Qual Quant DOI 10.1007/s11135-015-0237-6
Human mobility world lines on urban topologies Bruno Giorgini1,2 • Mariateresa Sartori3
Springer Science+Business Media Dordrecht 2015
Abstract In this paper we show some urban geometries generated by different human mobility types, in particular car and pedestrian mobility. These dynamical morphologies have been observed in many cities by working the Physics of the City Lab. Here we present two examples of the Torino car mobility network, some pedestrian trajectories in Marseille places, and crowding examples during the Venezia carnival. The pedestrian trajectories have been drawn by one of us, Mariateresa Sartori, a Venetian artist, using many video movies turned in a well defined spacetime framework, performing an artscience project on complex cities from Venezia to Marseille developed by us at IMERA, Marseille (2011–2012). In particular the investigations on walking pointed out which pedestrian world lines in general don’t follow Euclidean straight lines but more complex paths we guess due to the individual free will. Keywords Artscience Physics of the city Human mobility Pedestrian dynamics Drawing complex pedestrian trajectories Individual free will
Dioge`ne invente le the´ore`me fondamental de la connaissance, entendez parthe´ore`me ce qui permet de voir; et celui-ci dit: les choses a` voir, a` connaitre,celle qui font comprendre toutes les autres: eau, feu... sont ininte´ressantes. (Michel Serres)
1 Geometries Discussing the transition from the primeval universal chaos to the actual Cosmos (in ancient Greek meaning harmony), Plato writes (Timeus) that the agent of this changing is the Demiurge which is mathematician, i.e. master of the essence of Reason, and in the & Bruno Giorgini
[email protected];
[email protected] 1
Physics of the City Laboratory, CIG Bologna University, Bologna, Italy
2
INFN, Bologna, Emilia Romagna, Italy
3
Freelance Artist, Venice, Italy
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Simposium the agent ordering the world is Eros, i.e. the master of the essence of Passion. So we have two different agents for the evolution from the primeval chaos to the present complexity of Nature, which permits the earth being habitable by living individuals, especially human, in particular building up the cities. And it is significant that for Aristote, the physis (nature) of Cosmos is the same of Polis. Cosmos and Polis have the same geometry: the circle. So there is a unity between the sky and the earth, stars and human beings. In order to understand the connection between geometry, the geometrical forms, and polis, i.e. the politics forms, we can read Michel Serres: Dans Mythe et Pense´e chez le Grecs, Jean Pierre Vernant cherche et trouve des rapports entre ces premiers mode`les rigoureux du monde et telle re´volution bouleversant l’organisation politique et l’histoire sociale: (..) la ce´le`bre isonomie ou` e´galite´ de´mocratique des droits. A la fin de son discours, le parleur du centre se de´place vers le bord, et qui veut parler passe du bord au centre: liberte´ de mouvement et d’expression, dit-on. […]. Les discussions sur l’agora jaillissent d’une assemble´e circulaire: on a vu que celui qui de´clame se place au milieu: sur la circonfe´rence, voila` les re´cepteurs en position d’e´galite´, the circle being the perfect symmetric curve where all the points are equally distant from a one point, the centre, but Placez-vous en cercle pour mieux admirer son centre, vous tournez exactement le dos a` ceux qui, exclus, restent a` l’exte´rieur, and periphereia in ancient greek signifies exactly circumference. The circle is a figure defined on a homogeneous and isotropous space, in principle measurable via a Euclidean geometry, which was for the ancient Greeks also the best geometry from an ethical point of view (Aristote), where ethos means in classical Greek language, inhabitable. So the urban space can be described by a Euclidean geometry, assumed isomorphic with the inhabitants’ geometry. At this point we can give a geometrodynamical definition assuming the urban space as the set of all possible individual movements, that we call citizens world lines. Arriving from the ancient Greeks philosophers to the modern age, the Euclidean rationality is assumed as fundamental by one of the most important architects and urban planners, Le Corbusier that in «The City of Tomorrow and Its Planning», (1986, first edition 1927) enunciates a sort of ‘‘straight line axiom’’ coupled with a «pack donkey paradox». Man walks in a straight line because he has a goal and knows where he is going; he has made up his mind to reach some particular place and he goes straight to it. The pack-donkey meanders along, meditates a little in his scatter-brained and distracted fashion, he zigzags in order to avoid the larger stones, or to ease the climb, or to gain a little shade (…) But man governs his feelings by his reason. The pack-donkey’s way is responsible for the plan of every continental city (…) the modern city lives by the straight line (…) demands the straight lines; it is the proper thing for the heart of a city. The curve is ruinous, difficult and dangerous; it is a paralyzing thing (…). Geometry is the foundation. It is also the material basis on which we build those symbols which represents to us perfection and the divine. (..) The city of today is dying because it is not constructed geometrically.’’ Therefore the Euclidean geometry, in particular the straight lines assumed as the natural path for humans, becomes the foundation of the urban planning and building, which in this conception must be isomorphic with the straight line propension of the humans being rational. Moreover the Euclidean geometry of the straight line is considered in the Le Corbusier thinking a symbol for the ‘‘perfection and divine’’, and what he describes as ‘‘the March towards order’’ imposes the straight line discipline. But there is the ‘‘little’’ problem of the continental cities, that seem to be planned and constructed by a zigzagging pack-donkey; a veritable paradox because the origin and development of Reason, the Logos, is exactly located in ancient Greece and in the pack— donkey Polis, Athens for instance. Now it is interesting to note that the Le Corbusier axiom, assuming the pedestrian particles naturally walking along Euclidean lines, is also
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today the basis, explicit or implicit, for the pedestrian dynamics studies. But if the path from Plato to Le Corbusier runs along the linear Euclidean geometry, we can find also another way described in the Rerum Natura, the Lucrezio poem. Synthetically the atoms fall down along gravitational vertical parallel straight lines, but in order to constitute the matter, i.e. atoms agglomeration, the particles must collide having a deviation, in Latin: clinamen, from the straight line, so describing zigzagging trajectories. In this philosophy framework the transition from disorder to order could happen through turbulence (weak chaos) phenomena, i.e. twisters and/or whirls formation. It could be that also the ‘‘intelligent atoms’’ called pedestrian must have one or more ‘‘collisions’’ deviating from the straight line in order to create a citizens agglomeration- to say a complex system composed by individuals—if do you want, a Polis in ancient Greek civilization and/or a Civitas in Roman context until the modern citizenship in the third generation metropolis.
2 Mobility Mobility and transportation are a common need in many different natural systems, where individuals interact each other by cooperation and/or by competing for the same resources. For the social systems (not only the human ones) the features of mobility are closely related to the community structure, organization and evolution from various point of view, for instance individual freedom, energy consuming, pollution. Human mobility (Giorgini et al. 2007) today is also significant for planning, design of transportation systems, especially related to the inclusion exclusion dynamics, forecasting the diffusion of infectious diseases, for the populations’ conflicts, and war strategies. Synthetically mobility is fundamental for human being freedom, sociality and quality of life, and it is not a case if in the EU (European Union) a discussion is open on the possible definition of mobility as a basic human right. In the last years the studies on this field have strongly grown, considering the mobility policies as fundamental tools for the social governance. Specifying the human mobility in the urban systems, we must consider the street network and the different transport means. We define mobility as the propension of the single elementary component- the citizen- moving on a spacetime topology. It is therefore an individual property. Our main idea is that observing and modeling the citizens mobility we can enlighten and study, eventually understand and describe, the social background microscopic urban dynamics that in principle is invisible, i.e. not directly observable. Moreover we introduce the time as an essential variable via the chronotopoi. The city is studded with collective activities, time dependent, spatially located and defined (a hospital, a market, a university…). In planning language the chronotopoi are the spacetime representation of the urban time dependent activities. For us the chronotopoi are the primeval agents of the urban temporal dynamics, introducing correlations that would be absent without. Our definition permits to build up quantitative models that can be implemented on a computer, and tested with experiments in silico (Simulations) (Bazzani et al. 2009b). Now in Fig. 1 we show the picture of traffic, i.e. the vehicle mobility, in Torino, where the network structure is clearly visible. Figure 2 exhibits the Torino chronotopoi locations, where the intensity indicates the population density. It is evident the social transformation from an industrial city to a marketing and service one. Thirty years ago the larger density would be present in the Mirafiori and Lingotto (FIAT factories) area, and today it is not the case. Instead you can see that the higher densities are located in the super and hypermarkets, and trade centers areas.
