Cautiously bon-vivant

I keep developing on a few topics in parallel, with a special focus on two of them. Lessons in economics and management which I can derive for my students, out of my personal experience as a small investor in the stock market, for one, and a broader, scientific work on the civilizational role of cities and our human collective intelligence, for two.

I like starting with the observation of real life, and I like ending with it as well. What I see around gives me the initial incentive to do research and makes the last pitch for testing my findings and intuitions. In my personal experience as investor, I have simply confirmed an initial intuition that giving a written, consistent and public account thereof helps me nailing down efficient strategies as an investor. As regards cities and collective intelligence, the first part of that topic comes from observing changes in urban life since COVID-19 broke out, and the second part is just a generalized, though mild an intellectual obsession, which I started developing once I observed the way artificial neural networks work.

In this update, I want to develop on two specific points, connected to those two paths of research and writing. As far as my investment is concerned, I am seriously entertaining the idea of broadening my investment portfolio in the sector of renewable energies, more specifically in the photovoltaic. I can notice a rush on the solar business in the U.S. I am thinking about investing in some of those shares. I already have, and have made a nice profit on the stock of First Solar ( ) as well as on that of SMA Solar ( ). Currently, I am observing three other companies: Vivint Solar ( ),  Canadian Solar ( ), and SolarEdge Technologies ( ). Below, I am placing the graphs of stock price over the last year, as regards those solar businesses. There is something like a common trend in those stock prices. March and April 2020 were a moment of brief jump upwards, which subsequently turned into a shy lie-down, and since the beginning of August 2020 another journey into the realm of investors’ keen interest seems to be on the way.

Before you have a look at the graphs, here is a summary table with selected financials, approached as relative gradients of change, or d(x).

 Change from 01/01/2020 to 31/08/2020
Companyd(market cap)d(assets)d(operational cash-flow)
First Solar+23,9%-6%Deeper negative: – $80 million
SMA Solar+27,5%-10%Deeper negative: -€40 million
Vivint Solar+362%+11%Deeper negative: – $9 million
SolarEdge+98%0+ $50 million
Canadian Solar+41%+4%+ $90 million

There are two fundamental traits of business models which I am having a close look at. Firstly, it is the correlation between changes in market capitalization, and changes in assets. I am checking if the solar businesses I want to invest in have their capital base functionally connected to the financial market. Looks a bit wobbly, as for now. Secondly, I look at current operational efficiency, measured with operational cash flow. Here, I can see there is still a lot to do. Here is the link to You Tube video with all that topic developed: Business models in renewable energies #3 Solar business and investment opportunities [Renew BM 3 2020-09-06 09-20-30 ; ].

Those business models seem to be in a phase of slow stabilization. The industry as a whole seems to be slowly figuring out the right way of running that PV show, however the truly efficient scheme is still to be nailed down. Investment in those companies is based on reasonable trust in the growth of their market, and in the positive impact of technological innovation. Question: is it a good move to invest now? Answer: it is risky, but acceptably rational; once those business models become really efficient, the industry will be in or close to the phase of maturity, which, in turn, does not really allow expecting abnormally high return on investment.  

This is a very ‘financial’, hands-off approach to business models. In this case, business models of those photovoltaic businesses matter to me just to the extent of being fundamentally predictable. I don’t want to run a solar business, I just want to have elementary understanding of what’s going on, business-wise, to make my investment better grounded. Looking from inside a business, such an approach is informative about the way that a business model should ‘speak’ to investors.

At the end of the day, I think I am most likely to invest in SolarEdge. It seems to have all the LEGO blocks in place for a good opening. Good cash flow, although a bit sluggish when it comes to real investment.

As regards COVID-19 and cities, I am formulating the following hypothesis: COVID-19 has awakened some deeply rooted cultural patterns, which date back to the times of high epidemic risk, long before vaccines, sanitation and widespread basic healthcare. Those patterns involve less spatial mobility in the population, and social interactions within relatively steady social circles of knowingly healthy people. As a result, the overall frequency of social interactions in cities is likely to decrease, and, as a contingent result, the formation of new social roles is likely to slow down. Then, either digital technologies take over the function of direct social interactions and new social roles will be shaping themselves via your average smartphone, with all the apps it is blessed (haunted?) with, or the formation of new social roles will slow down in general. In that last case, we could have hard times with keeping up our pace of technological change. Here is the link to You Tube video which summarizes what is written below: Urban Economics and City Management #4 COVID and social mobility in cities [ Cities 4 2020-09-06 09-43-06 ;  ].

I want to gain some insight into the epidemiological angle of that claim, and I am passing in review some recent literature. I start with: Gatto, M., Bertuzzo, E., Mari, L., Miccoli, S., Carraro, L., Casagrandi, R., & Rinaldo, A. (2020). Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures. Proceedings of the National Academy of Sciences, 117(19), 10484-10491 ( ). As it is usually the case, my internal curious ape starts paying attention to details which could come as secondary for other people, and my internal happy bulldog follows along and bites deep into those details. The little detail in this specific paper is a parameter: the number of people quarantined as a percentage of those positively diagnosed with Sars-Cov-2. In the model developed by Gatto et al., that parameter is kept constant at 40%, which is, apparently, the average level empirically observed in Italy during the Spring 2020 outbreak. Quarantine is strict isolation between carriers and (supposedly) non-carriers of the virus. Quarantine can be placed on the same scale as basic social distancing. It is just stricter, and, in quantitative terms, it drives much lower the likelihood of infectious social interaction. Gatto el al. insist that testing effort and quarantining are essential components of collective defence against the epidemic. I generalize: testing and quarantine are patterns of collective behaviour. I check whether people around me are carriers or not, and then I split them into two categories: those whom I strongly suspect to host and transmit Sars-Cov-2, and all the rest. I define two patterns of social interaction with those two groups: very restrictive with the former, and cautiously bon vivant with the others (still, no hugging). As the technologies of testing will be inevitably diffusing across the social landscape, that structured pattern is likely to spread as well.    

Now, I pay a short intellectual visit to Jiang, P., Fu, X., Van Fan, Y., Klemeš, J. J., Chen, P., Ma, S., & Zhang, W. (2020). Spatial-temporal potential exposure risk analytics and urban sustainability impacts related to COVID-19 mitigation: A perspective from car mobility behaviour. Journal of Cleaner Production, 123673 . Their methodology is based on correlating spatial mobility of cars in residential areas of Singapore with the risk of infection with COVID-19. A 44,3% ÷ 55,4% decrease in the spatial mobility of cars is correlated with a 72% decrease in the risk of social transmission of the virus. I intuitively translate it into geometrical patterns. Lower mobility in cars means a shorter average radius of travel by the means of available urban transportation. In the presence of epidemic risk, people move across a smaller average territory.

In another paper (or rather in a commented dataset), namely in Pepe, E., Bajardi, P., Gauvin, L., Privitera, F., Lake, B., Cattuto, C., & Tizzoni, M. (2020). COVID-19 outbreak response, a dataset to assess mobility changes in Italy following national lockdown. Scientific data, 7(1), 1-7. , I find an enlarged catalogue of metrics pertinent to spatial mobility. That paper, in turn, lead me to the functionality run by Google: . I went through all of it a bit cursorily, and I noticed two things. First of all, countries are strongly idiosyncratic in their social response to the pandemic. Still, and second of all, there are common denominators across idiosyncrasies and the most visible one is cyclicality. Each society seems to have been experimenting with the spatial mobility they can afford and sustain in the presence of epidemic risk. There is a cycle experimentation, around 3 – 4 weeks. Experimentation means learning and learning usually leads to durable behavioural change. In other words, we (I mean, homo sapiens) are currently learning, with the pandemic, new ways of being together, and those ways are likely to incrust themselves into our social structures.    

The article by Kraemer, M. U., Yang, C. H., Gutierrez, B., Wu, C. H., Klein, B., Pigott, D. M., … & Brownstein, J. S. (2020). The effect of human mobility and control measures on the COVID-19 epidemic in China. Science, 368(6490), 493-497 ( ) shows that without any restrictions in place, the spatial distribution of COVID-19 cases is strongly correlated with spatial mobility of people. With restrictions in place, that correlation can be curbed, however it is impossible to drive down to zero. In plain human, it means that even as stringent lockdowns as we could see in China cannot reduce spatial mobility to a level which would completely prevent the spread of the virus. 

By the way, in Gao, S., Rao, J., Kang, Y., Liang, Y., & Kruse, J. (2020). Mapping county-level mobility pattern changes in the United States in response to COVID-19. SIGSPATIAL Special, 12(1), 16-26 ( ), I read that the whole idea of tracking spatial mobility with people’s personal smartphones largely backfired because the GDS transponders, installed in the average phone, have around 20 metres of horizontal error, on average, and are easily blurred when people gather in one place. Still, whilst the idea went down the drain as regards individual tracking of mobility, smartphone data seems to provide reliable data for observing entire clusters of people, and the way those clusters flow across space. You can consult Jia, J. S., Lu, X., Yuan, Y., Xu, G., Jia, J., & Christakis, N. A. (2020). Population flow drives spatio-temporal distribution of COVID-19 in China. Nature, 1-5.  ( .

Bonaccorsi, G., Pierri, F., Cinelli, M., Flori, A., Galeazzi, A., Porcelli, F., … & Pammolli, F. (2020). Economic and social consequences of human mobility restrictions under COVID-19. Proceedings of the National Academy of Sciences, 117(27), 15530-15535 ( ) show an interesting economic aspect of the pandemic. Restrictions in mobility give the strongest economic blow to the poorest people and to local communities marked by relatively the greatest economic inequalities. Restrictions imposed by governments are one thing, and self-imposed limitations in spatial mobility are another. If my intuition is correct, namely that we will be spontaneously modifying and generally limiting our social interactions, in order to protect ourselves from COVID-19, those changes are likely to be the fastest and the deepest in high-income, low-inequality communities. As income decreases and inequality rises, those adaptive behavioural modifications are likely to weaken.

As I am drawing a provisional bottom line under that handful of scientific papers, my initial hypothesis seems to hold. We do modify, as a species, our social patterns, towards more encapsulated social circles. There is a process of learning taking place, and there is no mistake about it. That process of learning involves a downwards recalibration in the average territory of activity, and smart selection of people whom we hang out with, based on what we know about the epidemic risk they convey. This is a process of learning by trial and error, and it is locally idiosyncratic. Idiosyncrasies seem to be somehow correlated with differences in wealth. Income and accumulated capital visibly give local communities an additional edge in the adaptive learning. On the long run, economic resilience seems to be a key factor in successful adaptation to epidemic risk.

Just to end up with, here you have an educational piece as regards Business models in the Media Industry #4 The gaming business[ Media BM 4 2020-09-02 10-42-44;]. I study the case of CD Projekt ( ), a Polish gaming company, known mostly for ‘The Witcher’ game and currently working on the next one, Cyberpunk, with Keanu Reeves giving his face to the hero. I discover a strange business model, which obviously has hard times to connect with the creative process at the operational level. As strange as it might seem, the main investment activity, for the moment, consists in terminating and initiating cash bank deposits (!), and one of the most important operational activities is to push further in time the moment of officially charging customers with some economically due receivables. On the top of all that, those revenues deferred into the future are officially written in the balance sheet as short-term liabilities, which CD Projekt owes to…whom exactly?   

Cruel and fatalistic? Weelll, not necessarily.


I am developing on one particular thread in my research, somehow congruent with the research on the role of cities, namely the phenomenon of collective intelligence and the prospects for using artificial intelligence to study human social structures. I am going both for good teaching material and for valuable scientific insight.

In social sciences, we face sort of an embarrassing question, which nevertheless is a fundamental one, namely how should we interpret quantitative data about societies. Simple but puzzling: are those numbers a meaningful representation of collectively pursued desired outcomes, or should we view them as largely random, temporary a representation of something going on at a deeper, essentially unobserved level?

I guess I can use artificial neural networks to try and solve that puzzle, at least to some extent. like starting with empirics, or, in plain human, with facts which I have observed so far. My most general observation, pertinent to every single instance of me meddling with artificial neural networks is that they are intelligent structures. I ground this general claim in two specific observations. Firstly, a neural network can experiment with itself, and come up with meaningful outcomes of experimentation, whilst keeping structural stability. In other words, an artificial neural network can change a part of itself whilst staying the same in its logical frame. Secondly, when I make an artificial neural network observe its own internal coherence, that observation changes the behaviour of the network. For me, that capacity to do meaningful and functional introspection is an important sign of intelligence.

This intellectual standpoint, where artificial neural networks are assumed to be intelligent structures, I pass to the question what kind of intelligence those networks can possibly represent. At this point I assume that human social structures are intelligent, too, as they can experiment with themselves (to some extent) whilst keeping structural stability, and they can functionally observe their own internal coherence and learn therefrom. Those two intelligent properties of human social structures are what we commonly call culture.

As I put those two intelligences – that of artificial neural networks and that of human social structures – back to back, I arrive at a new definition of culture. Instead of defining culture as a structured collection of symbolic representations, I define it as collective intelligence of human societies, which, depending on its exact local characteristics, endows those societies with a given flexibility and capacity to change, through a given capacity for collective experimentation.      

Once again, these are my empirical observations, the most general ones regarding the topic at hand. Empirically, I can observe that both artificial neural networks and human social structures can experiment with themselves in the view of optimizing something, whilst maintaining structural stability, and yet that capacity to experiment with itself has limits. Both a neural network and a human society can either stop experimenting or go haywire when experimentation leads to excessively low internal coherence of the system. Thence the idea of using artificial neural networks to represent the way that human social structures experiment with themselves, i.e. the way we are collectively intelligent. When we think about our civilisation, we intuitively ask what’s the endgame, seen from the present moment. Where are we going? That’s a delicate question, and, according to historians such as Arnold Toynbee, this is essentially a pointless one. Civilisations develop and degenerate, and supplant each other, in multi-secular cycles of apparently some 2500 – 3500 years each. If I ask the question ‘How can our civilisation survive, e.g. how can we survive climate change?’, the most rationally grounded answer is ‘Our civilisation will almost certainly fade away and die out, and then a new civilisation will emerge, and climate change could be as good an excuse as anything else to do that transition’. Cruel and fatalistic? Weelll, not necessarily. Think and ask yourself: would you like to stay the same forever? Probably not. The only way to change is to get out of our comfort zone, and the same is true for civilisations. The death of civilisations is different from extinction: when a civilisation dies, its culture transforms radically, i.e. its intelligent structure changes, yet the human population essentially survives.        

Social sciences are sciences because they focus on the ‘how?’ more than on the ‘why?’. The ‘why?’ implies there is a reason for everything, thus some kind of ultimate goal. The ‘how?’ dispenses with those considerations. The personal future of each individual human is almost entirely connected to the ‘how?’ of civilizational change and virtually completely disconnected from the ‘why?’. Civilisations change at the pace of centuries, and this is a slow pace. Even a person who lives for 100 years can see only a glimpse of human history. Yes, our individual existences are incredibly rich in personal experience, and we can use that existential wealth to make our own lives better, and to give a touch of betterment to the lives of incoming humans (i.e. our kids), and yet our personal change is very different from civilizational change. I will even go as far as claiming that individual human existence, with all its twists and turns, usually takes place inside one single cultural pattern, therefore inside a given civilisation. There are just a few human generations in the history of mankind, whose individual existences happened at the overlapping between a receding civilization and an emerging one.

On the night of July 6th, 2020, I had that strange dream, which I believe could be important in the teaching of social sciences. I dreamt of being pursued by some not quite descript ‘them’, in a slightly gangster fashion. I knew they had guns. I procured a gun for myself by breaking its previous owner neck by surprise. Yes, it is shocking, but it was just the beginning. I was running away from those people who wanted to get me. I was running through something like an urban neighbourhood, slightly like Venice, Italy, with a lot of canals all over the place. As I was running, I was pushing people into those canals, just to have freeway and keep running. I shot a few people dead, when they tried to get hold of me. All the time, I was experiencing intense, nagging fear. I woke up from that dream, shortly after midnight, and that intense fear was still resonating in me. After a few minutes of being awake, and whilst still being awake, I experienced another intense frame of mind, like a realization: me in that dream, doing horrible things when running away from people about whom I think they could try to hurt me, it was a metaphor of quite a long window in my so-far existence. Many a time I would just rush forward and do things I am still ashamed of today, and, when I meditate about it, I was doing it out of that irrational fear that other people could do me harm when they sort of catch on. When this realization popped in my mind, I immediately calmed down, and it was deep serenity, as if a lot of my deeply hidden fears had suddenly evaporated.

Fear is a learnt response to environmental factors. Recently, I have been discovering, and I keep discovering something new about fear: its fundamentally irrational nature. All of my early life, I have been taught that when I am afraid of something, I probably have good reasons to. Still, over the last 3 years, I have been practicing intermittent fasting (combined with a largely paleo-like diet), just to get out of a pre-diabetic state. Month after month, I was extending that window of fasting, and now I am at around 17 – 18 hours out of 24. A little bit more than one month ago, I decided to jump over another hurdle, i.e. that of fasted training. I started doing my strength training when fasting, early in the morning. The first few times, my body was literally shaking with fear. My muscles were screaming: ‘Noo! We don’t want effort without food!’. Still, I gently pushed myself, taking good care of staying in my zone of proximal development, and already after a few days, all changed. My body started craving for those fasted workouts, as if I was experiencing some strange energy inside of me. Something that initially had looked like a deeply organic and hence 100% justified a fear, turned out to be another piece of deeply ingrained bullshit, which I removed safely and fruitfully.

My generalisation on that personal experience is a broad question: how much of that deeply ingrained bullshit, i.e. completely irrational and yet very strong beliefs do we carry inside our body, like literally inside our body? How much memories, good and bad, do we have stored in our muscles, in our sub-cortical neural circuitry, in our guts and endocrine glands? It is fascinating to discover what we can change in our existence when we remove those useless protocols.

So far, I have used artificial neural networks in two meaningful ways, i.e. meaningful from the point of view of what I know about social sciences. It is generally useful to discover what we, humans, are after. I can use a dataset of common socio-economic stats, and test each of them as the desired outcome of an artificial neural network. Those stats have a strange property: some of them come as much more likely desired outcomes than others. A neural network oriented on optimizing those ‘special’ ones is much more similar to the original data than networks pegged on other variables. It is also useful to predict human behaviour. I figured out a trick to make such predictions: I define patterns of behaviour (social roles or parts thereof), and I make a neural network which simulates the probability that each of those patterns happens.

One avenue consists in discovering a hierarchy of importance in a set of socio-economic variables, i.e. in common stats available from external sources. In this specific approach, I treat empirical datasets of those stats as manifestation of the corresponding state spaces. I assume that the empirical dataset at hand describes one possible state among many. Let me illustrate it with an example: I take a big dataset such as Penn Tables. I assume that the set of observations yielded by the 160ish countries in the database, observed since 1964, is like a complex scenario. It is one scenario among many possible. This specific scenario has played out the way it has due to a complex occurrence of events. Yet, other scenarios are possible.      

To put it simply, datasets made of those typical stats have a strange property, possible to demonstrate by using a neural network: some variables seem to reflect social outcomes of particular interest for the society observed. A neural network pegged on those specific variables as output ones produces very little residual error, and, consequently, stays very similar to the original dataset, as compared to networks pegged on other variables therein.

