Thom/Eisenman

The issue of qualitative vs quantitative is to me one of most interesting aspects of Thom's catastrophe theory. It might be because his explanation of that aspect seemed very clear next to the deeply elaborated mathematically talk on the structural stability of form. Interestingly, while describing qualitative aspects Thom resorts to psychology, and intuition as arguments to use it in his mathematical model. In his example where a theoretical process is graphed along with two graphs of the recreated mathematical formulas, the one quantitatively closer is clearly a worse representation of the original proses - to a intuitively thinking person. "A natural tendency of mind" to put qualitative result over quantitative
As to the catastrophe theory itself, it was hidden deep under the math formulas of Thom's text. As far as I could gather from outside sources, it has more to do with mathematical description and analysis of events and dynamical systems than with geometry, although Thom elaborates on it in form and structural stability. It is more intuitive for me to think of it in terms of processes or systems that are affected by their evolution and their influencing parameters to produce a "disastrous effect" of "dicontinuity", or jumping the fold.
the catastrophe theory is suggested by Peter Eisenman as one of solutions to dealing with architecture in the age of mediation. He argues that the condition of the world today calls for departing from architecture based on Cartesian rationalism to one based on fold. Since Thom's theory combines fold and event it is best suited for such move. The fold is not simply reinterpretation of plan or section but a condition that exists in between others, for Eisenman - a new direction.