Villa Savoye/Mode Of The Axonometric

Template — 01. LOGIC OF THE PLAN VERSUS THE LOGIC OF AXONOMETRIC.

Is that architecture produces series of representation, even silent languages of governance. Representations in which the scope [or the agency] of the subject is spoken of?

I would think so.

Look for instance at the mode of the perspective verses the mode of the axonometric in architecture. If the view emerges from the eye of the perceiver, and emanates in an ocular pyramid (the perspective); or conversely vanishes into a point [metaphysics] the eye is by definition the eye-of-power. In the occident, ceremonial places, memorable places are founded on the principle of the vista (market square, the church, the palace). And the eye thus has a name: it is the eye-of-the-body. And this naming-of-the-eye has to do with occidental notions of the centre. On the other hand, there is parallel projection: the mode of the axonometric.

Now, the axonometric [i.e., parallel projection] considers the world as a machine. A world in which "I" am only a component. A function of the world-machine at the most. One’s agency is not, as in the case of the perspectival, infinite, but non-existent. ‘I’ is an-ant. Maybe a warrior ant (fortifications) maybe a worker-ant (the marketplace) maybe even the queen ant (the palace in the context of the axonometric drawing of a city).[1]

This then would be a simple distinction, an architecture on the ‘right’ would be an architecture of the perspectival; and an architecture of the ‘left’: of the axonometric. Freedom to configure the world [signification] in one case, freedom to partake in the project(s) of the world [(re-)production] in the other.

Logic of the Plan:

I have already articulated above as to how the axonometric sets a totally different principle of power as compared to the perspective. These are two variants of visibility generated by the optical, through mediation in the design process, a process known as drawing.

Even as Le Corbusier’s building is conceptualised using a Cartesian geometry, and dispersed along a point of origin, [x,y,z,], the logic of the plan is at work. By the logic of plan, I mean the traits built into design, as lines are manipulated along not a three dimensional ("x,y,z") space, but on a horizontal plane. Accepting the vertical and horizontal propensities of the drafting tool as a trammel—accepting the ‘x’, and ‘y’, axii. On which forms are ‘drawn’ and then extruded into three dimensions.

As regards the SEMANTIC ORDERING, let us accept this categorisation; the objects pertaining to the Dom-Ino frame (or, RCC construction methods) are organised along the "x,y,z," axial schema, they follow the basic cubical module and its derivations. E.g., the disposition of columns and beams which—being the main supports of the building, lend it it’s basic meaning. I have demonstrated, elsewhere, coherence of this system as a series: in a progression from ratio 1:1 through to 1:√2, and from there on to the proportion Ø, and so on…… the numbers increasing in their complexity as they approach the origin point, marked as ‘0,0,0’. One can also express this order as series 1 --> Ø. The transformation of this series into the vertical axis is an integral component of this geometry, using as the basic module the proportion ³√a, or ³√b. where a and b are dimensions etched on the horizontal planes. This entire maneuver could be demonstrated—at least in its general characteristic, as a single equation. Something true even of the façade. These linear elements, or the ‘skeleton’ do not strictly follow the logic of the plan.

By representing a mathematical equation, moreover, this system is free of the conventional triads (e.g., plan-mass-surface; or plan-section-elevation or, Ground-Structure-Ornament) which have functioned as unities of meaning in architecture. The triad being necessary for the formation of logic entailed by conventional ‘tests’ of coherence performed to validate the work.

The equation, on the contrary, validates itself: it is rather a form of the mechanisation of design. The meaning of the work would necessarily construe a tangent to this mechanisation. In other words, the plan is no longer necessary. Le Corbusier yet insists on the plan: inscribing it with quite another set of lines.

The order at this level is constituted of two coherences:

• First, a tri-axial system; corporeally represented by the RCC constructional frame: by its structural propensities (the building could not possibly exist without it), and by its material properties (an equation encompassing all possible numbers admitted as significant by Classical Western architecture) the primary level.
• Secondarily, there is the system constituted by the plan; as Colin Rowe has shown, validating this building’s existence as a particular instance of a type: an ideological-historical coherence.

The bodily-binding elements, on the other hand, are elements derived of the plan, that is to say, ‘freely inserted’ into the ensemble along the "x" , and "y" axii of the paper on which they were drawn. As figures (I) and (II) show, these membranes are then simply extruded vertically to suite requirements. The roof-top and entrance (glass) screens are examples to the point. Surprisingly, so is the staircase.

Given that the frame, which should always be understood as the ‘first’ principle of any of Le Corbusier’s (cubist-purist) buildings, given his obsession with the Dom-Ino, we should accept the plan (extruded) elements as elements of play. And the relation of the resultant ‘game’ to the primary semantic order is as dichotomous as the game of CHESS (the coded game, with "intrinsic properties from which their movements, situations and confrontations derive")—i.e., the game of State, the game of Striations versus the game of ‘go’—the game of the wall, the rhetorical elements standing-in as the element of confinement. It would be as if two very different games are being played out, respectively between the mechanical linear schema of the frame and the bodily binding "anonymous,…third person function(s)".

