Tekhnema 5 / "Energy and Chance"/ Fall 1999

The Folly of Structures: An Apology for Rigidity

Bernard Vaudeville

The principles of aggregation and disaggregation governing those objects one calls "Structures" are the subjects of this article. Speaking not from the point of view of a philosopher but of an engineer, I will be drawing on my experience of calculation and technical design to shed light on what is idiosyncratic about Structures. For starters, they are the product of a deliberate process of conceptualization and action (on the part of the engineer, the contractor, the architect...). This voluntarism has two consequences: it gives room for a potent concentration of energy, coagulated in matter and it does not take into consideration aleatory factors. This conjunction of accumulated energy and the exclusion of chance is what is proper to structural aggregation.

Having developed rapidly since the nineteenth century, Structures now populate our urban and industrial environment, whether they be in the form of bridges, pylons, railway stations, hangars or the skeletal frames of buildings. They form a particular category of technical objects: they are pure artifacts, premeditated before being constructed bit by bit. As my wish is to insist on the intellectual procedure which precedes any construction, I will purposely be using a restrictive definition of them. Structures will be defined against natural organisms (which are the result of aleatory action and physical or biological laws). A mountain, a skeleton, a tree, even though satisfying the criteria of solidity and stability, are not premeditated. The mechanical principles or laws governing their growth, which generate their specific shapes, are not to be assimilated to Structures. They stem from the matter itself rather than from a process that has managed to subject the matter to a particular form. These principles constitute an environment, a material milieu within which the natural object takes on its shape together with an irreducibly aleatory element. By defining Structure this way, against the type of organization at work within the natural object, I am going against the prevalent belief that natural formations have inherent Structures. Certain engineers have done their utmost to search for structural models within nature with a view to transposing them into their constructions.1 However this transposition is illusory as it neglects the radical difference between that which is the result of projection (i.e. a structure) and that which naturally arises from physical phenomena.

A Structure also differs from the "individuated" technical object, as defined by Gilbert Simondon. According to Simondon, the technical object is marked by a process of "concretization," an evolution from an originary state composed of elements simply assembled to its final stage as integrated object, dense and impenetrable like a diode or a clothes iron (Simondon 1989, 19-49). These objects tend towards an ideal fusion of their component parts into one whole, wherein material and function are joined together into one indivisible unity. By contrast, in a Structure it is the assemblage which counts, i.e. the initial state of the object before its fusion, before it is "concretized."

At once penetrable and indissociable, the Structure swings between milieu and technical object, closer to one or the other depending on the perspective of the observer. In 1928 Siegfried Giedion was fascinated by the double nature of Structures, brought to his attention by the striking iron structures characteristic of the nineteenth century, which are identifiable from the outside but which, once penetrated, lose their legibility for us.2 The user, once absorbed within an undefinable space, suspended between matter and atmosphere, discovers the world from a vertiginously novel perspective.3 As Giedion describes so vividly:

In the air-flooded stairs of the Eiffel Tower, better yet, in the steel limbs of a pont transbordeur [such as the one at Marseilles], we confront the basic aesthetic experience of today’s building: through the delicate iron net suspended in midair things, ships, sea, houses, masts, landscape and harbor. They lose their delimited form: as one descends, they circle into each other and intermingle simultaneously. (Giedion 1995, 91)

This article now goes on to test the strong and the weak points of this manner of composing matter which characterizes the Structure.
Sudden disintegration

The reticulated tower visible in the bottom corner of this journal which erects itself methodically, limb by limb, is a Structure. As such the images are a fairly typical representation, made up of bars and beams which could be made of iron. This Structure is not dissimilar to the Eiffel Tower or, even better, to the marvelous pylons of Suchov (see page 100).4 However, our Structure, once constructed, begins swaying, bending, springs back, a puppet in the hands of invisible forces. Then, at a decisive moment during which one element gives way, the incomplete structure caves in, immobilizes itself, lamentably dissipates into an unrecognizable state, so very different from its original form.

This tragi-comical playlet underlines the double character of Structures, at once pledges of solidity and rigidity and yet destined to collapse catastrophically. Being used to the numerous Structures which provide reassuring frameworks within which we evolve, we tend to repress all knowledge of this inherent risk. At most we experience a degree of giddiness, sensing the undercurrent of instability threatening us and our certitudes. Indeed, a principle of risk is lodged at the heart of the solid, a principle of disorder at the center of order itself. A Structure then appears as a one-way trip, whose destination can only be ruination despite the systematic planning and ingenuity informing its departure. We recognize therein a manifestation of the law of entropy, which translates as an irreducible tendency to become a heap, to find in formlessness the maximal degree of stability.

However, this destruction is striking in its suddenness and extreme brutality, contrasting with the methodical progress of the construction. It seems that the piling-up of materials is accompanied by a dangerous accumulation of potential energy which, once released, does so abruptly and irrevocably. A Structure does not disaggregate gradually, by erosion, as would a mountain or a rock. Instead it disintegrates all of a sudden (see page 101).

