Chaos and order in human action: do cities matter?

Towards new temporal geographies of… Encounters
October 12, 2016
Academic writing and the research problem
November 19, 2016



The cycle of social entropy and space, clockwise: from the high unpredictability of potential actions to a momentarily ordered system, as actions converge into places – only to dive in entropy again.



How do we put our chaotic individual actions together in a way to create a minimally organized society? How can individual actions develop into something like a working, coherent system of actions? Complex systems theorist João Meirelles, statistical physicist Fabiano Ribeiro and I developed a form to simulate social organization and the role of cities in it, and have just published a (preprint) paper on this.


In this paper, we attempt to answer this key question by suggesting that there is a role for cities in the way we coordinate seemingly chaotic decisions. We look into the elementary processes of social organisation exploring a particular concept: ‘social entropy’, or how social systems deal with uncertainty and unpredictability in the transition from individual actions to action systems. Examining ideas that (i) actions rely on informational differences latent in their environments, and that (ii) the city itself is an informational environment to actions, we propose that (iii) the city produces differences in the probability of interactions, becoming an essential part of the reduction of social entropy as a way to advance social organisation. We investigate this process through simulations of distinct scenarios of action orientations and spatial conditions. Finally, we suggest that states and fluctuations of social entropy are a vital part of social reproduction, and reveal a deep connection between social, informational and spatial systems.


A different way of looking into social organisation and cities

Recursive process that conducts the system from chaotic states (high entropy) into connections of actions in emergent coherent systems (low entropy).

I’ve been particularly interested in understanding things like ‘social complexity’ – how we live in with more information and possibilities of actions than ever before – and have been involved in a research team to capture it in relation to cities.

Entropy is clearly a phenomenon ‘beyond observation’ – we cannot see or touch entropy, even though we live it on a daily basis. We live entropy when we have to deal with unpredictable situations and with too much information – but we rarely realise it is the case.  We are not used to consciously think about the challenges we face in order to make our choices or put our actions together in any workable, coherent sense. And we as a collectivity can put our actions together as complex systems simply because such systems are open to new actions and new interactions. We know that we can somehow get to know other people as potential counterparts in interaction. We also know that we can find places where a certain action or activity is performed and might help us to get what we need. And we only do so because we have information about these activities. More than that: we have information systems that tell us about their existence, and where and how we can find them – and interact with them: cities themselves. These urban information systems are also systems of connection: we can ‘connect’ with certain persons or activities for a period of time. Cities are systems of communication in their own right.


Our point in this work is that cities and their spaces are a fundamental part of this story. In fact, they are the very historical condition that allowed such levels of information to be produced in the first place, and these connections to happen. Our proposition is that cities and their spaces are an essential part of the cyclical reduction of the entropy of actions, guiding their collective coordination.

We examine this proposition through computational experiments able to assess how social entropy relates to informational space. Ultimately, we argue that the forms in which social entropy is dealt with is one of the deep connections between the social and the physical city.

Linearising a process that in fact occurs simultaneously, the cycle of entropy of actions would take the following form:

(a) Think of the actions as lines moving in time, in an initial state free from space, when actors can do anything and we cannot foresee what they will do – a potential state of high entropy. The colours of the lines in the diagram on the left represent different orientations guiding actions.

(b) Then action lines converge into distinct positions of a spatial system – a system of informationally differentiated contents that is urban space (represented by the vertical strip in the diagram), arranged in distinct places and built forms. The colours of the action lines might have subtle differences in relation to the colours of the places they approach. Action lines converge in places by (informational and spatial) approximation.

(c) As action more lines approach places where interactions are supposed to happen, the initially unpredictable maze of lines becomes a more coordinated system: an actual system of interactions where actors cooperate and coordinate their actions.

(d) After each spatially held interaction, action lines move into a new stage where they may change according to new orientations or intentions of the actors. Accordingly, the colours of the lines may change. Our actions go again into a state of unpredictability, as possibilities of actions are presented to actors and some must be selected in action is to be actualised. Entropy increases.

(e) …And then action lines ‘refer’ again to positions in urban space, starting a new cycle of reduction of entropy via interaction and the connectivity of the system (see diagram):

These moments are theoretical, of course: in reality, these stages are likely to happen simultaneously, all the time. This cycle is a metaphor for the role of space in reducing the action of entropy: a complex tangle toward the cleanest streams, connected, where individual actions converge to coordinate interactions in urban places.


 Simulations in silico: how to see an invisible process

We examine this proposition through computational experiments able to assess how social entropy relates to semantic space, and how spatial patterns of materialised information changes possibilities – and the entropy – of actions. Ultimately, we argue that the forms in which social entropy is dealt with is one of the deep connections between society and space – and between the social and the physical city.

Evolution of entropy: colours in a RGB scale refer to parameter weights in decisions on actions to perform in a next time-step, and their impact on entropy levels in different simulations (under the friction of distance). In the palette triangle, each colour represents a specific combination of the three parameters. In each vertex, a parameter reaches maximum value while the others have minimum value. Results are averaged for 30 different runs for 125 parameter combinations.


I’ve published the theory as a book chapter in Brazil, available here: Cidade e Entropia Social

…and check out the new paper in English, with our Social Entropy model and simulations.

More on ongoing research.


By the way, the dynamic metaphor of a ‘social entropy loop’ increasing and decreasing entropy (or variety and unpredictability of actions and motivations) – and the place of a metaphoric space in coordinating actions (and reducing social entropy) was designed by Caio Cacholas, from a diagram of mine [thanks, Caio].

Other nice social entropy diagrams Caio created:



The cycle of social entropy and urban space: potential actions in a state free from space, with high unpredictability and entropy. Actions then converge into places, transitioning into a momentarily ordered interaction system – and then dive again in entropy.



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