Mathland: The Role of Mathematics in Virtual Architecture
This paper is dedicated to some arguments that could be of interest both for students and practicing architects. A short adventure in the reign of mathematics and culture. The example that I have chosen is that of the idea of space, how this idea and the perception of space around us has changed up to the point where it has arrived to the form of virtual architecture.
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This attitude is brought on by at least two causes related to the little space that mathematics
courses have in the architecture curriculum: there is an increasing tendency to reduce the number
of classroom hours, and a parallel tendency to reduce drastically the arguments treated.
I believe that the ideal mathematics course in the architecture curriculum is, for the large
majority of architects, a course in recipesto paraphrase Robert Musil in The Man without
Qualities , on the opinion of engineers regarding mathematicswhich are to be applied without
questioning why. The obvious corollary to this idea is that it would be better if the architects
themselves taught these recipe courses without troubling the mathematicians to make some
derivative or some integral. Although it is true that the mathematics courses serve as technical
courses for architects, it is also true that the attitude of a great number of the students and
professors of architecture is basically that in the end it is the engineers who have to deal with
structures.
It is certainly very difficult to collaborate with other professors in non-mathematics courses for
architecture given that the majority of these are ignorant (and prefer to be ignorant) of what could
be done in a mathematics course. I recall the first year that I began to teach in architecture at La
Sapienza , the University of Rome, in 1996. In presenting the courses the dean of the faculty
praised the architect as creative and artistic, describing the courses as a kind of support for future
architects for observing, gathering, feeling, almost sensing in the air the new tendencies in art and
architecture. Architects as creators. How then can that arid discipline mathematics be of use?
By chance I taught for a year in 1992 at the IUAV in Venice before transferring to the
University of Rome. After having taught for several years I posed myself the question, partly out of
boredom of having always taught the same things in the same way, of how things could be
changed radically. I left the architecture faculty and entered that of industrial design, hoping to
find more imagination. In any case, I believed that the best thing I could do was not write yet
another book on lessons and exercises in advanced calculus and analytical geometry (although
obviously the great advantage of writing such books is that hundreds of students are obliged to
buy them, to the great satisfaction of the authors) but instead to try to make comprehensible that
mathematics has an enormous cultural value, that it can change our way of thinking and therefore
the way that architects design in ways that they perhaps cannot even imagine.
The idea was born out of the project Matematica ed arte in 1976, and then in 1996 became
the much more vast Matematica e cultura [Emmer 2002, 2003, 2004a etc]. Taking as a point of
departure the ideas expressed in that deans presentation of the courses, my ambition was to make
it understood that among the many things to remember, observe, and understand there had to be
mathematics as well. Not only because mathematics is the essence of spirit, but because
mathematics can be an inexhaustible font of ideas and suggestions, not only of recipes. Besides, it
can be an extraordinary school of adaptation for problems that have not yet been encountered.
I did not want, however, to look at the questions in abstract (abstraction is one of the great
defects attributed to mathematicians by those who do not understand that this is instead one of
their great merits) [Osserman 1995]. Therefore I wanted to start with a concrete example in which
the relationship between mathematics and culture had profoundly changed our way to looking at
the world around us, and therefore also the architects way of thinking and acting. The theme was
that of space, of the mutation of our idea of space, using as the perfect guide the extraordinary
book Flatland by E. Abbot, a book published in 1884 but timely today if only one will penetrate
the surface and not consider it merely as a somewhat trite criticism of Victorian society. Having
made an animated film by the same title [Emmer 1994], I had had the experience of designing
the space that the book talks about, as well as the characters, the city, and the universe described by
the hero, the Square. This is the reason by the book that I wrote on this theme is entitled
Mathland [Emmer 2004b].
In the present paper I would like the refer to some of the arguments that this book discusses
that I believe are of interest to both student and practicing architects. This is a brief reading of
mans adv (...truncated)