Construction
Structure
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I walk around the city streets for days on end. I have come to see the world in wire-frame, always from multiple points of view: from plan, elevation, section, and sometimes from a birds-eye-perspective. I calculate the number of polygons, the needed texture maps, camera paths, and the radiosity factors required to construct and animate any given scene. I study the subtleties in light – its shimmering, almost hallucinatory mosaic refracting off intersecting planes of concrete, mirror, and glass, against the crush of urban landscape, amid the splinters of a broken sky.(1)
The space that architect John Beckmann describes to us here is far from empty. It is filled with information, action and structure. It is of course not – even though it could easily have been – a quote from a futurist manifest in the beginning of the 20th century, like the artist Umberto Boccioni, who in 1910 stated that “to paint a human figure you must not paint it; you must render the whole of its surrounding atmosphere.”(2) Beckmann’s space is found at the very end of the late 20th century. It is a space that cannot be considered a neutral medium or an empty atmosphere. It is a space with a strong structure beneath a dynamic surface of digital media.
The aim of this chapter is twofold. First, it is to show what the structures of an embedded space may be, and second, to show how these structures may control the dependency between the design process, the embedded space and its content in a constructive and operational manner. The chapter continues the argument from the previous chapter that media does influence such dependencies. The issue of structure is shared across many different kinds of media, as we shall see soon. There is, however, no doubt that the construction of design spaces has been greatly facilitated by the synthetic space of the computer, but they are not tied up to that medium.
Thus, I will suggest that an embedded space may be structured by a wide range of agents – by logic and reasoning (John Rajchman), information (Michael Benedikt), genetic form (Karl Chu) and topology (Rudy Rucker). Further, I will suggest that there is a difference between the structures of the embedded space itself and the structures of what is placed in that space. Such structures of the embedded space will be investigated and constructed in the experiments Different Rule(r)s, Space Flows and Virtual Tectonics that follow this chapter.
Effective and Affective SpaceIn the foreword to Max Jammer’s book Concepts of Space, The History of Theories of Space in Physics, Albert Einstein defines two concepts of space that may define the structures of embedded spaces. Einstein writes:
These two concepts of space may be contrasted as follows: (a) space as positional quality of the world of material objects; (b) space as container of all material objects. In case (a), space without a material object is inconceivable. In case (b), a material object can only be conceived as existing in space; space then appears as a reality which in a certain sense is superior to the material world. Both space concepts are free creations of the human imagination, means divised for easier comprehension of our sense experience.(3)
Even though Einstein argued on behalf of material objects, his two contrasted concepts may define our embedded spaces, which have the same paradoxal construction. The structures of an embedded space are only recognizable as the result of relations between the objects or operands, and yet they exist and can be constructed independent of such objects. This paradox was present in the way that R.M. Schindler’s Unit System only was traceable by its effect in his buildings as an index or imprint, and yet was defined and manipulated in the smallest detail. Or, in the way MVRDV define a diagrammatic structure of the concept FARMAX (Maximum Floor Area Ration), which was only seen by what it did to the relation between data, while it was not present in itself.
We can understand such spatial structure as the relations between aspects of space and the rules that govern these relations. In other words, if space had no structure it would be impossible to contain the variety of elements we saw in the previous chapter – the spatialized text, the spatial objects, the virtual interface or the real world artifacts. To these elements, the spatial structure act as a catalogue of parameters against which, each element must be defined, or as a set of rules that govern individual relations. Therefore, even though space may seem to be without structure just because it is without objects, it does indeed have structure right from the very beginning. It may be constructed even though it is without objects, as a container for structure.
