If we are to grasp Deleuze’s concepts of space, a few words should be said about his ‘political anthropology’, which is intended to replace Karl Marx’ political economy and historical dialectics as an analysis and guide in today’s political struggle. In his account of the historical process, Deleuze introduces an agent called ‘the nomad’, unknown to Marxism, who runs counter to ‘the State’ in the sense that the nomad is aggressively creative, while the State plays the more passive role of consolidator: the State thrives by capturing nomadic innovations and transforming them to fit its own needs, precisely in order to consolidate a certain state of affairs. On the other hand, every consolidated state induces renewed nomadic aggression and inventions that the State must absorb and adapt to its consolidating tissue, which, thus enriched, opens up paths for amplified nomadic action, and so on. In accordance with his philosophical style, Deleuze does not come up with a definition of the nomad, but puts the word into play in different contexts, and such that it never acquires a definite meaning, but rather is intended to serve as a conceptual nomad: an agent in unfinished philosophical, political, artistic and other business. This is not to say that the word is reduced to a metaphor or some other trope; the baffling thing is that the historical and anthropological nomads who used to roam the steppes and deserts, warring against the surrounding States, are indeed subsumed under the concept of the nomad at the same level as other nomads introduced along the way, including ‘mad’ physical particles, viruses and rats as well as craftsmen and engineers, and minorities involved in actions against the State. This means that real historical events, shreds of proper historiography, are every so often freely incorporated into a textual fabric that is about anything but history.
Something similar is true of Deleuze’s use of mathematical concepts: sometimes they are applied strictly, at other times they are let loose in the nomadic discourse without much concern for their proper scientific meaning. I believe that this is intentional, part and parcel of a philosophy dedicated to unbridled creativity and activism; one could say, then, that it is missing the point to confront Deleuze’s nomadic thinking with conceptualizations based on Piaget’s epistemology and psychology. Nevertheless, in this section I am going to pick up some threads from Deleuze’s most widely read book A Thousand Plateaus in order to figure out what Deleuzian concepts of space and evolution would look like from the point of view of the Piaget-inspired notion of cultural space. When the nomad/State opposition is applied to space, the basic principle is that nomad space is ‘smooth’ and heterogeneous, while State space is ‘striated’ and homogeneous. Deleuze illustrates these concepts with an example from technology: woven fabric is striated, that is, with the threads of warp and woof; felt is smooth, as it consists of entangled fibres; it is no accident, Deleuze comments, that the Mongolian nomads excel in using felt for their tents, clothing and even armoury. As a matter of fact, the very spaces inhabited by nomads – steppes and deserts – are smooth, and the same is true of the ice desert inhabited by Eskimos, and of the sea roamed by seafaring peoples. In these spaces orientations, landmarks and linkages are in continuous variation, Deleuze observes, and goes on: “there is no line separating earth and sky; there is no intermediate distance, no perspective or contour; visibility is limited; and yet there is an extraordinarily fine topology that relies not on points or objects, but rather on haecceities, on sets of relations (winds, undulations of snow or sand, the song of the sand, the creaking of the ice, the tactile qualities of both).” In contrast to this fluid state, the spaces inhabited by sedentary peoples – which are State spaces – are striated with walls, enclosures and roads that exhibit constancy of orientation and metric regularity. Deleuze’s description of the nomad’s environment is directly linked with a theory inspired by Worringer and Riegl of “nomad art and its successors (barbarian, Gothic, modern)”. It is generally held that nomads derive their art from the sedentary peoples with whom they come into contact, and it is a fact that much nomad art is purely geometrical; but Deleuze insists that the nomads have or have had their own ‘will to art’, which is expressed in a “streaming, spiralling, zigzagging, sneaking, feverish line”, as he describes it at one point. Although Deleuze repeatedly stresses the distinction between nomads and migrants, he insists on the point that the Goths who migrated into the Roman Empire in the 4th and 5th centuries were nomads, and connects these people and their art with the 12th century Gothic cathedrals and their builders, who were obviously not Goths; they were Franks. While Romanesque architecture is still striated, Deleuze observes, the Gothic is smooth. Agreeing in this, we would add that the Byzantines created an even smoother space, which deserves inclusion in the genealogy of nomad art. As for the ‘modern’ successors of nomad art, Deleuze does not elaborate in the pages referred to here, but what he has in mind is no doubt Expressionism rather than what is usually thought of as Modernism: Purism, Neoplasticism, Elementarism... whose spaces certainly are striated. What we know for sure is that Deleuze himself is philosophical inspired by a neo-Expressionist movement in art and architecture that took hold in the decades around the turn of the last century. Although the Baroque is not mentioned in the pages referred to here, in another work Deleuze describes the Baroque space in a way that richly qualifies the notion of smoothness. On our own account we would suggest that the space of Romanticism should be included in the nomadic-smooth genealogy, and there are in fact some places where Deleuze describes the mind of Romanticism as nomadic. As regards the striated State spaces, they presumably fill the gaps between the high points of nomadic smoothing, and are thus associated with Classical Antiquity, the Romanesque period, the Renaissance, Classicism and Classical Modernism. Deleuze’s account of the striation process hardly touches on art and architecture, and is extremely obscure, but I will try to paraphrase it in order to come up with a complete genealogy of architectural space in terms of the alternation between smoothing and striation. Before I present the genealogy, a few preliminary words should be said about Deleuze’s perception of geometrical space. In terms of the smooth/striated opposition, coordinate geometry as well as metric geometry in general describe striated, homogeneous spaces. Of geometrical smooth space it is said that it has no homogeneity except between infinitely proximate points, and that the linking of proximities is effected independently of any determined