Steven Fleming
University of Newcastle
Callaghan NSW 2308 AUSTRALIA
School of Architecture and the Built Environment

Klaus-Peter Gast claims that a method known as plan analysis reveals hidden geometrical patterns in almost all of Kahn's buildings. On first appraisal, Gast's analysis would In his recently published book Louis I. Kahn: The Idea of Order (Birkhäuser, 1998), appear to confirm claims by various scholars that Kahn was a Platonist. Jencks, Burton, Scully, Brownlee, De Long, Auer, and Danto have compared Kahn's tendency to conceive buildings as instances of "forms" to Plato's doctrine that particular things participate in what Plato calls Forms or Ideas. According to Gast, Kahn goes one step further by secretly inscribing his buildings with a geometrical kind of Platonic Form, the square.

Using simple mathematics, this paper demonstrates that Gast's geometrical analyses of three of Kahn's buildings do not to tally with the dimensions indicated on Kahn's working drawings for those projects. These discrepancies prompt an inquiry into Kahn's approach to number and geometry which takes its direction from scholarship linking Kahn's "form and design" theory to Plato's theory of Forms.

Before proceeding, two points of qualification are made. First, there is nothing in Plato to suggest that buildings should bear hidden inscriptions. Second, Plato's theory of Forms does not suggest that buildings should participate in Forms other than those corresponding to their class names. In other words, particular houses participate in The House Itself, but they needn't also participate in The Square Itself.

The treatment of the facade in the First Unitarian Church

In The Republic (524), Plato argues that the sensory perception of ones own fingers is sufficient to apprehend that we have five fingers on each hand. However, should we ask which of our fingers are large and which are small, given that these are relative terms, we're forced to use reason and consider the existence of the transcendent Forms, Largeness Itself and Smallness Itself. Hence the common sight of similar but non-identical units can be thought of as a challenge to empiricism, steering viewers towards Plato's rationalistic epistemology. As well as units, this rationale extends to plane and solid geometry as well, so that any ambiguity surrounding a building's shape may cause viewers to contemplate such Forms as The Square Itself and The Cube Itself.

On many levels, the visual apprehension of Kahn's Unitarian Church in Rochester causes mental distress and demands the operation of reason. Due to the radial distribution of light towers, viewers expect the auditorium to be square. Their discovery that it is not square after all, would, according to the logic of Plato's finger analogy, lead them to contemplate of The Square Itself. Similarly, glazing strips at The Kimbell Art Museum draw viewers' attention to the fact that the vaults are not elliptical as they might have at first expected. The façade treatment at Rochester also invites the use of reason, since the perception of any aspect, in the words of The Republic (524e), "seems to involve plurality as much as unity." Likewise, the scalelessness of Kahn's National Assembly in Dacca might cause viewers to ask if the buildings are large, and what is large.

This interpretation of number and geometry in Kahn's work may seem obscure, but it does provide an explanation of his intensions which is intrinsic to his own dualistic metaphysics. Kahn's buildings invite conflicting readings, reminding viewers not to trust their senses. As Kahn says, a great building evokes the "unmeasurable" realm of "form," just as the sight of fingers, according to Plato, evokes the purely intelligible realm of Forms.

ABOUT THE AUTHOR
This email address is being protected from spambots. You need JavaScript enabled to view it. is a lecturer in architectural history and theory at The University of Newcastle in Australia. As a PhD candidate, he is examining the Platonic nature of Louis Kahn's design philosophy. His research has involved a study trip to the Louis Kahn Collection in Philadelphia and an extensive study of Platonism as it pertains to architectural theory. Publications stemming from this work cover topics such as The Neoplatonic tradition in Western architecture, mimesis, "sacred" geometry, and the implications of Platonic philosophy to architecture.
Prior to commencing his doctoral studies, Steven had worked as an architect with the EJE Group in Newcastle, Australia, and with the Housing and Development Board (HDB) in Singapore, where he designed a 4.2 hectare neighbourhood park and a public housing project featuring 360 apartments in a sensitive military zone. He also managed three construction contracts featuring a total of 1450 apartments. Between 1989 and 1992, Steven operated a building design and documentation consultancy in Newcastle, primarily involved with redevelopment and repair work following the 1989 Newcastle earthquake. Steven's other interests include surfing, competitive cycling and naturism.

The correct citation for this article is:
Steven Fleming "Louis Kahn's Platonic Approach to Number and Geometry", pp. 95-107 in Nexus IV: Architecture and Mathematics, eds. Kim Williams and Jose Francisco Rodrigues, Fucecchio (Florence): Kim Williams Books, 2002.