The philosopher John Rajchman offers another way to structure an embedded space. He argues that there are two kinds of space, which are very different from Einstein’s:
We might distinguish between two kinds of spatial disposition, effective and affective. In the first, one tries to insert movement, figures, stories, activities into some larger organization that predates and survives them; the second, by contrast, seeks to release figures or movements from any such organization, allowing them to go off on unexpected paths or relate to one another in undetermined ways. We can already see that ‘construction’ and ‘intuition’ acquire different senses in the two cases. The first tries to draw all the lines of our various geometries from the fixed points on a prior system, while the second works through a more informal diagram that throws together odd features in a loose intuition that creates its own points as it goes along; and we may thus speak of two kinds of ‘geometry’. Yet, the distinction remains a conceptual one, for there is perhaps no building or city space in which both kinds of geometry do not exist at once, at least potentially. Any constructed space always reveals a tension between the two, the question being which one we put first.(4)
It would be easy to just categorize Rajchman’s effective disposition of space as total structure and his affective disposition as total lack of structure – but of course it is not so. The affective disposition of space does have just as many corridors, relations and guides as the effective does and as they mirror each other, they define their own spatial function and character. While the effective disposition is well known and well exposed in architectural production as efficient modules and grids, the affective disposition may turn out to be just as fruitful and fulfilling. With reference back to our previous investigations and unfoldings, we could observe these two dispositions of space in Schindler’s Unit System or Peter Eisenman’s almost neurotic order of anteriority, interiority and exteriority of architecture, on the one hand, and Edward W. Soja’s aleph or Lars Spuybroek’s dynamic generation of form, on the other. Schindler and Eisenman’s structures could be seen as systematic organizations in space, where each element, data object or operand has an optimum position, while Soja’s and Spuybroek’s systems could be seen as looser and more catalytic in nature, as they let their synthetic embedded spaces react and evolve along the way. Therefore, we may argue that just because a design space has a structure, it does not automatically mean that the structure is straight, predictable and without possibility for divergence.
If we compare Einstein’s and Rajchman’s structures, we can observe that structural concepts may be constructed just as our concept of space may. The two spatial structures that Einstein defines are categorically different, highly conceptual and deduced from rigorous logic, while the structures that Rajchman defines are functional, pragmatic and recognized by what they do.
Space of InformationThe architect and historian Michael Benedikt has a quite original proposal to the structure of space. He seeks deep into the constituent substance of space itself to make space operational, by giving it a ‘voice’ of its own, rather than just articulating a well-known description. In his paper “City Space, Cyberspace and The Spatiology of Information” from 1992, he argues that if space is filled with a substance – or in the terminology of Stephen Kern has a constituency – it is information.(5) Benedikt understands information as a “registering, tracing, questioning and remembering substance,” which is spread all around space, to offer architects the opportunity to manipulate and create space.(6) In this way, Benedikt makes the ‘immaterial’ space tangible – or in other words, constructs an index or imprint of space – and defines a new body of knowledge: spatiology. Since the information is spread evenly in space and since each ‘portion’ of information both has a discrete position in space and content in the form of information, that information takes the place of space. Instead of interacting directly with space, we may interact with information. Benedikt writes: “... Space itself is something not necessarily physical: rather ... it is a ‘field of play’ for all information, only one of whose manifestations is the gravitational and electromagnetic field of play that we live in, and that we call the real world.”(7) This resounds Einstein’s description of a reality superior to the material world, but it still has the affective character that Rajchman mentions.
To Benedikt such a space of information has a great potential, both for describing the way we perceive and manipulate space and for proposing ways to construct space, especially in the light of current media and synthetic spaces. Benedikt’s space of information serves as a bridge between the real and the imagined across language/myths, media technology, architecture and mathematics. He illustrated this potential in 1991 in his description of ‘cyberspace’:
Its corridors from wherever electricity runs with intelligence. Its chambers bloom wherever data gathers and is stored. Its depths increase with every image or word or number, with every addition, every contribution, of fact or thought. Its horizons recede in every direction‚ it breathes larger, it complexifies, it embraces and involves. Billowing, glittering, humming, coursing, a Borgesian library, a city; intimate, immense, firm, liquid, recognizable and unrecognizable at once.(8)
We may relate Benedikt’s information space to the ‘cineplastics’ that Vidler described above. Information is to this space both structure, content and rule, why a given information space just is one ‘layer’ or part of space with a specific set of parameters and information. Space is in that way defined by what information that can be derived from any given point in space. If the space seems to be manipulated and changed, it is in fact the way we observe or filter space that has changed.
