Mathland: The Role of Mathematics in Virtual Architecture

Nexus Network Journal, Nov 2005

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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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. - 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)


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Michele Emmer. Mathland: The Role of Mathematics in Virtual Architecture, Nexus Network Journal, 2005, pp. 73-88, Volume 7, Issue 2, DOI: 10.1007/s00004-005-0023-1