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Fig. 1 Vehicles mobility network in Torino built up with 5 millions of GPS data
Fig. 2 Chronotopoi in Torino
3 Pedestrian dynamics and crowding Pedestrian is one of the most important actors of social urban life, and the pedestrian dynamics is one of the principal sociality vectors. The walk, la promenade, can be considered the beginning of the citizen condition, when individuals don’t remain at home, a private space, but become public city spaces explorers and inhabitants. Walking and meeting each other in public open spaces, pedestrians build up a network of social micro
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interactions constituting one of the basically matters for the connective texture of urban society. There is a reciprocal action between pedestrian dynamics and public spaces, the pedestrian dynamics designing the public spaces and vice versa, but not in the sense of the Newton action reaction principle, where action and reaction have the same intensity, that it is not true being the interaction between citizens non linear. Pedestrians can be studied as particles subjected to forces or physical interactions, as a granular fluid, as walking and goal directed agents, as living reactive beings, as socially interactive individuals, as moving psychological entities, as cognitive ‘‘atoms’’, and so on, i.e. we are in presence of a highly complex actor, the pedestrian, moreover moving on a highly complex spacetime, the urban topology. A specific phenomenon emerging from the pedestrian dynamics is the crowd, in particular very relevant at least from the beginning of modern societies to the actual post modern ones, from different point of view: political, social, economical, cultural, sporting, religious and so on. From the first universal exhibition in the XIX century the big crowding events have been multiplied in the world so that many studies are today concentrated on the crowd managing and control, to avoid panic and to guarantee individuals security and safety. In other words the big events dynamics rarely can be foreseen, above all when crowd develops in highly non linear way with possible phase transitions, from order to chaos, with panic generalized behaviors. But this theoretical and applied studies flowering has not also produced a coherent and scientific community shared theory, because the high complexity degree and the need multidisciplinary approach, crowd dynamics remaining largely unpredictable. Moreover we can find in literature different definitions and types of crowding. In particular the Physics of the City Lab (Bazzani et al. 2009a) defines a crowding state when the people density is such that the individual social space can be invaded by others unknown persons. Concluding this very synthetically exposition on pedestrian dynamics, we underline that the basis paradigm remains the Le Corbusier straight line axiom, which in dynamical terms means that pedestrian walking naturally follows the minimum action (energy) principle. Now we will show a little sample of the many pedestrians’ paths drawn by Mariateresa Sartori using video movies, discovering that pedestrian mobility behaviour is more complex with respect to the Euclidean straight line axiom.