It is crucial to understand: these are board games. They unfold on the space of the drawing: in the geometricity of lines which relate to other lines. Their relation will be something else, as we would see later; if one considers the semiotic of the building in its corporeal state. If one thinks of the building as produced by labour. If one considers the semiotic of a building as perceived by the eye which travels inside the thing; or of a building coming to represent the technical conditions of its age.

The ‘eye’ is not in the picture throughout the consideration above.

The Axonometric:

What is the act of the plan? Is it primarily the act of naming space? (naming as it does, this-here, that-there. Specifying, numerically, relations amongst the various entailments: or the programme). How does it become ‘anonymous’ as in a game of ‘go’? is it the same as the act of geometry—geometry imposes a distance between the building and its architect: it inserts it’s own movements from the particular (this house, this wall, this thing… ) to the global (mathematics, geometry, conditions of knowledge…. Of ascertaining) it provides one with ways of verifying.

I think geometry—being a mythological form in Barthian terms—relates to the plan just as signification relates to the sign. First of all, it is a ‘stolen language’. It ‘steals’ the rôles of verification and the estrangement from the present (the laying of a ‘wedge’) from the plan. It ‘governs’ the plan thorough this stealing; and by stealing, it de-politises the plan. Grounds it ultimately in the metaphysical. One could safely call this elitist function of ordering the hegemonic function. Given it’s propensities towards overcoding, it is natural to assume the same purpose to power is at work here as it is in Barbarian or Imperial Representation. It’s function is the same as graphism in writing, and from quite another standpoint, the plan and proportioning systems could be shown to constitute the same relation as the voice and the graphism in imperial representation—well proportioned buildings are put to service by housing the functions of legislation, bureaucracy, accounting, the collection of taxes, the state monopoly…and in case of the Villa; as James Ackerman shows quite admirably; the Urban Man’s appropriation of the countryside.

It is crucial then to draw relations amongst the two diagramme represented; the Cartesian diagramme constitutive of the Primary semantic order of the villa: a pure architectural function, to the service of State Theory inasmuch as it transforms building through a peculiar Techné. A specialised sort of knowledge. And the Secondary semantic order: the bodily binding—wall—diagramme which would be termed the Euclidean schema.

Notes:

1. An understanding of parallel projection can take two basic forms: First, from Roger Becon, and Islam: that ‘things in the world have an eye by themselves’, or, "the universe from each of its points extends influences in all directions, rays and species, so that each points par se an active centre, a sort of an eye sending species over the entire universe and receiving them from the entire universe." A perception in which no human eye orders this world, for it is composed of an infinity of radiant points. Second, by assuming that it is derived from a peculiar Renaissance discussion on Optics. Where parallel projections are ‘obtained’ through an understanding of shadow. Which is seen as a representation of the thing placed in the parallel rays of the sun. or, in the eye of the sun. the parallel ‘ray’ anamorphises the thing onto the planar surfaces—the ‘screen’ of the gaze. J.Lacan develops this thematic as that of the gaze as an objet petit a, and the eye as a function of -Ø. A de-capitation, or a representation of death obtained through an anamorphic process. The symbolic ‘death’ of the anthropomorphic form is patent: the axonometric projection is often obtained by representing the death of the subject, at least a bodily death. Something sharing an affinity with certain of G.Bataille’s perceptions,…" mythologically expressed by a man slashing his own throat, as well as by an anthropomorphic being deprived of its head." [G.Bataille, The Rotten Sun.]
2. I use these terms ‘right’ and ‘left’ very loosely here. You may want to substitute them for other equivalents: ;super-' and 'sub' structures for example.
3. See Template—o1. Of Powers of the Eye and the Data Received by them.
4. See chapter – 01 section b.–i. The Mathematical ‘Language’. Codes of Unification, Linear Systems & the Active Field.
5. I am very aware, in writing this; of the last known writing by Le Corbusier, Nothing is Transmissible but Thought, in which he likens the creation of architectural objects to a ‘game’, of this house.
6. In the chapter from A Thousand Plateaux, entitled ‘1227: Treatise on Nomadology—the War Machine," Deleuze and Guattari analyse war by opposing chess and Go as game theories: ‘from the standpoint of the game pieces, the relations between the pieces and the spaces involved’ (1987, 34-52-3). Yet this concept of war involves processes within the subject was well as the most violent manifestations of social dynamics. While Deleuze and Guattari state that "Chess is a game of State, or of the court; the emperor of China played it" (352), we must also remember that chess tropes signifying systems that determine the socially-constituted subject, with rigid rules governing identity. Go pieces, on the other hand, ‘have only an anonymous, collective or third-person function,’ with ‘only a milieu of exteriorly, or extrinsic relations’. The properties of Go involve not semiotic precision but strategic flows that obey not cause and effect, as with chess, but dissemination that is contingent upon situation. They write, "it is a question of arraying oneself in an open space, of holding space, of maintaining the possibility of springing up at any point: the movement is not from one point to another, but becomes perpetual, without aim or destination. Without departure or arrival."
7. Anti-Œdipus, Capitalism and Schizophrenia. Pp. 200-17.