Euclid’s definition of space relies on the construction of points, lines and planes. These elements, when used in tandem, produce objects that are two-dimensionally grounded. By dividing his theories into definitions, postulates, and common notations, he is able to categorically define the objects constructed, explain their self-evident truths as related to mathematics and discuss the self-evident truths that are not specific to mathematics. By using Euclid’s definitions, postulates, and common notations, one is able to create a flat object, that in its nature is concerned with its form.
One of the major distinctions that Barr addresses when defining space is that topology isn’t focused on a form or shape so much as how it is put together. In Cartesian geometry the focus is on the aesthetic appeal of the object, which is defined by a multi-dimensional gird system. This system was passed down through the generations as a golden chalice. However, Euler’s Law radically changed the world’s perception of space placing emphasis on continuity as opposed to object appeal. Barr notes “a topologist is interested in those properties of a thing, that while they are in a sense geometrical, are the most permanent- the ones that will survive distortion and stretching.”
The specific properties of a thing that will survive distortion and stretching are its faces, edges and vertices. Through Euler’s Law, topological invariants can be used to bend geometric polyhedra from an aesthetic driven form into a continuous, self informed object. Through a series of scripted rules, topological geometry is capable of producing outcomes unimagined by Cartesian geometry. Space is no longer thought of as an inside/outside if/then statement, instead it is looked at as defined by faces, edges, and vertices.
Peter Eisenman takes it upon himself to outright reject Euclidian and Cartesian geometry for the likes of topology and the Catastrophe Theory. Through the research and analysis of Deleuze and Leibniz, Eisenman has equipped himself with an arsenal of weaponry that allowed him to reject previous Euclidian and Cartesian geometry for a more ‘event’ based form. Derived from Deleuze’s idea of continuous variation through a fold, Eisenmann proposes using these philosophical ideas as architectural matter. The concept of the fold allows for mediation between previous figure/ground strategies. The fold is neither figure nor ground yet it is capable of reconstituting both. Eisenman felt that the fold would allow for “an opportunity to reassess the entire idea of a static urbanism that deals with objects rather than events.”
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I think the thing I find most interesting about these ideas is how they consider motion.
ReplyDeleteThe classic Euclidean geometry and the cartesian geometry consider space and architecture as static. The points and elements of cartesian geometry are placed within a multi-dimensional grid, and stay there, solidly defined in their relation to other objects in the grid. The Euclidean geometry is concerned with (as Matt pointed out) flat objects, defined by their own forms.
In contrast, the topology experiments that Barr talks about are concerned with the elements that survive distortion. The distortion and stretching approaches objects from much more than a static ideology - the object can be defined by more than just its euclidean defined form located in a world of cartesian geometry. It can move, and yet still be the same object.
The same goes for the ideas in the writing by Eisenman. He is also concerned with a non-static definition of space. Eisenman uses the idea of an "event" and our modern ephemeral attention span to argue that "Hence architecture can no longer be bound by the static definitions of space and place".
As Matt pointed out, Eisenman also argues against the idea of a static form by way of attacking the traditional figure/ground relationship. He relates his ideas to the catastrophe theory where changes in equilibrium can be understood, and says that "These transformations do not allow any classical symmetry, and thus the possibility of a static object, because there is no privileged plane of projection." Again - motion.