4 Drawings Drawing trajectories it is not today usual in order to investigate path geometry, but we think in this case the drawings are able to make perceptible the pedestrian world lines, exactly for the intrinsic uncertainty of the pedestrian walking. In this sense the drawings are more realistic, i.e. more isomorphic to reality than the polite lines designed for example in the virtual universe when we perform simulations. Moreover this technique surely is not new in the natural philosophy research, remembering the Galileo designs of the sunspots and of the Moon Mountains, where a consistent part of the phenomena understanding was linked to the drawing ability to give a realistic representation of what the observers could watch by a telescope. So in this part we describe briefly the drawing technique performed by Mariateresa Sartori (in the following M.S.). For our IMe´RA project we collected a large amount of documentation about pedestrians’ movements: 72 h of video material for different Marseille public open spaces watched from above, a fixed camera defining our research universe, once and for all the time of our shot, in order to have a well established spacetime—a landscape with precise boundary conditions—where investigating the
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pedestrian dynamics. After we have analyzed and observed the whole material choosing the pieces of reality on which focus our work. This is the more delicate point because the decision is subjective, but we think not having too much twisted the real situation. More precisely, we have reduced the mapping of our investigations but not falsified the resulting geometry, because in our cases the pedestrian dynamics is individual, and/or of little groups, i.e. the single path is relatively independent from the others people walking. Obviously it had been different if we were tackling with a dense crowding. In this case, see the Piazza S. Marco drawing Fig. 15, we did not select any specific individual, and M.S. designed all people trajectories. Assuming a given space, we observe how it is created in its possible features by human presence, by its trajectories, its being motionless, its slowness and speed. The space therefore is for us analogous to a field of forces, where the boundaries delineate new figures each time (ubi materia ibi geometria—Kepler), in qualitative sense forces of attraction and repulsion, generated by human presence which fulfilled the empty space. Starting from the chosen pieces (generally along a time interval of about 15 min) M.S. did many drawings following a rudimentary, even crude procedure: she traced the pedestrians’ movements, drawing their paths with a felt-tipped pen on a transparent sheet placed over the computer monitor. The lines drawn in different directions create the space. Drawings are imprecise, but 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, the modalities of perception being imperfect, yet sufficiently perfect to make our existence possible. In this context M.S. used a computer, a high technological instrument, in a mechanical way, as the drawing process is mediated by human sense perception: the drawing hand is moving in sync with what the eye is seeing. So there is a perfect synchronicity between hand and eye. Therefore that one could say it is the hand that sees. The way how M.S. holds the pen in her hand is revealing: with the fingertips. Therefore you cannot have a perfect control on the sign and you have the physical sensation of being just a sensitive instrument. You feel yourself like a seismograph. M.S. wants to be a mere record, a relatively precise record of what occurred. Without to invent nothing, simply observing what has been and what is, and knowing 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 unspeakably beautiful. Observing reality, measuring phenomena through human senses is often the first step of the artistic research of M.S. investigating the discrepancy between reality perceived through the senses, and the truths of science. We know, they are true, but often we are not able to feel them true, we are not able to interiorize them as real things and not only abstract expressions of the scientific rationality. The artist M.S. works in, and feel, this intimate discordance. For this reason the hand becomes a seismograph that makes visible an organized complexity appearing alive in a very simple way: a drawing like a diagram is a help for thinking, like all well-made diagrams are, something that helps feel the representation in a simultaneous way: the drawing as economy of thought. The different figures are generated by a structure: they in principle are infinite, but not every figure is possible. The structure or rather the structures, i.e. the shape of the square, the planning elements and at last the human nature with its limits and its abilities delineate the figures. In the drawings every line is determined by different factors that make it inescapable. It has in itself its necessity. The videos of people seen from above in different public open spaces were not only the basis for the drawings. Through a particular way of framing we highlighted some situations which show a specific dynamic in the trajectories of the
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protagonists: a little dancer, a skater in the darkness, some volley-ball playing in the beach, a woman waiting in a desert square, people passing from shade to light. In Figs. 3 and 4 we show the trajectories of two young girls walking and running at Place Villeneuve Bargemon in Marseille during 15 min and 17 s from 5.08:00 to 5:23:17 pm Wednesday, 14 September 2011. It is perceptible the forms similitude between the two paths, that evidently are not linear. In Fig. 5 we see a sequence of pedestrian trajectories, very similar to a weak turbulence dynamics formation (limit cycle designed in the last square).
