1 introduction - intensity

What does topology change about our notion of "space?" (and remember mathematics has areas, "geometry," "algebra," etc. -- are these areas discovered? did they Naturally exist?). Read the text by Euclid, then read Barr's text on topology. Many of the "elements" are the same. But now consider, in what sense can we talk about "space" in Euclid? Therein lies one of the distinctions. For the moment, consider today's lecture on the Topological continuity between different polyhedra. The Klein bottle looks like any other object insofar as it seems to have things like boundaries. But in fact, when I asked to compare it to, say, a box, it became clear that one of the distinctions is that it doesn't have an inside and an outside -- it is continuous along its surface. Why is this of any relevance for architecture? Well, among other things, this kind of observation allows us to reconsider the notion of an architectural envelope and begin to PLAY with traditional architectural properties of inside and outside. A key concept is obviously the notion of folding spaces. We'll get to that a bit more later in relation to Deleuze, but for now it is a way of "complicating" space and thus making it more dynamic, more intense. As Rajchman points out, complicate is elborated from a Latin root pli, to fold.
When we look at many of the projects during the '90s by diller/scofidio, Lynn, Spueybroek, UnStudio, Koolhaas, etc., we see there are a series of these attempts at folding: folding of the inside and outside, folding of site and building, folding of ground and envelope. This changes the way in which we can experience and understand spatial relations in architecture -- they make it potentially more dynamic.
As I continue to write on this, keep in mind the last part of the lecture: topology has, among other things, enabled architecture to shift from the concept of the grid and metric space and bounded form to networks and folds. The latter introduce not limits and positions, but rather transitions and therefore intensities.