200 EAAE no 35 Teaching and Experimenting with Architectural Design: Advances in Technology and Changes in Pedagogy
niques do not produce static drawings or models ; most of the time, if it is to make
any sense, the project has to be performed, leading to demos that sound a bit like
cookery demonstrations on breakfast TV (I don’t have any videos of it with me).
There is, however, one project that I think did something with this in the end. The
projective plane of descriptive geometry features a missing quadrant if you like, which
does not exist in the sense that the 3 remaining three quadrants do. It is there only
as a concession to the continuity of paper as a material support, and mathematically
it is simply treated as the negative portion of the upper quadrant. But since it IS
there we figured we might just draw on it and generally behave like it’s an ordinary
projective quadrant. So my student Hoi-Chi Ng rushed into this tear in the material
fabric space and populated it with his own weird creations, leading to the develop-
ment of an analogical Tokyo ward, as part of a studio experiment titled learning
Japanese (2004). After this I chose to discontinue the line of pedagogical inquiry
for two reasons. The first is that too many people simply saw all this as some kind
of collage, and I don’t blame them because it does look like one. The second reason
is that the work was also often referred to as ‘folding’, a completely meaningless
and reductive formulation if there ever was one. By the time we completed learning
Japanese, we simply decided to move on to the fastest-growing area of our research,
the analytic surface.
Part II
Exploring the surface is for me primarily a problem of notation, and for some time
now I have chosen to approach it almost exclusively in writing. By writing I do not
mean writing emails, but approaching the subject through symbols and marks, rather
than figures and images. That is the nature of the analytic surface.
When it comes to creating new surfaces, writing takes on a different role altogether:
it implies a direct recourse to generative symbols and marks. This is about using
symbolic equations rather than ordinary surface software commands, or symbols rather
than buttons and sliders. Working in this manner requires a Zen-like mindset. In the
age of immediacy, super software and smooth person-machine interfaces, working with
parametric equations, as I and my students do, means choosing the arid discipline of
writing over the futile pleasures of modeling.
As this example clearly shows, the process of parametric generation produces a
continuous surface made of lines, or threads. There are two sets of threads, one for
i and one for j, and yes, these the symbols mentioned in the title of my book, IJP
the Book of Surfaces.
The bottom line is that the surface of contemporary mathematics is just lines, or
threads. Hence, the transition to materiality is usually straightforward. If the lines
are two-dimensional, we can use them to define centerlines for parallel laser-cut
material profiles, as shown on this slide by Asa Nilsson. The tectonic expression of
this model emphasizes the reading of the longitudinal threads, which form the full
body of the surface itself. The presence of the other range is somewhat obliterated: