I return to the project which I started in Spring this year (i.e. 2020), and which I had put aside to some extent: the book I want to write on the role and function of cities in our civilization, including the changes, which we, city slickers, can expect in the foreseeable future. As I think about it now, I guess I had to digest intellectually both my essential method of research for that book, and the core empirical findings which I want to connect to. The method consists in studying human civilization as collective intelligence, thus a collection of intelligent structures, able to learn by experimenting with many alternative versions of themselves. Culture, laws and institutions, technologies: I consider all those anthropological categories as cognitive constructs, which we developed over centuries to study our own collective intelligence and being de facto parts thereof.

Collective intelligence, in that perspective, is an overarching conceptual frame, and as overarching frames frequently do, the concept risks to become a cliché. The remedy I want and intend to use is mathematics. I want to write the book as a collection of conceptual developments and in-depth empirical insights into hypotheses previously formulated with the help of a mathematical model. This is, I think, a major originality of my method. In social sciences, we tend to go the other way around: we formulate hypotheses by sort of freestyling intellectually, and then we check them with mathematical models. I start with just a little bit of intellectual freestyling, then I formulate my assumptions mathematically, and I use the mathematical model which results from those assumptions to formulate hypotheses for further research.

I adopt such a strongly mathematical method because we have a whole class of mathematical models which seem to fit the bill perfectly: artificial neural networks. Yes, I consider artificial neural networks as mathematical models in the first place, and only then as algorithms. The mathematical theory which I associate artificial neural networks the most closely with is that of state space, combined with the otherwise related theory of Markov chains. In other words, whatever happens, I attempt to represent it as a matrix of values, which is being transformed into another matrix of values. The artificial neural network I use for that representation reflects both the structure of the matrix in question, and the mechanism of transformation, which, by the way, is commonly called σ – algebra. By ‘commonly’ I mean commonly in mathematics.

My deep intuition – ‘deep’ means that I understand that intuition just partly – is that artificial neural networks are the best mathematical representation of collective intelligence we can get for now. Therefore I use them as a mathematical model, and here comes a big difference between the way I use them and a typical programmer does. Programmers of artificial intelligence are, as far as I know (my son is a programmer, and, yes, sometimes we speak human lingo to each other), absolutely at home with considering artificial neural networks as black boxes, i.e. as something that does something, yet we don’t really need to understand what exactly that thing is, which neural networks do, and we essentially care about those networks being accurate and quick in whatever they do.

I, in my methodological world, I adopt completely different a stance. I care most of all about understanding very specifically what the is the neural network doing, and I draw my conclusions from the way it does things. I don’t need the neural network I use to be super-fast neither super accurate: I need to understand how it does whatever it does.

I use two types of neural networks in that spirit, both 100% hand made. The first one serves me to identify the direction a social system (collective intelligence) follows in its collective learning. You can see an application in this draft paper of mine, titled ‘Climbing the right hill’. The fundamental logic of that network is to take an empirical dataset and use the neural network to produce as many alternative transformations of that dataset as there are variables in it. Each transformation takes a different variable from the empirical dataset as its desired output (i.e. it optimizes all the other variables as instrumental input). I measure the Euclidean similarity (Euclidean distance) between each individual transformation and the source dataset. I assume that the transformation which falls relatively the closest to source empirical data is the best representation of the collective intelligence represented in that data. Thus, at the end of the day, this specific type of neural network serves me to discover what we are really after, as a society.

The second type of network is built as a matrix of probabilities, modified by a quasi-random factor of disturbance. I am tempted to say that this network attempts to emulate coincidence and quasi-randomness of events. I made it and I keep using it as pure simulation: there is no empirical data which the network learns on. It starts with a first, controlled vector of probabilities, and then it transforms that vector in a finite number of experimental iterations (usually I make that network perform 3000 experimental rounds). In the first application I made of that network, probabilities correspond to social roles, and more specifically to the likelihood that a random person in the society studied endorses the given social role (see ‘The perfectly dumb, smart social structure’). At a deeper, and, in the same time, more general a level, I assume that probability as such is a structural variable of observable reality. A network which simulates changes in a vector of probabilities simulated change in the structure of events.

