Marco Frascari
Virginia Tech, USA    

Livio Volpi Ghirardini
Mantua, ITALY

98-frascariAre architectural proportions metric, numeric, geometric or golden? Which ones among the many in a building are the markers that should be considered reference points for the proportioning of its parts? A golden or divine magnifying glass that distorts rather than clarifies has been applied to everything in the name of aesthetic and mystical impulses. A proportion called the Golden Mean has long been the only explanation for a successive melange of proportions in all the visual arts. This Golden Mean (also called the Divine Proportion) has been found repeatedly in the pictures of growth patterns embodied in natural events or in the pictures of human products. Since the last century it has so fascinated mathematicians and artists that is is proposed by many as the absolute aesthetic value.

By tracing lines onto pictures, this ideal proportion has been found in man-made artifacts and used to mark human achievements. As the acme of his mystically scientific process, pictures of the Parthenon with Golden sections traced on them have been exhibited as demonstrations of the beauty of its man-made, but nature-inspired, rational design. This graphic notion of beauty is so alluring and pervasive that it has been acritically forced upon us as an aesthetic paradigm since grade school.

The German, Apollonian search within the combined sciences of mathematics, philosophy and archaeology lies at the root of the scientific proposal of the Golden Mean as a panacea for explaining the composition of parts and foretelling the aesthetic future of man-made designs. German philosopher Adolf Zeising has made the Golden Mean the only possible principle of a scientific aesthetic and used the Parthenon with the usual diagram traced on it to provide the necessary archaeological authority for his theory of the omnipresence of the aesthetic guarantor phi. In 1876, in a ponderous article published in memory of Zeising, mathematician Siegmund Gunter reviewed Zeising's scientific aesthetics in a critical manner, but even he admitted that the presence of phi in ancient architecture, and notably in the Parthenon, was clear evidence of its being the powerful quintessence of classical aesthetic values. Without any doubt Zeising and Gunter were very skillful at measuring pictures, but it is clear that neither of them had ever measured a building following to tectonic principles.

The correct citation for this paper is:
Marco Frascari and Livio Volpi Ghirardini, "Contra Divinam Proportionem", pp. 65-74 in Nexus II: Architecture and Mathematics, ed. Kim Williams, Fucecchio (Florence): Edizioni dell'Erba, 1998.