While Benedikt clearly constructs the liquid space, defined by Spuybroek above, he also constructs a spatial structure, which shares many of the aspects of embedded spaces and design space. Benedikt confronts this abstract space with the real world through the actions of the observer or what he calls an ‘isovist’, who first decodes the information of the real and next creates a virtual model of it by manipulating that information in space. In other words, reverse engineering by the use of information – or in the larger context of this dissertation, a recursive process of embedding and disembedding operands in space.
The Structure of Modal SpaceThe architect Karl Chu has through intensive architectural investigations developed what he calls a ‘prespace’ or ‘modal space’. His investigations may be seen as part of a more general critique of the insistence upon buildability and the comfort in materiality, which obscures the crucial difference between buildability and constructability in architecture.(9) Chu states: “Even in the most limiting of cases, as in naïve realism, the definability and qualification of architecture can no longer simply be attributable to the empirical logic of buildability, but needs to be extended into the sphere of constructability in modal space.”(10) In other words, architecture shall not be judged on the merits of the final building alone, but just as well on the merits of its construction. Chu’s aim with this is not to exclude the empirical logic of buidability entirely, since he still wants his constructions to be realized and built. However, he argues that such an empirical logic is far too limiting and does not unfold the full potential of architecture.
Chu proposes two distinct applications of space, which may produce yet unimagined architecture(11) – as a space that serves as an ontological medium or plane between concept and object, or as a space with a mathematical structure and genetic logic. Space is both seen as a tool for understanding the world around us and as a tool for producing the material, which fills that world. Yet very complex, it may be seen as the structure of an embedded space with both descriptive and prescriptive potentials, as it was the case with Benedikt.
Chu constructs a spatial diagram, which he calls a ‘cone of immanenscendence’. This serves as an ontological lens describing what architects do, when they bring concepts and ideas into being through the construction of objects – real or virtual. Chu positions his prespace or plane of immanence precisely in the middle of the cone – between the concept and the object. He explains:
The plane is conceived as neither a concept nor an object but as a necessary abstraction that establishes the plane of immanence as the invisible tablet upon which a host of interrelated concepts is actively played out to form a machinic philosophy of multiplicities … The plane of immanence therefore is an ontological construction of the possible spheres of being compressed onto a single plane of thought … To think the plane of immanence anew is to start from the unthought within suppositions: prespace that is prior to any thought of being.(12)
The embedded space of Chu does not only serve as a location for thought, but also as an immanent structure for being and thinking, and as a spatial structure for relating all the information, operands and objects that will be embedded. We could say that Chu’s cone provides a structure, which generates architecture through activating the wide range of operands in the embedded space. He describes this activity by comparing it to the theoretical computation machine of the mathematician Alan Turing:
(The Universal Turing Machine) … is an instrument that discloses the deep embedded structures of reality through a recursive generation of bits, but leaves open the semiological dimension of meaning, which it is incapable of computing. It is an irony of the Turing Machine that it can write only under erasure in order to arrive at significance or logical depth.(13)
We may logically imagine computing the distance between every atom in the universe, but it is physically impossible. By establishing an imagined mathematical pre-space, we may escape such physical constraints and produce unthought architecture. On the scale and complexity of mathematical space, Chu quotes the computer scientist Tomasso Toffoli for stating, “we never perform a computation, we just merely hitch a ride on the great Computation that is going on already,” and the mathematician Steven Smale for arguing that the physical world could not contain all the fractals that are in fractal geometry.
Karl Chu’s pre-space may therefore be seen as a link between the mathematical reality and the architectural reality, letting the unlimited source of mathematic logic present itself in architectural form through space.
