Euclid speaks about space as a two dimensional platform, which he uses to define geometrical position. He starts off with a description of point that I think implies single isolated element ready to behave and give geometry but in itself is not equal to anything of organization, thus he needs to define lines, surfaces etc. The categories of Euclid I think are different in terms of quantity and types of elements forming geometries, both setting up specific conditions of formal recognition of such geometries not and much beyond that. A category (from Wikipedia.org) “is a fundamental and abstract way to describe mathematical entities and their relationships”. Barr calls out mathematical fields (pg2) in his study that incline a dynamic performance of elements in space. He also refers to continuity of space (P. Eisenman -folds) in that other dimension vaguely omitted from observation and recognition. I think this could go hand in hand with science of system of human receptors, which daily absorb millions of information and selectively identify those paid attention too at specific moments in space. As the class syllabus states “Peter Eisenman rejects Euclidean and Cartesian geometry for Catastrophe theory, Calculus, and Typology.” This rejection is caused by the static figure-ground conditions formed by Cartesian system and that “point is not the smallest element” but a fold. He concludes so from studies that architecture not a display for fast growing, electronic media but a source of consumption, and boundaries defining geometrical models in space are much more advanced and complex than a class, set or function of an equation in geometrical positions.
Euclid speaks about space as a two dimensional platform, which he uses to define geometrical position. He starts off with a description of point that I think implies single isolated element ready to behave and give geometry but in itself is not equal to anything of organization, thus he needs to define lines, surfaces etc. The categories of Euclid I think are different in terms of quantity and types of elements forming geometries, both setting up specific conditions of formal recognition of such geometries not and much beyond that. A category (from Wikipedia.org) “is a fundamental and abstract way to describe mathematical entities and their relationships”.
ReplyDeleteBarr calls out mathematical fields (pg2) in his study that incline a dynamic performance of elements in space. He also refers to continuity of space (P. Eisenman -folds) in that other dimension vaguely omitted from observation and recognition. I think this could go hand in hand with science of system of human receptors, which daily absorb millions of information and selectively identify those paid attention too at specific moments in space.
As the class syllabus states “Peter Eisenman rejects Euclidean and Cartesian geometry for Catastrophe theory, Calculus, and Typology.” This rejection is caused by the static figure-ground conditions formed by Cartesian system and that “point is not the smallest element” but a fold. He concludes so from studies that architecture not a display for fast growing, electronic media but a source of consumption, and boundaries defining geometrical models in space are much more advanced and complex than a class, set or function of an equation in geometrical positions.