New book re‑thinks ideas on proportionality

Professor Matthew Cohen works from scaffolding on a building.
Professor Matthew Cohen measures the Baptistery of Florence from scaffolding that he rented for the purpose.

It’s been nearly 30 years since Matthew Cohen, an architecture professor in the School of Design and Construction, first took a tape measure to an early Renaissance-era basilica in Florence, Italy, for a graduate student presentation.

His curiosity about the measurements he made that day led him on a long academic career path and to the publication of a new book, Proportional Systems in the History of Architecture: A Critical Reconsideration.

The book reconceives the idea of proportional systems, which are often numerical ratios or easily constructed geometrical shapes formed from the dimensions used to build a structure.

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.

According to orthodox theories, proportional systems are conceived a certain way to express beauty in architectural structures. For example, in Renaissance buildings, many historians view the dimensions of a proportional system as a series of musically harmonious ratios that the human brain interprets as visual beauty.

Cohen’s book, edited with Maarten Delbeke of ETH Zurich, deconstructs that view in favor of a more scientific and evidence-based approach.  It argues that rather than affecting the aesthetic appearance of architecture, proportional systems served as objects of belief and modes of iconographical communication. These ancient and diverse belief systems infiltrated architectural thinking in subtle and sometimes surprising ways.

Closeup of Matthew Cohen with his new book.
Matthew Cohen

For example, when Cohen measured the Basilica of San Lorenzo in Florence, he found that the church’s dimensions did not match written descriptions by scholars. When he converted his measurements to braccia, the unit of measure used by Renaissance architects, he noticed a pattern—the ratio of one to the square root of two, an irrational ratio, was dominant.

“These are intellectual ratios; why did the architect choose one to the square root of two?,” he wondered.

That question may never be fully answered, but Cohen has theories that are based on religious philosophy at the time.

“Here is a moment where a geometrical structure cannot be described in terms of numbers; it defies the religious notion at the time that God created a consistent world,” he said. “The architect for this building, Filippo Brunelleschi, nevertheless found a way to express this irrational ratio though architecture, by calculating an extremely accurate approximation of it in terms of whole numbers.”

The book is comprised of papers written by experts in the field, with the introduction and conclusion written by Cohen. It comes out of an international conference that Cohen organized in Leiden, the Netherlands, in 2011.

Cohen said the topic has generated controversy among scholars who prefer established ways of looking at proportional systems.

“People get nervous when you suggest there’s a different way to look at problems they think have been solved,” he said. “I hope this leads to a larger reckoning by looking at proportional systems with factual evidence.”

The book is published by the Leiden University Press, and is distributed by The University of Chicago Press. Excerpts are available on Cohen’s Academia website.

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