We could compare Chu’s use of space as an ontological medium or diagram to the space that the urban geographer Edward W. Soja constructs of the postmodern city through the aleph.(14) Compared to Soja’s space, which is all-inclusive and ‘dirty’, Chu’s space seems to be all-exclusive and ‘clean’, insisting on a pure position, levitating between concept and object. Even though Chu’s plane eventually will be embedded with structures, it is ‘born’ as an empty and clean state of immanence, where Soja’s aleph contains all projections and presences from the very beginning. We could stretch this comparison a little, and argue that Chu is a modern purist with a new digital medium, and Soja is a postmodern pragmatic with a productive story borrowed from Jorge Luis Borges. This may be a quick comparison of the two structures, also relative to Rajchman’s effective and affective structures of space, but I will argue that Chu is inherently modern. He believes that it is possible to produce architecture, which has not yet been thought, whereby he may deny the presence of history in everything we do. On the other hand, Soja has a firm belief in a historical accumulation in the urban territory, which makes the production of ‘new’ architecture impossible, as it quite literally is a matter of reuse, redistribution and reference.
The structure of Chu’s prespace may therefore be more helpful to us than his ontological medium. It is still positioned – or in the terms of Chu projected – upon the plane of immanence between concept and objects, but it is at the same time an example of bringing the unthought into being. Chu constructs a space for designing, which has no ties to a traditional architectural design process – it is unpredictable and filled, yet controlled and simple. He writes:
The internal logic of modal constructivism would include the notion of complementarily, forms of computation, generative systems, selforganisations, ensemble theories, nonlinear dynamics, morphogenetic potentials, statistical models of configuration space at different regimes of reality, combinatorials, artificial life, complexity, metrology, theory of limits and category and set theory at the very least.(15)
This is quite a mouthful – at the very least – and seems to be far from the pure and simple position between concepts and object that Chu is looking for. However, it shows that structures of an embedded space may be constructed without constructing the material as such, but rather constructing the space – the parameters, the fields, the rules and the energies – that the operands will be embedded in. In this sense, Karl Chu’s use of a genetic process is different from that of Greg Lynn as described above, which is based on a biological and anatomic logic of the mechanical transformation of bodies in space.
Therefore, I will argue that there is a difference between using objects (bodies) as a medium in the architectural design process and using space (algorithm). The dynamics of Lynn are objective through a reliance on anatomic and biological (de)formations of the body as their context, while Karl Chu’s structures of space are mathematical and computational.
Operational Structures of the Kappa-Tau CurveThe concept of topology describes a very fundamental structure of space.(16) Topology is the branch of mathematics and geometry that deals with the aspects of space, which are not changed by elastic deformation like stretching, twisting, rotation, scaling and so on. It describes the structural likeness between geometric or spatial ‘types’. A circle, a square and a triangle are identical topologically because they are constructed by a continuous boundary and an even surface, while a compact disc, a ring and a donut are identical because they are spatial objects with a hole in the center. No matter how we move, distort or scale space, its topologic character will stay the same – it will still be possible to identify the donut as a donut, since the topological structure will be unaltered.
Usually we do not question the topology of space, but take its fundamental characters, like the possibility for discrete positions and containment, for granted. However, just as we may construct a space with an endless number of dimensions, to accommodate the need of our particular embedded space, we can imagine and find topologies that contradict these fundamental characters. For instance, the possibility of discrete positions in space, that each position in space is unique, is not the case in a quantum mechanical space of probabilities. In that space, positions may be shared so an object can be present in multiple positions at the same time. Another contradictory structure could be the possibility of containment; that a given object may be fully contained and described in space. This is not the case for one- and two-dimensional ‘flatlands’ as described by the mathematician Edwin A. Abbott in 1884. In such a space, objects that are described by three or more dimensions would be truncated, so that we only would experience a one- or two-dimensional representation of that object.(17) Practically all form and transform functions in design applications may be considered elastic deformations of space. However, it is possible to construct non-elastic deformations in computer applications like MAYA, through evaluation logarithms (limits) that prope every position in space to produce a discontinuous space.
