I am generalizing from the article which I am currently revising, and I am taking a broader view on many specific strands of research I am running, mostly in order to move forward with my hypothesis of collective intelligence in human social structures. I want to recapitulate on my method – once more – in order to extract and understand its meaning. 

I have recently realized a few things about my research. Firstly, I am using the logical structure of an artificial neural network as a simulator more than an optimizer, as digital imagination rather than functional, goal-oriented intelligence, and that seems to be the way of using AI which hardly anyone else in social sciences seems to be doing. The big question which I am (re)asking myself is to what extent are my simulations representative for the collective intelligence of human societies.

I start gently, with variables, hence with my phenomenology. I mostly use the commonly accessible and published variables, such as those published by the World Bank, the International Monetary Fund, STATISTA etc. Sometimes, I make my own coefficients out of those commonly accepted metrics, e.g. the coefficient of resident patent applications per 1 million people, the proportion between the density of population in cities and the general one, or the coefficient of fixed capital assets per 1 patent application.

My take on any variables in social sciences is very strongly phenomenological, or even hermeneutic. I follow the line of logic which you can find, for example, in “Phenomenology of Perception” by Maurice Merleau-Ponty (reprint, revised, Routledge, 2013, ISBN 1135718601, 9781135718602). I assume that any of the metrics we have in social sciences is an entanglement of our collective cognition with the actual s**t going on. As the actual s**t going on encompasses our way of forming our collective cognition, any variable used in social sciences is very much like a person’s attempt to look at themselves from a distance. Yes! This is what we use mirrors for! Variables used in social sciences are mirrors. Still, they are mirrors made largely by trial and error, with a little bit of a shaky hand, and each of them shows actual social reality in slightly disformed a manner.

Empirical research in social sciences consists, very largely, in a group of people trying to guess something about themselves on the basis of repeated looks into a set of imperfect mirrors. Those mirrors are imperfect, and yet they serve some purpose. I pass to my second big phenomenological take on social reality, namely that our entangled observations thereof are far from being haphazard. The furtive looks we catch of the phenomenal soup, out there, are purposeful. We pay attention to things which pay off. We define specific variables in social sciences because we know by experience that paying attention to those aspects of social reality brings concrete rewards, whilst not paying attention thereto can hurt, like bad.

Let’s take inflation. Way back in the day, like 300 years ago, no one really used the term of inflation because the monetary system consisted in a multitude of currencies, mixing private and public deeds of various kinds. Entire provinces in European countries could rely on bills of exchange issued by influential merchants and bankers, just to switch to other type of bills 5 years later. Fluctuations in the rates of exchange in those multiple currencies very largely cancelled each other. Each business of respectable size was like a local equivalent of the today’s Forex exchange. Inflation was a metric which did not even make sense at the time, as any professional of finance would intuitively ask back: ‘Inflation? Like… inflation in which exactly among those 27 currencies I use everyday?’.

Standardized monetary systems, which we call ‘FIAT money’ today, steadied themselves only in the 19^th century. Multiple currencies progressively fused into one, homogenized monetary mass, and mass conveys energy. Inflation is loss of monetary energy, like entropy of the monetary mass. People started paying attention to inflation when it started to matter.

We make our own social reality, which is fundamentally unobservable to us, and it makes sense because it is hard to have an objective, external look at a box when we are staying inside the box. Living in that box, we have learnt, over time, how to pay attention to the temporarily important properties of the box. We have learnt how to use maths for fine tuning in that selective perception of ours. We learnt, for example, to replace the basic distinction between people doing business and people not doing business at all with finer shades of how much business are people doing exactly in a unit of time-space.   

Therefore, a set of empirical variables, e.g. from the World Bank, is a collection of imperfect observations, which represent valuable outcomes social outcomes. A set of N socio-economic variables represents N collectively valuable social outcomes, which, in turn, correspond to N collective pursuits – it is a set of collective orientations. Now, my readers have the full right to protest: ‘Man, just chill. You are getting carried away by your own ideas. Quantitative variables about society and economy are numbers, right? They are the metrics of something. Measurement is objective and dispassionate. How can you say that objectively gauged metrics are collective orientations?’. Yes, these are all valid objections, and I made up that little imaginary voice of my readers on the basis of reviews that I had for some of my papers.

