IaaC Bit 5.1.1

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Implementing Advanced Knowledge


5.1.1 Ruled Surface Edouard Cabay

Ruled Surface

and the condition of indetermination in spatial organisation

“Let go of a certain kind of control to let other things happen.” Cage, John A line drawn on piece of paper, from one side to another separates the space of the paper into two areas. While one might say that a line can act as the geometrical figure that relates points, as a direction or a path, in the language of the architectural drawing it generally has the property to isolate one space from another, therefore to cut space into two parts. It is deterministic, in a top down manner and, as a consequence, it creates a yes/no or an on/off condition. On one side of the line an activity is supposed to happen, while on the other, a different one. It could be argued that one could sleep outside of the bedroom and yet, when the space is planned - or the line is drawn - there is a clear design that relates the space and its use - the place and the event - which usually is not done in a flexible manner: in this case the line seeks clarity and order. An architectural drawing, although primarily used to represent a spatial environment yet to be constructed (what differentiates it from a map, which shows an existing spatial environment) shows a static condition. It does not integrate the dimension of time and is therefore not bound to respond to the behaviour of the user or to consider the evolution of its very structure. It reduces the role of the user to passively inhabit rather than to participate; it does not integrate dimensions of unexpectedness, chance or indetermination. We will examine different case studies that provide examples of the temporal and spatial organisation of events in a conditioned environment that consider the dimension of the unexpected, integrating “accidents” and exist only through indetermination. The predominant example is the situation of public space in an urban context, where a peculiar antagonism occurs between the space used by people and the one attributed to cars. A line separates the two; materially it merely shows a very slight topographical drop the size of a step, but in terms of spatial protocols, the two spaces on either side of the line function in an opposing manner. The surface of the car space is rigidly ruled to dictate behaviours; the pedestrian counterpart is a flat surface, not less ordered and yet a permanent stage of unpredictable events. The conceptual difference between these two environments and their Cover - Glories Regenerative Systems. Rana Abdulmajeed, Tobias Deeg, Martin Hristov, Peter Magnus, Utsav Mathur, Nour Mezher, Jean Sebastian Munera and Lili Tayefi. Institute for Advanced Architecture of Catalonia. 2015. 2

operational modes are central to the argument developed in this article. In urban space, the car is a threat to people, mainly due to its speed. As a result of this danger, the open space of the city has been divided into two areas: one for the pedestrian and the other for motorised traffic. A subtle yet abysmal ten centimetre vertical shift creates a topographical cut that separates people from cars. There are two territories, with partial and controlled incursions of one into the other, notably the pedestrian crossing, temporally regulated by a flashing red or green light. The space of the car has an order of its own, commanding an adherence to strict rules – a code - often represented by white lines painted on it’s surface. Indetermination is the enemy of this space, a environment that does not permit actions outside of its strict rules.

The line and the surface

A line defines an on/off condition. In an architectural drawing, the line reductively states that actions or events happen on either side. For example, a line encloses a room in which one is supposed to sleep, the bedroom. The line delimits an area in which it is understood that the user will be sleeping, while outside the user is not suppose to sleep. While most interior spaces are conceived in such a way where the line is constructed as a wall that isolates and creates privacy, in the open space of the urban public realm, that strategy is far more questionable. In the case of the urban environment, there is a line that rigidly separates the car space from the pedestrian space. Let´s consider that in the future, this limit will no longer be relevant; that it is destined to be transformed into something that does not create an on/off condition, but rather allows events and activities to occur on a single surface. This hypothesis serves as a premise for the question: Does a line invariably need to define a spatial boundary? How can we contest its deterministic quality as to integrate the parameter of chance and unpredictability and trigger authenticity in the unfolding of events in space? In a drawing of the Jardin du Luxembourg, a surface of 20x20 metres features a typical Parisian public space, an apparently generic planar area covered by gravel, a homogeneous surface that contains neither obstacles nor attractors. On this surface the author has rigorously mapped the path of people walking through the space also recording their age. A scientific theorem proposing a direct relationship between the age of a person and the energy that he/she emits enabled the author to graphically transform the line into a network of radiating lines representing the quantity of Joules. The map no longer features the path employed by the wanderers, it precisely shows the amount of human bodily energy emitted at any given point of the surface of action. Through this drawing, the author has not only depicted the particular



