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).
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.
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:
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.
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.