Once again, then. We measure the things we care about, and we go to great lengths in creating accurate scales and methods of measurement for the things we very much care about. Collective coordination is costly and hard to achieve. If we devote decades of collective work to nail down the right way of measuring, e.g. the professional activity of people, it probably matters. If it matters, we are collectively after optimizing it. A set of quantitative, socio-economic variables represents a set of collectively pursued orientations.

In the branch of philosophy called ethics, there is a stream of thought labelled ‘contextual ethics’, whose proponents claim that whatever normatively defined values we say we stick to, the real values we stick to are to be deconstructed from our behaviour. Things we are recurrently and systematically after are our contextual ethical values. Yes, the socio-economic variables we can get from your average statistical office are informative about the contextual values of our society.

When I deal with a variable like the % of electricity in the total consumption of energy, I deal with a superimposition of two cognitive perspectives. I observe something that happens in the social reality, and that phenomenon takes the form of a spatially differentiated, complex state of things, which changes over time, i.e. one complex state transitions into another complex state etc. On the other hand, I observe a collective pursuit to optimize that % of electricity in the total consumption of energy.

The process of optimizing a socio-economic metric makes me think once again about the measurement of social phenomena. We observe and measure things which are important to us because they give us some sort of payoff. We can have collective payoffs in three basic ways. We can max out, for one. Case: Gross Domestic Product, access to sanitation. We can keep something as low as possible, for two. Case: murder, tuberculosis. Finally, we can maintain some kind of healthy dynamic balance. Case: inflation, use of smartphones. Now, let’s notice that we don’t really do fine calculations about murder or tuberculosis. Someone is healthy or sick, still alive or already murdered. Transitional states are not really of much of a collective interest. As it comes to outcomes which pay off by the absence of something, we tend to count them digitally, like ‘is there or isn’t there’. On the other hand, those other outcomes, which we max out on or keep in equilibrium, well, that’s another story. We invent and perfect subtle scales of measurement for those phenomena. That makes me think about a seminal paper titled ‘Selection by consequences’, by the founding father of behaviourism, Burrhus Frederic Skinner. Skinner introduced the distinction between positive and negative reinforcements. He claimed that negative reinforcements are generally stronger in shaping human behaviour, whilst being clumsier as well. We just run away from a tiger, we don’t really try to calibrate the right distance and the right speed of evasion. On the other hand, we tend to calibrate quite finely our reactions to positive reinforcements. We dose our food, we measure exactly the buildings we make, we learn by small successes etc.  

If a set of quantitative socio-economic variables is informative about a set of collective orientations (collectively pursued outcomes), one of the ways we can study that set consists in establishing the hierarchy of orientations. Are some of those collective values more important than others? What does it even mean ‘more important’ in this context, and how can it be assessed? We can imagine that each among the many collective orientations is an individual pursuing their idiosyncratic path of payoffs from interactions with the external world. By the way, this metaphor is closer to reality than it could appear at the first sight. Each human is, in fact, a distinct orientation. Each of us is action. This perspective has been very sharply articulated by Martin Heidegger, in his “Being and Time”.    

Hence, each collective orientation can be equated to an individual force, pulling the society in a specific direction. In the presence of many socio-economic variables, I assume the actual social reality is a superimposition of those forces. They can diverge or concur, as they please, I do not make any assumptions about that. Which of those forces pulls the most powerfully?

Here comes my mathematical method, in the form of an artificial neural network. I proceed step by step. What does it mean that we collectively optimize a metric? Mostly by making it coherent with our other orientations. Human social structures are based on coordination, and coordination happens both between social entities (individuals, cities, states, political parties etc.), and between different collective pursuits. Optimizing a metric representative for a collectively valuable outcome means coordinating with other collectively valuable outcomes. In that perspective, a phenomenon represented (imperfectly) with a socio-economic metric is optimized when it remains in some kind of correlation with other phenomena, represented with other metrics. The way I define correlation in that statement is a broad one: correlation is any concurrence of events displaying a repetitive, functional pattern.