A law turned into matter

Into the category of that which stands, which maintains an erect position, we have just introduced a fundamental distinction between Structure and Mountain.5 The latter is often regarded as the epitome of stability. By contrast, what characterizes a Structure is less its solidity than the law organizing its material. This law confers a specific identity on the Structure as a distinguishable whole, turning it into something which is much more than the simple addition of composite elements. Stability is only one particular aspect of the Structure, one dependent on a fortuitous coming together of circumstances.

The notion of Structure as a systematic and organizing conception of matter has its own history. One can situate its appearance in eighteenth-century Europe. It was particularly developed by engineers, those bearers of technological modernity, who profited from mathematical inventions and the experimentation with iron as a construction material. Towards 1850 Viollet-le-Duc theorized this contribution of Structure to architectural thinking which he considered to be a major progress and whose seeds he traced back to the Gothic cathedrals. He described the principles governing structural order in the following fashion:

If one studies with attention and without prejudice, the stone constructions of the thirteenth and fourteenth centuries, one soon recognizes that Structure is not solely composed of independent elements, each one carrying out their specific function. They are no longer, as is still the case of Romanesque architecture, homogeneous concrete masses. Instead they are a sort of organism in which all constituent parts have not only an assigned role, but also a direct, sometimes even proactive action to bring to bear—as is the case, for example, with flying buttresses and arches. (Viollet-le-Duc 1986, 60)

Viollet-le-Duc’s definition of a "structural organism" is underpinned by the image of Gothic constructions and nineteenth-century iron buildings. In both cases these Structures take the form of skeletons, capable of being represented by schemas. This "structuralist" vision of Structures is restrictive as it does not permit us to take account of more recent constructions, such as concrete shells, membranes, nets (used in aviaries) which cannot be decomposed into their constituent parts. These are nonetheless Structures, according to our definition, as each one of them is subjected to a rule which assures their cohesion. This rule is just as rigorous, but more elaborated, than the hierarchized schemas of Viollet-le-Duc. In the case of concrete shells (see overpage), it draws on the mathematical equations governing surfaces, or, in the case of membranes and nets—those surfaces called "films of soap"—on research into the minimal nature of surface.

By their very shape Structures are the reflection of the underlying laws governing them. This reciprocal influence of shape and calculation is often ignored by architectural historians who generally stick to a formalist or functionalist analysis of structural phenomena. In truth the history of Structures runs parallel to the history of calculation and the arrival of new structural types, always significant for architecture, is the corollary of a new conceptual approach containing the aesthetic seed of a new Structure.6 The Structure is above all a law, subsequently made of matter and displayed in space.

The confrontation of two laws and the mediation of calculation

The subjection of the structural object to a law which orders it is not an end in itself. It only has meaning if it exists in respect to another law, representative of the physical and mechanical phenomena which solicit it. It is the confrontation of these two very different laws which permits us to lay hands on the stability of an object. One without the other would remain at the level of pure formal speculation. What use could be made of Newton’s beautiful theory of Mechanics in relation to the undifferentiated mass of a Mountain?

Inversely, a sophisticated structural schema which is lacking the scientific tools necessary for its analysis would remain an empty shell. This was the case for the Gothic vault ribs which were ahead of their time, predating the mechanical theories which could have affirmed their role. The utility of these ribs, intuitively imagined by the builders of cathedrals as an element contributing to the structuration of the arch, is actually poorly defined and as a consequence still keenly debated by historians. Whereas some Gothic ruins conserve their ribs intact when the vaults themselves have already collapsed (thereby apparently attesting to their structural efficacy), others still have their vaults in place even though the ribs themselves have fallen (thereby suggesting their structural superfluity). Erwin Panofsky highlights this unresolvable contradiction when he notes that "the Gothic ribs began to articulate something before they were capable of acting upon it" (Panofsky 1986, 111). However, such anachronisms are rare. More usually the evolution of the conception of Structures accompanies and stimulates the development of the mechanical and mathematical theories.

In order to grasp the stability of an object, the two laws (the one governing the Structure and the other representing the mechanical and physical phenomena7) must be formulated to the same level of abstraction. In particular the object must become a Structure: i.e. the constituent elements which contribute to its stability must be organized according to an explicit rule. Stability arises from the momentary compatibility of these two independent laws which are not of the same order. The first is an edict and imposes a geometric order and the characteristics of the materials of the Structure to be. The second is a formalization of phenomena with the aid of concepts such as: force, elasticity, stress and strain. Being of a scientific nature this second law differs from the structural law in the sense that it necessitates a legitimization through experience. It does not impose itself on, but instead tries to embrace, the phenomenal reality.

Between these two laws calculation is at work. Calculation is a thought process which aims at anticipating the stability of the Structure. By definition, anticipation cannot be carried out on the object itself. It necessitates a transposition into an abstract plane wherein a simulacrum of the confrontation between the future object and the external circumstances is played out. This is what is called "modelization." It should be noted that only a prognosis can be made of external circumstances and, consequently, anticipation is limited to the field of the predictable. This limitation contributes to one of the weak spots of Structures.

