The Physics of the City


Mariateresa Sartori et Bruno Giorgini

date de sortie



Arts et études des arts

La città per Agostino è in itinere, è una società peregrina, una sorta di rappresentazione esterna di questa inquietudine interiore caratterizzata anch’essa dall’essere itinerante. Neppure la verità di questa città è esterna ad essa ma concresce nella realtà (..) la città europea è una città itinerante, pellegrina, ed è una civitas perplexa (complessa diremmo noi adesso).

M. Cacciari


The Physics of the City


Cities are the nodes of the human civilization network from Neolithic until today, when more than half of the whole world-wide population is composed by individuals that live in urban systems, from towns to metropolis. So it is obvious that many learning from policy to aesthetics, from sociology to philosophy, from planning to architecture, from engineering to psychology have applied to understand, plan and build up the city development; but not physics. It was not always the case; in the ancient times Aristotle thought that the physis (nature) of the polis (city) was the same physis of the cosmos. But at a certain moment of the history, this harmony between earth and sky, city and cosmos, was broken. From one hand there are human sciences based on the free will and insofar unpredictable and mathematically undetermined; from the other natural sciences, essentially geometry, physics and astronomy, in principle exactly determinate by measuring and/or calculating, and predictable at least in principle because based on invariant symmetries, and whose empirical observations and experiments can be repeated by everyone, to verify the results. Here we are in presence of a bifurcation point from which two completely separated branches, the humanistic one and the scientific, seem to go away. But in the last three, four decades the discover and development of complexity changed the landscape, in the double sense both that many phenomena must be investigated with a multidisciplinary approach if we want really to understand them, and that also in the physics domain a complex paradigm allows us a deeper knowledge of the richness and variety of nature at our human scales.


As matter of fact from one hand many natural events do not respect the deterministic laws neither in physics dominion, from the other one the behaviour and the evolution of human beings are almost in part governed by free will, intrinsically non deterministic. So a completely ordered world appears too much inert and lifeless, and the completely disordered one would make the life and the human culture development impossible. From any point of view the order/disorder duality risks to wear us in a blind alley. Complexity can be conceived as the exit strategy invented by nature to escape from this duality, discovering that many natural phenomena are organized but not deterministic, that is also a characteristic of the social systems, especially the democratic ones.


Roughly speaking complexity is a sort of no man’s land intermediate between order and disorder, where life can survive and evolve, perhaps where life could be originated. Moreover complexity via networks and information suggests that nature and culture coevolve together. Claude Levi-Strauss defined the city as an “aggregate of beings that hold their biological history into its borders and model it within all their intentions proper to thinking creatures, the city results at the same time by the biological generation, the organic evolution, and the aesthetics creativity. The city is contemporary a natural object and a subject of culture”, where clearly emerges the complex nature of every urban system, that today it is generally accepted and considered in order to study the city, its development and evolution. Let’s stop for a moment to consider the city as an extremely intertwined set of flows, information and forms. The city shows itself to be polymorphous, polysemic and polyglot, stratified in time and crossed by actors and objects whose dynamics are extremely different and can be conflictive, often engendering a feeling of chaos, i.e. we can say that cities live at the edge of chaos and the problem is exactly to govern the system emerging complexity and not chaos. If we want to try to express the quality of this complexity in quantitative terms, using the instruments of the exact sciences, without losing its texture, we must reduce the semantic, logical, syntactic and phenomenological field in which to articulate the possibilities of constructing models able to be descriptive, explanatory and, at least to some extent, predictive. A simple consideration can help us in the reduction process: regardless of the variety and complexity of flows, forms and information, an urban system exists insofar as it is inhabited. In our aim a city is not even definable without citizens, elementary components common to any urban system, from the Neolithic Catal Hoyuk to the modern New York, only changing over the time the complexity degree. Therefore our physics of the city will be essentially physics of the inhabited city, and given the large number of elementary components, this means non-equilibrium statistical physics, because the town is an open system. Moreover, given that the elementary components move in urban spacetime, this also means the physics of dynamic systems and since the individuals in the system have free will, we are also talking about probabilistic physics (Pascal firstly modelled the human free will by the probability function, using the game of chance as paradigm). To finish, since the elementary components have memory and are able to draw information from the environment, processing it according to intentions, choices and decisions, the physics of the city must also be intentional, cognitive and decisional. Furthermore cities can be also considered as adaptive complex systems. In fact the cities conserve coherence and persistence over a long time, nevertheless being open and far from equilibrium. If you think for example to Rome you can see that the urbe aeterna, the eternal city, develop continuously a sort of recognizable and dynamical identity.