behaviours of use of this apparently homogenous space; more importantly, she has used a graphical language that creates a map of gradual intensities. As a result, the space is not understood as a place where energy is being emitted or not, but provides an accurate representation of where the energy is emitted and in what amount. The space is not cut in two or more areas, but rather unfolds as a surface with different intensities of use. Both graphically and spatially, the figure unfolds as a field; it is not linear but gradual. Traces left on a generic object can express how it has been used. In so, it describes the relationship between the frame in which an action is provoked and the deviations that occur while it happens. A table that has been repeatedly used for cutting paper or cardboard retains, for each act, a cut as a trace or a scar, signifying the passage of the knife. As we see in the image, the cuts do not occur in the same place. Furthermore, no two are the same and yet, many of them are similar in the position they occupy and the direction of their course. Similar to the drawing of the Jardin du Luxembourg, from a certain distance one recognises a pattern of use in a gradient scale of white to black. In the photograph, the centre and the very edges of the table remain whiter; suggesting regions of the surface used less for cutting. As one cuts on a table, the need to maintain a level of practical-corporal comfort in the action results in the use of the surface near its edge; the size and shape of the table in relation to the particularities of the body in the action of cutting determines the space of interaction between the two. The table demonstrates the relationship between an object designed to be used in a certain manner, and the complexity of the occurring action - cutting - leads to results which are alike yet always different. In other words, they are partially determined but not fully predictable. Furthermore, the tabletop is a surface with no apparent feature or hierarchy. In this sense, it creates a condition - the horizontal plane - with a degree of liberty in which the action (the use) takes place, leaving place for indetermination. If we were open to detect and observe traces of daily organic actions in the seemingly most trivial situations, a table, a market place, we could possibly find less static and intentional models in order to enhance an element of life to somehow dead environments.

The condition and the event

In Reunion John Cage experiments with indetermination within the event space. Reunion is a theatre performance, which was performed in Toronto in 1968. On stage an electronically enhanced board, created by Lowell Cross, records the moves of a chess game being played by John Cage and Marcel Duchamp; it transforms them into sounds simultaneously played Figure 1 - Energy map, Jardin du Luxembourg, drawing by Shujie Chen. Atelier Re-, Ecole SpÊciale d’ Architecture, Paris. 2013. Figure 2 - Cutting table. Photograph by Anthony Boguszewski.

to the audience by eight speakers distributed around the room. While the rules of the performance are written and strictly followed during event, the progress, or form of the chess game cannot be anticipated. The performance is therefore subject to a variable force or order, and the spatial event that is triggered is therefore unique. The play has a life of it’s own, it can neither be predicated nor repeated, yet it is not arbitrary: it is orchestrated. It contains, and celebrates serendipity, a condition with which Cage plays. On the one hand he clearly defines the rules and on the other, he brings the element of chance and this is what really affects the play or the events; it gives it its originality. In another disciple, in a series called the Cage Paintings, painter Gerard Richter lays paint on the canvas and uses a wooden scraper to spread it from one side of the canvas to the other. He repeats the operation as many times as necessary until a convincing result emerges and the process comes to a halt whereby he abandons the process and the art piece is finalised. Initially, the texture of the canvas, the viscosity of paint, the unevenness of scraper and later, the influential presence of the previous layer beneath creates an unpredictable repartition of the colours along the surface. This work has the particularity that the uppermost layer can only exist because of the previous ones, layers that contain accumulated irregularities - accidents. The process, rather than minimising what would often be considered a mistake, cultivates and even amplifies them until finally, they compose the painting. As with John Cage, Richter relies on chance. The design is controlled, but he is not able to fully predict the result of his acts. We can say that both artists dissociate the action of creating (curated) from the form of the result (uncontrolled). In their work, unpredictability is therefore central: it is deliberately sought and expressed. Across time or through repetition, they carefully navigate between order and chaos, between the intentional and the arbitrary. Richard Long’s A line made by walking, 1967, is an art piece under the form of an event documented by a photograph that shows an ephemeral line created by walking repeatedly back and forth in a field resulting in the flattening of the grass. The line is the direct consequence of a determined action: the rigorous walking from A to B, without any exception. Long was interested in recording his physical intervention within the landscape and the line is the trace of human movement. If the rule was not clearly set (walk from A to B in a straight line), the result would have been relatively different. Not only would the outcome likely not be straight, furthermore, Figure 3 -A line made by walking 1967. Photograph by Richard Long. Property of Tate Modern Figure 4 -Marcel and Alexia Duchamp and John Cage in Reunion. Toronto, 1968. image credit: musicworkds magazine. 8