Modelization can be carried out by experimentation on reduced-scale models or on samples, calculation being necessary for interpreting and transposing the results of these measures to a real-life situation. Such a procedure was followed by Brunelleschi when designing the Florence dome and, more recently, Gaudi, when building the arches of the Guell Park or Sagrada Familia.8 However, calculation took on another dimension when, as from the eighteenth century, one began to want to economize on scale models and lighten the work of modelization by situating it primarily on an intellectual level.9 Instead of confronting the material representation of the Structure with simulated external actions, calculation now brought face-to-face two conceptual representations, the law organizing the structure and the law of mechanics. It looks for the zone of empathy between these two laws which corresponds to the stability of the Structure. Calculation intervenes here as a mediator, reconciler, a tool of synthesis between an object and its context which have a priori nothing in common.

As for the method adopted, calculation proceeds with the immersion of the structural schema in the mechanical theory, thereby tracing the immersion of the real structural object into the seething realm of real physical phenomena. Before this virtual immersion can be enacted, the descriptive law of the Structure and the descriptive law of the phenomena must be translated into a common language with the aid of adequate concepts. This translation necessitates successive transformations of the Structure, taking it to the point where mechanical concepts become operative. The transformations undergone by the Structure when modeled can be best explained by taking the case of one of the simplest Structures, i.e. a teepee in a storm, and charting step by step the changes effectuated. The operations to be carried out would be the following, in this order:

Strip the load-bearing structure by removing each element which does not participate in its stability. This takes place in a wind-free locality.

Schematize this structure by substituting its constituent elements with typical elements (bars, beams) linked up by typical connections (pins, encastrements), resting on typical supports.

Represent the action of the wind blowing on the teepee by horizontal vectors applied to the nodes of the structure.10

Substitute the structural elements with the vector-forces going in the same direction. At this stage only the vectors remain, to be added in accordance with the principles of vectorial algebra to prove the equilibrium of the teepee.

For a more complete analysis, the vectors are replaced by their algebraic expression, equilibrium being represented by the resolution of a system of equations.

Two remarks impose themselves at this stage. At first it seems that during this convergence it is the Structure which does all the work. But it only appears this way as, in order to permit the analysis of the Structure, the mechanical law itself must be expressed by concepts appropriate to the specificity of this Structure. Thus the concept of force, represented by the vector, is adapted to a reticulated Structure made up of bars. This is less the case when a structure is a continuous surface, for example, when it comes in the shape of a shell which would be analyzed by means of the notion of pressure. One sees therefore that the work is shared: the mechanical theory offers a conceptual framework which suits the analyzed Structure; the Structure is itself modeled according to concepts made available by the mechanical theory.

In other respects the modelization of the Structure appears like a gradual transformation towards ever increasing abstraction, to the point where it becomes unrecognizable. The aggregation of matter, transformed by successive filtering into a system of equations, loses its legibility in the burgeoning of inexpressive cabalistic signs. It is the theoretical and therefore abstract concepts, which permit an analysis of the Structure, that impose their abstraction on the Structure.

Calculation is indissociably linked to the notion of Structure, i.e. to the conformation of the construction to an organizing law. From this follows that the calculation is also tied to the built form as reflection of the structural principle. Calculation is the operation which permits a prediction of the stability of a Structure, however it does not constitute for all that a passage obligé to attain stability. Indeed, natural formations, such as Mountains, and numerous artificial constructions prove themselves to be solid and stable despite not having been the object of calculation or bearing the characteristics of Structures. If calculation is not the condition for stability, why submit oneself to this laborious, time-consuming and inelegant decanting? Why design structured objects at all when objects could be conceived otherwise, i.e. as inert masses?

The first reason one might think of could be the need to economize on building materials. It is true that the technique of Structures, notably those built from the second half of the nineteenth century onwards which use highly efficient materials such as steel and concrete, has permitted a considerable lightening of structures. However, the wish to cut back on, and not unnecessarily squander, materials is an inadequate reason for explaining our fidelity to structures as calculation and structural order are not indispensable to the search for economy. Let us imagine our Mountain excavated little by little until it resembles Swiss cheese; or a wall pierced until it becomes as transparent as lace (like a Moorish window). In this case there is a reduction of the materials used without there being a vision of the whole of the structural behavior. Material is economized through incrementation, by progressing from one state of tested stability to the next, slightly less stable stage. At each stage the operation can be interrupted and the risk is proportional to the quantity of removed material. To use the terms of the Mechanics of Rupture, it is a question of an "approach from the inside,"11 that is to say, a progressive nibbling away until a "limit-state," in opposition to a conception which, from the "outside," envisages from the outset the limit-state (i.e. instability).