Long story short, I have two neural networks for making precise hypotheses: one uncovers orientations and pursued values in sets of socio-economic data, whilst the other simulates structural change in compound probabilities attached to specific phenomena. When I put that lot to real computational work, two essential conclusions emerge, sort of across the board, whatever empirical problem I am currently treating. Firstly, all big sets of empirical socio-economic data are after something specific. I mean, when I take the first of those two networks, the one that clones an empirical dataset into as many transformations as there are variables, a few of those transformations, like 1 ÷ 3 of them, are much closer to the original, in Euclidean terms, than all the rest. When I say closer, it is several times closer. Secondly, vectors of probabilities are tenacious and resilient. When I take the second of those networks, the one which prods vectors of probabilities with quasi-random disturbances, those probabilities tend to resist. Even if, in some 100 experimental rounds, some of those probabilities get kicked out of the system, i.e. their values descend to 0, they reappear a few hundred of experimental rounds later, as if by magic. Those probabilities can be progressively driven down if the factor of disturbance, which I include in the network, consists in quasi-randomly dropping new events into the game. The phenomenological structure of reality seems to be something very stable, once set in place, however simple I make that reality a priori. It yields to increasing complexity (new phenomena, with their probabilities coming to the game) rather than to arbitrary reduction of the pre-set phenomena.

I generalize those observations. A collective intelligence, i.e. an intelligent social structure, able to learn by experimenting with many alternative versions of itself, can stay coherent in tat experimentation and seems to stay coherent because it pursues very clear collective outcomes. I am even tempted to reframe it as a condition: a human social structure can evolve as a collectively intelligent structure under the condition of having very clear collectively pursued values. If it doesn’t, it is doomed to disintegrate and to be replaced by another collectively intelligent social structure, which, in turn, is sufficiently oriented to stay internally coherent whilst experimenting with itself. As I descend to the level of human behaviour, observed as the probability of an average individual endorsing specific patterns of behaviour, those behavioural patterns are resilient to exogenous destruction, and, in the same time, quite malleable when new patterns emerge and start to compete with the old ones. When a culture starts from a point A, defined as a set of social roles and behavioural patterns with assorted probabilities of happening, that point A needs a bloody long time, or, in other words, a bloody big lot of collectively intelligent experimentation, to vanish completely.

Now, I want to narrow down the scope of hypotheses I intend to formulate, by specifying the basic empirical findings which I have made so far, and which make the foundations of my research on cities. The first empirical finding does not come from me, but from the CIESIN centre at the Columbia University, and it is both simple and mind blowing: however the formal boundaries of urban areas are being redefined by local governments, the total surface of urban areas, defined as abnormally dense agglomerations of man-made structures and night-time lights, seems to have been constant over the last 30 years, maybe even more. In other words, whilst we have a commonly shared impression that cities grow, they seem to be growing only at the expense of other cities. You can check those numbers via the stats available with the World Bank (https://data.worldbank.org/indicator/AG.LND.TOTL.UR.K2 ). As you will be surfing with the World Bank, you can also call by another metric, the total surface of agricultural land on the planet (https://data.worldbank.org/indicator/AG.LND.AGRI.K2 ) and you will see that it has been growing, by hiccups, since 1960, i.e. since that stat is being collected.

To complete the picture, you can check the percentage of urban population in the total human population on the planet (https://data.worldbank.org/indicator/SP.URB.TOTL.IN.ZS ) and you will see that we have been becoming more and more urban, and right now, we are prevalently urban. Long story short, there are more and more urban humans, who apparently live in a constant urban space, and feed themselves out of a growing area of agricultural land. At the end of the day, cities seem to become increasingly different from the countryside, as regards the density of population: urban populations on Earth are becoming systematically more dense than rural ones.

I am cross breeding my general observations from what my two neural networks tend to do, with those main empirical findings about cities, and I am trying to formulate precise hypotheses for further research. **Hypothesis #1**: cities are purposeful demographic anomalies, with a clear orientation on optimizing specific social outcomes. **Hypothesis #2**: if and to the extent that the purpose of cities is to create new social roles, through intense social interaction in a limited physical space, the creation of new social roles involves their long coexistence with older social roles, and, therefore, the resulting growth in social complexity is exponential. **Hypothesis #3**: the COVID-19 pandemic, as an exogenous factor of disturbance, is likely to impact us in three possible ways: a) it can temporarily make disappear some social roles b) on the long run, it is likely to increase social complexity, i.e. to make us create a whole new set of social roles and c) it can change the fundamental orientation (i.e. the pursued collective values) of cities as demographic anomalies.

In your spare time you can also watch this video I made a few weeks ago: ‘**Urban Economics and City Management #1 Lockdowns in pandemic and the role of cities’ : ****https://youtu.be/fYIz_6JVVZk**** . **It recounts and restates my starting point in this path of research. I browse through the main threads of connection between the pandemic of COVID-19 and the civilisational role of cities. The virus, which just loves densely populated places, makes us question the patterns of urban life, and makes us ask question as for the future of cities.