Fig. 3 Young girl 1
Fig. 4 Young girl 2
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Fig. 5 Vieux Port, Place Peri
5 Some others examples The following drawings represent the actual trajectory traced by people going in Place Jean Jaure`s, Marseille, September 16, 2011, from 6:48:00 to 7:03:52 pm. In Figs. 6, 7 and 8 we have distinguished people going alone from people moving in pairs and/or in three or more. It is perceptible the people that goes alone filling the space in a more wide spreading way than coupling and triadic. In other words, the singles show a more free mobility with respect to the couples and the trio, which is congruent with the smaller number of freedom degrees because the constraints in the case of couples and trio. We can also think that the individual free will is more ‘‘free’’ for walking singles than for tied couples and trio. In Fig. 9 we show all people together. The drawings below show the actual trajectory traced by people going on the beach de Corbie`res in Marseille, September 18, 2011, from 4:33:00 to 4:38:40.pm. Here we have distinguished different direction flows and different areas. In Fig. 10 we watch people tracking quasi linear paths, i.e. the minimal Euclidean distance, going to the beach. In Fig. 11 we can perceive the difference between these paths and walking on the beach, which show a feature similar to a tree structure, common to many other complex phenomena. Moreover in Fig. 12 you can see also the dynamics going in the water much more fractured due to the passage from solid to fluid matter. Finally in Fig. 13 we put all the different movements’ drawings emerging the entire complexity of pedestrian trajectories going to the beach, moving on, and at the borders between sea and land.
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Fig. 6 People going alone
Fig. 7 People going in pairs
Now looking for Venezia, we like to quote a sentence by Italo Calvino (Invisibles Cities – Vintage Books – London). In Smeraldina, city of water, a network of canals and a network of streets span and intersect each other. To go from one place to another you have always the choice between land and boat: and since the shortest distance between two points is not a straight line but a zigzag that ramifies in tortuous optional routes, the ways that open to each passerby are never two, but many, and they increase further for those who alternate a stretch by boat with one by land. And so Esmeraldina’s inhabitants are spared the boredom of following the same streets every day.(..) The most fixed and
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Fig. 8 People going in three or more
Fig. 9 All people going
calm lives are spent without any repetition (Invisible cities - Vintage Books London).
6 Venezia and crowding And Walter Benjamin write: La nature, par la foule, exerce son droit fondamental sur la ville. For crowding in Fig. 14 it is possible to watch the pedestrian fluxes obtained by the Physics of the City Lab (Omodei et al. 2012) using GPS signals recorded during the Venezia Carnival (2007). We can observe that the larger part of the city is quasi empty (with a low individuals density), also during a big event as the Carnival.
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Fig. 10 People going on the path to the beach
Fig. 11 People going on the path and people going on the beach
In the following Fig. 15 we show the M.S. drawings tracking the pedestrian trajectories in Piazza S. Marco during the Carnival. Some lines are quasi straight, and roughly speaking can be interpreted as the paths covered by the individuals having an agenda strictly determined for example by working, and moreover often being commuters, with a timetable more rigidly defined also for taking into account the transportation delay. The others as tourists, visitors, flaneurs are walking along more complex and unpredictable world lines. This different behaviour can be understood if we take into account the individual free will. It is obvious that when we are obliged going to work at office hours, our free will
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Fig. 12 People going on the path, on the beach and in the water
Fig. 13 People going on the path, on the beach, in the water and from strand to water and from water to strand
usually has a narrow action range. More precisely during the trajectory from home to work we assume a free will state level near to zero, choosing the best paths that minimize distances and/or times, with a minimum energy consuming. Nevertheless when the freedom degrees grow giving us a larger spectrum of possibilities, our individual free will returns to play a consistent role choosing the paths, not only the minimal, but for instance the more beautiful, or passing where we know there is a nice coffee shop etc.…and so the world lines become more complex and the walking morphology more various, rich and
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Fig. 14 The pedestrian fluxes in Venezia during the Carnival constructed using GPS signals collected in 2006 and 2007
Fig. 15 All people going, Piazza San Marco, Venezia, from 2:05:00 to 2:07:43 pm, 26 February 2006, 170 9 240 cm, pen on paper, 2009
interesting. Looking the figure you can perceive the complexity of the dynamical space fulfilled by so different and various individual trajectories designing this irregular net. Finally in Fig. 16 we present a snapshot of the fluxes in Dorsoduro, a Venetian Sestiere, simulated with a software built up by the Physics of the City Lab, collaborating with the
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Fig. 16 Screenshot of the graphic interface of the software. The sliders on the right allow the user to change the control parameters of the system, like the social temperature and the number of people coming in from the bridges and the boats
Architecture and Planning IUAV University (Mamoli et al. 2010), and you can see a sort of simple order created by the choice of working at the level of the fluxes, i.e. with mean values having a physical sense only for the statistical equilibrium and steady states. So you have the strange situation, for which the individual walking drawings are more suggestive in order to perceive complexity of the individuals’ behaviour, yet to mathematically model and simulate predicting, you must operate with some averaged abstract quantities. In other words between the human perception of the phenomena, especially complex phenomena, and the mathematical representation and computing there exists a dyscrasia that the modern algorithmic and computer science today is unable to solve.
