around all that, works differently in different types of populations, regarding their density. It works the most logically, in economic terms, in the densest populations. The percentage of renewable energy in the final basket of consumption depends nicely and positively on the accumulation of production factors and on the supply of money. The more developed the local economic system, the better are the chances of going greener and greener in that energy mix.

In economics, demographic variables tend to be considered as a rich and weird cousin. The cousin is rich, so they cannot be completely ignored, but the cousin is kind of a weirdo as well, not really the kind you would invite risk-free to a wedding, so we don’t really invite them a lot. This nice metaphor sums up to saying that I tried to find a purely economic interpretation for those changes I observed when controlling for the density of population. My roughest guess was that money matters the most when we have really a lot of people around us and a lot of transactions to make (or avoid). With hardly any people around me (around is another simplification here, it can be around via Internet), money tends to have less importance. That’s logical. In other words, the velocity of money depends on the degree of development in the market we consider. The more developed a market is, the more transactions are there to finance, and the more money we need in the system to make that market work. Right, this works for any market, regardless whether we are talking about long-range missiles, refrigerators or spices. Now, how does it matter for this particular market, the market of energy? Please, notice: I used the ‘how?’ question instead of ‘why?’. Final consumption of energy is a lifestyle and a social structure doing its job. If the factors determining the percentage of renewable energies in said final consumption work differently in different classes of density in the population, those classes probably correspond to different lifestyles and different types of local social structures.

I imagined a local community, where people progressively transition towards the idea of renewable energies. In the beginning, there are just a few enthusiasts, who, with time, turn into a few hundred, then a few thousands and so on. From then on, I unhinged my mind a bit. I equalled the local community at the starting point, when nobody gives a s*** about green energy, as a virgin land. As new settlers come, new social relations emerge, and new opportunities to transact and pay turn up. Each person, who starts actively to use renewable energies, is like a pioneering settler coming to that virgin land. The emergence of a new market, like that of renewable energy, in an initially indifferent population, is akin to a growing density in a population of settlers. So, I further speculated, the nascence and development of a new market can be represented as a growing density in the population of customers. I know: at this point, it could be really hard to follow me. I even have trouble following myself. After all, if there are like 150 people per square kilometre in a population, according to my database, there are just them in that square kilometre, and no one else. It is not like they are here, those 150 pioneers, and a few hundred others, who are there, but remain kind of passive. Here, you have an example of the kind of mindfuck a researcher deals all the time. Data exploration is great, but data tends to have sharp edges. There is a difference, regarding the role of money in going green in our energies, between a population of 100 per km2 and a population of 5000 per km2. The difference is there, it jumps to my eye, but what does it mean? How does it work? My general intuition is that the density of population, as control variable, controls for the intensity of social interactions (i.e. interactions per unit of time). The degree of maturity in a market is the closest economic meaning I can associate with that intensity of interactions, but there could be something else.