Another basic ingredient of physics, besides the elementary components, is a spacetime where the dynamics can evolve. So we can ask if it is possible to identify a spacetime structure proper to a generic urban system. Obviously we can describe the streets network, and the different morphologies with a spatial metric that usually it is not Euclidean, but this it is not sufficient to develop an urban dynamics. We need also of a clock, a time structure scale invariant. This structure can be modelled by the chronotopoi (literally, places of time), the primal agents of urban temporal dynamics able to generate time correlations that would not exist without them. In the planning language, the chronotopoi are defined as areas where are implanted temporal scheduled activities, for example an hospital, the university, a shopping center and so on, that generate/attract mobility. Urban topology thus becomes chronotopic and the interaction between the individual’s agenda and the chronotopoi pulsations produces complex urban mobility. Shortly we must tackle with an automata gas, i.e. a gas of individuals that can assume and process information, the automaton being a sort of perceptive and “intelligent” atom; more precisely a particle, with mass, size, velocity, vision, social space and with a cognitive internal state.


The Venezia Bridges


Obviously investigating urban dynamics, we studied and modelled different mobility types, essentially private cars, public transportations means, and pedestrians. In particular the pedestrian dynamics and crowd phenomena evolve continuously in the space, the individual trajectories generally are not Euclidean, i.e. the pedestrians’ particles often do not respect the minimum action principle, and constitute a strong sociality vector. Moreover this dynamics can enlighten the human behaviour: “in no time he was fascinated, seeing how unselfconscious people were in their movements, how unique each man’s movements were, and how much of the person they revealed” (V. S. Naipaul).


We observed and studied the pedestrian dynamics and crowd phenomena on the Venezia network, in normal situation and during the Venezia Carnival or others big events. The Physics of the City Laboratory collaborating in a common research programs PRIN with the Sociology Dept. of the Milano Bicocca University, the IUAV (Istituto Universitario di Architettura di Venezia), the Politecnico di Milano, Facoltà d’Architettura, and others partners, collected long time series of data with GPS and video movies, building up 1) a microscopic pedestrian dynamics modeling and simulations, 2) a differential equation which points out the existence of a critical threshold for the possible transition to chaos which can be interpreted as the emergence of panic. This limit in principle is calculable by measuring the control parameters, i.e. the utility function for the cooperative behaviours and the social temperature which measures the individual free will and selfish behaviour. But in order to describe, understand and predict, at least in a statistical sense, the global dynamics on the Venezia network, we considered the bridges as crucial points where the problem of opposite flows crossing each other is particularly evident. In this way we have seen that the bridges pedestrian flows are statistically correlated. Moreover analyzing a portion of city, Punta della Dogana, i.e. reducing the complexity, we were able to write a statistical linear theory with exact steady state solutions, which was a guideline to construct a software for the flows. In this virtual environment we performed many in silico experiments in good agreement with empirical data. Finally we measured the Venetian network complexity, via Information Centrality, finding a power law distribution, which is a typical complexity signature.