Under this angle of approach, I ascribe an ontological interpretation to the stats I work with: I assume that each distinct socio-economic variable informs about a distinct phenomenon. Mind you, it is just one possible interpretation. Another one, almost the opposite, claims that all the socio-economic stats we commonly use are essentially facets (or dimensions) of the same, big, compound phenomenon called social existence of humans. Long story short, when I ascribe ontological autonomy to different socio-economic stats, I can use a neural network to establish two hierarchies among these variables: one hierarchy is that of value in desired social outcomes, and another one of epistatic role played by individual variables in the process of achieving those outcomes. In other words, I can assess what the given society is after, and what are the key leverages being moved so as to achieve the outcome pursued.

Another promising avenue of research, which I started exploring quite recently, is that of using an artificial neural network as a complex set of probabilities. Those among you, my readers, who are at least mildly familiar with the mechanics of artificial neural networks, know that a neural network needs empirical data to be transformed in a specific way, called standardization. The most common way of standardizing consists in translating whatever numbers I have at the start into a scale of relative size between 0 and 1, where 1 corresponds to the local maximum. I thought that such a strict decimal fraction comprised between 0 and 1 can spell ‘probability’, i.e. the probability of something happening. This line of logic applies to just some among the indefinitely many datasets we can make. If I have a dataset made of variables such as, for example, GDP per capita, healthcare expenditures per capita, and the average age which a person ends their formal education at, it cannot be really considered in terms of probability. If there is any healthcare system in place, there are always some healthcare expenditures per capita, and their standardized value cannot be really interpreted as the probability of healthcare spending taking place. Still, I can approach the same under a different angle. The average healthcare spending per capita can be decomposed into a finite number of distinct social entities, e.g. individuals, local communities etc., and each of those social entities can be associated with a probability of using any healthcare at all during a given period of time.

That other approach to using neural networks, i.e. as sets of probabilities, has some special edge to it. I can simulate things happening or not, and I can introduce a disturbing factor, which kicks certain pre-defined events into existence or out of it. I have observed that once a phenomenon becomes probable, it is not really possible to kick it out of the system, yet it can yield to newly emerging phenomena. In other words, my empirical observation is that once a given structure of reality is in place, with distinct phenomena happening in it, that structure remains essentially there, and it doesn’t fade even if probabilities attached to those phenomena are random. On the other hand, when I allow a new structure, i.e. another set of distinct phenomena, to come into existence with random probabilities, that new structure will slowly take over a part of the space previously occupied just by the initially incumbent, ‘old’ set of phenomena. All in all, when I treat standardized numerical values – which an artificial neural network normally feeds on – as probabilities of happening rather than magnitudes of something existing anyway, I can simulate the unfolding of entire new structures. This is a structure generating other structures.

I am trying to reverse engineer that phenomenon. Why do I use at all numerical values standardized between 0 and 1, in my neural network? Because this is the interval (type) of values that the function of neural activation needs. I mean there are some functions, such as the hyperbolic tangent, which can work with input variables standardized between – 1 and 1, yet if I want my data to be fully digest for any neural activation function, I’d better standardize it between 0 and 1. Logically, I infer that mathematical functions useful for simulating neural activation are mathematically adapted to deal with sets of probabilities (range between 0 and 1) rather than sets of local magnitudes.    

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What can be wanted only at the collective level


I am recapitulating on my research regarding cities and their role in our civilization. In the same time, I start preparing educational material for the next semester of teaching, at the university. I am testing somehow new a format, where I precisely try to put science and teaching content literally side by side. The video editorial on You Tube plays an important part here, and I sincerely invite all my readers to watch it.  

I am telling the story of cities once again, from the beginning. Beginning of March 2020. In Poland, we are going into the COVID-19 lockdown. I am cycling through the virtually empty streets of Krakow, my hometown. I slowly digest the deep feeling of weirdness: the last time I saw the city that inanimate, it was during some particularly tense moments in the times of communism, decades ago. A strange question keeps floating on the surface of my consciousness: ‘How many human footsteps per day does this place need to be truly alive?’.

Cities are demographic anomalies. This is particularly visible from space, when satellite imagery serves to distinguish urban areas from rural ones. Cities are abnormally dense agglomerations of man-made architectural structures, paired with just abnormally dense clusters of night-time lights. We, humans, we agglomerate in cities. We purposefully reduce the average social distance, and just as purposefully increase the intensity of our social interactions. Why and how do we do that? The ‘why?’ is an abyssal question. If I attempt to answer it with all the intellectual rigor possible, it is almost impossible to answer. Still, there is hope. I have that little theory of mine – well, not just mine, it is called ‘contextual ethics’ – namely that we truly value the real outcomes we get. In other words, we really want the things which we actually get at the end of the day. This could be a slippery slope. Did Londoners want to have the epidemic of plague, in 1664? I can cautiously say it wasn’t on the top list of their wildest dreams. Yet, acquiring herd immunity and figuring out ways of containing an epidemic outbreak: well, that could be a valuable outcome in the long perspective. That outcome has a peculiar trait: it sort of can be wanted only at the collective level, since it is a collective outcome par excellence. If we pursue an outcome like this one, we are being collectively intelligent. It would be somehow adventurous to try and acquire herd immunity singlehandedly. 

Cities manifest one of the ways we are collectively intelligent. In cities, we get individual outcomes, and collective ones, sort of in layers. Let’s take a simple pattern of behaviour: imitation and personal style. We tend to imitate each other, and frequently, as we are doing so, we love pretending we are reaching the peak or originality. Both imitation and pretention to originality make any sense only when there are other people around, and the more people are there around, the more meaningful it is. Imagine you have a ranch in Texas, like 200 hectares, and in order to imitate anyone, or to pretend being original, you need to drive for 2 hours one way, and then 2 hours back, and, at the end of the day, you have interacted with maybe 20 people.

Our human social structures are machines which make other social structures, and not only sustain the current humans inside. A lot of behavioural patterns make any sense at all when the density of population reaches a reasonably required minimum. Social interactions produce and convey information which our brains use to form new patterns. As I think about it, my take on collective intelligence opens up onto the following claim: we have cities in order to make some social order for the future, and order made of social roles and group identities. We have a given sharpness of social distinction between cities and the countryside, e.g. in terms of density in population, in order to create some social roles and group identities for the future.

We, humans, had discovered – although we might not be aware of what we discovered – that certain types of social interactions (not all of them) can be made into recurrent patterns, and those patterns have the capacity to make new patterns. As long as I just date someone, it is temporary interaction. When I propose, it takes some colours: engagement can turn into marriage (well, it should, technically), thus one pattern of interaction can produce another pattern. When I marry a woman, it opens up a whole plethora of new interactions: parenthood, agreement as for financials (prenuptial contracts or the absence thereof), in-law family relations (parents-in-law, siblings-in-law). Have you noticed that some of the greatest financial fortunes, over centuries, had been accumulated inside family lineages? See? We hit the right pattern of social interactions, and from there we can derive either new copies of the same structure or altogether new structures.

Blast! I have just realized I finally nailed down something which I have been turning around in my mind for months: the logical link between human social structures and artificial neural networks. I use artificial neural networks to simulate collective intelligence in human societies, and I have found one theoretical assumption which I need to put in such a model, namely that consecutive states of society must form a Markov chain, i.e. each individual state must be possible to derive entirely from the preceding state, without any exogenous corrective influence.

Still, I felt I was missing something and now: boom! I figured it out. Once again: among different social interactions there are some which have the property to turn into durable and generative patterns, i.e. they reproduce their general structure in many local instances, each a bit idiosyncratic, yet all based on the same structure. In other words, some among our social interactions have the capacity to be intelligent structures, which experiment with themselves by producing many variations of themselves. This is exactly what artificial neural networks are: they are intelligent structures able to experiment with themselves by generating many local, idiosyncratic variations and thereby nailing down the variation which minimizes error in achieving a desired outcome.

When I use an artificial neural network to simulate social change, I implicitly assume that the social change in question is a Markov chain of states, and that the society under simulation has some structural properties which remain consistent over all the Markov chain of states. Now, I need to list the structural properties of artificial neural networks I use in my research, and to study the conditions of their stability. An artificial neural network is a sequence of equations being run in a loop. Structure of the network is given by each equation separately, and by their sequential order. I am going to break down that logical structure once again and pass its components in review. Just a general, introductory remark: I use really simple neural networks, which fall under the general category of multi-layer perceptron. This is probably the simplest that can be in terms of AI, and this is the logic which I connect to collective intelligence in human societies.

The most fundamental structure of an artificial neural network is given by the definition of input variables – the neural stimuli – and their connection to the output variable(s). I used that optional plural, i.e. the ‘(s)’ suffix, because the basic logic of an artificial neural network assumes defining just one output variable, whilst it is possible to construe that output as the coefficient of a vector. In other words, any desired outcome given by one number can be seen as being derived from a collection of numbers. I hope you remember from your math classes in high school that the Pythagorean theorem, I mean the a2 + b2 = c2 one, has a more general meaning, beyond the simple geometry of a right-angled triangle. Any positive number we observe – our height in centimetres (or in feet and inches), the right amount of salt to season shrimps etc. – any of those amounts can be interpreted as the square root of the sum of squares of two other numbers. I mean, any x > 0 is x = (y2 + x2)0,5. Logically, those shady y and z can be seen, in turn, as derived, Pythagorean way, from even shadier and more mysterious entities. In other words, it is plausible to assume that x = (y2 + x2)0,5 = {[(a2 + b2)0,5]2 + [(c2 + d2)0,5]2}0,5 etc.

As a matter of fact, establishing an informed distinction between input variables on the one hand, and the output variable on the other hand is the core and the purpose of my method. I take a handful of variables, informative about a society or a market, and I make as many alternative neural networks as there are variables. Each alternative network has the same logical structure, i.e. the same equations in the same sequence, but is pegged on a different variable as its output. At some point, I have the real human society, i.e. the original, empirical dataset, and as many alternative versions thereof as there are variables in the dataset. In other words, I have a structure and a finite number of experiments with that structure. This is the methodology I used, for example, in my paper on energy efficiency.

There are human social structures which can make other social structures, by narrowing down, progressively, the residual error generated when trying to nail down a desired outcome and experimenting with small variations of the structure in question. Those structures need abundant social interactions in order to work. An artificial neural network which has the capacity to stay structurally stable, i.e. which has the capacity to keep the Euclidean distance between variables inside a predictable interval, can be representative for such a structure. That predictable interval of Euclidean distance corresponds to predictable behavioural coupling, the so-called correlated coupling: social entity A reacts to what social entity B is doing, and this reaction is like music, i.e. it involves moving along a scale of response in a predictable pattern.

I see cities as factories of social roles. The intensity of social interactions in cities works like a social engine. New businesses emerge, new jobs form in the labour market. All these require new skillsets and yet those skillsets are expected to stop being entirely new and to become somehow predictable and reliable, whence the need for correspondingly new social roles in training and education for those new skills. As people endowed with those new skills progressively take over business and jobs, even more novel skillsets emerge and so the wheel of social change spins. The peculiar thing about social interactions in cities are those between young people, i.e. teenagers and young adults up to the age of 25. Those interactions have a special trait, just as do the people involved: their decision-making processes are marked by significantly greater an appetite for risk and immediate gratification, as opposed to more conservative and more perseverant behavioural patterns in older adults.

Cities allow agglomeration of people very similar as regards the phase of their personal lifecycle, and, in the same time, very different in their cultural background. People mix a lot inside generations. Cities produce a lot of social roles marked with a big red label ‘Only for humans below 30!’, and, in the same time, lots of social roles marked ‘Below 40, don’t even think about it!’. Please, note that I define a generation in sociological terms, i.e. as a cycle of about 20 ÷ 25 years, roughly corresponding to the average age of reproduction (I know, first parenthood sounds kind’a more civilized). According to this logic, I am one generation older than my son.

That pattern of interactions is almost the exact opposite of rural villages and small towns, where people interact much more between generations and less inside generations. Social roles form as ‘Whatever age you are between 20 and 80, you do this’. As we compare those two mechanisms of role-formation, in turns out that cities are inherently prone to creating completely new sets of social roles for each new generation of people coming with the demographic tide. Cities facilitate innovation at the behavioural level. By innovation, I mean the invention of something new combined with a mechanism of diffusing that novelty across the social system.

These are some of my thoughts about cities. How can I play them out into my teaching? I start with a staple course of mine: microeconomics. Microeconomics sort of nicely fit with the topic of cities, and I don’t even have to prove it, ‘cause Adam Smith did. In his ‘Inquiry Into The Nature And Causes of The Wealth of Nations’, Book I, Chapter III, entitled ‘That The Division Of Labour Is Limited By The Extent Of The Market’, he goes: ‘[…] There are some sorts of industry, even of the lowest kind, which can be carried on nowhere but in a great town. A porter, for example, can find employment and subsistence in no other place. A village is by much too narrow a sphere for him; even an ordinary market-town is scarce large enough to afford him constant occupation. In the lone houses and very small villages which are scattered about in so desert a country as the highlands of Scotland, every farmer must be butcher, baker, and brewer, for his own family. In such situations we can scarce expect to find even a smith, a carpenter, or a mason, within less than twenty miles of another of the same trade. The scattered families that live at eight or ten miles distance from the nearest of them, must learn to perform them- selves a great number of little pieces of work, for which, in more populous countries, they would call in the assistance of those workmen. Country workmen are almost everywhere obliged to apply themselves to all the different branches of industry that have so much affinity to one another as to be employed about the same sort of materials. A country carpenter deals in every sort of work that is made of wood; a country smith in every sort of work that is made of iron. The former is not only a carpenter, but a joiner, a cabinet-maker, and even a carver in wood, as well as a wheel-wright, a plough-wright, a cart and waggon-maker. The employments of the latter are still more various. It is impossible there should be such a trade as even that of a nailer in the remote and inland parts of the highlands of Scotland. Such a workman at the rate of a thousand nails a-day, and three hundred working days in the year, will make three hundred thousand nails in the year. But in such a situation it would be impossible to dispose of one thousand, that is, of one day’s work in the year […]’.     

Microeconomics can be seen as a science of how some specific social structures, strongly pegged in the social distinction between cities and the countryside, reproduce themselves in time, as well as produce other social structures. I know, this definition does not really seem to fall close to the classical, Marshallian graph of two curves, i.e. supply and demand, crossing nicely in the point of equilibrium. ‘Does not seem to…’ is distinct from ‘does not’. Let’s think a moment. The local {Supply <> Demand} equilibrium is a state of deals being closed at recurrent, predictable a price. One of the ways to grasp the equilibrium price consists in treating it as the price which clears all the surplus stock of goods in the market. It is the price which people agree upon, at the end of the day. Logically, there is an underlying social structure which allows such a recurrent, equilibrium-making bargaining process. This structure reproduces itself in n copies, over and over again, and each such copy is balanced on different a coupling between equilibrium price and equilibrium product.

Here comes something I frequently remind to those of my students who have enough grit to read any textbook in economics: those nice curves in the Marshallian graph, namely demand and supply, don’t really exist. They represent theoretical states at best, and usually these are more in the purely hypothetical department. We just guess that social reality is being sort bent along them. The thing that really exists, here and now, is the equilibrium price that we strike our deals at, and the corresponding volumes of business we do at this price. What really exists in slightly longer a perspective is the social structure able to produce local equilibriums between supply and demand, which, in turn, requires people in that structure recurrently producing economically valuable, tradable surpluses of physical goods and/or marketable skills.

Question: how can I know there is any point in producing an economically valuable surplus of anything? Answer: where other people make me understand they would gladly acquire said surplus. Mind you, although markets are mostly based on money, there are de facto markets without straightforward monetary payment. The example which comes to my mind is a structure which I regularly observe, every now and then, in people connected to business and politics, especially in Warsaw, the capital of my home country, Poland. Those guys (and gals) sometimes call it ‘the cooperative of information and favour’. You slightly facilitate a deal I want to strike, and I remember that, and later I facilitate the deal you want to strike. We don’t do business together, strictly speaking, we just happen to have mutual leverage on each other’s business with third parties. I observed that pattern frequently, and the thing really works as a market of favours based on social connections and individual knowledge. No one exchanges money (that could be completely accidentally perceived as corruption, and that perfectly accidental false perception could occur in a prosecutor, and no one wants to go to jail), and yet this is a market. There is an equilibrium price for facilitating a $10 million deal in construction. That equilibrium price might be the facilitation of another $10 million deal in construction, or the facilitation of someone being elected to the city council. By the way, that market of favours really stirs it up when some kind of elections is upcoming.

Anyway, the more social interactions I enter into over a unit of time, the more chances I have to spot some kind of economically valuable surplus in what I do and make. The more such social interactions are possible in the social structure of my current residence, the better. Yes, cities allow that. The next step is from those general thoughts to a thread of teaching and learning. I can see a promising avenue in the following scheme:

>>> Step 1: I choose or ask my students to choose any type of normal, recurrent social interaction. It can be interesting to film a bit of city life, just like that, casually, with a phone, and then use it as empirical material.

>>> Step 2: Students decompose that interaction into layers of different consistency, i.e. separate actions and events which change quickly and frequently from those which last and recur.

>>> Step 3: Students connect the truly recurrent actions and events to an existing market of goods or marketable skills. They describe, with as much detail as possible, how recurrent interactions translate into local states of equilibrium.

Good. One carryover done, namely into microeconomics, I try another one, into another one of my basic courses at the university: fundamentals of management. There is something I try to tell my students whenever I start this course, in October: ‘Guys, I can barely outline what management is. You need to go out there, into that jungle, and then you learn. I can tell you what the jungle looks like, sort of in general’. Social interactions and social roles in management spell power, hierarchy, influence, competition and cooperation on the top of all that. Invariably, students ask me: ‘But, sir, wouldn’t it be simpler just to cooperate, without all those games of power and hierarchy inside the organization?’. My answer is that yes, indeed, it would be simpler to the point of being too simple, i.e. simplistic. Let’s think. When we rival inside the organization, we need to interact. There is no competition without interaction. The more we compete, the more we interact, and the more personal resources we need to put in that interaction.

Mind you, competition is not the only way to trigger intense, abundant human interaction. Camaraderie, love, emotional affiliation to a common goal – they all can do the same job, and they tend to be more pleasant than interpersonal competition. There is a caveat, though: all those forms of action-generating emotional bonds between human beings tend to be fringe phenomena. They happen rarely. With how many people, in our existence, can we hope to develop a bond of the type ‘I have your back and you have my back, no matter what’? Just a few, at best. Quite a number of persons walk through their entire life without ever experiencing this type of connection. On the other hand, competition is a mainstream phenomenon. You put 5 random people in any durable social relation – business, teamwork, art etc. – and they are bound to develop competitive behaviour. Competition happens naturally, very frequently, and can trigger tacit coordination when handled properly.

Yes, right, you can legitimately ask what does it mean to handle competition properly. As a kid, or in your teenage years, have you ever played a competitive game, such as tennis, basketball, volleyball, chess, computer games, or even plain infantile fighting? Do you know that situation when other people want to play with you because you sometimes score and win, but kind of not all the time and not at all price? That special state when you get picked for the next game, and you like the feeling? Well, that’s competition handled properly. You mobilise yourself in rivalry with other people, but you keep in mind that the most fundamental rule of any competitive game is to keep the door open for future games.      

Thus, I guess that teaching management in academia, which I very largely do, may consist in showing my students how to compete constructively inside an organisation, i.e. how to be competitive and cooperative in the same time. I can show internal competition and cooperation in the context of a specific business case. I already tend to work a lot, in class, with cases such as Tesla, Netflix, Boeing or Walt Disney. I can use their business description, such as can be found in an annual report, to reconstruct an organisational environment where competition and cooperation can take place. The key learning for management students is to understand what traits of that environment enable constructive competition, likely to engender cooperation, as opposed to situations marked either with destructive competition or with a destructive absence thereof, on the other hand.