The oblique, liberation and uprooting

The notion of Structure and calculation permit a short-circuiting of the gradual, step-by-step approach; of this groping around proper to the "approach from the inside." Therein lies their efficiency and true raison d’être. The economy of building materials is a mere, though happy, consequence of them. Calculation, viewed as a systematic reflection on the conditions of stability of a Structure, permits an anticipation of complex equilibria and thereby enlarges the field of what is possible. An uncalculated construction is necessarily built with limited visibility, without anticipation, implying a repetition of well-worn shapes combined through juxtaposition or stacking-up. This is what, according to Viollet-le-Duc, handicapped the Romanesque constructions. His vision was certainly oversimplified and it would be wrong to deny the existence of an inventive thinking of construction before the Gothic period. However, it is true that the order which presided over the erection of such constructions arose more from composition than from an actual system. The notion of system implies the interaction of the parts so that they form an indissociable whole. When this is missing, the only forms of structural composition possible are the simplest ones: those of superposition or juxtaposition, the one developing along the vertical plane, the other following the horizontal. Also, the only operations governing calculation are those of addition and subtraction, used to evaluate the loads, the requisite quantity of building material and the cost. The stability of these non-structures is self-evident as there is no interaction between the elements (except by a straightforward piling-up of one element onto another), and only the most immediate forms of corporeal intuition are called upon. Eleventh-century European Romanesque basilica were constructed in this manner, being a succession of projected spaces (the narthex, the nave, the choir, the apse) and a superposition of strata in elevation.

With Gothic cathedrals suddenly an oblique element, the flying buttress, is introduced into building strategies. This puts into question and troubles the sedate equilibrium of the Romanesque church. Once subjected to the laws of gravity, the oblique does not possess its own stability, its equilibrium depends on adjacent elements. The oblique is the indication that we are no longer confronted with a simple principle of piling-up but with a structural system governed by an organizing law which encompasses all the edifice. Even though the Gothic oblique is not yet supported by a coherent method of calculation, this new thinking in terms of systems makes possible the vertiginous elevation of the stone vaults found in cathedrals and the enlargement of the stained glass windows until they reduce the stone walls to interstitial pillars. This radical departure from traditional ways of building constitutes an opening towards new architectural forms. More fundamentally, this represents an uprooting, an irremediable break with our corporeal experience, our orientation in terms of the vertical and the horizontal. Henceforth we resort to our intellects to understand the edifice. In his defense for a utopian architecture of the oblique written one century after Viollet-le-Duc and eight centuries after the Gothic era, Paul Virilio attests to the conceptual radicality that the oblique represents:

We are confronted with the pressing necessity of accepting as a historical fact the end of the vertical as an axe of elevation, the end of horizontal as a permanent plane, in favor of the oblique axis and the inclined plane which fulfil all the conditions necessary for the creation of a new urban order. This will permit a total reinvention of architectural vocabulary. This crucial shift of emphasis must be recognized for what it is: the third spatial possibility of architecture. (Virilio & Parent 1966, n. 1)

The new architectural forms, here conceived in most utopian terms, respond to the profusion of structural forms suddenly made possible by this uprooting. Born of an abstract intellectual process, they surprise us, they even exceed the expectations of their inventors. They are shocking for common sense as they are not affiliated to any tradition. Indeed it suffices to remember those enflamed pamphlets by eminent intellectuals, such as Maupassant and Dumas, who took it upon themselves to defend "beautiful Paris" and "French taste" against that "monstrous" and undignified intrusion, the Eiffel Tower (Lemoine 1984, 96). Maybe one of the reasons why we feel we are hostages to fortune when surprised by Structures is that they are made in the image of the mind’s precocious anticipations which project them. Hence they are projections upwards (as is the case with towers), across an obstacle (bridges) or following audacious curbs (concrete shells). This uprooting of the mind enabled a tremendous liberation of forms which fascinated the nineteenth century and occupied a major place in aesthetic debate.

The irreducible fragility of structures

However, this uprooting is also a sore point for the engineering profession due to the aridity of calculation and, above all, the loss of sentient contact with the projected object. The disembodiment of the project by calculation has put off many an engineer.12 Unable to draw on intuition and far removed from a tactile experience of the materials employed, these engineers felt (and continue to feel) alienated by the reduction of Structure to an impoverished list of mathematical equations. Consequently, other avenues for conceiving Structures are sought, ones which have less recourse to abstraction and which favor experimentation. One of the most striking examples of this resistance to calculation is provided by Frei Otto’s study for the tensile net for the Olympic Stadium in Munich (see overpage).13 For over a year several teams of young architects and engineers took turns in working day and night to build model after model, each one more precise than its precedent, in order to measure as accurately as possible the stresses and strains in the structure. Despite their concerted efforts they did not succeed since their models, however sophisticated, always concealed imperfections which marred the measurements. This experimental phase was useful as far as the maturing of the conception of the project was concerned, but calculations (in this case computer processing) were nevertheless indispensable for adjusting the dimensions of the definitive structure.
Beyond the engineer’s chagrin, provoked by this unavoidable dependency on a calculation alien to the experience of body and matter, there is an even more fundamental worry: the giddiness evoked earlier that stems from the catastrophic collapses to which Structures sometimes succumb and which our flip book depicts in slow motion. We have to accept that Structures are essentially fragile, despite our explicit investment in them as stable points of anchorage. This fragility should not surprise us, one could object, as Structures which are economical with building materials are left with less of a reserve of material at their disposal in case of emergency and therefore with less strength than a Mountain. But this matter-of-fact approach neglects the truth that it is the very law governing Structures that betrays itself as the origin of structural fragility. This treachery manifests itself in the way in which Structures collapse, in comparison with the emblematic case of non-structures, such as Mountains.