But what was completely unexpected has been the empathy between the Physics of the City Lab researches and the artistic milieu of Venezia. So one of us (Bruno Giorgini) was called to become member of the Cantiere di Lavoro-Venezia Biennale, titled Città Mobilità Cultura (City Mobility Culture) discussing during three years (2007-2009) completely friendly and free with artists, sociologists, historians… as Alberto Abruzzese, Giorgio Busetto, Anna Detheridge, Paolo Fabbri, Gian Piero Jacobelli, Michelangelo Pistoletto, Ame-rigo Restucci. This work produced three books, and above all our —between Bruno Giorgini and Mariateresa Sartori— actual collaboration based on the common strong interesting on pedestrian movements. The first step was video movie “sistemi complessi” (Complex Systems) and a series of designs created by Sartori utilizing the physical empirical data of the Lab. (see pictures). We report here the words of Sartori, explaining the core of his artistic work. “I traced the pedestrians’ movements, drawing their paths with a felt tipped pen on a transparent sheet placed over the computer monitor. I then faithfully transferred the results onto ordinary large sheets of paper. The procedure is rudimentary and imprecise. Nevertheless it is an imprecision that is not so approximate, in so much as the movements are recorded in a “relatively” faithful manner, in other words as faithful as human sense perception can allow. I am very interested in the modalities of perception, which are imperfect, yet sufficiently perfect to make our existence possible.

• I want this to be a record, a relatively precise record of what occurred.

• Invent nothing, observe what has been and what is, and know that is exactly how things went, even though everything could have gone differently.

• Quietly record, trying to convey that incredible complexity that makes our strange world beautiful.”


The Marseille Agoras Project


The second our collaboration step is the Project that we are developing at IMèRA on Marseille, a city with a high degree of complexity: it has a great harbour for the global trades, a port of destination for many people especially from Africa and MO, it is a node of the immigration path networks, an interface between different civilizations, a critical observation point for the melting pot, the multiethnic and multicultural society, and the civil cohabitation. Moreover Marseille is one of the most important cities of the European Mediterranean area, with Barcelona, Genova, Napoli, and Venezia which have many similar characteristics. Our main idea is to discover and describe the Marseille Agoras dynamics as counterpart of the ghetto dynamics. In a provisional definition, the agoras as open chronotopoi highly significant, places where different people(s) can friendly meet, converse, discuss, picnic, play foot or basket and eventually decide civil action in order to take part at the policy life and planning: shortly the agoras are chronotopoi where selforganization dynamical processes and cooperation structures can emerge. In our conception a beach, a garden, a concert can be chronotopic, i.e. time dependent, agoras. Moreover we would also design the agoras network, and finally arrive to set up an atlas of the Marseille Agoras, with images, measures and “theorems” (“Entendez par théorème ce qui permet de voir”, Michel Serres).




The human mobility is essential for civilizations evolution and individual freedom, and we think that investigating the crowding and pedestrian movements in order to enlighten the “hidden” underlying dynamics, it could be possible to understand more on the social, cultural and also politic behaviours, in our case focusing on citizens and urban systems. With an eternal question in the background: if it exist general natural laws and features governing human mobility, a sort of fundamental level, or if the human mobility is essentially defined by the social, cultural and politics specific conditions.

B. Giorgini, « Philosophie naturelle de la causalité et du hasard dans un modèle de mobilité urbaine » in Chaos et systèmes dynamiques, S. Franceschelli, M. Paty and T .Roque (éds), Editions Hermann, 2007, p. 259.
A. Bazzani, B.Giorgini and S. Rambaldi (eds), Physics and the City, Advances in Complex Systems, 10, Issue 2 (2007).
A. Bazzani, B. Giorgini and S. Rambaldi, Traffic and Crowd Dynamics: the Physics of the City, Encyclopaedia of Complexity and Systems Science, Springer, Part 20 (2009).
Mariateresa Sartori, Le ragioni della scienza/The Reasons of Science, La Corte Arte Contemporanea Firenze, Galleria studio g7 Bologna, Venezia 2002.
Mariateresa Sartori, Tutte le pause del mondo, Galleria Michela Rizzo, Venezia 2006.
Mariateresa Sartori, Il suono della lingua, Fondazione Querini Stampalia Onlus, Venezia, 2008.

Bruno Giorgini est physicien, chercheur au CIG Bologna University and Istituto Nazionale di Fisica Nucleare (Bologne, Italie). Mariateresa Sartori est artiste. Ils ont monté ensemble le projet The Physics of the City à l’IMéRA de Marseille.



21/05/2012 - 13:30 - 18:00


Sciences de la matière
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