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The balance between intelligence and the way we look in seasoned black leather


After having devoted some of my personal energy to reviewing other people’s science (see Second-hand observations), I return to my own science, i.e. to my book on the civilizational role of cities. Reviewing that manuscript in the field of energy management gave me some inspiration. I realized that the core message I wanted to convey in the book was that human societies have collective intelligence, that intelligence manifests itself in typical, recurrent patterns, and cities are one of those patterns, where creating a demographic anomaly allows creating new social roles for a growing population, and assuring functional partition between two types of settlements: agricultural land for producing food, on the one hand, and urban land for producing new social roles and new technologies, on the other hand. Moreover, cities are the base of markets, and of the market-based economy. The whole social system based on the development of skills and technologies, so as to produce tradable surpluses, that whole system is precisely based on the role of cities. Maybe there are other social structures to obtain the same result, but we haven’t figured them out yet. With the creation of cities, we developed a pattern of further development, where apparently fundamental markets interweave with the apparently futile ones, and the whole system facilitates technological change and the creation of new social roles. The social system based on cities is like a social vortex, largely powering its own momentum and sucking new people into it.

That overview of my thinking brings me one more time to the issue of collective intelligence and to the big methodological question: to what extent can neural networks be used to simulate collective intelligence in human societies? I know, I know, this is some n-th time I return to that thing. Still, it is important, both methodologically and fundamentally. There is a whole big stream of research, including my own, where neural networks are used as mathematical tool for validating theoretical model. I can see that neural networks tend to replace the classical methods, such as GARCH, ARIMA or the good old Ordinary Least Squares. All that stuff works with the same basic data, i.e. with residual errors which inevitably appear as we try to apply our grand ideas to the brutal reality of life. Still, the way that neural networks process those errors is fundamentally different from stochastic models. The latter just cut through the entire set of data with one line (or curve, for that matter), which minimizes the sum total of residual errors, all in one go. Neural networks are more patient, and they minimize error by error, case by case. Neural networks learn.

The point is that when I use a neural network to validate a theoretical model in social sciences, I should substantiate the claim that the network represents the way of learning in the given society. The best theory of learning which I have found so far is the Interface Theory of Perception (Hoffman et al. 2015[1]; Fields et al. 2018[2]; see also I followed my suspects home). I rephrase it shortly and I try to put it against (or next to) my own methodology.

When an aggregate socio-economic variable, such as e.g. GDP per capita or energy consumption per capita, changes over time, it allows assuming a society doing something differently as time passes. In other words, those aggregate variables are manifestations of collective decisions and collective action. Question: how are those collective decisions being taken and how are they being turned into action? Some sort of a null assumption is that we have no way to guess anything about that process. Still, I think I can make a slightly stronger assumption, namely that we collectively know what we are doing, we just know it imperfectly. Therefore, when I observe a variable such as GDP per capita, or the average number of hours worked per person per year, change over years, I can assume it manifests a collectively intelligent adaptation: we do something together, we contemplate the outcomes, we say ‘Blast! It is not exactly what we meant. Folks! Get ready! We adapt! That rate of secondary education has to change! We are running a civilisation here, aren’t we?’, and we engage into another set of decisions and actions.

Collective decisions and collective action mean that people argue and diverge in what they say they intend to do, in what they really do, and in what they claim they have just done. We diverge from each other and we lie to each other on the top of it, and we lie to ourselves, and yet that whole business of civilisation seems to be working. We have a set N = {se1, se2, …, sen} of n social entities (people, basically, or various agglomerations thereof), and they all cheat, lie, and egoistically get after it, in the presence of a set R = {r1, r2, …, rm} of m external stressors (viruses, presidents, wars, bad crops etc.). Mind you, as long as n > 1, i.e. as long as there are many social entities, probably at least one of them is doing things sufficiently well to survive in the presence of m stressors.

We have those n social entities trying to get by in the presence of m external stressors, and one could wonder how that lot can learn anything? I subtly change the shade of the question ‘how?’ into ‘how can we know that?’. How can we know that a social entity has learnt anything in the presence of external stressors? Learning can be understood from two perspectives: subjective internal impression of having learnt something, on the one hand, and objective, externally observable fact of having acquired new skills. When I prepare the same sauce 30 times, 20 times it is completely spoilt, 9 times it sort of approaches the ideal, and 1 time, the final one, I have the impression I nailed it. I have the impression I have learnt something, however it does not mean other people think the same.  

I need a gauge to assess learning. One possible method, more specifically the one used in artificial neural networks, consists in checking how close my social entities are to a pre-defined desired outcome. In more elaborate artificial neural networks, the pre-defined component might be just the method of setting the desired outcome. That outcome can be simply survival or something more, such as achieving a certain amount of something valuable.

Good, so I have those n social entities, and the stressor they act under is the pressure to achieve a desired outcome, i.e. to obtain a certain payoff. The social entity sei which gets the closest to that outcome, or which, in other words, collects the greatest payoff, can be considered as the most successful. Life is reproduction. People die, and new people are born. Governments change. On the long run our set N = {se1, se2, …, sen} of n social entities is interesting to the extent that it reproduces into another set Nk of n(k) social entities. Social change can be viewed as an (almost) ever-lasting chain of sets, each with social entities inside: N1 transforms into N2, which turns into N3 etc.

I think I have just nailed an important point (involuntarily, to be clear). When I study any kind of social change, I can make one of the two alternative assumptions: continuity of social entities versus their generational reproduction. Social structures can be seen such as I have just described it: as changing sets of social entities. Under that angle, the 38 million people in my native Poland today are a different set of people from the roughly 36 million who were around when I was 10, i.e. in 1978. It does not necessarily mean that each person present in 1978 died and has been replaced by someone else; I am pretty sure I didn’t die. However, some people died, some new people have come to the fore, some people changed significantly etc. On the whole, the set N2020 is different from the set N1978. There is a different angle for looking at the same reality: people in Poland, 2020, are the same big social entity as the one in Poland, 1978, and it is just the internal structure of that entity that has changed. 

What is the practical (well, theoretical) difference between those two angles of approach to the same theatre of social change, i.e. consecutive sets of small entities as opposed to consecutive states of one big entity? When I simulate social change as a sequence of sets, where individual components can change their properties, a long sequence of that type is like a journey of discovery. Each consecutive set Nk comes out of learning that occurred in its predecessor Nk-1. The transformation of one set into another certainly follows some constraints, yet a long sequence of such transformations is like a long hike up a hill: we have to take turns around boulders and ravines, we have to choose between paths of different difficulty, and usually an easier path is a less steep one, thus a longer and slower one. This type of change, social or biological, is known as adaptive walk in rugged landscape in Kaufman & Levin 1987[3]. Mathematically, it is a Markov chain, i.e. a chain of states, where the properties of each consecutive state are determined just by the properties of the previous state as well as by the algebra of transformation from one state to another (the so-called σ-αλγεβρα, oops! Excuse me, I wanted to say σ-algebra).

When I take the other approach to a social structure, i.e. when I study it as one big, perennial social entity which undergoes structural change inside, that change is something like different shapes of the same thing. I noticed strong marks of such an approach in that scientific paper entitled ‘Evolutionary Analysis of a Four-dimensional Energy- Economy- Environment Dynamic System’, which I was reviewing recently on the request of  the International Journal of Energy Sector Management (ISSN1750-6220). In that paper, a complex system of relations between economy, energy and society is represented as four gradients of change in, respectively, volume of pollution x, real economic output y, environmental quality z and energy reduction constraints w. I know it is a bit abstract, at this point, yet I want to make an effort and explain it. Imagine an irregular quadrilateral, i.e. a rectangle with broad intellectual horizons. Four angles, four edges, yet the angles do not have to be right and the edges do not have to be parallel in pairs. Just four of each lot. The length of each edge corresponds to the gradient of change in one of those 4 variables: x, y, z, and w. Any substantial change in that system is a change in lengths of those 4 edges, and, as it is a closed polygon, it entails a change in angles between edges.

As I am trying to grasp fundamental differences between those two views upon social change, namely sequence of sets as opposed to an internally changing perennial entity, I think the difference is mostly epistemological. As a matter of fact, I don’t know s**t about reality as it is, and, let’s be honest, neither do you, my dear readers. We just make many possible Matrixes out of the real stuff and settle for the one that offers the greatest rewards. This is the stance adopted in the Interface Theory of Perception (Hoffman et al. 2015[4]; Fields et al. 2018[5]), as well as in classical Western empiricism (see William James’s ‘Essays in Radical Empiricism’, 1912). This holds for social reality as well as for anything else. When I see social change, I see most of all change in itself, and only secondarily, in my spare moments, I can try to figure out what exactly is that thing that changes. This is science, or philosophy, depends on the exact method I adopt, and this is hard, and time-consuming. Most of the times, I just use a ready-made explanation, conveyed in my culture, that what is changing is, for example, the market or the constitutional order, or the set of cultural stereotypes. Still, at the bottom line, those labels are just labels. What I am really experiencing, is change in itself.

When I assume that social change is a Markov chain of sets made of small social entities, I study social change as change in itself, i.e. as the say σ-algebra of that chain. I do not pretend to know exactly what is happening, I just observe and give the account of the passage from one state to another. Conversely, when I assume that social change is structural recombination inside a big, perennial social structure, I pretend to know the limits and the shape of that big structure. This is a strong assumption, probably an overstated one.    

Now, I connect the dots. I am linking my thinking about cities with my thinking about collective intelligence, and all that I serve in a sauce peppered with the possibility to use artificial neural networks for studying the whole business. I can study the civilizational role of cities under those two angles, i.e. as a Markov chain of states which I barely understand, yet which I can observe, on the one hand, or as internal reshuffling inside a finite, big social entity called ‘civilisation’, with nicely outlined contours. I am honest: I am not even going to pretend I can outline the precise contours of the civilisation we live in. With all the s**t going out there, i.e. leftist extremists in Germany erecting an illegal statue of Lenine, in response to #BlackLivesMatter in United States, and neo-Nazi extremists from The Base organization receiving orders from a leader who is an American with an Italian name, currently living in Russia: man, I do not feel up to trace the external contours of that thing.  

I know that I can and want study the phenomenon of cities as change in itself, and I assume that the change I see is an aggregation of local changes in small social entities sei. As those small sei’s change locally, their local transformations translate and manifest as the passage from the aggregate set Nk = {se1, se2, …, sen} into another set Nk+1 = {se1, se2, …, sen}. The next hurdle to jump over is the connection between sets of the type Nk = {se1, se2, …, sen} and aggregate socio-economic variables commonly used as so-called statistics. Those ‘statistics’ tend to have one of the 4 possible, mathematical forms: averages, totals, frequencies, or rates of change. When they are averages, e.g. GDP per capita, they are expected values of something. When the come as aggregate totals, e.g. aggregate headcount of population, they stand for the size of something. As they take the form of frequencies, e.g. the percentage of people with secondary education, they are simple probabilities. Finally, as rates of change, they are local first derivatives over time in some functions, e.g. the function of economic growth.

Each of those mathematical forms can be deemed representative for a heterogenous set of small phenomena, like small social entities sei. I assume that each set Nk = {se1, se2, …, sen} of n social entities manifests its current state in the form of a complex vector of variables: expected mean values, total sizes, simple probabilities of specific phenomena, and first derivatives over time in the underlying functions of change. Any set of socio-economic variables is an imperfect, epistemic representation of current local states in the individual social entities sei included in the set Nk = {se1, se2, …, sen}.  

As I go through my notes and blog updates from the last 2 months, something emerges. The social entities I focus on, thus my sei‘s, are individual people endorsing individual social roles. set Nk = {se1, se2, …, sen} is essentially a set of people, i.e. a population. Each of those people has at least two coordinates: their place of residency (mostly defined as city vs countryside), and their social role. I messed around with a set like that in a neural network (see The perfectly dumb, smart social structure). The current state of the whole set Nk manifests itself as a vector Vse of socio-economic variables.

So far and by far, the most important variable I have identified is the density of population in cities, denominated over (i.e. divided by) the general density of population. I named this variable [DU/DG] and I assume it shows the relative social difference between cities and the countryside (see Demographic anomalies – the puzzle of urban density). The coefficient [DU/DG] enters into interesting correlations with such variables as: consumption of energy per capita, income per capita, surface of agricultural land, cereal yield in kg per hectare of arable land, number of patent applications per 1 million people, and finally the supply of money as % of the GDP. On the other hand, by studying the way that urban land is distinguished from the rural one and from wildlife, I know there is a correlation between density of urban population and the density of man-made structures, as well as the density of night-time lights.

Good. I have a set Nk = {se1, se2, …, sen} of n social entities, which changes all the time, and a vector Vse = {DU/DG; energy per capita; income per capita; surface of agricultural land; cereal yield; patent applications; supply of money} of variables pertinent regarding cities and their role. Between the two I insert my mild obsession, i.e. the set SR = {sr1, sr2, …, srm} of ‘m’ social roles.

Now, I go pictographic. I use pictures to make myself spit out the words I have in mind. I mean, I know I have words in mind, only I don’t know what exact words are these. Pictures help. In Figure 1 I am trying to convey the idea of proportion between the headcount of population and the range of social roles available to endorse. My basic assumption is that we, humans, are fully socialized when we endorse social roles that suit our basic personal traits, such as intelligence, extroversion vs introversion, neuroticism, conscientiousness, the way we look in seasoned black leather etc. The state of society can be explained as a balance between the incremental headcount of humans, on the one hand, and the incremental range of social roles to take. If the headcount of humans is n, and the number of social roles available is m, we are talking about ∆n/∆m.  

When both sets, i.e. Nk and SR change at the same pace, i.e. ∆n/∆m (t0) = ∆n/∆m (t1), the society is in some sort of dynamic equilibrium, like a constant number of humans per one social role available. When the set SR of social roles burgeons faster than the pace of demographic growth, I mean when ∆n/∆m (t0) > ∆n/∆m (t1), logically there is less and less humans per one social role. This is social change by differentiation. New, idiosyncratic skillsets and behavioural patterns emerge. This is like an absorptive state, which can suck new humans in like easy.

On the other hand, when demographic growth in the set Nk races far ahead, and the set SR of social roles lags behind, i.e. ∆n/∆m (t0) < ∆n/∆m (t1), there is consistently more and more humans per one social role. That favours standardization and institutional definition of those roles, in the form of professions, public offices, ritualized social statuses etc. Society settles down into a nice order. Still, each such institutionalized social role grows barriers to entry around itself. You need to pass some exams, you need to be appointed or elected, you need to invest some capital… New humans coming to the world encounter those barriers, and some of them end up by saying: ‘F**k it! I stay outside of everything’.  This is the tipping point, when social change is needed, so as to make social room for new humans.   

Figure 1

Now, I transition into the role of cities in that social pattern. I am trying to picture the idea in Figure 2. If the state of social differentiation, we need some pattern for generating diversity. We need social interaction. Cities can be seen as a social contrivance which facilitates such interaction. Still, it comes to my mind sort of right now, we don’t really know (yet), to what extent digital interaction between humans can replace the real one in that specific respect, i.e. as a mechanism of creating new social roles. My gut feeling is that digital technologies can be at least imperfect substitutes of real social interaction. You Tube or Instagram may replace cities in their civilizational role of creating new social room for new homo sapiens. We might just be evolving from a civilization of city slickers living next to rednecks, into a civilisation of city slickers, rednecks and homo onlinus.  

Figure 2

In the next step, I am wrapping my mind around the math side of the problem, which I try to picture in Figure 3.  I guess that what I have in terms of empirical data to put in a neural network is mostly the vector Vse of social outcomes, which I can enrich with the headcount of population, and that would be the real-life material that a neural network could learn from. What that network could try and optimize could be the gradient ∆n/∆m or some variation thereof, as the exact number of social roles is technically unobservable with the current state of technology. When I think about the practical way of doing it, I can imagine a network pegged on optimizing some sort of hard-nailed output variable, such as the average number of hours worked per person per year (solid stuff, as it comes out of my so-far research). I drop the gradient ∆n/∆m among the input variables, and I try to discover what value thereof the network would yield after a few thousands laborious trials to produce artificial history.

Another angle of approach that comes to my mind is to take all the known empirical variables as input, and the gradient ∆n/∆m as the output. Then I make different clones of the network, with ∆n/∆m going various ways, like gently up, steep up, down a bit etc. I can check which of the clones displays the closest Euclidean distance to the source empirical dataset.    

Figure 3

Now, the final step: I connect the concept of social role with that of conscious agent, as represented in the Interface Theory of Perception (Hoffman et al. 2015[1]; Fields et al. 2018[2]). Figure 4 represents my pictographic thinking about it. Social roles are temporary outcomes of learning and social interaction between Conscious Agents (CA). In other words, social roles form as humans exchange information about their conscious experience, which serves to translate objectively existing states of the world into material possible to process by our brain, so as to decide whether to run away from the tiger or maybe rather kill the tiger and take the antelope. We take action consequently, we contemplate its consequences, and we talk about it, and we show to each other how we can learn new stuff.

Figure 4

Discover Social Sciences is a scientific blog, which I, Krzysztof Wasniewski, individually write and manage. If you enjoy the content I create, you can choose to support my work, with a symbolic $1, or whatever other amount you please, via MY PAYPAL ACCOUNT.  What you will contribute to will be almost exactly what you can read now. I have been blogging since 2017, and I think I have a pretty clearly rounded style.

In the bottom on the sidebar of the main page, you can access the archives of that blog, all the way back to August 2017. You can make yourself an idea how I work, what do I work on and how has my writing evolved. If you like social sciences served in this specific sauce, I will be grateful for your support to my research and writing.

‘Discover Social Sciences’ is a continuous endeavour and is mostly made of my personal energy and work. There are minor expenses, to cover the current costs of maintaining the website, or to collect data, yet I want to be honest: by supporting ‘Discover Social Sciences’, you will be mostly supporting my continuous stream of writing and online publishing. As you read through the stream of my updates on , you can see that I usually write 1 – 3 updates a week, and this is the pace of writing that you can expect from me.

Besides the continuous stream of writing which I provide to my readers, there are some more durable takeaways. One of them is an e-book which I published in 2017, ‘Capitalism And Political Power’. Normally, it is available with the publisher, the Scholar publishing house ( ). Via , you can download that e-book for free.

Another takeaway you can be interested in is ‘The Business Planning Calculator’, an Excel-based, simple tool for financial calculations needed when building a business plan.

Both the e-book and the calculator are available via links in the top right corner of the main page on .

You might be interested Virtual Summer Camps, as well. These are free, half-day summer camps will be a week-long, with enrichment-based classes in subjects like foreign languages, chess, theater, coding, Minecraft, how to be a detective, photography and more. These live, interactive classes will be taught by expert instructors vetted through Varsity Tutors’ platform. We already have 200 camps scheduled for the summer.

[1] Hoffman, D. D., Singh, M., & Prakash, C. (2015). The interface theory of perception. Psychonomic bulletin & review, 22(6), 1480-1506.

[2] Fields, C., Hoffman, D. D., Prakash, C., & Singh, M. (2018). Conscious agent networks: Formal analysis and application to cognition. Cognitive Systems Research, 47, 186-213.

[1] Hoffman, D. D., Singh, M., & Prakash, C. (2015). The interface theory of perception. Psychonomic bulletin & review, 22(6), 1480-1506.

[2] Fields, C., Hoffman, D. D., Prakash, C., & Singh, M. (2018). Conscious agent networks: Formal analysis and application to cognition. Cognitive Systems Research, 47, 186-213.

[3] Kauffman, S., & Levin, S. (1987). Towards a general theory of adaptive walks on rugged landscapes. Journal of theoretical Biology, 128(1), 11-45

[4] Hoffman, D. D., Singh, M., & Prakash, C. (2015). The interface theory of perception. Psychonomic bulletin & review, 22(6), 1480-1506.