The "destruction" of a Mountain can only happen if material is taken away gradually by erosion or excavation. This will eventually result in the leveling or subsidence of the Mountain. By contrast, the collapse of a Structure inevitably happens abruptly, effacing all of a sudden its shape and identity, only conserving a heap of rubble as a trace of its former glory. This annihilation only rarely occurs because of a lack of material. It is mainly caused by the disappearance of an element however small (a single voussoir is missing and the whole vault collapses), or by the break in an internal link (a simple cut with a saw suffices to destroy a wooden beam), or by excessive geometric distortion (i.e. buckling). In each of these cases the ruin follows on from a transgression of the organizing law of the Structure, whether the infringement is to be situated at the level of topology, internal hierarchy or geometry.

The proper law of a Structure pledges its stability. However, we see that at the same time it constitutes a shackle which imprisons structural expressivity by swiftly sanctioning reckless escapades. The Structure is, so to speak, house-bound by its own law. The Structure is either integrated into the dominion of the law or it disintegrates. Between these two states there is no possible compromise or intermediary position. Fortunately, real structures have a thickness, a materiality which sometimes damages their chances of survival but at other times saves them from brittle fragility by permitting them to adapt and to edge their way towards stability. In this astute adaptation they are mountain-like. But the more the Structure embraces the law, the more it lays itself bare for an unrelenting punishment if it dares to venture an infringement. It would therefore appear that fragility is the product of an excess of coherence.

Viollet-le-Duc had drawn attention to this paradox and, despite the increase in fragility which accompanies this new structural thinking, he detected in it a progress:

Just because you can remove a pillar from a concretized Roman construction without causing the edifice to fall, and just because you cannot remove a voussoir from a flying buttress of a Gothic nave without ruining it, it does not follow that, within the structural hierarchy, the Gothic monument does not constitute a step forward compared to the Roman monument. This proves rather that in the Gothic edifice all the organs are necessary, indispensable, hence the structure is actually more perfect. Man who passes for the most perfect of organized beings is also the most sensitive to any kind of lesion, unlike many other mammals. His arms do not grow again as do the claws of crayfish when cut off. A heightened sensitivity and fragility is one of the conditions of progress for an organism in the order of creation. This also applies to Man’s right-hand creation that we call construction. The more Man subjugates inert matter, the more he forces it to comply to his needs, the more the organs (if you will allow the expression) of his creations must be indispensable, delicate, and by consequence, fragile. The calculation of new laws of equilibrium, of weighting, counterpoint and opposed forces replace the immobile mass, stable in itself. (Viollet-le-Duc 1986, 77)

Viollet-le-Duc presents here a demiurgic vision of construction whose perfection necessitates a submission of matter to the structural order imposed by the creator (implicitly the engineer or architect). With this act of authority, he infuses a dynamism into "inert matter," dragging matter away from its state of amorphic stupor so as to get it to engage with a dynamic equilibrium. This dynamic, organic characteristic of the Structure permits Viollet-le-Duc to venture a parallel with the human race, considered to be the pinnacle of evolutionary perfection and to justify thereby the superiority of the structural order.

Darwinian-inspired theories of evolution have done much damage to the anthropocentric certainties and human vanity implicit in Viollet-le-Duc’s comments. The human race does not represent the marvelous culmination of a long process of biological sophistication.14 Much more modestly, it is only one branch of evolution, the fruit of chance, a complex but incomplete construction. It is exactly this very incompleteness which fuels the motor of evolution and which permits life-forms to adapt to new conditions. François Jacob makes a pertinent comparison when he explains that evolution is the product of bricolage rather than of engineering, since each life form is the result of a collage of fragments of genotype some of which are devoid of utility (Jacob 1981, 65). These shards are "bits of useless anatomy" to use Darwin’s words as cited by Jacob, which permit mutation and the adaptation to otherwise unforeseen contingencies. Nothing in these biological constructions resembles the characteristics of Structures. On the contrary, the difference between the former and the latter is further emphasized: due to their submission to an all too strict law Structures are incapable of change; their sterility is the outcome of their purity.

This detour via genetics highlights the opposition between these two contrary and competing forms of aggregated matter: the structure and the "collage" (used as a generic term to signify all types of assemblage by addition, accumulation, juxtaposition, superposition or stacking-up). The "collage" represents a more basic, poorer form of assemblage than the Structure. The Mountain, a simple heap of matter, is an example of this. This simplicity, this degree zero of assemblage, seems to be associated with the chaotic and haphazard formation of the Mountain which has succumbed to the effects of terrestrial convulsions. But "collage" also imposes itself as a form of organization in more sophisticated realms, such as those pertaining to genetics or economics. In fact it presents strategic advantages related to its capacity for malleability, permitting a greater absorption of contingency. Paradoxically these advantages result from the absence of calculation, of any law governing the assemblage and from the weak link between the parts and the whole. The slightest complexity of object or organism constituted by collage (i.e. the degree zero assemblage) permit it to pose a passive, though efficient resistance to the unknown (as is the case for the crayfish or the lizard capable of jettisoning their limbs to predators so as to make good their escape) and to increase its flexibility in the face of the need to adapt by adding or cutting back.