Even though structures or topologies of space may be elusive and rarely brought into question, they may, just as space in general, be an active partner in the construction of design spaces, which we can form, define and design for our specific embedding needs.
Rudy Rucker from the Department of Mathematics and Computer Science at San Jose State University offers a topological structure for our design space. Rucker, who worked with John Walker (founder of AutoDesk as mentioned above) from 1988-92, has described a kappa-tau space curve that is based on the theories by Alexis-Claude Clairaut in the 1731 book Recherche sur les Courbes a Double Courbure.
This kind of space curve is not defined by the use of an absolute spatial reference like an x,y,z coordinate system with an absolute origin in 0,0,0 that maps every point on the curve in absolute space, or in space as a container, to borrow Einstein’s description from above. Instead, the curve is defined as the positional qualities relative to the point’s position just prior as it moves along the curve in a specific direction. At every instance of space, the point is described as a set of three vectors – the tangent (T), the normal (N) and the binormal (B). The curve is removed from an overall system of spatial positions as T, N and B define a moving trihedron of a space curve, which provides each instance on the space curve with its own coordinate system to control the space that lies ahead.
However, the local coordinate system does not provide structure, but rather a mathematical way to relate three parameters. To construct a structure of space, Rucker suggests two properties that relate different points on a given curve. First, the curvature (kappa), which is the rotation in the plane of the tangent with a curve to the left as a positive curve. The curvature (kappa) is defined as 1/R, with R being the radius of the circle that the curve may ‘follow’ – a small radius would mean a ‘tight’ curvature and a high kappa value. Second, torsion (tau), which is the rotation in the plane of the binormal with a torsion to the left or ‘up’ from the tangent as a positive torsion. The torsion (tau) is defined as 1/H, with H being the turn-height for a full revolution – a small turn-height would mean a ‘harder’ torsion and a high tau value. In this way, the kappa-tau curve offers a very dynamic structure of space – one that is not pre-determined or ‘observed’ from an absolute 0,0,0 position at every step of the way, but rather one that is affective, dynamic and develops as it goes along from one instance to the next.
Even though this may seem mind bogging, it provides us with a spatial structure that does exist freely in space, not locked up in an overarching system of reference. Rucker applies the kappa-tau space curve to the flight path of a housefly, which is characterized by high values of both curvature and torsion. This application may not be within the scope of our endeavor, but it is important to remember that it is a mathematical description of a dynamic spatial structure, which is generated through an open ended process, like the flock of birds that the architects Maurice Nio and Lars Spuybroek mentions:
You can not create a flock (of birds) but you can ‘breed’ it. You can make a large number of black dots move in a certain direction (towards the south) on a computer. You can provide each of these dots with a couple of simple alogorithmic rules: don’t bump into any other dots, keep up with the dot next to you and don’t stray. Then you set the program in motion and suddenly a flock has come about out of nothing – you havn’t designed it, you’ve generated it.(18)
Compared to other curves, the kappa-tau space curve is highly relative. It is not a pre-defined curve, as Nurbs or Bezier curve that are constructed by specific positions in space with weighted control points. The spatial structure of the kappa-tau curve is defined relative to the characteristics of the curve itself, which makes the spatial structure highly dynamic, instantaneous and unpredictable. Greg Lynn describes in Animated Form, how this:
… shift from a passive space of static coordinates to an active space of interactions implies a move from autonomous purity to contextual specificity … Rather than as a frame through which time and space pass, architecture can be modeled as a participant immersed within dynamic flows. In addition to the special-effects and animation industries, many other disciplines such as aeronautical design, navel design, and automobile design employ this animate approach to modeling form in a space that is a medium of movement and force.(19)
If we relate the structures of the mathematical kappa-tau space curve to the potential of parametric modeling applications like MAYA, there are several functions to support the construction of such spatial structures. In the medium of synthetic space, we may construct the structures of space rather than the structures of material objects. It is possible to randomly emit particles or vectors in space with random direction and speed. The particles can be affected by force fields that will ‘distort’ their otherwise straight space curve through space, and thereby manipulating the curvature and torsion of a kappa-tau curve. In other words, we can construct a parametric design space and let the space be controlled by structures similar to those that Rucker suggests. Even though the spatial structures and their constructions are entirely mathematical, they display a remarkably degree of liveliness and unpredictability. The only parameters that we control are the relation between the specific spatial structure and the energy clusters that are positioned in a generic space. This will be the issue for the construction Different Rule(r)s.
