Mathematics as a Design Tool: The Case of Architecture Reconsidered

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Although the body of this essay is confined to discussion of architectural design; the issue in question, namely, the role of mathematics, concerns the realm of in its broadest sense. In modern usage, the word design owes much to its Italian progenitor disegno, concept first systematically worked out in 15thand 16thcentury art theory. Disegno, in its original and most literal sense, referred to drawing, and was often contrasted, particularly in discussions of painting, with colorito, or coloring. Inherent in this contrast is the distinction between the sensual (coloring) and the intellectual (drawing); and, thus, the term disegno gradually came to signify the creative idea existing in the mind of the artist, and only secondarily, the preliminary drawing in which the idea was first embodied. is important to note that the theory of disegno was developed during the Renaissance to support the artist's claim to be considered as practitioner of liberal art and, therefore, as an intellectual rather than manual laborer. In the preface to his De re aedificatoria, Alberti distinguishes the work of the architect from the work of the builder, saying that the latter consists of manual operations, while the former is of thought and invention. According to Alberti, this distinction is grounded in the assumption that the architect possesses science and, therefore, knows the causes of things; while the manual worker, who has only the knowledge that experience imparts, does not. But what is this science that enables the architect to know the causes of design? Paralleling his distinction between the architect and the builder, Alberti divides the art of building into two parts: (lineamentum: literally, line; derivatively, drawings) and structure. He says that, It is the property and business of the to appoint to the edifice and all its parts their proper places, determinate number, just proportion, and beautiful order; so that the whole form of the structure be proportionable.' And he defines as a right and exact adapting and joining together the lines and angles which compose and form the face of the building.2 Clearly, the science that the architect must possess is mathematics; more particularly, geometry, the science of lines. At the root of the divisions Alberti makes between the architect and the builder, and between and structure, is the Platonic-Aristotelian distinction between matter and form. In book This essay has been adapted from sections