It is also a mode of organization which seems to suit the industrial economy best. Industrial products, individualized and standardized, can be technically highly sophisticated. Simondon would call these perfected objects "concretized" (Simondon 1989, 19-49). But in order to allow their maximal diffusion, one must be able to combine them with other products using the weakest, most neutral and less specific links. Taking into consideration the rapid obsolescence of industrial products, one must be able to cut these links so as to replace a section without endangering the rest. Industry therefore imposes in all of its domains an organization which is based on juxtaposition, superposition or stratification of components. This greatly influences our environment which organizes itself on every level according to a principally additional mode of functioning (an "and... and... and..."). Cities, for example, become agglomerations, stretching themselves out into long, ill-defined suburbs, collecting within their amorphous confines the "boxes" housing the amalgams which amount to commercial centers; buildings are constructed in successive layers: insulation, plus air-conditioning ducts, plus power supplies, plus cladding and "wall-curtain"; furniture is assembled in kit-form; computers themselves are nothing but connecting points for interchangeable electronic cards. This form of "collage" pervades even the realm of gastronomy whose most emblematic contemporary icon is the hamburger, that simple, though highly industrialized, stacking-up of one scarcely edible foodstuff on another.

Confronted with all this, Structures, hemmed in by their internal laws, appear to be downright inflexible and rather quaint. Their lack of malleability, coupled with their intrinsic fragility, finds its cause in the calculation which, to be sure, permits a circumscription of the risks at large in the domain of the predictable, but does not prepare them for a confrontation of unpredictable circumstances. Behind this tautology lies a real paradox: the more the field of prediction enlarges itself (the more calculations perfect themselves), the more complex and specialized the Structure becomes so as to respond to this challenge and, by so doing, the less able it is to adapt to the unpredictable. The fundamental characteristics of a Structure thereby declare themselves: it constitutes a radical caesura which separates not only the material but also the future events which it has to affront. It is a one-way street with no escape routes, an autonomous strategy, closed to unforeseen solicitations and to hazards. Chance is alien to the structural(ist) idea, or at least is always encountered as a catastrophe. Therein lies the Structure’s strength and its weakness. It has permitted the Structure to extirpate the inertia of, to use Viollet-le-Duc’s terms cited above, "concretized and homogeneous masses" through centuries of continuous intellectual effort. However it also means that the Structure is threatened with a return to the simplistic—but more supple—form of aggregation, characteristic of the "collage."

The pathos of Structures

Structures are basically pathetic objects. Proud and defiant erections in steel or concrete, they are condemned to a disconcerting ruination. We wrongly turn them into the image of all that is reassuring. All too ready are we to embrace them as stable elements, points of anchorage, permanent pedestals when they are on the contrary future-less eruptions, dangerous peaks of potential energy on the point of explosive release. It is within this ambivalence that the complex aesthetic of Structures is to be situated. This aesthetic draws on three coexisting, yet contradictory principles which can only arouse mixed feelings.

First principle: we admire the work, the patient accumulation of material; we have respect for the intelligence, the skilful geometry or assemblage of a Structure. We at once appreciate the order, i.e. the subjection of matter, and the sophistication of this order as we would admire the beauty of a diamond. However, this order can become disturbing if the Structure capitalizes on all the liberties calculation offers it. We have seen that corporeal points of orientation are lost, the weighty vertical or horizontal hierarchies of the classical tradition are thrown off balance. The impudence of the new forms which are thereby engendered by Structures have always shocked, from the nineteenth century through to today (just think of the reserved, if not outrightly hostile, response to the Centre Pompidou when it was first opened).

Second principle: through their novelty and dynamism, structures express fluidity, élan, also an overcoming and a form of heroism. The miracle of synergy offers itself to sight and touch with a capacity to arouse moving feelings as strong as those provoked by the vision of a united people advancing together in, to use Kracauer’s term, the same "mass ornament" (Kracauer 1995, 75-88). In physically demonstrating that a collectivization of individual energies can give rise to grand realizations, Structures offer a socialist vision of which the ex-Eastern Block countries, which elevated such Structures to the rank of total works of art and urban spectacles, were keenly aware.

The third principle of structural aesthetics is the opposite of such pious admiration. It is the secret jubilation associated with the repressed consciousness of risk, of the heralded end, that a Structure evokes in its flirtatious encounter with instability. Structures do not make "beautiful ruins," unlike heavy and ungainly constructions.15 But their ruin nevertheless makes for a beautiful spectacle. The collapse of a tower, the break-up of a bridge (as in Tacoma, famous for the amplitude of its thrilling oscillations), the shuddering caused by an earthquake; the explosive demolition of a high-rise block of flats (which always pulls in the crowds) and even the bombardments of a city (the transfixed fascination for this lethal form of firework display), all these catastrophic events attract our attention, not just because of our morbid pleasure in negativity but also because they reveal the tragic dimension of this accumulated energy susceptible to the risk of sudden annihilation. Structures thereby, without even having to actually collapse, accrue a certain dark beauty.