7 Conclusions We have shown some forms related to human mobility, traffic and pedestrian dynamics, obtained by different techniques, video movies, GPS signals, drawings and simulations. In particular the pedestrian dynamics phenomena, observed by video movies and drawings in Marseille and Venezia, falsify the usual item that the natural pedestrian walking is along a straight line and performed with a constant velocity. The pedestrians’ particles move in a more complex way because the humans are endowed with free will and emotions. As the writer Naipaul said: 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. In a different language we can conclude that the complex pedestrian paths describe forms enlightening a background social microscopic dynamics, in principle invisible. Moreover at the present the observed real pedestrian world lines are too complex and/or irregular in order to be represented only in a strictly mathematical and/or algorithmic way. So mixing different tools, from drawing to simulations, with a common point of departure, the empirical observations, seems to us a good strategy for feeling, perception and understanding the strange and charming particle called pedestrian.
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Human mobility world lines on urban topologies Acknowledgments We thank very much the IMERA Institute for the nice hospitality and the interesting discussions in particular with Samuel Bordreuil, James K Gimzewski, Scott Gresham—Lancaster, Kathryn Gresham- Lancaster, Robert Ilbert, Roger Malina, Victoria Vesna. Moreover we are glad to thank le groupedunes which organized the exhibition Agoras de Marseille/Visions et geometries (11 July 2012 at La Friche de Marseille) where we had shown to a public of artists and scientist some results of our common work. A particular thinking by BG for Robert Ilbert that during the time of B.G. residence organized some interdisciplinary seminars on the chronotopoi in different context, and for various times scaling phenomena.
References Bazzani, A., Giorgini, B., Rambaldi, S.: Traffic and Crowd Dynamics: The Physics of the City—Encyclopaedia of Complexity and System Science, Editor-in-chief R.A. Meyers, pp. 00641, ISBN 978-0387-75888-6, Springer, Berlin (2009a) Bazzani, A., Giorgini, B., Rambaldi, S., Turchetti, G.: In: Diamantini, D., Martinotti, G (Eds.), The Physics of the City: Modeling Complex Mobility. Urban civilization from yesterday to the next day, pp. 215–249. ScriptaWeb, Napoli (2009b) Giorgini, B., Bazzani, A., Rambaldi, S.: In: Giorgini, B., Bazzani, A., Rambaldi, S. (Eds.), Editorial: Physics and the City. In: Physics and the City Special Issue of Advances in Complex Systems ACS 10(2): pp 215–221). World Scientific Publishing Company, Singapore (2007) Mamoli, M., Michieletto, P., Bazzani, A., Giorgini, B.: Venice as pedestrian city and tourist magnet. In: Proceedings of the Venice Transport International (2010) Omodei, E., Bazzani, A., Rambaldi, S., Michieletto, P., Giorgini, B.: The Physics of the City : Pedestrian Dynamics and Crowding Panic Equation in Venezia (1–41). Qual Quan Int J Methodol, Springer, Electronic version ISSN 1573-78452012 doi:10.1007/s11135-012-9773-5 (2012)
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