DescartesDurandBalmond
The comparison with Balmond and Durand is important. Why should we say one is rational? Is Balmond right to make a straw-man out of the Cartesian grid?
Well, what does the grid mean? Look at it this way: What Descartes invented was a coordinate system. He engaged algebra with geometry – previously two separate systems in mathematics.
Often the grid is referred to as the “Cartesian” grid. But Descartes never really constructed a grid. He invented a coordinate system that later came to be defined by a graph that we refer to as a “grid.” Descartes’ first discussion of the coordinate system is anecdotal rather than illustrative. It appears in the Discourse on Method, which begins with an observation about architecture. During a stay in Germany Descartes considered the difference between an emergent urban space and a planned one: “ancient cities which, from being at first only villages, have become, in course of time, large towns, are usually but ill laid out compared with the regularity constructed towns which a professional architect has freely planned on an open plain; so that although the several buildings of the former may often equal or surpass in beauty those of the latter, yet when one observes their indiscriminate juxtaposition, there a large one and here a small, and the consequent crookedness and irregularity of the streets, one is disposed to allege that chance rather than any human will guided by reason must have led to such an arrangement...“[1]
The tension between these two systems is an internal problematic in architecture; it is the difference between two forms of mathematical logic: constructive (geometry), and symbolic (algebra). Neither, Descartes asserts, are sufficient in and of themselves, thus he cross-breeds the two.
Then as to the analysis of the ancients and the algebra of the moderns, besides that they embrace only matters highly abstract, and, to appearance, of no use, the former is so exclusively restricted to the consideration of figures, that it can exercise the understanding only on condition of greatly fatiguing the imagination; and, in the latter, there is so complete a subjection to certain rules and formulas, that there results an art full of confusion and obscurity calculated to embarrass, instead of a science fitted to cultivate the mind. By these considerations I was induced to seek some other method which would comprise the advantages of the three and be exempt from their defects.[2]
The principles of “method” in Descarte’s Discourse on Method are an attempt to complete the two imperfections of geometry and algebra: “In this way I believed that I could borrow all that was best both in geometrical analysis and in algebra, and correct all the defects of the one by help of the other.”[3] I believe that this introduces an important lesson for architecture, which is the constant negotiation between two different kinds of operations – for example, between generative scripting and analytical simulations. The invention of calculus and the way in which it problematized Cartesian coordinate systems by introducing curvature and rates of change introduced a new kind of coordinate system that dealt with events rather than spatial relationships or forms. This would have a drastic effect on architecture, one which has only started to play itself out through computation.
Durand: ok, look at the visual documents. Look at the base geometrical grammar – this is Hernandez’s point, the analytical features of the process. Could one even use terms like process or method before Durand? I mean could one use them in such an abstract way? The primitives are the original set and then there are the permutations – left to right. But they are all combinations of circle and square. Then follows more complex arrangements, functions architectural.
The grid is a base from which to compose – so one doesn’t really compose according to a model, but rather an algorithmic-like procedure. The question of Eisenman and Chomsky is important here. In Hernandez: the relation between “no preconceived idea of form [and here the question of Durand’s former professor Boulleee is important]” and the conception of the system as grammatical and syntactical.
What I am missing here – someone borrowed my book on Durand and it is MIA -- is the part of the text that deals with the problem of drawing. Namely: by virtue of this new system, one doesn’t have to deal with the illusionary features of draughtsmanship to make architecture.
Then the question of what Balmond is doing with Chemnitz stadium in opposition to the Cartesian grid vis a vis Durand is important. Another kind of grid. So are we comparing absolutes?
Descartes invented a coordinate system. So what are the consequences of this? Read the article, but essentially he reduced geometry to symbolic notation. Now, think of what it is for us to do scripting. Now think of what Durand was proposing in contrast to the tradition and history of drawing. . . .
These things are linked.