Thus, when I study the force of a given variable as a collective orientation in a society, I take this variable as the hypothetical output in the process (of collective orientation, and I simulate that process as the output variable sort of dragging the remaining variables behind it, by the force of functional coherence. With a given set of empirical variables, I make as many mutations thereof as I have variables. Each mutated set represents a process, where one variable as output, and the remaining ones as input. The process consists of as many experiments as there are observational rows in my database. Most socio-economic variables come in rows of the type “country A in year X”.  

Here, I do a little bit of mathematical cavalry with two different models of swarm intelligence: particle swarm and ants’ colony (see: Gupta & Srivastava 2020[1]). The model of particle swarm comes from the observation of birds, which keeps me in a state of awe about human symbolic creativity, and it models the way that flocks of birds stay collectively coherent when they fly around in the search of food. Each socio-economic variable is a collective orientation, and in practical terms it corresponds to a form of social behaviour. Each such form of social behaviour is a bird, which observes and controls its distance from other birds, i.e. from other forms of social behaviour. Societies experiment with different ways of maintaining internal coherence between different orientations. Each distinct collective orientation observes and controls its distance from other collective orientations. From the perspective of an ants’ colony, each form of social behaviour is a pheromonal trace which other forms of social behaviour can follow and reinforce, or not give a s**t about it, to their pleasure and leisure. Societies experiment with different strengths attributed to particular forms of social behaviour, which mimics an ants’ colony experimenting with different pheromonal intensities attached to different paths toward food.

Please, notice that both models – particle swarm and ants’ colony – mention food. Food is the outcome to achieve. Output variables in mutated datasets – which I create out of the empirical one – are the food to acquire. Input variables are the moves and strategies which birds (particles) or ants can perform in order to get food. Experimentation the ants’ way involves weighing each local input (i.e. the input of each variable in each experimental round) with a random weight R, 0 < R < 1. When experimenting the birds’ way, I drop into my model the average Euclidean distance E from the local input to all the other local inputs.   

I want to present it all rolled nicely into an equation, and, as noblesse oblige, I introduce symbols. The local input of an input variable x_i in experimental round t_j is represented with x_i(t_j), whilst the local value of the output variable x_o is written as x_o(t_j). The compound experimental input which the society makes, both the ants’ way and the birds’ way, is written as h(t_j), and it spells h(t_j) = x₁(t_j)*R* E[x_i(t_j-1)] + x₂(t_j)*R* E[x₂(t_j-1)] + … + x_n(t_j)*R* E[x_n(t_j-1)].    

Up to that point, this is not really a neural network. It mixes things up, but it does not really adapt. I mean… maybe there is a little intelligence? After all, when my variables act like a flock of birds, they observe each other’s position in the previous experimental round, through the E[x_i(t_j-1)] Euclidean thing. However, I still have no connection, at this point, between the compound experimental input h(t_j) and the pursued output x_o(t_j). I need a connection which would work like an observer, something like a cognitive meta-structure.

Here comes the very basic science of artificial neural networks. There is a function called hyperbolic tangent, which spells tanh = (e^2x – 1)/(e^2x + 1) where x can be whatever you want. This function happens to be one of those used in artificial neural networks, as neural activation, i.e. as a way to mediate between a compound input and an expected output. When I have that compound experimental input h(t_j) = x₁(t_j)*R* E[x_i(t_j-1)] + x₂(t_j)*R* E[x₂(t_j-1)] + … + x_n(t_j)*R* E[x_n(t_j-1)], I can put it in the place of x in the hyperbolic tangent, and I bet tanh = (e^2h  – 1)/(e^2h  + 1). In a neural network, error in optimization can be calculated, generally, as e = x_o(t_j) – tanh[h(t_j)]. That error can be fed forward into the next experimental round, and then we are talking, ‘cause the compound experimental input morphs into:

>>  input h(t_j) = x₁(t_j)*R* E[x_i(t_j-1)]*e(t_j-1) + x₂(t_j)*R* E[x₂(t_j-1)] *e(t_j-1) + … + x_n(t_j)*R* E[x_n(t_j-1)] *e(t_j-1)   

… and that means that each compound experimental input takes into account both the coherence of the input in question (E), and the results of previous attempts to optimize.