Therefore, we can argue that this use of space curves and animated structures, calls for a more active role for space. Even though the kappa-tau curve is a topological construction, it provides us with a structure we may use in the description and manipulation of the formal potentials of a design space.
The Structure of ConstructionsIt has become evident to me that a central issue to the construction of embedded spaces is structure. The very structure of a design space may be used as generator of spatial form and to control the path through that space. This was evident in the works that R.M. Schindler produced through his reference frames in space, but also in current design methodology by Lars Spuybroek, Karl Chu and Greg Lynn.
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(1) John Beckman (1998), “Merge Invisible Layers,” in The Virtual Dimension, ed. John Beckmann (1998), New York, NY: Princeton Architectural Press, p. 1.
(2) Quoted in Kern, Stephen (1983), The Culture of Time and Space, Cambridge, MA: Harvard University Press, p. 163.
(3) Einstein, Albert in Jammer, Max (1993 Dover Edition (1954)), Concepts of Space, The History of Theories of Space in Physics, New York, NY: Dover Publications, Inc, p. XV.
(4) Rajchman, John (1998), Constructions, Cambridge, MA: The MIT Press, p. 93.
(5) See Benedikt, Michael (1993), “Cityspace, Cyberspace and The Spatiology of Information,” from http://www.ar.utexas.edu/benedikt_articles/cityspace.html. The paper was a manuscript for an invited lecture at the New Urbanism Symposium at Princeton University in October 1992.
(6) Ibid., p. 1.
(7) Benedikt, Michael (1991), “Introduction,” in Cyberspace: First Steps, ed. Michael Benedikt (1991), Cambridge, MA: The MIT Press, p. 20.
(8) Ibid., p. 2.
(9) Karl Chu shares this point with Stanford Kwinter, Greg Lynn, Lars Spuybroek and others. See Kwinter, Sanford (1998), “Leap in the Void: A New Organon?,” in AnyHow, ed. Cynthia C. Davidson (1998), Cambridge, MA: The MIT Press, p. 22.
(10) Chu, Karl (2003), “Modal Space,” from http://synworld.t0.or.at/level3/text_archive/modal_space.htm, n. p.
(11) Chu, Karl (1998), “The cone of Immanenscendence,” in Any 23, Diagram Work, 1998.
(12) Ibid., p. 39. Reference to Gilles Deleuze and Félix Guattari, What Is Philosophy? (1991, translated to English 1994).
(13) Ibid., p. 42.
(14) See the part A New View on Space for a more on the concept of aleph.
(15) Chu (2003), art. cit., n. p.
(16) The concept of topology has been a vital issue at the Danish Center for Integrated Design, in the form of efforts to optimize the topology of architectural constructions (beams, columns etc.) and thus reach a higher level of integrated design. Further, the idea of topology-design is also present in the development of the application TOPOS in the research project WorkSpace at University of Aarhus.
(17) See Abbott, Edwin A. (1884), Flatland, from http://www.alcyone.com/max/lit/flatland/.
(18) Nio, Maurice & Lars Spuybroek (1996), “The Strategy of the Form,” from http://www.v2.nl/DEAF/96/nodes/NOX/text1.html, n. p.
(19) Lynn, Greg (1999), Animate Form, New York, NY: Princeton Architectural Press, p. 11.
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