[5] Fields, C., Hoffman, D. D., Prakash, C., & Singh, M. (2018). Conscious agent networks: Formal analysis and application to cognition. Cognitive Systems Research, 47, 186-213.

We suck our knowledge about happening into some kind of patterned structure


It’s done. I am caught in the here and now with my writing. As I am writing these words, on June 10th 2020, George Floyd’s funeral in Minneapolis, U.S., is just over. I am Polish, I live in Poland, and I am essentially a bystander as regards the events taking place in United States. Yet, those events resonate in my country, and I think I can express an opinion.

I have a few words to say about the idea of defunding the police force. We had the same idea in Poland, when we were transitioning from communism to democracy, from 1989 on. As communism collapsed, we would intuitively associate police force in general with an oppressive regime. It was a pattern inherited from the communist system: the police force was a tool of oppression in the hands of a totalitarian state. In parallel, the new democratic Poland had to rebuild its fiscal base almost from scratch, and for quite a few years, the government went very largely bankrupt. Defunding the police force came as sort of handy, both economically and politically, and so we did.

We expected more freedom with less cops in the streets. Still, instead of freedom, gangs crept in. Gangsters took control of entire cities, within months. One year after the fall of communism, in summer 1990, it was already impossible to run any substantial business without being racketed, pardon, without paying for “protection services”, and you were lucky if just one gang claimed that tribute from you. Sometimes, you would find yourself in disputed terrain between rivalling gangs, and then you were really f**ked. In 1995, a friend of mine died of a horrible death, in a cartel-style execution, because he was unlucky enough to be a bouncer in a club which two rivalling gangs tried to take over and control. It took us like a decade to re-establish a relatively normal social order, around 2001 – 2002.

Thus, guys, a message to those of you who think that the police force is your worst enemy. With all the due respect, you’re wrong. The police force is like a shield between us, normal folks, and a social fringe of truly evil sociopaths. Once again, believe me, you have no idea what true evil is until you look it straight in the face. You remove the shield, and you get exposed to real monsters, and those monsters are surprisingly well organized. I am tempted to quote Jean – Jacques Rousseau, the French thinker commonly associated with the theory of social contract. Rousseau stated very clearly that what we see as civil rights and freedoms really works only to the extent that we have a government strong enough to guarantee them.

The world is changing. I am doing my best to wrap my mind around those changes. As social media swell with contrary tides of ideas, I try to keep my mind open to all kinds of opinions. A strange memory floats up to the surface of my consciousness. I think I was like 10 years old, so it must have been 1978, communist Poland, of course. We already had in place a system of food rationing, especially as regards meat and fruit. My father was in the communist party and was a fervent acolyte thereof. I remember seeing in the official news, on TV, a reportage on how fantastically buoyant our agriculture and the food sector were. Mountains of delicious fresh food loomed on the TV screen. I asked my father: ‘Dad, how come we have such amounts of food on TV, but in day to day life we have so little meat and fresh fruit, and what we can buy in food stores is mostly industrial sugar and industrial pasta?’. My dad answered: ‘This is because our entire society, in line with the doctrine of the Party, we are committed to support the emancipation of black Americans in the United States’. ‘Oh, so we send them our pork meat, to the United States?’ – I would reply – ‘Cool. I didn’t know. But, dad, couldn’t we help those black Americans a little less and eat a little better? I think it is called a compromise…’. ‘Don’t you dare questioning the policy of the Party! There are no compromises in promoting international social justice’. Yes, it was the usual closure to such conversations, at the time. You never knew who was listening.

Of course, it was bullshit. We were not helping black Americans, we simply had a f**ked up economic system, based on ideology instead of entrepreneurship, and black Americans were just an excuse. I wonder how much of handy excuse are black Americans now, serving to cover various mistakes in people who would lose a lot, should they have to endorse those mistakes, and serving ambitions in other people (or maybe in the same people). As I read business news, I can see, here and there, some top corporate executives, all white, being suddenly fired by other top corporate executives, white as well, because of ‘racial hate speech’ etc.    

I can see society slightly shaking around me, and I realize how strongly I am attached, in my psyche, to relative stability in the social space. I realize how easy it is to fall for either path: ‘Let’s do revolution!’ is just as tempting as ‘Western civilization is dying!’. Both offer easy space for unloading stress, which accumulates as I see social rituals changing all of a sudden. Good. This thread of thinking, i.e. thinking about social stability versus social change, is a good avenue to lead me back towards my research on the role of cities in our civilisation. I build up intellectual distance by referring once again to Arnold Toynbee’s ‘Study of History’ (abridged version: Somervell &Toynbee 1946[1]). In the introduction, Arnold Toynbee writes: ‘If the argument of this chapter is accepted it will be agreed that the intelligible unit of historical study is neither a nation state nor (at the other end of the scale) mankind as a whole but a certain grouping of humanity which we have called a society’.

That excursion into Arnold Toynbee’s theory serves me as a pretext to open up on a more current topic: cities in Asia, and more specifically in China. I had the opportunity to visit some of the Chinese cities and I was baffled with how different they are from the European ones. Under a superficial layer of similarity, a completely different social order dwells. When I wrote that cities are made of movement and human connection, I should take it to square power in the Chinese case. In Chinese cities, even buildings go faster than European ones. Hardly anyone conserves buildings in China the way we do it in Europe. In Europe, we are used to maintaining constructed architectural substance as a sort of skeleton, and to organizing our social activity around it. In China, buildings are like cars: when used up, no one bothers to renovate them, they are just being replaced with new ones. Chinese cities are all movement.      

Cities have grown, across the globe, in strict economic connection to the surrounding countryside. The city creates social roles, and therefore a market for agricultural products, and the countryside provides a stable food base. That connection by partition is fascinatingly different between China and Europe. European agriculture developed as pretty much a closed loop between people, livestock, and vegetal farming. Livestock eats, livestock shits, and thus livestock fertilizes. In China, historically, there has been much less livestock in agriculture, and much more cereals, mostly rice. There is a historical detail about the connection between rice and cities in China. This is one of those details we just don’t talk about, as it sounds awkward: Chinese cities had been fertilizing their neighbouring rice fields with human excrements from cities, with comparatively little amount of animal manure (see for example Braudel 1992[2]). The kind of loop that European humans made with their livestock and their cereal fields, Chinese humans made directly with their rice fields, without inviting cattle to the party.

As you can easily guess, looping our food base on our own excrements gives clear incentives to increase the amount of the latter. Cities can grow much bigger than in Europe. Bigger cities, and faster growth in their population mean more new social roles being created per unit of time, whence new social space for greater a population. Greater a population defecates more, and the loop spirals up.

Chinese cities, including their ancient, peculiar relation to the rice they buy from the countryside, seem to favour hyper-growth in size. Au & Henderson (2006[3]) claim that Chinese cities, such as they emerged as the Chinese economy after its progressive transition towards market economy, are still too small regarding the economic incentives for growth they offer (or rather used to offer 15 years ago). Au & Henderson claimed that Chinese cities create exceptional economic incentives for demographic growth. On the other hand, as we observe the way that Chinese cities function today, they have an outstanding ability to attract new investment. The bottom line under this specific thread of my writing is that social difference between cities and the countryside is strongly idiosyncratic. Why?

The ‘why?’ question is usually an abyssal one. You have logical coherence and functional correlation entangled around the assumption that things which happen later are the outcome of things that happened earlier. I prefer tricking myself by asking ‘How?’ instead of ‘Why?’. How does the idiosyncratic social difference between cities and the countryside develop? How does it start? What are the distinctive steps in the process? Is there any threshold of saturation?

How does a city start? The basic answer is: slowly and with a lot of struggle, when a local population needs to organize itself. A demographic anomaly forms: a collection of man-made structures, apparently pointless from the point of view of warfare and agriculture, and yet functional for trade, business and politics. Some folks discover that it pays off to construct a few buildings close to each other instead of spreading them across the countryside. Those folks deliberately shrink their respective physical territories, from farm-wide to store-wide, in order to have additional benefits from exchange.

I jump back to the present and the current, and to the #BlackLivesMatter protests. In Seattle, U.S., protesters created (well, they didn’t create anything, they occupy somebody else’s property, but ‘created’ sounds better) an autonomous zone. They created a town. Similar episodes are happening across Western Europe as well. People who, objectively speaking, are anarchists and therefore postulate to destroy the incumbent social order, put in place their own social structure as soon as they are satisfied with apparently having destroyed the old one. This is amazingly coherent with what I discovered in my experiments with a neural network, which was supposed to simulate a system of social roles. When social cohesion, i.e. social distance between distinct social roles, gets a bit of loose in the shoulders, the incumbent social roles disappear at first. Yet, after an initial phase of entropy, that very simple set of equations learns how to bring social roles back (see The perfectly dumb, smart social structure).

Maybe this is how cities formed in the past, i.e. they formed in momentary windows of social entropy, when nobody new s**t, and some people said: ‘OK, guys, as no one really knows what to do, we are going to do urban life. This is how intelligence works: knowing what to do when we have no clue what to do’.  

Now, a few more words of explanation as regards my stance on #BlackLivesMatter. By reading what I have just written, you can guess I am a moderate conservatist. Yes, indeed I am, and, on the top, of that, I like asking embarrassing questions and cutting bullshit out of the answers. When people gather in large numbers, what they want most of all is gathering in itself. They want to experience community. Defining a common enemy – those ugly privileged whites and ugly cops – helps reinforcing the oxytocin loops that gathered people trigger with each other. The pandemic and the lockdown have shaken a bit the sense of social cohesion – people stopped going to work, children stopped going to school, habits got shaken – and slogans like ‘Society must change!’, shouted and yelled, actually reflect a post factum acknowledgment of facts (‘F****k! Society changes! Heeeeelp!’).

Sometimes, I have the impression that anarchist movements like this one are a necessary pain in the ass when we want to absorb important exogenous stressors. Maybe we train for the BIG adaptation to climate change?

Cities are distinctive from the countryside by their abnormally high density of population, which is a proportion between population and the territory it occupies. There are two distinct methods of measuring both: administrative and GPW (Gridded Population of the World). I am sharpening my understanding of these two approaches so as to understand the dynamics of urban structures as such. My approach is empiricist. I hope to understand better the boundary between cities and the countryside through understanding the fine distinctions as regards the way we perceive that boundary. Here, one more excursion into current events. Have you noticed that CHaz (Capitol Hill Autonomous Zone) in Seattle is precisely in Seattle and not in the countryside? Logically, if you want to cut ties with the ugly incumbent social order, forming a commune out there, in the fields and woods, could be a tempting idea. Yet, these specific protesters decided to constitute Chaz in the city. They claimed it because they need it.   

Underneath the cognitively acknowledged social rituals, maths dwell. Before we started to remember what we had forgotten about life in the presence of epidemic risk, our set SR = {sr1, sr2, …, srm} of ‘m’ social roles was congruent with and logically equivalent to such other sets as, for example, the set IN = {in1, in2,…, inz} of ‘z’ typical levels observable in annual income, or the set R = {r1, r2, …, ro} of ‘o’ places of residence. Social contacts had been kind of going along and coming with the social role at hand. Now, our set of social roles has suddenly become significantly congruent with and logically equivalent to a set ßC = {ßc1, ßc2, …, ßcn} of ‘n’ observable levels in epidemic risk derived from social contacts.

Before, the daily mathematical life of our culture consisted in feeding into itself a set of individual experiences regarding income, housing, cars owned etc., and pitching the resulting mix against the benchmark of what we consider as collectively desired outcomes. Life is made of chaos and order, and we mix it. We have things we know we do, i.e. our relative preference for different social roles SR = {sr1, sr2, …, srm}, and that preference manifests itself as the probability p(sri) that a randomly selected human endorses the social role sri. We acknowledge chaos as random, local occurrences ε(t) of something barely conceptualized. Our social roles happen as temporary instances of a general cultural frame, i.e. as SR(t) = {ε(t)*p(sr1), ε(t)*p(sr2), …, ε(t)*p(sri)}. Each ε(t) in that temporary occurrence SR(t) is different. Remember: that ε(t) is just a civilized mask we put on the pretty scary face of barely acknowledged chaos.

We, humans, we are obstinately ordered. Things happen to us in a hurricane of phenomenal chaos, and we take great care to react in an orderly, patterned way. We don’t have enough money? Good, there are patterns to follow: save, invest, get a better job… The catalogue is actually definite, at least for most of us. We feel a bit down on our physical condition? Good. Exercise, sleep more, pay attention to what you eat. Once again, the repertoire of reactions is finite. We need someone else in charge? Well, let’s see… Elections? No? Then maybe a corporate structure and appointment by the strongest players? No? Doesn’t fit the bill either? Well, then we stay with limited options… Structurally unstable dictatorship disguised as democracy where we buy people’s votes with the money they haven’t earned from other people ‘cause we were the first to snatch that money? Good? We go on with this one? Good…

There is another trait of orderliness in our civilization: we are strongly coherent and cohesive in our social ways. Have you ever noticed how frequently those people, who present themselves as outsiders and non-conformists, take great care of fitting into a precise mould of ready-made ideas and behaviours? I remember going to a wedding, in 2018, where the bride and the groom were much younger than I, just as most of their friends. As the wedding party was starting, the young couple announced that ‘this party is a celebration of freedom and independent thinking, without any false moral limitations; do whatever pleases you to do’. The actual consummation of that principle looked stiffer than a reception at the Buckingham Palace. Everybody was eyeing everybody else, how free and independent they appear, and tried to fit exactly into the same model of freedom and independence. This is what we humans do, socially: we eye each other, and we conform. Even when we claim we don’t conform, we actually conform to some other pattern. This is not some innate stupidity: this is how being a social species manifests itself. We hold parties in the same basic way our distant ancestors would hunt the woolly mammoth. We coordinate, and much of this coordination is tacit, i.e. not expressed explicitly.        

The provisional bottom line of this little intellectual excursion into the realm of weddings is that, on the top of distinctive traits observable in particular social roles, our collective intelligence feeds into itself information about mutual coherence between those social roles.

We have those patterns. Whatever happens, we suck our knowledge about happening into some kind of patterned structure. Patterning starts with aggregation of idiosyncrasies. We collectively make some kind of simple metric about reality. Let’s call it h. The simple h can suck reality into itself in many mathematical ways. The h can emerge as h = ε(t)*p(sr1) +  ε(t)*p(sr2) +  … + ε(t)*p(srm), or it can go into the fancy realms of matrix maths, like h = [ε(t)*p(sr1)/ ε(t)*p(sr2)] + [ε(t)*p(sr1)/ ε(t)*p(sr3)] + … + [ε(t)*p(sr1)/ ε(t)*p(srm)]. Whatever. It boils down to taking a lot of largely chaotic reality and squeezing it into the magic hat of culture, so as to pull a nicely structured rabbit afterwards.

Have you noticed that the rabbit always comes up from the magic hat, and never falls down from it? As a collective intelligence, we have patterned ways of drawing conclusions from aggregate existential chaos. There is something at the base – the hat – and something – the rabbit – comes up from that base. As you browse through neural activation functions, which we use in artificial neural networks to represent what we think intelligence is, at the bottom line you most frequently fall either on the mathematical constant e = 2,71828 elevated to the power h of aggregate chaos, with some kind of additional parameters, or on the square root of 1+ h elevated to some arbitrary power. The idea is that our way of being intelligent contains some kind of constant root, such as e = 2,71828 or √(1 + h2). By the way, the constant root e = 2,71828 is a collection of steps towards reverted infinity of dimensions, i.e. e = (1/1) * (1/1) *( ½) * … * 1/(n → ∞).    

Thus, when we think about the way that intelligence works, thus when we project our own thinking about our own intelligence, we assume there is a constant root in that intelligent cognition. At the very base of what we think, we sort of always think the same, and aggregate chaos of daily existence comes as a modifier to that constant root. We think almost the same we used to think before, just with a small drift.

I feel like partly summing it up. We go through that chaos called life by being smartly social. We endorse SR = {sr1, sr2, …, srm} social roles and we discriminate among them by experimenting with their local probabilities p(sri), whilst acknowledging random disturbances ε(t) and producing local instances SR(t) = {ε(t)*p(sr1), ε(t)*p(sr2), …, ε(t)*p(sri)} of our framework social structure. We aggregate our experience with those local variations into simple metrics, like h = [ε(t)*p(sr1)/ ε(t)*p(sr2)] + [ε(t)*p(sr1)/ ε(t)*p(sr3)] + … + [ε(t)*p(sr1)/ ε(t)*p(srm)], digestible to our big, patterned institutions, which maintain a baseline continuity and allow some drift as circumstances happen.

The inevitable failure to achieve what we collectively want, largely resulting from the apparently intrinsic inability to define what we really, collectively want, generates learning about the margin of error as regards perfect happiness. We feed that error forward in time, into the next episode of existence, and we backpropagate that error along the logical structure of our civilisation, and it all plays out over and over again. Now, we enrich our collectively subconscious, mathematical life with data about epidemic risk attached to individual social roles, and by that means, to general categories of social roles. We feed into our culture our observation of that risk, we make it a functional part of the social order, and we keep pushing.

OK, change of tangent. I think I have pretty much circled the ideas I want to develop in my book on cities and their civilizational role. Here comes the list:

>>> Idea 1: Cities are demographic anomalies, which we, humans, have devised in order to accommodate a growing population.

>>> Idea 2: Seen as social contrivances, cities have three essential functions. Firstly, they allow rapid multiplication of social roles, which facilitates social structuring of a growing population. Secondly, that creation of new social roles allows the existence of many parallel, social hierarchies, which, in turn, facilitates the moderation of social conflicts. Thirdly, the development of cities allows, as strange as it could seem at the first sight, systematic development of agriculture.

>>> Idea 3: Cities enhance the collective intelligence of human societies, i.e. they enhance our collective ability to experiment with many local, alternative instances of our fundamental social structures. Cities allow systematic development of correlated behavioural coupling, which, in turn, largely eliminates randomness and excessive rigidity in the process of collective learning.    

>>> Idea 4: Technological change as such is a manifestation of collective intelligence rather than the individual one. Our technologies change at the pace allowed by the intensity of social interaction. Artificial intelligence is a good example of a technology that reflects collective intelligence.

>>> Idea 5: Cultures built around and on the basis of urban life display a characteristic pattern, centred on demonstrable social activity, correlated behavioural coupling supported by financial markets, and complex institutional systems.

>>> Idea 6: Cities form, as demographic anomalies, when a factor of disturbance temporarily distorts social cohesion, and then a new process of defining social roles emerges, with a cohesion of its own.  

Those 6 ideas coincide with some basic empirical regularities which I have noticed. Here they come:

*** Fact 1: Since 2008, the global human society has become prevalently urban and the process of urbanisation continues.

*** Fact 2: There is an interesting discrepancy between the administratively defined extent of urban land, on the one hand, and measurements based on satellite imagery, on the other hand. Whilst some cities in the world officially grow in space (i.e. their officially defined territories spread), the total surface of urban land in the world seems to be constant – at least for now – and cities grow into that de facto urban space rather than out of it.

*** Fact 3: The density of urban population, measured on the basis satellite-assessed extent of urban land, demonstrates intriguing properties as socio-economic variables. Those properties become even more interesting when the density of urban population is being denominated in units of general density in population. That compound variable, i.e. urban social density divided by general social density, which essentially measures the social difference between cities and the countryside, grows in an unusually monotonous, linear manner, and demonstrates intriguing correlations with such variables as income per capita, energy consumption per capita or agricultural productivity. When compared cross-sectionally, i.e. between countries, that variable seems to be hitting some kind of sweet spot around the value of 20 ÷ 22, i.e. when urban populations are approximately between twenty and twenty-two times denser than the general population. Anything significantly below or beyond that value seems to be less functional.      