Here, I am a bit stuck. I need to explain, how exactly the fact of computing the error of optimization e = x_o(t_j) – tanh[h(t_j)] is representative for collective intelligence.

[1] Gupta, A., & Srivastava, S. (2020). Comparative analysis of ant colony and particle swarm optimization algorithms for distance optimization. Procedia Computer Science, 173, 245-253. https://doi.org/10.1016/j.procs.2020.06.029

I continue revising my work on collective intelligence, and I am linking it to the theory of complex systems. I return to the excellent book ‘What Is a Complex System?’ by James Landyman and Karoline Wiesner (Yale University Press, 2020, ISBN 978-0-300-25110-4, Kindle Edition). I take and quote their summary list of characteristics that complex systems display, on pages 22 – 23: “ […] which features are necessary and sufficient for which kinds of complexity and complex system. The features are as follows:

1. Numerosity: complex systems involve many interactions among many components.

2. Disorder and diversity: the interactions in a complex system are not coordinated or controlled centrally, and the components may differ.

3. Feedback: the interactions in complex systems are iterated so that there is feedback from previous interactions on a time scale relevant to the system’s emergent dynamics.

4. Non-equilibrium: complex systems are open to the environment and are often driven by something external.

5. Spontaneous order and self-organisation: complex systems exhibit structure and order that arises out of the interactions among their parts.

6. Nonlinearity: complex systems exhibit nonlinear dependence on parameters or external drivers.

7. Robustness: the structure and function of complex systems is stable under relevant perturbations.

8. Nested structure and modularity: there may be multiple scales of structure, clustering and specialisation of function in complex systems.

9. History and memory: complex systems often require a very long history to exist and often store information about history.

10. Adaptive behaviour: complex systems are often able to modify their behaviour depending on the state of the environment and the predictions they make about it”.

As I look at the list, my method of simulating collective intelligence is coherent therewith. Still, there is one point which I think I need to dig a bit more into: that whole thing with simple entities inside the complex system. In most of my simulations, I work on interactions between cognitive categories, i.e. between quantitative variables. Interaction between real social entities is most frequently implied rather than empirically nailed down. Still, there is one piece of research which sticks out a bit in that respect, and which I did last year. It is devoted to cities and their role in the human civilisation. I wrote quite a few blog updates on the topic, and I have one unpublished paper written thereon, titled ‘The Puzzle of Urban Density And Energy Consumption’. In this case, I made simulations of collective intelligence with my method, thus I studied interactions between variables. Yet, in the phenomenological background of emerging complexity in variables, real people interact in cities: there are real social entities interacting in correlation with the connections between variables. I think the collective intelligence of cities the piece of research where I have the surest empirical footing, as compared to others.

There is another thing which I almost inevitably think about. Given the depth and breadth of the complexity theory, such as I start discovering it with and through that ‘What Is a Complex System?’ book, by James Landyman and Karoline Wiesner, I ask myself: what kind of bacon can I bring to that table? Why should anyone bother about my research? What theoretical value added can I supply? A good way of testing it is talking real problems. I have just signalled my research on cities. The most general hypothesis I am exploring is that cities are factories of new social roles in the same way that the countryside is a factory of food. In the presence of demographic growth, we need more food, and we need new social roles for new humans coming around. In the absence of such new social roles, those new humans feel alienated, they identify as revolutionaries fighting for the greater good, they identify the incumbent humans as oppressive patriarchy, and the next thing you know, there is systemic, centralized, government-backed terror. Pardon my French, this is a system of social justice. Did my bit of social justice, in the communist Poland.

Anyway, cities make new social roles by making humans interact much more abundantly than they usually do in a farm. More abundant an interaction means more data to process for each human brain, more s**t to figure out, and the next thing you know, you become a craftsman, a businessperson, an artist, or an assassin. Once again, being an assassin in the countryside would not make much sense. Jumping from one roof to another looks dashing only in an urban environment. Just try it on a farm.