We have briefly traced the history as well as the problematic pertaining to Structures. This material form is not atemporal, but it is always linked to a culture, it derives from a form of thought. This thought is rational, but it is not very reasonable, a sort of "folly,"16 one that is translated materially and with élan in the organized follies that we call large bridges, reticulated towers, sky-scrapers, taut concrete shells. Appearing two centuries ago, these follies appear to us to be a definitive acquisition of technical progress, entirely integrated into modern technical culture, and subject to continuous development.

But this perpetuity is not a given. Not only is the idea of Structure put in jeopardy by the disadvantageous terms of its competitivity with the most supple forms of "collage," it is also undermined from within through the eruption of new forms of computer modelization.

Contrary to appearance, calculation has already lost the match.

The tensile roofing of the Olympic Stadium in Munich marked the failure of experimentation on a large scale. At the same time it ratified the superiority of computerized calculation. From the 1960s onwards the strength of computers has permitted a very exact modelization of the behavior of Structures as complicated as that of Frei Otto, being based on the principle of a "calculation of finite elements."17 This method consists in a multiplication and a universalization of calculation, the Structure or the object to be calculated being chopped up into a multitude of smaller elements, all identical or attached to a limited number of types, related to each other by standardized mechanical links. This multiplication of the operations at work within calculation in the computer should not deceive us: here it is not a question of a definitive victory by calculation. On the contrary, it is a denaturalization which profoundly modifies the relationship with the calculated object. The infinitesimal brick, the universal element which serves as a basis for all calculations, confirms the disappearance of intermediary concepts of force, moment, pressure, in favor of the basic concepts of stress and strain.18 The modelization of the Structure itself is reduced to its simplest expression, the singular hierarchy proper to each Structure is flattened. With this manner of composing calculations in totally general terms, the Structure loses that which singularized it in the calculations. It is now just treated as a continuum of matter, and matter itself is only specified by a symbol attached to each brick within the modelization. It is therefore the very concept of Structure which is put into question as aggregated matter is modeled as a milieu, without us having to force it to comply with a law in order to calculate it.

Pre-computerized calculation consisted in paving a way, step by step, through mathematical penury (mathematical tools being rarely equal to the structural problems needing resolution), astutely searching for an exit and modeling the Structure itself in relation to the possibilities of calculation. By contrast, computerized calculation opens up the scope; it advances like a trawler net sweeping up all peculiarities within the Structure, treating the smallest cranny of a Structure with the same systematism as the principle members (pillars, trusses, guys, etc.). The presentation of the results completes the lamination of calculation by eliminating all visibility from the process of calculation: the algorithm and the number become invisible, gobbled up into the depths of the microprocessor. The infinitesimal brick itself dissolves into a shading of colors. The only remaining item on the screen is the smoothed-out and colored radioscopy of the simulated (we can no longer use the word "calculated") object (we no longer venture to employ the word "Structure"). A creature of the virtual, calculation no longer exacts the same intellectual investment as before.

The phenomenal power of computerized calculation spawns fascination by reason of the facility with which it becomes possible to fabricate forms and to verify their solidity and stability. This new situation is experienced by numerous architects and engineers as a liberation of intellectual categories which necessarily surround the conception and calculation of a structure, just as the invention of the structural idea constituted a liberation from corporeal a prioris. The most recent tendency in architecture rests on the creation of designedly a-structured forms, free forms, ovoid and complex forms which seem to have generated themselves spontaneously. Certain of these constructions reveal a vibrant poetic power due to their very incongruity—we are thinking here of the Guggenheim Foundation building in Bilbao (by Gehry), where the mediation of the computer was crucial for inserting a skeletal structure into turbulent shapes. However, once out of the brilliant glare of such projects, we cast doubt on the long term influence of this mode of construction. The same exacerbated formalism can be detected in industrial engineering: for example, each new model of car is now calculated like an undifferentiated block, integrating the bodywork, the windscreen, seats, accessories, sometimes even the dummies (for the simulated collisions).

It seems to me that the formal opening and liberation that the computer authorizes is today accompanied by a form of regression. The new models are too slick for thought to attach itself to them. Thought needs resting-places, stages, intermediary concepts, stumbling blocks, names for designating objects.

The problem lies not in a hypothetical rivalry between Humanity and Machine wherein the former sees Its creative prerogative stolen from It. The problem comes from what, behind the apparent infinity of forms suddenly rendered possible, imposes itself: a unique order founded on the undifferentiated accumulation of infinitesimal bricks and on the equivalence between all material elements—fluid and solid, skeletal frame and cladding, organic and mineral matter. Like collage, the mode of aggregation introduced by the new computerized ways of calculating neutralizes radical singularities. It limits risk up to a certain point, but at the same time forecloses a thinking of greater risks. What is understood is that it is not the computer’s fault but our complacent short-sightedness and the lamentable absence of any reflective thinking with which to oppose the immanence of computerized models.

The concept of Structure must be saved through adaptation. It is only by so doing that we can overcome crass formal ramblings and continue to imagine and to construct the more radical follies which Structures represent. Structures, absolutely unique, unredeemably destined to ruination.