Discover Social Sciences is a scientific blog, which I, Krzysztof Wasniewski, individually write and manage. If you enjoy the content I create, you can choose to support my work, with a symbolic $1, or whatever other amount you please, via MY PAYPAL ACCOUNT.  What you will contribute to will be almost exactly what you can read now. I have been blogging since 2017, and I think I have a pretty clearly rounded style.

In the bottom on the sidebar of the main page, you can access the archives of that blog, all the way back to August 2017. You can make yourself an idea how I work, what do I work on and how has my writing evolved. If you like social sciences served in this specific sauce, I will be grateful for your support to my research and writing.

‘Discover Social Sciences’ is a continuous endeavour and is mostly made of my personal energy and work. There are minor expenses, to cover the current costs of maintaining the website, or to collect data, yet I want to be honest: by supporting ‘Discover Social Sciences’, you will be mostly supporting my continuous stream of writing and online publishing. As you read through the stream of my updates on , you can see that I usually write 1 – 3 updates a week, and this is the pace of writing that you can expect from me.

Besides the continuous stream of writing which I provide to my readers, there are some more durable takeaways. One of them is an e-book which I published in 2017, ‘Capitalism And Political Power’. Normally, it is available with the publisher, the Scholar publishing house ( ). Via , you can download that e-book for free.

Another takeaway you can be interested in is ‘The Business Planning Calculator’, an Excel-based, simple tool for financial calculations needed when building a business plan.

Both the e-book and the calculator are available via links in the top right corner of the main page on .

You might be interested Virtual Summer Camps, as well. These are free, half-day summer camps will be a week-long, with enrichment-based classes in subjects like foreign languages, chess, theater, coding, Minecraft, how to be a detective, photography and more. These live, interactive classes will be taught by expert instructors vetted through Varsity Tutors’ platform. We already have 200 camps scheduled for the summer. .

[1] Royal Institute of International Affairs, Somervell, D. C., & Toynbee, A. (1946). A Study of History. By Arnold J. Toynbee… Abridgement of Volumes I-VI (VII-X.) by DC Somervell. Oxford University Press.,

[2] Braudel, F. (1992). Civilization and capitalism, 15th-18th Century, Vol. I: The structure of everyday life (Vol. 1). Univ of California Press., pp. 145 – 158.

[3] Au, C. C., & Henderson, J. V. (2006). Are Chinese cities too small?. The Review of Economic Studies, 73(3), 549-576.

How much of a collective intelligence we are? The case of cities and agricultural land


I continue to work on the role of cities in our civilisation and on the changes that the current COVID-19 pandemic can possibly bring to our ways of living in cities. Initially, when I started writing this update, on June 6th, I intended to explore the connection between technological change and the civilizational role of cities. Further in this update, I do go down that avenue, yet for now, in those initial paragraphs, I want to share another strand of my thinking, which I already signalled last time, namely my impressions from reading Daniel Defoe’s ‘Journal of The Plague Year’, published in 1665. That book was published in 1665 and gives the account of events which took place in London, in 1664, during the epidemic outbreak of plague. It was 356 years ago, and yet, when I read it, especially the initial chapters, I have the impression of going through news feeds from the last 4 months, like from February until now, of course in relation to the COVID-19 pandemic. The sequence of events described by Daniel Defoe, the patterns of human reactions to the epidemic disease – all that is so incredibly similar to what we experience today that I have hard times to realize that what Daniel Defoe described took place 18 generations ago (if we count 25 years for one generational shift, by sociological standards).

That striking similarity gives tons of hope. Eighteen generations ago, people had just a small fraction of science and technology that we have today, and yet they pushed themselves through that deep shit, and there was another sunrise. It was plague, not COVID-19. It was a monster. Yet, there was another sunrise. What impressed me the most, I think, is the very end of that book, and I allow myself to quote it: “It was a common thing to meet people in the street that were strangers, and that we knew nothing at all of, expressing their surprise. Going one day through Aldgate, and a pretty many people being passing and repassing, there comes a man out of the end of the Minories, and looking a little up the street and down, he throws his hands abroad, ‘Lord, what an alteration is here! Why, last week I came along here, and hardly anybody was to be seen.’ Another man—I heard him—adds to his words, ‘’Tis all wonderful; ’tis all a dream.’ ‘Blessed be God,’ says a third man, and and let us give thanks to Him, for ’tis all His own doing, human help and human skill was at an end.’ These were all strangers to one another. But such salutations as these were frequent in the street every day; and in spite of a loose behaviour, the very common people went along the streets giving God thanks for their deliverance. It was now, as I said before, the people had cast off all apprehensions, and that too fast; indeed we were no more afraid now to pass by a man with a white cap upon his head, or with a cloth wrapt round his neck, or with his leg limping, occasioned by the sores in his groin, all which were frightful to the last degree, but the week before. But now the street was full of them, and these poor recovering creatures, give them their due, appeared very sensible of their unexpected deliverance; and I should wrong them very much if I should not acknowledge that I believe many of them were really thankful”.  (Excerpt From: Daniel Defoe. “A Journal of the Plague Year / Written by a Citizen Who Continued All the While in London”. Apple Books.”)

As I am rereading that book by Daniel Defoe, and as I meditate over it, I realize how bloody tough we, humans, are. The city of London (where the events described by Daniel Defoe take place) is still there. It is thriving. We moan, we bicker, we take grand moral stances over events we don’t even have full knowledge about, and yet, at the bottom line, when the shit hits the fan, we just clench our teeth, dig our heels into the sand, and survive. Wonderful.

I am going into a slightly different path of thinking, as compared to my recent updates. The initial hypothesis of that entire thread of research is 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 focus on the connection between cities and the countryside, at the aggregate level. In Figure 1, below, you can see indexed trends in three aggregate variables: a) density of urban population denominated in units of general density in population (which I will further designate, for the sake of presentational convenience, as [DU/DG]) b) cereal yield in kg per hectare, and c) total surface of agricultural land. In order to assure comparability, I represented all those three metrics as constant-base indexes, where values from the year 2000 make 1.

As you can see, I provided direct links (to the database of the World Bank) as regards two variables out of the three. I did it because the first variable is a compound construct of my own, made out of primary data supplied by the World Bank. I took the numbers regarding aggregate urban population, and I divided it by the aggregate surface of urban land, which yields the coefficient of density in urban population. In the next step, I want to use that coefficient so as to measure the relative social difference between cities and the countryside. In order to do so, I divide the coefficient of density in urban population by the coefficient of general density in population. In other words, I check how many general densities of population we need in order to have one unit of density in urban population.

Since 1961 through 2016, the relative social distance between cities and the countryside, measured at the planetary level, has been growing steadily, almost in a straight line. As a matter of fact, that line is so straight that it is hardly believable. When you find a straight line of trend, which sort of cuts across waves and bumps in other variables, you are either completely wrong or deeply right. Linear change over time is a rare beast in the realm of measurable phenomena. However, as I measure local growth rates in that [DU/DG] metric, they keep sticking to 1% a year. Yes, since 1961, the average social distance between cities and the countryside has been growing at a nearly constant rate of 1% a year.

Against that almost suspiciously consistent change in the density of urban populations across the planet, agriculture has been changing at two different speeds. Cereal yield per hectare has grown, at the end of the day, yet its growth has been happening at a much more familiar, bumpy rate, sort of two steps forward, one step back. The aggregate surface of agricultural land presents a stairway type of change: two plateaus separated by a sudden jump in the beginning of the 1990ies.

Summing up, as social density in cities has been hyper-consistently drifting away and above general social density, agriculture kept adapting, mostly by consistent growth in agricultural productivity. Interestingly, all three trends, although different in shape, are strongly correlated, which is shown in Table 1, below Figure 1. Those correlations are so strong that it all looks like one compound phenomenon, with just a little entropy inside.  

As local expansions of agricultural land have kept happening, yet they also kept being compensated, at the global scale, by decreases in other parts of the world. On the long run, between 1961 and 2016, the total surface of agricultural land in the world has grown by 11,4 millions of square kilometres. Apparently, more than 55% of that aggregate growth happened in the short window between 1989 and 1992 seems to be only moment since 1961 when the total global surface of agricultural land unequivocally went up. That big leap in agricultural land, by about 6,3 millions of additional square kilometres, happened mostly in countries classified as ‘Middle Income’, and was prevalently concentrated in two of them: Kazakhstan and Russian Federation. The long-term geography of change in agricultural land, between 1961 and 2016, is shown in the form of a map in Figure 2. Kazakhstan, Russian Federation and China keep the podium. A freakish idea comes to my mind. Between 1989 and 1992, a dramatic increase happened in the surface of agricultural land on the planet. It happened mostly in the former Soviet Union, which, precisely then, was dissolving. Are the two phenomena connected? Is it possible that the dissolution of the biggest country in the world was a collectively intelligent response of our planetary human species to the necessity of having more land to grow food?  

Figure 1

Table 1 – Pearson correlation between density of urban population, agricultural land, and cereal yield per hectare

 Density of urban population, denominated in units of general density in population: World
Surface of agricultural land, km2 : World0,927149105
Cereal yield, kg per hectare of arable land: World0,984881004

Figure 2

Now, I focus on the ‘technological change’ part and I formulate two other hypotheses. Firstly, I claim that technological change manifests collective intelligence in human societies. Secondly, Artificial Intelligence, the development of which marks technological change of the last two decades, emulates collective intelligence much more than individual one.

Why do I claim at all that technological change manifests collective human intelligence? Isn’t it rather individual intelligence saying, at some point in time, something like ‘Enough! Enough of those stupid sleighs. We need wheels!’? It is true to some extent, more specifically to the extent that individually expressed ideas really push technology forward. Still, those ideas work similarly to the way that a ball is being played in a team game. When we play basketball, most individual actions with the ball are effective and efficient only to the extent of cooperation from the part of other players in the team. An innovative idea is like that ball: its needs to be passed around and collectively played.

Collective intelligence can be described as the ability to collectively figure out what to do when we collectively have no clue what to do. This is a very synthetic description of mechanisms which require a deeper insight. We collectively experience problems when we share collective beliefs, acceptably grounded in empirical facts, that something happens the way most of us doesn’t want it to happen. This is the gap between expectations and reality. Collective experience is that something doesn’t work as we would like it to work.

Now, let’s introduce the distinction between simple discomfort with reality, on the one hand, and the experience of inefficiency in our behaviour, on the other hand. Life is brutal, in general. Yes, it is beautiful as well, and yet we experience beauty largely by opposition to ugliness. We perceive the brutal beauty of existence mostly as gradients of change, and not really as absolute states of things (see, for example: We really don’t see small change). We are uncomfortable with some changes in reality, and sometimes that discomfort triggers collectively coordinated action. That’s the first moment of assessment as regards us being collectively smart: can we coordinate to take action, or cannot we? The next level is being efficient in that action. Have we achieved the results we expected to achieve?

We have two levels of collective ambition, whence two possible levels of collective frustration, namely with the failure to coordinate, or with the insufficient outcomes of coordination. Both failures incite to do something about that imperfect social coordination of ours. When we dig a bit into the depth of the problem, we usually discover at least one of the two things: we are either too rigid or too random in coupling individual behaviours into the beautiful dance of well-rounded teamwork. Too rigid means that person A always does what person B expects them to do, whence nearly perfect a stationarity of their common action. Too much randomness manifests as the person A hardly ever doing what person B expects them to do, whence a well-understandable frustration in the person B and a lack of trust in coordination.

Good coordination relies on a behavioural pattern called correlated coupling, which manifests as the person A responding flexibly and yet predictably to signals sent by person B, and vice versa. Being both flexible and predictable in my response to other people’s signals means that my own action takes a recurrent form – which sends other people the reassuring signal ‘I get it, guys, carry on’ – and yet that form is somehow scalable. When I am an engineer and my boss asks me ‘to give that engine a bit of nerve’, he or she can trust – if my behaviour is correlatedly coupled with theirs – that I will come up with a range of possible solutions for said nerve, and I will select the most appropriate.

We are collectively intelligent when, as a collective, we have the ability to spot recurrent cases of too rigid behavioural coupling, or too much randomness in collective coordination, and transform those situations into correlated coupling. Let’s take the example of a simple, old technology: the use of windmills to power querns, instead of grinding cereal grain by hand. I think it was some 20 years ago: I messed around a bit with a reconstructed, man-powered quern (you now, two flat stones on a common rotating axis), just to see how it felt, centuries ago. When I gave it a try, I understood why the baking of bread became really widespread across Europe only with the diffusion of windmills and watermills. Grinding grain into flour by the sheer force of human muscle is, at the end of the day, a zero-sum activity, energy-wise. You burn approximately as much energy when grinding as you can have from the flour you obtain.    

Technologies give us flexibility and predictability. The wind-powered quern, back in the day, as compared to the man-powered one, assured smooth grinding of grain and scalability: faster or slower, greater quantity per day or a smaller one etc. Technologies allow replacing fixed coupling in behaviour, or a random one, with the functional elegance of correlated coupling.

Now, let’s get into the process of implementing new technologies. When I do it individually, it is a sequence of trials and errors. I try something, and it works smoothly, it works just sort of, or it doesn’t work at all. Depending on the exact outcome, either I say ‘Hooray! Nailed it!’, or I go ‘Well, it needs some improvement’, or, finally, I say things I could be ashamed, later on, of having said at all. When I need improvement, it slows me down, obviously. Still, when my new contrivance seems to be working just perfectly, it can slow me down even more. I am satisfied with immediate outcomes, and a prolonged chain of satisfactory results can prevent me from seeing an entirely different, alternative way of doing things.

When lots of ‘I’ do the same thing – after all, each human is an ‘I’ – it is different. Each ‘I’ comes up with somehow different results, and these can be instantaneously compared. The ‘I’s which do the best job stick out of the crowd. Their ways are likely to be reproduced by other people, whilst the clearly suboptimal methods fall into oblivion. Many humans experimenting with solutions to the same problem are like as many living organisms attempting to mutate in the presence of an exogenous stressor. The more organisms experiment with themselves, the greater the likelihood of successful mutations. In biology, this mechanism is called ‘adaptive walk in rugged landscape’ and can be applied in social sciences. When many social entities experiment with themselves in order to cope with an exogenous pressure, such as the pressure to survive or to climb the ladder of social hierarchy, some of those entities (e.g. persons, businesses, political parties) are more successful than others. Best practices are retained and reproduced in the future. This is collective intelligence in solving collective problems.

Cities facilitate technological change because they reinforce that sort of next-to-my-neighbour innovation. In cities, due to high density of population, it is simply easier to observe others, to emulate their successes or steer clear of the way they failed. It is easier to navigate through the muddy waters between conformism and individuation. Cities are instances of enhanced collective intelligence.

I use simple neural networks to emulate the way that our human collective intelligence works. I used it in this specific thread of research (see The perfectly dumb, smart social structure), you can find it in a published article on energy efficiency, and in another, unpublished paper. As I keep meddling with neural networks, I am more and more convinced that artificial intelligence emulates the collective intelligence of human societies much more than individual intelligence of one human being. Why do I make such a claim? Because neural networks work well when they can experiment with quasi-random combinations of weights assigned to many input variables, i.e. many different phenomena. With just one input variable, a neural network usually goes completely bananas. No learning whatsoever. The necessity of multiple input makes me think about many social entities trying to do something, rather than just one human.     

Discover Social Sciences is a scientific blog, which I, Krzysztof Wasniewski, individually write and manage. If you enjoy the content I create, you can choose to support my work, with a symbolic $1, or whatever other amount you please, via MY PAYPAL ACCOUNT.  What you will contribute to will be almost exactly what you can read now. I have been blogging since 2017, and I think I have a pretty clearly rounded style.

In the bottom on the sidebar of the main page, you can access the archives of that blog, all the way back to August 2017. You can make yourself an idea how I work, what do I work on and how has my writing evolved. If you like social sciences served in this specific sauce, I will be grateful for your support to my research and writing.

‘Discover Social Sciences’ is a continuous endeavour and is mostly made of my personal energy and work. There are minor expenses, to cover the current costs of maintaining the website, or to collect data, yet I want to be honest: by supporting ‘Discover Social Sciences’, you will be mostly supporting my continuous stream of writing and online publishing. As you read through the stream of my updates on , you can see that I usually write 1 – 3 updates a week, and this is the pace of writing that you can expect from me.

Besides the continuous stream of writing which I provide to my readers, there are some more durable takeaways. One of them is an e-book which I published in 2017, ‘Capitalism And Political Power’. Normally, it is available with the publisher, the Scholar publishing house ( ). Via , you can download that e-book for free.

Another takeaway you can be interested in is ‘The Business Planning Calculator’, an Excel-based, simple tool for financial calculations needed when building a business plan.

Both the e-book and the calculator are available via links in the top right corner of the main page on .

You might be interested Virtual Summer Camps, as well. These are free, half-day summer camps will be a week-long, with enrichment-based classes in subjects like foreign languages, chess, theater, coding, Minecraft, how to be a detective, photography and more. These live, interactive classes will be taught by expert instructors vetted through Varsity Tutors’ platform. We already have 200 camps scheduled for the summer. .

Fringes and layers: how do cities develop resilience


There is a collective intelligence, I mean a lot of us, humans, indulge in thinking how smart we are, and this collective intelligence strives to sustain long-term access to cappuccino, which, in turn, most frequently, requires the presence of cities, conveniently disposed across the landscape. The access to cappuccino is put in jeopardy by secondary outcomes of a new pathogen making itself comfortable in the social space made of human interactions. Some human interactions become riskier than others. At first, we think all human interactions are dangerous, we entrench and yield to fear. Then, both science and individual capacity to learn step in and allow defining those reasonably safe social contacts, conveying low risk of infection, and we start distinguishing them, more and more finely every month, from the risky human interactions. As a matter of fact, we had been doing it for millennia, and stopped just recently, around 1970, when widespread vaccination made us progressively forget the terror of typhoid, polio, tuberculosis etc. Before we started forgetting, we used to follow some simple principles. Hang out with people whom you know and can observe for the time sufficient for an infection to manifest itself. Come close to those who are manifestly healthy. Shake hands, hug, kiss, share kitchenware and have sex only with those whom you can expect to be like really healthy. When you need to make acquaintance with complete strangers, select those whom you can be introduced to (or who can be introduced to you, depends on the arrow on the vector) by a person from the former category of knowingly healthy persons in your social circle. When hanging out with strangers, use all kinds of Ninja tricks: veils, hats with large brims, scarves nonchalantly put around the lower part of the face, fancy silken or leather gloves etc. Arrange the space indoors so as to separate rooms with doors and curtains, whilst putting many windows in external walls. That allows partly independent circulation of air in separate spaces. If you happen to become someone important, like a prince or a wealthy merchant, a lot of people will have some business to talk to you about, and then be smart enough to receive their visit in a space with significant social distance, like you sitting on an ornate, elevated stool and them a few yards in front, lower than you and breathing into the floor, not in front of them. It is fascinating and bemusing, how similar is our present experience with COVID-19 to historically documented episodes of plague in European cities. Reading Daniel Defoe’s ‘Journal of The Plague Year’, published in 1665, offers a lot of interesting insights in that respect, including the problem of asymptomatic carriers (!).  