path. To Deleuze, the epitome of this kind of space is the space of Riemannian geometry; but as distinct from metric space, vectorial, projective and topological spaces are also smooth. There is a problem here with projective space, because although Deleuze repeatedly makes it a point that projection amounts to smoothing, in one crucial place it is stated that striated space is defined by, among other things, “the constitution of central perspective”. Deleuze does not put this casual observation to much use, and is very vague about what he means by ‘the constitution of central perspective’. I think that this deprives Deleuze’s ideas about space of analytical and narrative power, and will therefore elaborate a little on the difference between metric and projective space. In psychogenetic terms, the difference between metrics and projection is that the straight line is mastered in two different ways: as a ‘base line’ that structures metric space, and as a ‘line of sight’ that structures projective space. In the most elementary psychological sense, the straight line of metrics is the line that connects and denotes the distance between two points. When one notes the shortest distance by means of an actual movement, one acquires the idea of the straight line as something that denotes a fixed distance. Eventually, this experience is encoded as a general mental scheme that works automatically in all situations. When we move things around in our imagination so that their relative positions are changed in a regular manner, while their metric identities remain unchanged, the idea gradually emerges of a system of co-ordinates as a regular frame of reference for a metric space that can be expanded to include bigger and bigger entities. In the same process, a general notion of orientation emerges from which there first arises the idea of parallelism, then the idea of ‘point of view’ and recognition of the line of sight that structures projective space. The meaning of this is vividly illustrated by one of Piaget’s experiments. In order to show how the projective line is acquired by way of the sight principle, Piaget asks his young subjects to place small sticks – stuck into a base of plasticine – on a straight line between two sticks placed in advance on a table. The youngest children place them close together in a random cluster or curves. When children of this age are shown a straight line and a curved line, they can easily tell the difference, but in their mental space there is no difference between straight and curved, and it is this condition that finds expression in the way the sticks are placed. Around the age of six or seven, children get better at producing a straight line, but not until around the age of nine is the child capable of successfully completing the task, because it now discovers ‘the sight principle’: you make the sticks stand in a straight line by adjusting them to the line of sight that connects your eye with the two sticks placed in advance. The discovery of the sight principle has the effect that the child discovers that it has a point of view of its own, which is the starting point for an understanding of the fact that other points of view also exist. And, Piaget says, projective perception of space consists precisely of the ability to coordinate an infinite numbers of viewpoints. In Deleuzian terms, then, metric and projective coordination should be considered as two modes of striation, which would first have to produce the straight line from a primordial, topologically fluid smooth space. Metric coordination is actualized progressively as spatial units are related to more and more regular grids of parallel lines. The projective line is actualized as a horizontal axis and is progressively deepened, as it were, until finally reaching the ‘point at infinity’ that corresponds to the vanishing point of the perspective construction. With the projective line follows, first, bilateral symmetry, and later higher degrees of symmetry. To complete the picture, two potentials for striation which in fact precede metric and projective coordination should be mentioned. Firstly, in a discussion of the space of physics, Deleuze correctly points out that the primordial element of striation is the vertical line that corresponds to the direction of gravitation in our normal environment. In architectural space, too, the vertical is the first geometrically structuring element to appear, and from then on the most persistent one. Not only because gravitation is of obvious importance to the construction of buildings, but also because the vertical direction coincides with the main axis of the body and has particular emotional effects: fear of depth, and the experience of height as ‘elevated’. For these reasons the vertical easily acquires a strong symbolic meaning denoting ‘centres’ – the axis mundi of much mythology. For Deleuze, the centre assumes the more dramatic role “of casting into the loathsome deep, the abode of the dead, anything smooth or unmeasured that may have remained.” The second potential for striation is related to the fact that the human body has a front and back, and that the head-on direction, or the frontal position in relation to other people and objects, in general has a particular psychological importance and easily acquires symbolic meaning too. Psychologists, anthropologists, and philosophers, even linguists, have observed the peculiarity of these two directions, vertical and head-on, and together they are designated ‘the canonical directions’ which, as inherent properties of the human body, provide the natural basis for spatial structuring. In the Deleuzian scenario, too, the canonical directions are thought of as primordial, but here depth in the head-on sense (the ‘third’ dimension added to ‘height’ and ‘breadth’) and in the vertical sense (the ‘loathsome deep’) are conflated into what Deleuze calls depth, which is the virtual intensity from which the extensive, actual space is unfolded (on the concepts of virtual/actual and intensive/extensive, see section 4: Piaget, DeLanda and Deleuze). I suggest that the reader, with these observations in mind, look at the plates in the picture gallery, which present an overview of the evolution of architectural space. The development takes off from a primordial smooth space, upon which striation is gradually imposed, in the first place metrically (plates 3, 4), then projectively (plate 5). From then on, smoothing and striation follow in more or less regular alternation up to the present day. On the face of it at least, although not with regard to the political meaning of Deleuze’s philosophy, this would seem to fulfil the aim stated toward the end of A Thousand Plateaus: “What interests us in striation and smoothing are precisely the passages and combinations: how the forces at work within space continually striate it, and how in the course of its striation it develops other forces and emits new smooth spaces...” |