Now, an intellectual challenge. How can humans, who essentially don’t know what to do collectively, can interact so as to create emergent complexity which, in hindsight, looks as if they had known what to do? An interesting approach, which hopefully allows using some kind of neural network, is the paradigm of the maze. Each individual human is so lost in social reality that the latter appears as a maze, which one ignores the layout of. Before I go further, one linguistic thing is to nail down. I feel stupid using impersonal forms such as ‘one’, or ‘an individual’. I like more concreteness. I am going to start with George the Hero. George the Hero lives in a maze, and I stress it: he lives there. Social reality is like a maze to George, and, logically, George does not even want to get out of that maze, ‘cause that would mean being lonely, with no one around to gauge George’s heroism. George the Hero needs to stay in the maze.

The first thing which George the Hero needs to figure out is the dimensionality of the maze. How many axes can George move along in that social complexity? Good question. George needs to experiment in order to discover that. He makes moves in different social directions. He looks around what different kinds of education he can possibly get. He assesses his occupational options, mostly jobs and business ventures. He asks himself how he can structure his relations with family and friends. Is being an asshole compatible with fulfilling emotional bonds with people around?  

Wherever George the Hero currently is in the maze, there are n neighbouring and available cells around him. In each given place of the social maze, George the Hero has n possible ways to move further, into those n accessible cells in the immediate vicinity, and that is associated with k dimensions of movement. What is k, exactly? Here, I can refer to the theory of cellular automata, which attempts to simulate interactions between really simple, cell-like entities (Bandini, Mauri & Serra 2001[1]; Yu et al. 2021[2]). There is something called ‘von Neumann neighbourhood’. It corresponds to the assumption that if George the Hero has n neighbouring social cells which he move into, he can move like ‘left-right-forward-back’. That, in turn, spells k = n/2. If George can move into 4 neighbouring cells, he moves in a 2-dimensional space. Should he be able to move into 6 adjacent cells of the social maze, he has 3 dimensions to move along etc. Trouble starts when George sees an odd number of places to move to, like 5 or 7, on the account of these giving half-dimensions, like 5/2 = 2.5, 7/2 = 3.5 etc. Half a dimension means, in practical terms, that George the Hero faces social constraints. There might be cells around, mind you, which technically are there, but there are walls between George and them, and thus, for all practical purposes, the Hero can afford not to give a f**k.

George the Hero does not like to move back. Hardly anyone does. Thus, when George has successfully moved from cell A to cell B, he will probably not like going back to A, just in order to explore another cell adjacent thereto. People behave heuristically. People build up on their previous gains. Once George the Hero has moved from A to B, B becomes his A for the next move. He will choose one among the cells adjacent to B (now A), move there etc. George is a Hero, not a scientist, and therefore he carves a path through the social maze rather than discovers the maze as such. Each cell in the maze contains some rewards and some threats. George can get food and it means getting into a dangerously complex relation with that sabre-tooth tiger. George can earn money and it means giving up some of his personal freedom. George can bond with other people and find existential meaning and it means giving up even more of what he provisionally perceives as his personal freedom.

The social maze is truly a maze because there are many Georges around. Interestingly, many Georges in English give one Georges in French, and I feel this is the point where I should drop the metaphor of George the Hero. I need to get more precise, and thus I go to a formal concept in the theory of cellular automata, namely that of a d-dimensional cellular automaton, which can be mathematically expressed as A = (Z^d, S, N, Sⁿ⁺¹ -> S). In that automaton A, Z^d stands for the architecture of the maze, thus a lattice of d – tuples of integer numbers. In plain human, Z^d is given by the number of dimensions, possibly constrained, which a human can move along in the social space. Many people carve their paths across the social maze, no one likes going back, and thus the more people are around, and the better they can communicate their respective experiences, the more exhaustive knowledge we have of the surrounding Z^d.