All those small smart details of daily life sum up to paying particular attention to epidemic risk. Each of us, average hominids knowing what a cappuccino is, become more and more likely to endorse social roles involving recurrent, predictable interactions with knowingly healthy people, and just a fringe of society, those lords Byron-like types, or the really-f**ked types, as a matter of fact, remain likely to step into shoes that require abundant, haphazard interactions   with people of unknown exposure to the pathogen currently in fashion. At the easily conceptualizable level, we strive to sustain systemic access to cappuccino – i.e. to sustain the market-based, open economy which we know just works – whilst progressively modifying our social roles so as to operate in closed social circles, with precisely defined points of contact with other circles, and barriers to contact with non-circled people.

Cities are demographic anomalies, and inside those anomalies the density of population is abnormally high. According to my research, the wealthier the country, and the greater the consumption of energy per capita in that country, the smaller the difference between urban density of population and the non-urban one. That difference shrinks down to a point, which looks like a threshold: developed social structures hardly descend below urban density of population twice as high as the general density of population (see Demographic anomalies – the puzzle of urban density). Cities define themselves, and this is one side of the coin. Throughout history, cities have been emerging in specific places because some people, dwelling in those places, wanted a city to be around. The other side of the coin is visible from space, i.e. from satellites: urban land displays a specific agglomeration of man-made structures visible during the day, and a high concentration of night-time lights. Once again, there is a threshold in that agglomeration of structures and lights, beyond which your average alien, observing Earth from a distance, could informingly say to another alien: ‘Look, Jkitths, they have a city over there! I wonder how much is a four-star hotel night’.    

Interestingly, the two sides of this coin usually don’t match. The stretch of land qualifiable as urban satellite-wise is usually larger than the officially proclaimed expanse of urban territory in that place. Cities usually define themselves inside a de facto urban territory, and ‘inside’ means there is a margin between the physical boundaries of that typically urban agglomeration of structures and night-time lights, on the one hand, and the legally defined boundaries of the city. Normally, cities define themselves by acknowledging the urban nature of a place, not by arbitrarily declaring a place urban. There are exceptions, such as the programme of new cities in Egypt (Attia et al. 2019[1]) or the founding of the city of Gdynia, in my native Poland, in 1926.

An interesting question emerges: to what extent does new epidemic risk, such as that generated by COVID-19, modify the objectively observable agglomeration of structures and night-time lights? On the other hand, how does epidemic risk affect the way that cities define themselves? Intuitively, I would say that acknowledged epidemic risk leads to spreading ourselves over a larger territory, i.e. to temporary slowdown in the speed of growth in the density of urban population, or even to a temporary reversal towards lower density.   

Life in the presence of epidemic risk had been city slickers’ daily bread for centuries, and yet cities have grown up from existing as demographic anomalies to being demographically dominant in our today’s civilisation (55,27% of mankind lived in cities in 2018).

In 2016, I visited Colchester , reputedly the oldest city in Britain. I was bemused to observe the contrast between something which, fault of a better expression, I can describe as multiple layers of being a city. There is that old castle, dating back to Middle Ages, surrounded by the Old Town. It all looks like a really old car with new covers on the seats. Really strange. In a wider radius around the old core, various types of peripheral structures stretch. There is the not-as-old-yet-quite-old a part, which I tentatively date at like the 18th century. There is a district which looks like a model industrial city from the 1970ies, i.e. an expanse of virtually identical, small terraced houses without apparent centre of gravity. There are patches of more modern buildings, like shopping malls or apparently recent residential blocks. There is the academic campus, displaying layers of its own: old concrete architecture from the 1970ies, combined with the most recent forms of wood and concrete structures (those latter ones look like Hobbiton, I swear). Colchester makes me think about people who have been resolute to be a city, in this specific place, and over centuries they were inventing and superimposing different ways and technologies to serve that purpose.

As I think about it, all the cities I know which have some solid history in them are like that. They are layered patchworks of physical structures. It is interesting. People who will come after us, centuries from now, are most likely to superimpose their urban structures over our contemporary ones, rather than put them somewhere else. Cities seem to be like cores of coagulation in civilization. Why? Why does it work this way? How does it apply to the possible adaptations of our urban space to the newly emergent epidemic risk?

As I read Adam Smith’s ‘Lectures on Justice’ (1766, published in 1896[2]), I realize that historically, cities have been allowed to make their own laws, and that legislative power has been so prominent over centuries that some classics of legal sciences, such as, for example, Herbert Hart, use the expression ‘municipal law’ to designate national legal systems, as opposed to international law. For centuries, cities have been largely defining themselves as demographic anomalies endowed with idiosyncratic, local institutions and jurisdictions. As a matter of fact, the last two centuries have seen a progressive transfer of those legislative powers from cities to national governments.

The impression that cities make is not necessarily identical with their real size and importance. In Richard Cantillon’s ‘Essay on Commerce’ , dating from 1755, we can find the following claim: ‘It is generally supposed that half the inhabitants of a State subsist and have their homes in the town, the other half in the countryside’. Yet, in Fernand Braudel’s ‘Civilisation and Capitalism’, we can find a completely different estimation, namely some 16% of the French population being urban in mid-18th century. What we think is urban, around us, is not necessarily as urban as we think.

Sometimes, cities define their own existence in strange, apparently counterintuitive places, such as the city of Mulhouse AKA Mulhausen, in Alsace, France.  According to Albert Metzger (Metzger 1883[3]), the city of Mulhouse was just in the middle of a territorial conflict since its very beginnings, around the year 1150. Founding a city there was economically logical, with the proximity of the river Rhine, and yet, politically, it was like asking for trouble. On some occasions, such risky locations turn into permanent failures. If one day you visit the city of Frombork, in Northern Poland, where Nicolaus Copernicus wrote his book ‘De revolutionibus orbium coelestium’, you will immediately understand why he was so much into writing this book. Besides the big cathedral, whose estate Nicolaus Copernicus was in charge of, there is hardly anything else there. Yes, there is a commercial port, and quite an old one, by the way, still the city founders were obstinate to locate that port, and make it prosper, between two other big ports: Gdansk and Elblag. As soon as Frombork had established any kind of presence in the trade across the Bay of Gdansk, one of those two big neighbours (sometimes both) would send an armed expedition in order to explain the delicate nuances of trade in a small market. It was like trying to start a small electronic business in a market, where you have just Tesla and General Electric. Doomed to fail. Never been much of a city, Frombork. Ambitions are not enough. The final ‘and yet’ of the story, though, is that despite all the false starts and adversities, Frombork has kept being a city, and it technically still is a city, although it looks like a village with a big church in the middle.

When cities grow and give birth to new social roles, some of those social roles are ugly. This is the dark side of urbanisation: the growth of crime. Here comes an interesting book, written by William Howe and Abraham Hummel, and equipped with arguably one of the longest titles in the history of literature: ‘Danger! A True History of a Great City’s Wiles and Temptations. The Veil Lifted, and Light Thrown on Crime and its Causes, and Criminals and their Haunts. Facts and Disclosures’ (Howe & Hummel 1886). The book focuses on the city of New York – which can be safely deemed as the Incredible Hulk of urban expansion – and shows, in a casual and completely non-scientific way, how cities allow the burgeoning of social pathologies in many ways. Cities provide good shelter against weather, and thus allow the phenomenon of slumming: people living technically indoors, but not quite, some of them just sometimes, some of them homeless and yet not as much exposed to the dangers of sleeping outdoors as they would be in the countryside. You need to be tough like boot to be homeless in Siberia, but all you need in order to be homeless in Paris is a bad divorce or depression.

Cities give shelter to people who could hardly survive, and certainly not thrive in the countryside. Cities give opportunities to sociopaths and psychopaths, too, and this is another thread explored by Howe and Hummel. The abnormally high density of population in cities offers unusual opportunities to people with deranged personalities, prone to violence and manipulation. They can grow as kingpins, or seconds thereto. In the countryside they would much more likely expect the local community to put an end to their vile life through a completely accidental fire in their house.      

An interesting, recent article by Kostas Mouratidis (Mouratidis 2019[4]) suggests that cities develop and change through a cyclical sinewave in the density of urban population. As density grows, in the presence of relatively constant technological base, subjective well-being of city dwellers decreases, and they sprawl around. As they radiate towards comfortable suburbs, said suburbs lose much of their charm, and, with time, living in those suburbs boils down to spending more time in traffic jams. The phenomenon, known as urban sprawl, creates potential energy for a reverse movement, from peripheries back to the city centre, and that movement comes along with significant technological change, mostly in technologies accessible to the average city slicker in the form of urban infrastructure.   

I found at least one author who develops a path of research similar to mine: I am talking about Sir Peter Hall (Hall 2000[5]; Hall 2003[6]). He argues that cities give peculiar incentives to the emergence of cultural industries, i.e. industries marked by quick race for dominant position, based on creativity and innovation. Emergence is different from continuous development: Peter Hall observes, with the example of selected British cities, that creative industries tend to be an economic fringe in cities, rather than the mainstream of business. There seems to exist a threshold of 5% share in the city’s GDP, which creative industries can grow within. Anything over and above those 5% is apparently doomed to disappear shortly. Interestingly, that creative fringe of economic life in cities tends to specialize. Peter Hall names three big, typical vectors thereof: art (e.g. Paris, Florence), industry (e.g. Silicon Valley or Manchester), and finally urban creativity in itself (once again, Paris comes as an example, although places like Vienna or Prague seem to fit the same mould).

New social roles emerge in cities due to the phenomenon of emergent fringes. Cities allow significant growth at the tails of statistical distribution. Fringe patterns of behaviour can thrive, both as creative industries, and as social pathologies. This is how cities adapt and stay resilient to exogenous disturbances, epidemic risk included. I intuitively feel that cities of today will be adapting to the pandemic of COVID-19 in a similar way: fringe behaviours will emerge, both at the desirable creative end of the spectrum spread over the scale of ethical values, and at the undesirable end of social pathologies. The latter seem to be attached to the former, like the price of progress. Probably, we will temporarily spread in space: urban sprawl will advance for a certain time. We will be seeking more space around us, so as to reduce epidemic risk, and a new generation of technologies, such as vaccines, testing and decontamination, is likely to counter that sprawling propensity, bringing city dwellers a bit more densely together, one more time. 

Discover Social Sciences is a scientific blog, which I, Krzysztof Wasniewski, individually write and manage. If you enjoy the content I create, you can choose to support my work, with a symbolic $1, or whatever other amount you please, via MY PAYPAL ACCOUNT.  What you will contribute to will be almost exactly what you can read now. I have been blogging since 2017, and I think I have a pretty clearly rounded style.

In the bottom on the sidebar of the main page, you can access the archives of that blog, all the way back to August 2017. You can make yourself an idea how I work, what do I work on and how has my writing evolved. If you like social sciences served in this specific sauce, I will be grateful for your support to my research and writing.

‘Discover Social Sciences’ is a continuous endeavour and is mostly made of my personal energy and work. There are minor expenses, to cover the current costs of maintaining the website, or to collect data, yet I want to be honest: by supporting ‘Discover Social Sciences’, you will be mostly supporting my continuous stream of writing and online publishing. As you read through the stream of my updates on , you can see that I usually write 1 – 3 updates a week, and this is the pace of writing that you can expect from me.

Besides the continuous stream of writing which I provide to my readers, there are some more durable takeaways. One of them is an e-book which I published in 2017, ‘Capitalism And Political Power’. Normally, it is available with the publisher, the Scholar publishing house ( ). Via , you can download that e-book for free.

Another takeaway you can be interested in is ‘The Business Planning Calculator’, an Excel-based, simple tool for financial calculations needed when building a business plan.

Both the e-book and the calculator are available via links in the top right corner of the main page on .

You might be interested Virtual Summer Camps, as well. These are free, half-day summer camps will be a week-long, with enrichment-based classes in subjects like foreign languages, chess, theater, coding, Minecraft, how to be a detective, photography and more. These live, interactive classes will be taught by expert instructors vetted through Varsity Tutors’ platform. We already have 200 camps scheduled for the summer. .

[1] Attia, S., Shafik, Z., & Ibrahim, A. (2019). New Cities and Community Extensions in Egypt and the Middle East. Springer Berlin Heidelberg,.

[2] Smith, A. (1896). Lectures on justice, police, revenue and arms: Delivered in the University of Glasgow. Oxford: Clarendon Press.

[3] Metzger, A. (1883). La république de Mulhouse, son histoire, ses anciennes familles bourgeoises et admises à résidence, depuis les origines jusqu’à 1798. Henri Georg.

[4] Mouratidis, K. (2019). Compact city, urban sprawl, and subjective well-being. Cities, 92, 261-272,

[5] Hall, P. (2000). Creative cities and economic development. Urban studies, 37(4), 639-649.

[6] Hall, P. (2003). Cities in civilization: culture, innovation and urban order. Journal of Irish Urban Studies, 2, 1-14.

The knowingly healthy people


I am returning to the thread of research devoted to cities and their role in the human society. My goal is to outline an informed prediction as regards the impact of COVID-19 pandemic on our civilisation, and the prediction is based on a stylized fact I can observe: the most severe outbreaks of COVID-19 take place in densely populated areas, cities or conurbations.

As I connect two threads of my writing and blogging, namely research on cities and collective intelligence, on the one hand, and my investment strategy, on the other hand, one big coin dropped, with ‘logistics’ stamped in that place where traditional coins would display the profile of some king or queen. If my intuition is correct, i.e. if COVID-19 is really forcing us and is going to force us even more into a spatial rearrangement of our settlements, logistics will be a pivotal industry. Here comes that funny coincidence. In Poland, we have that express delivery company, Integer Capital Group, which has pretty much revolutionized the landscape of parcel deliveries. In United States, there is another Integer, namely Integer Holdings Corporation, specializing in portable medical devices, such as neuro- and cardio- modulators. Unfortunately, only the second Integer has its stock publicly listed and available to small investors. Still, there are stocks such as Deutsche Post (the mothership of DHL), UPS or Fedex, which are all booming, stock-price-wise, and them booming seems to have strong foundations in the economic environment. Cool. Looks like I have just found another wave to ride (see The moment of reassessment for the underlying logic of the concept). The strategy I am forming in my mind consists in selling out my positions in Airway Medix and Bioton, whose fundamentals seem a tiny bit wobbly, then take the next rent I collect from that apartment in town, and invest it all in a basket of stock made of four companies, all of them doing logistics: Deutsche Post, UPS, Wisetech, and XPO Logistics. This time, under those hyperlinked names of companies, instead of the habitual ‘investors relations’ websites, my readers can find Excel workbooks with the technical analysis I did, i.e. moving average price (the ‘Mov’), mean reverted price and volumes traded (under the ‘MR’ label), and extrapolated return on the last closing price (‘Return’), whilst in the spreadsheet labelled ‘Sheet1’ you can find the source data with equations that I use to transform it. 

Right, I went off track. I was supposed to focus on cities, COVID-19 and stuff. Still, what do you want: things just connect in surprising ways. The entire topography of those surprising ways is called life. Now, as my internal curious ape is back on track of the serious science to do, I am formalizing my scientific take on two issues: the measurement of urban space, and geographic patterns of the COVID-19 pandemic. Here comes an interesting paper, still at the stage of preprint: ‘Time, Space and Social Interactions: Exit Mechanisms for the Covid-19 Epidemics’ by Scala et al. 2020[1]. The authors attempt to trace the possible scenarios of SARS-Cov-2’s epidemic spread in Italy after the lockdowns are lifted. They use a simple compartmental epidemic model, and I use their model as base for my own thinking about the long-term impact of COVID-19 on our society, mostly on the way that cities live their life. What? Cities are not alive? They don’t live any life, they just function? Well, just go, one day, and observe a city at dawn, as people inside it start going about their business. Just look how those streaks of light, at sunrise, move through that giant urban body, akin to a bloodstream. Those things (i.e. cities) are alive, and we are alive in them.

Scala et al. 2020 stroll down the same cognitive avenue which I am taking: they assume that our exposure to COVID-19 is a combination of three types of factors: biological (our biology vs that of the virus), technological (the really available science we have), and social, i.e. the way we interact and hand the virus over to each other. This distinction is useful to remember. The way most countries go through the epidemic curve is mostly social. We observe a mounting wave of contagion, at first, then a peak comes, which we pass over, and the curve starts to flatten. All that plays out over something like 8 ÷ 11 weeks. Technology did not change during those 11 weeks. I mean, even in Star Trek it wouldn’t. Biology stays more or less the same, both on our part and on the part of the virus. What makes that specific shape of the epidemic curve is our behaviour.

This pandemic paved the way to fame for a previously shy coefficient, the R0. Hello everybody, I am R0. I am the average number of people that can be infected by one already infected and infectious person. I am the proportion between the coefficient β of transmission, and the coefficient γ of removal. The latter means either recovery or death. Whichever happens, the given person is removed from the ranks of those susceptible to infection. Thus, I, R0, spell: R0 = β/γ. The γ is essentially made of biology and technology. It is all about the way our body responds to the pathogen, and the way that doctors can have a few words to say about it. On the other hand, the coefficient β of transmission is a mixture of biology and social behaviour. It is about the way we can infect each other by coughing, and about the odds that we have any opportunity to cough at each other. The β can spell β = , where C is the rate of social contact between people, and λ is the likelihood of infection once such contact happens.

Lockdowns have driven the C factor down, in response to an alarmingly rapid increase number O of clinically observed patients with acute symptoms of COVID-19. It is important to understand: as societies, we do not react to the number of people infected and we do not even react to the number of people with acute symptoms. When was it the last time we closed all the roads and cancelled all traffic thereon because of the number of people injured in traffic-related accidents? Have we ever been tempted to do so in the view of people getting serious cardio-vascular problems as a result of them spending hours a day in their cars and being, most of those hours, viscerally pissed about the way they are? No, we just make more comfortable cars and roads, because all those bad things in traffic happen at pretty a constant rate. We, humans, are programmed to notice gradients of change rather than absolute states (see e.g. We really don’t see small change and The kind of puzzle that Karl Friedrich was after). The pandemic introduced a new gradient of disquieting change into our social system, and we reacted by taking cover. 

Social response to the pandemic can be represented very simply as elasticity of social contacts to change in the occurrence of acute COVID-19 cases, or ∆C/[∆(O/N)] (once again, O stands for the aggregate number of acute, clinically observed cases). In the presence of epidemic danger – and this specific danger is going to stay with us for a while – we react by inducing a sinusoid pattern into our ∆C: we lock down, then we release etc. As I said before, I deeply believe that lockdowns as such manifest panic behaviour at the collective level rather than a rational response. They are not sustainable economically, and even psychologically. Whatever we reward, we reinforce, and whatever we reinforce grows. If we reward fear of social contact, that fear is going to grow and our European history tells us very explicitly what happens next: isolated colonies of (allegedly) sick people, erosion of socially cohesive behaviour, lynching etc. Question: how can we develop a collectively rational reaction to the pandemic, whilst staying functional as a society? Answer: by modifying our set of social roles so as to be flexible in the ∆C department, and so as to get healthier and more resilient to infections, thus to drive down the λ likelihood of serious infection due to social contact.

Question: are there any historical precedents of societies purposefully changing their repertoires of social roles so as to achieve those two outcomes? Well, yes, and we keep doing it all the time. A good person is clean, right? We don’t like interacting with smelly people, and we socialize easily with folks who are visibly clean in their personal hygiene and wear clean clothes. We like the company of manifestly healthy people much more than the company of someone obviously sick. We shake hands only when we have reasonable chances to shake a clean hand. We sustain an elaborate game of social rivalry where a higher position in hierarchy means a bigger personal space indoors, both at work and at home.

