The idea of the grid is of something to be extruded into. Grids are seen as marking space, that is creating an arbitrary but useful division of space which organizes an intrusion upon it. The mentality of the grid is one of imposition – not the imposition of axes, mind you, which are implied, but the further imposition of geometry upon an already existing infinite space. If we're talking about architectural creation, then the architect has already lost control. The project becomes bound to a system, defined by a system, which is not of the architect's creation. Or more accurately, if it is of the architect's creation, it is a creation with implicit axioms and assumptions about the operating principles of space.
By "Cartesian space" and "grid systems," I don't necessarily mean right-angled working lines, or linear geometry. Grids may exist as deformations (Reinmennian geometry, or spherical, or hyperbolic geometry, to name some examples) and may even be self-contained. What I mean more specifically is the Modern mentality – "Modern" in the technical sense, or "Modernist" if you like – that the nature of space is rational and neutral, that space exists at all in an infinite and pervasive way, such that grid lines may be drawn upon it, and coordinates may be plotted upon it.
The difference is between geometry and arithmetic, in the historical sense of the terms. Euclid (nor Phidias and Iktinos, for that matter) was not Cartesian in this way – the operations of the compass the straightedge and the pen all grow from within themselves. Each circle drawn on paper (or marble!) viciously creates both the circle and the space to which it relates. The relationship between the two only exists because they were created – further, the circle and its center only exist by an act of force. The plane itself, arguably Cartesian and arguably a geometrical concept necessary in the creation of the circle, is created by an act of force. The infinite did not exist beforehand, but exists within itself and within the representation of itself, and is contained only within the representation of itself.
It is the rational which is impossible to grasp. It flits away and slips sideways – it is impossible to proceed one from the next without an act of destruction, a jump from the scratched and tangible surface of the vellum sheet, through a point in the air, to begin again another world unrelated to the first except through that point in the air. The rational procreates in one next to the other, not touching but dimly aware of the other's existence.
I feel that there is a much more elegant way to put this, but perhaps words are not the correct medium. The larger point for architecture is simple: grids and grid systems carry assumptions about the operations of space, which become inextricably tied to assumptions about the organization of space, which is to say program, circulation, &c., which is to say architecture. Part of the great dissonance I feel towards the mentality outlined in a previous post about the Columbia GSAPP is this dissonance – that such projects claim to have broken the grid system while remaining entrapped within a Cartesian system. Claims about intrusion, elbowing out, growing from the center, architecture developing from itself and pushing itself violently into the world just inherently don't work if it is assumed that these operations create architecture upon existing space.
No, rather, it is the act of creation which is a violent event. The tabula rasa is only catastrophic as an afterthought, while the true creation of space from within itself (and into no thing) is the implied catastrophe embodied in an event. It's the reason that the Greek Temple works so fantastically, why the Parthenon speaks today as an incredible crystaline carving out of space itself, while the French Neoclassical fails so spectacularly in the same goal – the Pantheon in Paris tries to be all about support and the application of structural logic to form, but in the end is all about grids. It's the difference between Jenson and Didot, in a sense the same difference between the Carolingian and Neoclassical scripts, between the high French Gothic and La Madeleine.
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