There is a finite set S of states in that social space Z^d, and that finitude is connected to the formally defined neighbourhood of the automaton A, namely the N. Formally, N is a finite ordered subset of Z^d, and, besides the ‘left-right-forward-back’ neighbourhood of von Neumann, there is a more complex one, namely the Moore’s neighbourhood. In the latter, we can move diagonally between cells, like to the left and forward, to the right and forward etc. Keeping in mind that neighbourhood means, in practical terms, the number n of cells which we can move into from the social cell we are currently in, the cellular automaton can be rephrased as as A = (Z^d, S, n, Sⁿ⁺¹ -> S). The transition Sⁿ⁺¹ -> S, called the local rule of A, makes more sense now. With me being in a given cell of the social maze, and there being n available cells immediately adjacent to mine, that makes n +1 cells where I can possibly be in, and I can technically visit all those cells in a finite number of Sⁿ⁺¹ combinatorial paths. The transition Sⁿ⁺¹ -> S expresses the way which I carve my finite set S of states out of the generally available Sⁿ⁺¹.       

If I assume that cities are factories of new social roles, the cellular automaton of an urban homo sapiens should be more complex than the red-neck-cellular automaton in a farm folk. It might mean greater an n, thus more cells available for moving from where I am now. It might also mean more efficient a Sⁿ⁺¹ -> S local rule, i.e. a better way to explore all the possible states I can achieve starting from where I am. There is a separate formal concept for that efficiency in the local rule, and it is called configuration of the cellular automaton AKA its instantaneous description AKA its global state, and it refers to the map Z^d -> S. Hence, the configuration of my cellular automaton is the way which the overall social space Z^d mapes into the set S of states actually available to me.

Right, if I have my cellular automaton with a configuration map Z^d -> S, it is sheer fairness that you have yours too, and your cousin Eleonore has another one for herself, as well. There are many of us in the social space Z^d. We are many x’s in the Z^d. Each x of us has their own configuration map Z^d -> S. If we want to get along with each other, our individual cellular automatons need to be mutually coherent enough to have a common, global function of cellular automata, and we know there is such a global function when we can collectively produce a sequence of configurations.

According to my own definition, a social structure is a collectively intelligent structure to the extent that it can experiment with many alternative versions of itself and select the fittest one, whilst staying structurally coherent. Structural coherence, in turn, is the capacity to relax and tighten, in a sequence, behavioural coupling inside the society, so as to allow the emergence and grounding of new behavioural patterns. The theory of cellular automata provides me some insights in that respect. Collective intelligence means the capacity to experiment with ourselves, right? That means experimenting with our global function Z^d -> S, i.e. with the capacity to translate the technically available social space Z^d into a catalogue S of possible states. If we take a random sample of individuals in a society, and study their cellular automatons A, they will display local rules Sⁿ⁺¹ -> S, and these can be expressed as coefficients (S / Sⁿ⁺¹), 0 ≤ (S / Sⁿ⁺¹) ≤ 1. The latter express the capacity of individual cellular automatons to generate actual states S of being out of the generally available menu of Sⁿ⁺¹.

In a large population, we can observe the statistical distribution of individual (S / Sⁿ⁺¹) coefficients of freedom in making one’s cellular state. The properties of that statistical distribution, e.g. the average (S / Sⁿ⁺¹) across the board, are informative about how intelligent collectively the given society is. The greater the average (S / Sⁿ⁺¹), the more possible states can the given society generate in the incumbent social structure, and the more it can know about the fittest state possible. That looks like a cellular definition of functional freedom.

[1] Bandini, S., Mauri, G., & Serra, R. (2001). Cellular automata: From a theoretical parallel computational model to its application to complex systems. Parallel Computing, 27(5), 539-553. https://doi.org/10.1016/S0167-8191(00)00076-4

[2] Yu, J., Hagen-Zanker, A., Santitissadeekorn, N., & Hughes, S. (2021). Calibration of cellular automata urban growth models from urban genesis onwards-a novel application of Markov chain Monte Carlo approximate Bayesian computation. Computers, environment and urban systems, 90, 101689. https://doi.org/10.1016/j.compenvurbsys.2021.101689