We have a set SR = {sr1, sr2, …, srm} of ‘m’ social roles. Each social role sri is characterized by a frequency of direct, potentially infectious social interactions – the coefficient C(sri) – and by a probability p(sri) that any given individual endorses that specific role. The overall intensity C of such interactions in the given society is a weighted average of individual intensities and comes as C = ∑ [p(sri)*C(sri)]. At this point, I return to the assumption I phrased out in ‘City slickers, or the illusion of standardized social roles’: social roles are essentially individual and idiosyncratic. Categorial social roles, such as ‘a doctor’, ‘a housewife’ etc. are cognitive simplifications that we build in order to save bandwidth in our brain. Therefore, the C(sri) coefficient is really local and individual, and the summation sign ∑ in the C = ∑ [p(sri)*C(sri)] expression has a lot of summing work to do.  

When we want to cut down our overall C, and do it more sensibly than by closing all hairdressers for 2 years, we need to reshape our C = ∑ [p(sri)*C(sri)], i.e. we need to increase the prevalence p(sri) of social roles with relatively low C(sri), and reduce the occurrence of those who go the opposite, contact-abundant way in their C(sri). Yes, ‘who go’, and not ‘which go’. They are idiosyncratic phenomena in individual people, remember? 

In my update entitled ‘The perfectly dumb, smart social structure’, I sketched a piece of artificial intelligence supposed to simulate the interplay of social roles, and I ran a few experiments with it. Those experiments indicate that it is not really possible to kick selected social roles out of the system. Even if we attempt to, they end up by coming back, through one hole or another. On the other hand, the emergence of new social roles can naturally push the incumbent ones out of the system, as long as the society tries to keep all its marbles together and assures coherence between those newcomers and the incumbent ones.

The way out of the shitty spot which we are currently in, some place between the epidemic spread running amok, with reins dangling loosely on its neck, on the one hand, and the how-much-longer-can-we-stay-in-lockdown absence of sensible strategy, on the other hand, consists in triggering the creation of new social roles, endowed with relatively low incidence C(sri) of infectious social contacts, whilst maintaining as much social cohesion as possible.

We are facing a functional paradox. Cities are the only social contrivance that we have invented, so far, in order to speed up the creation of new social roles, and cities are demographic anomalies, displaying abnormally high density of population, thus by abundant social contacts. Now, with the pandemic around, we need to create new social roles with lower typical occurrence C(sri) of potentially infectious social contacts. Can we induce lower intensity of social interactions and maintain social cohesion in an environment which is naturally made for rich social interactions?

A thread of observation has come to my mind. We have had cities for quite a long time, right? Quite a long time means centuries and even millennia. We have also had epidemics in the past, and, as a matter of fact, we tend to forget how many of them we had, and how brutal they used to be. We tend to be anti-vaccine because we have been spoilt by the prevalence of vaccines and by the absence of serious epidemic outbreaks. Anyway, cities have been there for a long time, and epidemics had been there for a long time, sort of hand in hand, and cities have been and still are the most privileged spot of infection. Does it make sense? Somehow it does, and I want to understand how exactly.

Potentially infectious social contacts fall in two categories: contacts with people whom we don’t know or haven’t checked on for a long time, for one, and contacts with people heavily exposed to other infectious contacts in their environment. Thus, I need to introduce a scale of infectious risk in social interactions associated with any social role sri in the set SR = {sr1, sr2, …, srm}. I obtain something like the Itô calculus: an integral of social interactions inside the integral of a social role. It looks complicated, but we can simplify it by assuming that any set SR = {sr1, sr2, …, srm} of ‘m’ social roles is coupled with a set SC = {sc1, sc2, …, scn} of ‘n’ social interactions. The set SC is structured over an axis (dimension) of infectious risk. I can approach risk in a classical way, called the VaR method AKA Value-at-Risk: risk is a quantity, which, in turn, results from associating a given magnitude of damage with a probability of happening. In the case of an epidemic disease, the magnitude of damage ranges along a scale of severity in symptoms combined with their durability.

The so-far collective behaviour during the COVID-19 pandemic indicates that societies tend to minimize aggregate epidemic risk, defined as the arithmetical product: ‘likelihood of infection * severity of symptoms’. In the case of each infected person, the real danger are the most acute symptoms, and thus, in our practical perception of epidemic risk, severity of symptoms can be considered as a subjective constant: we are afraid of the worst that can possibly happen to us. When we reduce the epidemic risk by lockdowns and social distancing, we control the likelihood of infection.

In the presence of prolonged pandemic, and COVID-19 is likely to play out precisely this way, we are likely to minimize epidemic risk by remodelling our social roles. We can maximize the occurrence of predictable social interactions with knowingly healthy people, and minimize haphazard interactions with people of unknown exposure to infection. With a bit of science, we can reasonably narrow down the category of ‘knowingly healthy people’ to those whom we can categorize as non-symptomatic of COVID-10 for a sufficiently long time to assume they are non-symptomatic because they are either non-infected or they have successfully battled the infection, and not because they are asymptomatic. In plain terms, we discreetly observe someone for 3 weeks and we can make and educated guess as for what likelihood of infection that person conveys. Of course, this is just partly scientific, as we never quite know, and yet I think this is the way that people in the past – when epidemic diseases were daily bread, so to say – used to identify those whom they can reasonably hang out with.   

At this point, I am going back to the very definition of urban structures, and to the strange and interesting discrepancy in the assessment of what actual, present-time cities are (see Demographic anomalies – the puzzle of urban density). Cities are distinctive from the countryside by their abnormally high density of population, which is a proportion between population and the territory it occupies. There are two distinct methods of measuring both: administrative and GPW (Gridded Population of the World). I am sharpening my understanding of these two approaches so as to understand the dynamics of urban structures as such. My approach is empiricist. I hope to understand better the boundary between cities and the countryside through understanding the fine distinctions as regards the way we perceive that boundary.

Administratively, towns and cities are being defined by the law. In Antiquity and in the feudal society, legal definition of a town was that of a general privilege. City dwellers were allowed to do things, which people living in the countryside couldn’t do. It was frequently about holding a regular marketplace, and some sort of local government, incorporated as city council and/or the office of mayor. That privilege-based approach to the legal definition of a city seems to have vanished during the 19th century, when cities became nests of large-scale industry, and, interestingly, the number of officially defined cities seems to have frozen approximately at the same time. At some point in time – in Europe it could be around 1900 – the process of legal-administrative identification of urban settlements came to a virtual standstill. Further changes consisted in spatial extension of the already defined towns and cities. Interestingly, that pivotal moment coincided with the progressive elimination of epidemic diseases, through sanitation, healthcare, vaccination etc.

Discover Social Sciences is a scientific blog, which I, Krzysztof Wasniewski, individually write and manage. If you enjoy the content I create, you can choose to support my work, with a symbolic $1, or whatever other amount you please, via MY PAYPAL ACCOUNT.  What you will contribute to will be almost exactly what you can read now. I have been blogging since 2017, and I think I have a pretty clearly rounded style.

In the bottom on the sidebar of the main page, you can access the archives of that blog, all the way back to August 2017. You can make yourself an idea how I work, what do I work on and how has my writing evolved. If you like social sciences served in this specific sauce, I will be grateful for your support to my research and writing.

‘Discover Social Sciences’ is a continuous endeavour and is mostly made of my personal energy and work. There are minor expenses, to cover the current costs of maintaining the website, or to collect data, yet I want to be honest: by supporting ‘Discover Social Sciences’, you will be mostly supporting my continuous stream of writing and online publishing. As you read through the stream of my updates on , you can see that I usually write 1 – 3 updates a week, and this is the pace of writing that you can expect from me.

Besides the continuous stream of writing which I provide to my readers, there are some more durable takeaways. One of them is an e-book which I published in 2017, ‘Capitalism And Political Power’. Normally, it is available with the publisher, the Scholar publishing house ( ). Via , you can download that e-book for free.

Another takeaway you can be interested in is ‘The Business Planning Calculator’, an Excel-based, simple tool for financial calculations needed when building a business plan.

Both the e-book and the calculator are available via links in the top right corner of the main page on .

You might be interested Virtual Summer Camps, as well. These are free, half-day summer camps will be a week-long, with enrichment-based classes in subjects like foreign languages, chess, theater, coding, Minecraft, how to be a detective, photography and more. These live, interactive classes will be taught by expert instructors vetted through Varsity Tutors’ platform. We already have 200 camps scheduled for the summer. .

[1] Scala, A., Flori, A., Spelta, A., Brugnoli, E., Cinelli, M., Quattrociocchi, W., & Pammolli, F. (2020). Time, Space and Social Interactions: Exit Mechanisms for the Covid-19 Epidemics. arXiv: Physics and Society.

The perfectly dumb, smart social structure


I am developing directly on the mathematical model I started to sketch in my last update, i.e. in Social roles and pathogens: our average civilisation. This is an extension of my earlier research regarding the application of artificial neural networks to simulate collective intelligence in human societies. I am digging down one particular rabbit-hole, namely the interaction between the prevalence of social roles, and that of disturbances to the social structure, such as epidemics, natural disasters, long-term changes in natural environment, radically new technologies etc.

Here comes to my mind, and thence to my writing, a mathematical model that generalizes some of the intuitions, which I already, tentatively, phrased out in my last update. The general idea is that society can be represented as a body of phenomena able to evolve endogenously (i.e. by itself, in plain human lingo), plus an external disturbance. Disturbance is anything that knocks society out of balance: a sudden, massive change in technology, a pandemic, climate change, full legalization of all drugs worldwide, Justin Bieber becoming the next president of the United States etc.

Thus, we have the social structure and a likely disturbance to it. Social structure is a set SR = {sr1, sr2, …, srm} of ‘m’ social roles, defined as combinations of technologies and behavioural patterns. The set SR can be stable or unstable. Some of the social roles can drop out of the game. Just checking: does anybody among my readers know what did the craft of a town crier consist in, back in the day? That guy was a local media industry, basically. You paid him for shouting your message in one or more public places in the town. Some social roles can emerge. Twenty years ago, the social role of an online influencer was associated mostly with black public relations, and today it is a regular occupation.

Disappearance or emergence of social roles is one plane of social change, and mutual cohesion between social roles is another one. In any relatively stable social structure, the existing social roles are culturally linked to each other. The behaviour of a political journalist is somehow coherent with the behaviour of politicians he or she interviews. The behaviour of a technician with a company of fibreoptic connections is somehow coherent with the behaviour of end users of those connections. Yet, social change can loosen the ties between social roles. I remember the early 1990ies, in Poland, just after the transition from communism. It was an odd moment, when, for example, many public officers, e.g. maires or ministers, were constantly experimenting with their respective roles. That very loose coupling of social roles is frequently observable in start-up businesses, on the other hand. In many innovative start-ups, when you start a new job, you’d better be prepared to its exact essence and form taking shape as you work.

In all that story of social cohesion I essentially tap into swarm theory (see Correlated coupling between living in cities and developing science; Xie, Zhang & Yang 2002[1] ; Poli, Kennedy & Blackwell 2007[2] ; Torres 2012[3]; Stradner et al. 2013[4]). I assume that each given pair of social roles – e.g. the First Secretary of The Communist Party of China and a professional gambler in Las Vegas – can be coupled at three levels: random, fixed, and correlated. A relative loosening of social cohesion means that random coupling grows in relative importance, at the expense of the fixed, strictly ritualized coupling, and of the correlated one.

All in all, I hypothesise four basic types of social change in an established structure, under the impact of an exogenous disturbance. Scenario A assumes the loosening of cohesion between social roles, under the impact of an exogenous disturbance, with a constant catalogue of social roles in place. Scenario B implies that external stressor makes some social roles disappear, whilst scenarios C and D represent the emergence of new social roles, in two different perspectives. In Scenario C, new social roles are not coherent with the established ones, whilst Scenario D assumes such a cohesion.

Mathematically, I represent the whole thing in the form of a simple neural network, a multi-layer perceptron. I have written a lot about using neural networks as representation of collective intelligence, and now, I feel like generalising my theoretical stance and explaining two important points, namely what exactly I mean by a neural network, and why do I apply a neural network instead of a stochastic model, such as e.g. an Ito drift.

A neural network is a sequence of equations, which can be executed in a loop, over a finite sequence ER = {er1, er2, …, ern} of ‘n’ of experimental rounds, and that recurrent sequence of equations has a scalable capacity to learn. In other words, equation A takes input data, transforms it, feeds the result into equation B, which feeds into equation C etc., and, at some point, the result yielded by the last equation in the sequence gets fed into equation A once again, and the whole sequence runs another round A > B > C > …> A etc.. In each consecutive experimental round erj, equation A taps into raw empirical data, and into the result of the previous experimental round ej-1. Another way of defining a neural network is to say that it is a general, logical structure able to learn by producing many specific instances of itself and observing their specific properties. Both definitions meet in the concept of logical structure and learning. It is quite an old observation in our culture that some logical structures, such as sequences of words, have the property of creating much more meaning than others. When I utter a sequence ‘Noun + Verb + Noun’, e.g. ‘I eat breakfast’, it has the capacity to produce more meaning than a sequence of the type ‘Verb + Verb + Verb’, e.g. ‘Eat read walk’. The latter sequence leaves more ambiguity, and the amount of that ambiguity makes that sequence of words virtually useless in daily life, save for online memes.  

There are certain peg structures in the sequence of equations that make a neural network, i.e. some equations and sequences thereof which just need to be there, and which the network cannot produce meaningful results. I am going to present the peg structure of a neural network, and then I will explain its parts one by one.

Thus, the essential structure is the following: [Equation of random experimentation  ε* xi (er1)] => [Equation of aggregation  h = ∑ ε* xi (er1)] => [Equation of neural activation  NA = (a*ebh ± 1) / (a*ebh ± 1) ] => {Equation of error assessment  e(er1) = [O(er1) – NA(er1)]*c} => {[Equation of backpropagation]  [Equation of random experimentation + acknowledgement of error from the previous experimental round]  [ε* xi (erj) + e(er1)]} => {Equation of aggregation  h = ∑ [ε* xi (erj) + e(er1)]} etc.          

In that short sequential description, I combined mathematical expressions with formal logic. Brackets of different types – round (), square [] and curly {} – serve to delineate distinct logical categories. The arrowed symbols stand for logical connections, with ‘’ being an equivalence, and ‘=>’ and implication. That being explained, I can start explaining those equations and their sequence. The equation of random experimentation expresses what an infant’s brain does: it learns, by trial and error, i.e. my mixing stimuli in various hierarchies and seeing which hierarchy of importance, attached to individual pieces of sensory data, works better. In an artificial neural network, random experimentation means that each separate piece of data is being associated with a random number ε between 0 and 1, e.g. 0,2 or 0,87 etc. A number between 0 and 1 can be interpreted in two ways: as a probability, or as the fraction of a whole. In the associated pair ε* xi (erj), the random weight 0 < ε < 1 can be seen as hypothetical probability that the given piece xi of raw data really matters in the experimental round erj. From another angle, we can interpret the same pair ε* xi (erj) as an experiment: what happens when we cut fraction ε from the piece of data xi. it can be for one, or as a slice cut out of that piece of data.

Random experimentation in the first experimental round er1 is different from what happens in consecutive rounds erj. In the first round, the equation of random experimentation just takes the data xi. In any following round, the same equation must account for the error of adjustment incurred in previous rounds. The logic is still the same: what happens if we assume a probability of 32% that error from past experiments really matters vs. the probability of 86%?

The equation of aggregation corresponds to the most elementary phase of what we could call making sense of reality, or to language. A live intelligent brain collects separate pieces of data into large semantic chunks, such as ‘the colour red’, ‘the neighbour next door’, ‘that splendid vintage Porsche Carrera’ etc. The summation h = ∑ ε* xi (erj) is such a semantic chunk, i.e. h could be equivalent to ‘the neighbour next door’.

Neural activation is the next step in the neural network making sense of reality. It is the reaction to the neighbour next door. The mathematical expression NA = (a*ebh ± 1) / (a*ebh ± 1) is my own generalisation of two commonly used activation functions: the sigmoid and the hyperbolic tangent. The ‘e’ symbol is the mathematical constant e, and ‘h’ in the expression ebh is the ‘h’ chunk of pre-processed data from the equation of aggregation. The ‘b’ coefficient is usually a small integer, e.g. b = 2 in the hyperbolic tangent, and -1 in the basic version of the sigmoid function.

The logic of neural activation consists in combining a constant component with a variable one, just as a live nervous system has some baseline neural activity, e.g. the residual muscular tonus, which ramps up in the presence of stimulation. In the equation of hyperbolic tangent, namely NA = tanh = (e2h – 1) / (e2h + 1), the constant part is (e2 – 1) / (e2 + 1) = 0,761594156. Should my neural activation be the sigmoid, it goes like NA = sig = 1 / (1 + e-h), with the constant root of 1 / (1 + e-1) = 0,731058579.

Now, let’s suppose that the activating neuron NA gets excited about a stream of sensory experience represented by input data: x1 = 0.19, x2 = 0.86, x3 = 0.36, x4 = 0.18, x5 = 0.93. At the starting point, the artificial mind has no idea how important are particular pieces of data, so it experiments by assigning them a first set of aleatory coefficients – ε1 = 0.85, ε2 = 0.70, ε3 = 0.08, ε4 = 0.71, ε5 = 0.20 – which means that we experiment with what happens if x3 was totally unimportant, x4 was hardly more significant, whilst x1, x2 and x3 are really important. Aggregation yields h = 0,19*0,85 +0,86*0,70 + 0,36*0,08 + 0,18*0,71 + 0,93*0,20 = 1,10.

An activating neuron based on the hyperbolic tangent gets into a state of NA = tanh = (e2*1,10 – 1) / (e2*1,10 + 1) = 0.801620, and another activating neuron working with the sigmoid function thinks NA = sig = 1 / (1 + e-1,10) = 0,7508457. Another experiment with the same data consists in changing the aleatory coefficients of importance and seeing what happens, thus in saying  ε1 = 0.48, ε2 = 0.44, ε3 = 0.24, ε4 = 0.27, ε5 = 0.80 and aggregating h = 0,19*0,48 +0,86*0,44 + 0,36*0,24 + 0,18*0,27 + 0,93*0,80 = 1,35. In response to the same raw data aggregated in a different way, the hyperbolic tangent says NA = tanh = (e2*1,35 – 1) / (e2*1,35 + 1) = 0,873571 and the activating neuron which sees reality as a sigmoid retorts: ‘No sir, absolutely not. I say NA = sig = 1 / (1 + e-1,35) = 0,7937956’. What do you want: equations are like people, they are ready to argue even about 0,25 of difference in aggregate input from reality.

Those two neural reactions bear a difference, visible as gradients of response, or elasticities of response to a change in aggregate output. The activating neuron based on hyperbolic tangent yields a susceptibility of (0,873571 – 0,801620) / (1,35 – 1,10) = 0.293880075, which the sigmoid sees as an overreaction, with its well-pondered (0,7937956 – 0,7508457) / (1,35 – 1,10) = 0,175427218. That’s an important thing to know about neural networks: they can be more or less touchy in their reaction. Hyperbolic tangent produces more stir, and the sigmoid is more like ‘calm down’ in its ways.

Whatever the neural activation NA produces, gets compared with a pre-set outcome O, or output variable. Error is assessed as e(erj) = [O(erj) – NA(erj)]*c, where ‘c’ is na additional factor, sometimes the local derivative of NA. It just serves to put c there: it can amplify (c > 1) or downplay (c < 1) the importance of local errors and therefore make the neural network more or less sensitive to making errors.                