there would not have been a localised accumulation of steps and therefore no continuous flattening of the vegetation and no trace left on the ground. In nature, where animals make their way in the landscape, a similar process happens. The situation however is different in the sense that behaviours are governed by different and more complex dynamics and evolve over time. Initially there is no trail. As the first animals walk, they will seek the most convenient path. Progressively, their steps will flatten the ground and define an area, which will serve as a sign, a suggestion of use, for the others. The more the path is being used, the more it will physically transform and indicate, or even impose, its use. This line can be both seen as the sign of past events and as the condition to influence future ones, it is created by the action itself and for the action. Created within the context of an academic studio on drawing and energy at the Institute for Advanced Architecture of Catalonia, Automated Drawing is an experiment in which students where asked to produce a drawing without using their own hand or body. The exercise, resulting in drawings with close to calligraphic qualities – what usually caries the complex particularities of a human gesture-, demonstrates that a space subject to simple yet clearly determined conditions provokes actions that embed a certain level of freedom and therefore produce indeterminate results. Here, accidents do happen and are necessary. Two students, Tobias Deeg and Martin Hristov, constructed a pendulum equipped with a magnet and a pen oscillating above a surface of paper fitted with magnets. Due to the magnetic force, the repelling magnets on the page affect the trajectory of the pendulum, inducing a movement close to a dance. The pendulum, ending in a pen, continuously registers that movement under the form of a single sinusoidal line. The pen is less likely to reach the space occupied by the fixed magnets, practically never reaching it, readable as white zones on the drawing. Not allowed in certain areas, the pen tends to occupy more the resulting space, seen as the darker zones. While at the beginning of the experiment, the pen seems to be moving randomly -that line could still be considered accidental-, the longer the experiment is carried through, the longer the sinusoidal line grows, and so the clearer the reading of the pattern of occupation becomes. The resulting drawing becomes a description of the conditions of the environment. Time and repetition are necessary. Figure 4 -Automatic drawing, line in drawn in a magnetic field. Automatic drawing. Tobias Deeg and Martin Hristov. Institute for Advanced Architecture of Catalonia. 2015. Figure 5 -Automatic drawing, line in drawn in a magnetic field. Automatic drawing. Tobias Deeg and Martin Hristov. Institute for Advanced Architecture of Catalonia. 2015. 10

The line, as a mean to organise, is a tool, which is determinant and tends to restrain the organisation of space. When drawn, it attempts to abolish any sort of ambiguity. It cuts the surface of action into sectors, fragments, and often subject by strict protocols of use. The line, as a singular figure, fixes time and only operates on the scale of the instant. It cannot integrate the dimension of transformation or evolution. When time and use enter, the line, if seen as the trace of an event, repeats itself and its singularity leaves place to the collective, integrating complexity and leading to another figure which is the gradient. A figure which cuts the surfaces is so many fragments that they are no longer perceived as pieces, but rather renders the surface as a filed of intensities. Space is indeterminate; the surface is a matrix of potential of uses. On that surface of intensities, events don’t happen either here or there, but potentially anywhere influenced by a suggestive protocol. The condition is not restrictive, but orchestrates a carefully designed set of rules in which indeterminate events happen, or are even provoked; the reverse to the manner of the car space, a strict top-down overruled spatial model. Chance leads to unpredictable situations and constructive accidents. A system that cannot be controlled, but provides another dimension to the space, permitting the user (and its unpredictable behaviour) to be a central governing figure and allowing the surface to evolve, to self-organise itself over time. Rules, or conditions, do on first sight create a limit, but by doing that they originate events, actions, life.