Translated by Diane Morgan

Reference matter

Giedion, S. 1995: Building in France, Building in Iron, Building in Ferro-Concrete, Santa Monica: Getty Center.
Headley, G. and W. Meulenkamp. 1990: Follies: A Guide to Rogue Architecture in England, Scotland and Wales, London: Jonathan Cape Ltd.
Gould, S. 1997: Life’s Grandeur: The Spread of Excellence from Plato to Darwin, London: Vintage.
Jacob, F. 1981: Le jeu des possibles, Paris: Fayard.
Kracauer, S. 1995: The Mass Ornament: Weimar Essays, trans. T. Levin, Cambridge MA: Harvard U.P.
Lemoine, B. 1984: Gustave Eiffel, Paris: Hazan.
Mimram, M. 1983: Structures et formes: étude appliquée à l’oeuvre de Robert le Ricolais, Paris: Bordas.
Otto, F. 1985: Architecture et bionique: constructions naturelles, Denges: Editions Delta & Spes.
Panofsky, E. 1986: Architecture gothique et pensée scolastique, Paris: Les éditions de minuit.
Picon, A. ed. 1997: L’art de l’ingénieur: constructeur, entrepreneur, inventeur, Paris: Centre Georges Pompidou/Le Moniteur.
Speer, A. 1981: Inside the Third Reich, New York: Collier Books.
Viollet-le-Duc, E. 1986: Entretiens sur l’architecture, Bruxelles: Pierre Mardaga.
Virilio, P. and C. Parent. 1966: Architecture principe, Besançon: Les éditions de l’imprimeur.


1 See, for example, Otto 1985, on the work of Le Ricolais, Mimram 1983.
2 The passage by Giedion will be later cited by Benjamin in Passagenwerk (1982).
3 On this subject see D. Morgan, "Survival through Design: Vertiginous Dangers and Modernist Architecture" on the work of Richard Neutra (forthcoming).
4 Notably the Moscow Radio Tower (1922). Suchov, one of the greatest Russian engineers at the beginning of the century, was a pioneer of light structures made of steel nets.
5 My remarks deliberately assume the guise of a parable, whose two protagonists-the Structure and its protagonists-are purposively simplified so as to aid clarification. I am not denying that structures and mountains are in reality complex entities which cannot be simply reduced to two paradigms.
6 For example, the experimentation with concrete shells (by Candela, Torroja and Lafaille and others) was made possible thanks to the development of the mathematical theory of differential analysis.
7 Such phenomena include not only external considerations such as the wind, snow, gravity but also the material characteristics of the object itself: its elasticity, its strength.
8 Gaudi perfected an experimental method of conferring an efficient shape (called "funicular") on vaults for a given distribution of loads and supports. This method consists in representing the vault upside down, by a suspended net, in order only to subject it to traction and to let it assume its natural shape. This shape was then traced, turned back up and used to constitute the vault.
9 This was made possible by the concomitant development of mathematical theories, notably differential analysis.
10 Vectors are mathematical objects linked to a space, characterized by a direction and an intensity. In the plane or 3-D space, they are usually represented by an arrow whose length represents intensity.
11 This is a mechanical theory developed by M. Salençon of L'Ecole Polytechnique in the 1970s.
12 For example, the great engineer Eugène Freyssinet (1879-1962), inventor of pre-stressed concrete, always remained reserved about the representativity of calculation and consistently emphasized the primacy of experimentation.
13 Research for the stadium began in 1967 and the inauguration of the project took place in 1972.
14 See Gould 1997 for a clear exposition of these ideas.
15 Here we refer to the "Theory of Ruin Value" proposed by Hitler's architect, Albert Speer. Speer presented a philosophy of construction in direct opposition with the idea of Structure promulgated by Viollet-le-Duc. Speer explains his concept as follows: "The idea was that buildings of modern construction were poorly suited to form that 'bridge of tradition' to future generations which Hitler was calling for. It was hard to imagine that rusting heaps of rubble could communicate these heroic inspirations which Hitler admired in the past. My 'theory' was intended to deal with this dilemma. By using special materials and by applying certain principles of statics, we should be able to build structures which even in a state of decay, after hundreds or (such were our reckonings) thousands of years would more or less resemble Roman models" (Speer 1981, 56). Structures resist a putting-to-work in the name of an ideologically motivated symbolization of duration and permanence.
16 Here the term 'folly' evokes the eighteenth-century usage for designating an eclectic category of construction prevalent in landscape gardens. Such follies have been described, most unsatisfactorily, as "big, Gothic, ostentatious, over-ambitious and useless structures" which indulge in "a natural urge to express eccentricity" (Headley & Meulenkamp 1990, XIX). A more profound analysis of follies would highlight their self-conscious and eminently rational staging of philosophical ideas and socio-cultural debates raging at that time and their equally thought-provoking ruminations on ruination, utopianism and the aesthetic as symbolic vehicle. This re-reading of follies would permit an interesting rapprochement with the exegesis of Structure proposed here.
17 This a method of computer calculation elaborated from the 1950s notably by O. C. Zienkewicz. For further information see Picon (ed.) 1997, 166.
18 The mechanical notion of 'moment' refers to the capacity of a force to rotate a body. This concept has nothing to do, even etymologically, with a temporal moment.