Before I pass to discussing the practical application of that whole logical structure to the general problem at hand, i.e. the way that a social structure reacts to exogenous disturbances, one more explanation is due, namely the issue of backpropagation of error, where said error is being fed forward. One could legitimately ask how the hell is it possible to backpropagate something whilst feeding it forward. Let’s have a look at real life. When I learn to play piano, for example, I make mistakes in my play, and I utilise them to learn. I learn by repeating over and over again the same sequence of musical notes. Repetition is an instance of feeding forward. Each consecutive time I play the same sequence, I move forward one more round. However, if I want that move forward to be really productive as regards learning, I need to review, each time, my entire technique. I need to go back to my first equation and run the whole sequence of equations again. I need to backpropagate my mistakes over the whole sequence of behaviour. Backpropagating errors and feeding them forward calls two different aspects of the same action. I backpropagate errors across the logical structure of the neural network, and I feed them forward over consecutive rounds of experimentation.   

Now, it is time to explain how I simulate the whole issue of disturbed social structure, and the four scenarios A, B, C, and D, which I described a few paragraphs earlier. The trick I used consists in creating a baseline neural network, one which sort of does something but not much really, and then making mutants out of it, and comparing the outcomes yielded by mutants with that produced by their baseline ancestor. For the baseline version, I have been looking for a neural network which learns lightning fast on the short run but remains profoundly stupid on the long run. I wanted quick immediate reaction and no capacity whatsoever to narrow down the error and adjust to it. 

The input layer of the baseline neural network is made of the set SR = {sr1, sr2, …, srm} of ‘m’ social roles, and one additional variables representative for the hypothetical disturbance. Each social role sri corresponds to a single neuron, which can take values between 0 and 1. Those values represent the probability of occurrence in the social role sri. If, for example, in the experimental round e = 100, the input value of the social role sri is sri(e100) = 0.23, it means that 23% of people manifest the distinctive signs of that social role. Of course, consistently with what I perceive as the conceptual acquis of social sciences, I assume that an individual can have multiple, overlapping social roles.

The factor of disturbance RB is an additional variable in the input layer of the network and comes with similar scale and notation. It takes values between 0 and 1, which represent the probability of disturbing occurrence in the social structure. Once again, RB can be anything, disturbing positively, negatively, or kind of we have no idea what it is going to bring about.

Those of you who are familiar with the architecture of neural networks might wonder how I am going to represent the emergence of new social roles without modifying the structure of the network. Here comes a mathematical trick, which, fortunately enough, is well grounded in social sciences. The mathematical part of the trick consists in incorporating dormant social roles in the initial set SR = {sr1, sr2, …, srm}, i.e. social roles assigned with arbitrary 0 value, i.e. zero probability of occurrence. On the historically short run, i.e. at the scale of like one generation, new social roles are largely predictable. As we are now, we can reasonably predict the need for new computer programmers, whilst being able to safely assume a shortage of jobs for cosmic janitors, collecting metal scrap from the terrestrial orbit. In 20 years from now, that perspective can change – and it’d better change, as we have megatons of metal crap on the orbit – yet, for now, it looks pretty robust.

Thus, in the set SR = {sr1, sr2, …, srm}, I reserve k neurons for active social roles, and l neurons for dormant ones, with, of course, k + l = m. All in all, in the actual network I programmed in Excel, I had k = 20 active social roles, l = 19 dormant social roles, and one neuron corresponding to the disturbance factor RB.            

Now, the issue of social cohesion. In this case, we are talking about cohesion inside the set SR = {sr1, sr2, …, srm}. Mathematically, cohesion inside a set of numerical values can be represented as the average numerical distance between them. Therefore, I couple the input layer of 20k + 19l + RB = 40 neurons is coupled with a layer of meta-input, i.e. with a layer of 40 other neurons whose sole function is to inform about the Euclidean distance between the current value of each input neuron, and the values of the other 39 input neurons.

Euclidean distance plays the role of fitness function (see Hamann et al. 2010[1]). Each social role in the set SR = {sr1, sr2, …, srm}, with its specific probability of occurrence, displays a Euclidean distance from the probability of occurrence in other social roles. The general idea behind this specific mathematical turn is that in a stable structure, the Euclidean distance between phenomena stays more or less the same. When, as a society, we take care of being collectively cohesive, we use the observation of cohesion as data, and the very fact of minding our cohesion helps us to maintain cohesion. When, on the other hand, we don’t care about social cohesion, then we stop using (feeding forward) this specific observation, and social cohesion dissolves.

For the purposes of my own scientific writing, I commonly label that Euclidean distance as V, i.e. V(sri; ej) stands for the average Euclidean distance between social role sri, and all the other m – 1 social roles in the set SR = {sr1, sr2, …, srm}, in the experimental round ej. When input variables are being denominated on a scale from 0 to 1, thus typically standardized for a neural network, and the network uses (i.e. feeds forward) the meta input on cohesion between variables, the typical Euclidean distance you can expect is like 0,1 ≤ V(sri; ej) ≤ 0,3. When the social structure loses it, Euclidean distance between phenomena starts swinging, and that interval tends to go into 0,05 ≤ V(sri; ej) ≤ 0,8. This is how the general idea of social cohesion is translated into a mathematical model.

Thus, my neural network uses, as primary data, basic input about the probability of specific social roles being played by a randomly chosen individual, and metadata about cohesion between those probabilities. I start by assuming that all the active k = 20 social roles occur with the same probability of 0,5. In other words, at the starting point, each individual in the society displays a 50% probability of endorsing any of the k = 20 social roles active in this specific society. Reminder: l = 19 dormant social roles stay at 0, i.e. each of them has 0% of happening, and the RB disturbance stays at 0% probability as well. All is calm. This is my experimental round 1, or e1. In the equation of random experimentation, each social role sri gets experimentally weighed with a random coefficient, and with its local Euclidean distance from other social roles. Of course, as all k = 20 social roles have the same probability of 50%, their distance from each other is uniform and always makes V = 0,256097561. All is calm.

As I want my baseline AI to be quick on the uptake and dumb as f**k on the long-haul flight of learning, I use neural activation through hyperbolic tangent. As you could have seen earlier, this function is sort of prone to short term excitement. In order to assess the error, I use both logic and one more mathematical trick. In the input, I made each of k = 20 social roles equiprobable in its happening, i.e. 0,50. I assume that the output of neural activation should also be 0,50. Fifty percent of being anybody’s social role should yield fifty percent: simplistic, but practical. I go e(erj) = O(erj) – NA(erj) = 0,5 – tanh = 0,5 – [(e2h – 1) / (e2h + 1)], and I feed forward that error from round 1 to the next experimental round. This is an important trait of this particular neural network: in each experimental round, it experiments adds up the probability from previous experimental round and the error made in the same, previous experimental round, and with the assumption that expected value of output should be a probability of 50%.

That whole mathematical strategy yields interesting results. Firstly, in each experimental round, each active social role displays rigorously the same probability of happening, and yet that uniformly distributed probability changes from one experimental round to another. We have here a peculiar set of phenomena, which all have the same probability of taking place, which, in turn, makes all those local probabilities equal to the average probability in the given experimental round, i.e. to the expected value. Consequently, the same happens to the internal cohesion of each experimental round: all Euclidean distances between input probabilities are equal to each other, and to their average expected distance. Technically, after having discovered that homogeneity, I could have dropped the whole idea of many social roles sri in the database and reduce the input data just to three variables (columns): one active social role, one dormant, and the disturbance factor RB. Still, I know by experience that even simple neural networks tend to yield surprising results. Thus, I kept the architecture ’20k + 19l + RB’ just for the sake of experimentation.

That whole baseline neural network, in the form of an Excel file, is available under THIS LINK. In Table 1, below, I summarize the essential property of this mathematical structure: short cyclicality. The average probability of happening in each social role swings regularly, yielding, at the end of the day, an overall average probability of 0,33. Interesting. The way this neural network behaves, it represents a recurrent sequence of two very different states of society. In odd experimental rounds (i.e. 1, 3, 5,… etc.) each social role has 50% or more of probability of manifesting itself in an individual, and the relative cohesion inside the set of social roles is quite high. On the other hand, in even experimental rounds (i.e. 2, 4, 6, … etc.), social roles become disparate in their probability of happening in a given time and place of society, and the internal cohesion of the network is low. The sequence of those two states looks like the work of a muscle: contract, relax, contract, relax etc.

Table 1 – Characteristics of the baseline neural network

Experimental roundAverage probability of input  Cohesion – Average Euclidean distance V in input  Aggregate input ‘h’  Error to backpropagate
1           0,5000 0,25011,62771505-0,4257355
2           0,0743 0,03720,029903190,47010572
3           0,5444 0,27231,79626958-0,4464183
4           0,0980 0,04900,051916330,44813027
5           0,5461 0,27321,60393868-0,4222593
6           0,1238 0,06190,093201450,40706748
7           0,5309 0,26561,59030006-0,4201953
8           0,1107 0,05540,071570250,4285517
9           0,5392 0,26981,49009281-0,4033418
10           0,1359 0,06800,113017960,38746079
11           0,5234 0,26181,51642329-0,4080723
12           0,1153 0,05770,062083680,43799596
13           0,5533 0,27681,92399208-0,458245
14           0,0950 0,04760,036164950,46385081
15           0,5589 0,27961,51645936-0,4080786
16           0,1508 0,07550,138602510,36227827
17           0,5131 0,25671,29611259-0,3607191
18           0,1524 0,07620,122810620,37780311
19           0,5302 0,26521,55382594-0,4144146
20           0,1158 0,05790,063916620,43617027
Average over 3000 rounds0,33160,16590,81130,0000041
Variability*0,60920,60920,901297 439,507

*Variability is calculated as standard deviation, i.e. square root of variance, divided by the average.

Now, I go into the scenario A of social change. The factor of disturbance RB gets activated and provokes a loosening of social cohesion. Mathematically, it involves a few modifications to the baseline network. Activation of the disturbance RB involves two steps. Firstly, numerical values of this specific variable in the network needs to take non-null values: the disturbance is there. I do it by generating random numbers in the RB column of the database. Secondly, there must be a reaction to disturbance, and the reaction consists in disconnecting the layer of neurons, which I labelled meta-data, i.e. the one containing Euclidean distances between the raw data points.

Here comes the overarching issue of sensitivity to disturbance, which goes across all the four scenarios (i.e. A, B, C, and D). As representation of what’s going on in social structure, it is about collective and individual alertness. When a new technology comes out into the market, I don’t necessarily change my job, but when that technology spreads over a certain threshold of popularity, I might be strongly pushed to reconsider my decision. When COVID-19 started hitting the global population, all levels of reaction (i.e. governments, media etc.) were somehow delayed in relation to the actual epidemic spread. This is how social change happens in reaction to a stressor: there is a threshold of sensitivity.

When I throw a handful of random values into the database, as values of disturbance RB, they are likely to be distributed under a bell-curve. I translate mathematically the social concept of sensitivity threshold as a value under that curve, past which the network reacts by cutting ties between errors input as raw data from previous experimental rounds, and the measurement of Euclidean distance between them. Question: how to set this value so as it fits with the general logic of that neural network? I decided to set the threshold at the absolute value of the error recorded in the previous experimental round. Thus, for example, when error generated in round 120 is e120 = -0.08, the threshold of activation for triggering the response to disturbance is ABS(-0,08) = 0,08. The logic behind this condition is that social disturbance becomes significant when it is more prevalent than normal discrepancy between social goals and the actual outcomes.

I come back to the scenario A, thus to the hypothetical situation when the factor of disturbance cuts the ties of cohesion between existing, active social roles. I use the threshold condition ‘if RB(erj) > e(erj-1), then don’t feed forward V(erj-1)’, and this is what happens. First of all, the values of probability assigned to all active social roles remain just as uniform, in every experimental round, as they are in the baseline neural network I described earlier. I know, now, that the neural network, such as I designed it, is not able to discriminate between inputs. It just generates a uniform distribution thereof. That being said, the uniform probability of happening in social roles sri follows, in scenario A, a clearly different trajectory than the monotonous oscillation in the baseline network. The first 134 experimental rounds yield a progressive decrease in probability down to 0. Somewhere in rounds 134 ÷ 136 the network reaches a paradoxical situation, when no active social role in the k = 20 subset has any chance of manifesting itself. It is a society without social roles, and all that because the network stops feeding forward meta-data on its own internal cohesion when the disturbance RB goes over the triggering point. Past that zero point, a strange cycle of learning starts, in irregular leaps: the uniform probability attached to social roles rises up to an upper threshold, and then descends again back to zero. The upper limit of those successive leaps oscillates and then, at an experimental round somewhere between er400 and er1000, probability jumps just below 0,7 and stays this way until the end of the 3000 experimental rounds I ran this neural network through. At this very point, the error recorded by the network gets very close to zero and stays there as well: the network has learnt whatever it was supposed to learn.

Of course, the exact number of experimental rounds in that cycle of learning is irrelevant society-wise. It is not 400 days or 400 weeks; it is the shape of the cycle that really matters. That shape suggests that, when an external disturbance switches off internal cohesion between social roles in a social structure, the so-stimulated society changes in two phases. At first, there are successive, hardly predictable episodes of virtual disappearance of distinct social roles. Professions disappear, family ties distort etc. It is interesting. Social roles get suppressed simply because there is no need for them to stay coherent with other social roles. Then, a hyper-response emerges. Each social role becomes even more prevalent than before the disturbance started happening. It means a growing probability that one and the same individual plays many social roles in parallel.

I pass to scenario B of social change, i.e. the hypothetical situation when the exogenous disturbance straightforwardly triggers the suppression of social roles, and the network keeps feeding forward meta-data on internal cohesion between social roles. Interestingly, suppression of social roles under this logical structure is very short lived, i.e. 1 – 5 experimental rounds, and then the network yields an error which forces social roles to disappear.

One important observation is to note as regards scenarios B, C, and D of social change in general. Such as the neural network is designed, with the threshold of social disturbance calibrated on the error from previous experimental round, error keeps oscillating within an apparently constant amplitude over all the 3000 experimental rounds. In other words, there is no visible reduction of magnitude in error. Some sort of social change is occurring in scenarios B, C, and D, still it looks as a dynamic equilibrium rather than a definitive change of state. That general remark kept in mind, the way that the neural network behaves in scenario B is coherent with the observation  made regarding the side effects of its functioning in scenario A: when the factor of disturbance triggers the disappearance of some social roles, they re-emerge spontaneously, shortly after. To the extent that the neural network I use here can be deemed representative for real social change, widely prevalent social roles seem to be a robust part of the social structure.

Now, it is time to screen comparatively the results yielded by the neural network when it is supposed to represent scenarios C and D of social change: I study situations when a factor of social disturbance, calibrated in its significance on the error made by the neural network in previous experimental rounds, triggers the emergence of new social roles. The difference between those two scenarios is in the role of social cohesion. Mathematically, I did it by activating the dormant l = 19 social roles in the network, with a random component. When the random value generated in the column of social disturbance RB is greater than the error observed in the previous experimental round, thus when RB(erj) > e(erj-1), then each of the l = 19 dormant social roles gets a random positive value between 0 and 1. That random positive value gets processed in two alternative ways. In scenario C, it goes directly into aggregation and neural activation, i.e. there is no meta-data on the Euclidean distance between any of those newly emerging social roles and other social roles. Each new social role is considered as a monad, which develops free from constraints of social cohesion. Scenario D establishes such a constraint, thus the randomly triggered probability of a woken up, and previously dormant social role is being aggregated, and fed into neural activation with meta-data as for its Euclidean distance from other social roles.    

Scenarios C and D share one important characteristic: heterogeneity in new social roles. The k = 20 social roles active from the very beginning, thus social roles ‘inherited’ from the baseline social network, share a uniform probability of happening in each experimental round. Still, as probabilities of new social roles, triggered by the factor of disturbance, are random by default, these probabilities are distributed aleatorily. Therefore, scenarios C and D represent a general case of a new, heterogenous social structure emerging in the presence of an incumbent rigid social structure. Given that specific trait, I introduce a new method of comparing those two sets of social roles, namely by the average probability attached to social roles, calculated over the 3000 experimental rounds. I calculate the average probability of active social roles across all the 3000 experimental rounds, and I compare it with individual, average probabilities obtained for each of the new social roles (or woken up and previously dormant social roles) over 3000 experimental rounds. The idea behind this method is that in big sets of observations, arithmetical average represents the expected value, or the expected state of the given variable.

The process of social change observed, respectively, in scenarios C and D, is different. In the scenario C, the uniform probability attached to the incumbent k = 20 social roles follows a very calm trend, oscillating slightly between 0,2 and 0,5, whilst the heterogenous probabilities of newly triggered l = 19 social roles swing quickly and broadly between 0 and 1. When the network starts feeding forward meta-data on Euclidean distance between each new social role and the others, it creates additional oscillation in the uniform probability of incumbent social roles. The latter gets systematically and cyclically pushed into negative values. A negative probability is logically impossible and represents no real phenomenon. Well, I mean… It is possible to assume that the negative probability of one phenomenon represents the probability of the opposite phenomenon taking place, but this is really far-fetched and doesn’t really find grounding in the logical structure of this specific neural network. Still, the cycle of change where the probability of something incumbent and previously existing gets crushed down to zero (and below) represents a state of society, when a new phenomenon aggressively pushes the incumbent phenomena out of the system.

Let’s see how those two processes of social change, observed in scenarios C and D, translate into expected states of social roles, i.e. into average probabilities. The first step in this analysis is to see how heterogeneous are those average expected states across the new social roles, triggered out of dormancy by the intrusion of the disturbance RB. In scenario C, new social roles display average probabilities between 0,32 and 0,35. Average probabilities corresponding to each individual, new social role differs from others by no more than 0.03, thus by a phenomenological fringe to be found in the tails of the normal distribution. By comparison, the average uniform probability attached to the existing social roles is 0,31. Thus, in the absence of constraint regarding social cohesion between new social roles and the incumbent ones, the expected average probability in both categories is very similar.

In scenario D, average probabilities of new social roles oscillate between 0,45 and 0,49, with just as little disparity as in scenario C, but, in the same time, they push the incumbent social roles out of the nest, so to say. The average uniform probability in the latter, after 3000 experimental rounds, is 0.01, which is most of all a result of the ‘positive probability – negative probability’ cycle during experimentation.

It is time to sum up my observations from the entire experiment conducted through and with a neural network. The initial intention was to understand better the mechanism which underlies one of my most fundamental claims regarding the civilizational role of cities, namely that cities, as a social contrivance, serve to accommodate a growing population in the framework of an increasingly complex network of social roles.

I am focusing on the ‘increasingly complex’ part of that claim. I want to understand patterns of change in the network of social roles, i.e. how can the complexity of that network evolve over time. The kind of artificial behaviour I induced in a neural network allows identifying a few recurrent patterns, which I can transform into hypotheses for further research. There is a connection between social cohesion and the emergence/disappearance of new social roles, for one. Social cohesion drags me back into the realm of the swarm theory. As a society, we seem to be evolving by a cycle of loosening and tightening in the way that social roles are coupled with each other.      

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[1] Xie, X. F., Zhang, W. J., & Yang, Z. L. (2002, May). Dissipative particle swarm optimization. In Proceedings of the 2002 Congress on Evolutionary Computation. CEC’02 (Cat. No. 02TH8600) (Vol. 2, pp. 1456-1461). IEEE.

[2] Poli, R., Kennedy, J., & Blackwell, T. (2007). Particle swarm optimization. Swarm intelligence, 1(1), 33-57.

[3] Torres, S. (2012). Swarm theory applied to air traffic flow management. Procedia Computer Science, 12, 463-470.

[4] Stradner, J., Thenius, R., Zahadat, P., Hamann, H., Crailsheim, K., & Schmickl, T. (2013). Algorithmic requirements for swarm intelligence in differently coupled collective systems. Chaos, Solitons & Fractals, 50, 100-114.