Prior to the advent of modern structural engineering, architects and builders used proportional systems to imbue their works with a general condition of order that was integral to notions of beauty and structural stability. These mostly invisible intellectual frameworks ranged from simple grids and symbolic numbers, to sly manipulations of geometry and numbers that required privileged knowledge and arithmetical calculations to access. Since the origins of architectural history, proportional systems have served as objects of belief and modes of iconographical communication. Whether they are capable of fulfilling more tangible functions remains a matter of debate today, but as the contributors to this volume show, these ancient and diverse belief systems continue to infiltrate architectural thinking in subtle and sometimes surprising ways today.
 

Matthew A. Cohen is a licensed architect and professor of architecture at Washington State University. Maarten Delbeke is chair in the history and theory of architecture at the Institute for the History and Theory of Architecture at ETH Zürich.