This article was written in the context of Active Public Space, a design studio at the Institute for Advanced Architecture of Catalonia directed by Edouard Cabay and assisted by Rodrigo Aguirre, in 2015. The studio explored consequences of the removal of motorised traffic in the main squares of the city of Barcelona, with a focus on strategies to program the large surface of reclaimed space. Besides the difficulty of the scale, it implies a complex set of issues: the organisation of a public space needs to integrate time (the hour, day, season, decade), both in its function and evolution. The user is in transit, the condition is continuously changing. As a consequence, fixed objects - from furniture to buildings - are inadequate, rapidly become obsolete. A proposal developed for one of the central squares, Plaza de las Glories Catalanes provides a possible solution. The plaza is an urban centre, which has always struggled to define itself. It was initially designed to become the city´s central square; however, its role of traffic hub has turned it into a car park covered by an elevated roundabout. Recently, the city of Barcelona 12

has undertaken its transformation into a public park. The project proposes to integrate waste management on the square as a means to provoke events in order to activate the space. The process of recycling transforms rubbish into usable matter (substances, materials, parts, objects and even building components), that is used directly on the square: organic matter serves as bio-fuel and compost for local orchards, polymers become the primary material for 3D-printed urban furniture and small building components such as market stalls‌. Actions engender actions; the system feeds back into itself. The form and the future of the project cannot be determined as the daily quantity of waste arriving, and consequently what will be produced from it is unpredictable. As a result we cannot anticipate the kind of events that the recycling will provoke, where, and for how long. Since the arrival of waste never stops, the system has to continuously absorb it, and is therefore in endless transformation. The space ceaselessly constructs itself. The waste is the indeterminate input, as is Duchamp and Cage’s chess game in the performance, Reunion. The form of the project is therefore unknown. However, as in the paintings of Richter, the game needs to be played to produce results; provoked by the rules set by the authors of the project and played by the user, certain patterns of use will start to appear on the surface.

Figure 6 - Glories Regenerative Systems. Rana Abdulmajeed, Tobias Deeg, Martin Hristov, Peter Magnus, Utsav Mathur, Nour Mezher, Jean Sebastian Munera and Lili Tayefi. Institute for Advanced Architecture of Catalonia. 2015.


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Manuel Gausa, IaaC Dean

EDITORIAL COORDINATOR Jordi Vivaldi, IaaC bits Editorial Coordinator

EDITORIAL TEAM Manuel Gausa, IaaC Dean Mathilde Marengo, Communication & Publication Jordi Vivaldi, IaaC bits Editorial Coordinator

ADVISORY BOARD: Areti Markopoulou, IaaC Academic Director Tomas Diez, Fab Lab Bcn Director Silvia Brandi, Academic Coordinator Ricardo Devesa, Advanced Theory Concepts Maite Bravo, Advanced Theory Concepts

DESIGN: Ramon Prat, ACTAR Editions

IAAC BIT FIELDS: 1. Theory for Advanced Knowledge 2. Advanced Cities and Territories 3. Advanced Architecture 4. Digital Design and Fabrication 5. Interactive Societies and Technologies 6. Self-Sufficient Lands

Nader Tehrani, Architect, Director MIT School Architecture, Boston Juan Herreros, Architect, Professor ETSAM, Madrid Neil Gershenfeld, Physic, Director CBA MIT, Boston Hanif Kara, Engineer, Director AKT, London Vicente Guallart, Architect, Chief City Arquitect of Barcelona Willy Muller, Director of Barcelona Regional Aaron Betsky, Architect & Art Critic, Director Cincinnati Art Mu­seum, Cincinnati Hugh Whitehead, Engineer, Director Foster+ Partners technology, London Nikos A. Salingaros, Professor at the University of Texas, San Antonio Salvador Rueda, Ecologist, Director Agencia Eco­logia Urbana, Barcelona Artur Serra, Anthropologist, Director I2CAT, Barcelona

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