Proof: How The World Became Geometrical, by Amir Alexander
There is something deeply ironic in this book. The irony exists on several levels. Some of the book’s ironies are intentional, such as the way the author spends most of his time talking about the way that geometry of a precise and planar form informed the artistic and gardening and architectural worldview of an absolutist European kind that also serves at the basis of Washington DC’s own design, demonstrating its imperialist ambitions in spatial organization, with a surprise ending of sorts that discusses non-Euclidian geometry as destroying the supposed perfection of planar geometry and its assumptions. Not all of the book’s ironies are intentional, for all of the author’s desire to show himself superior to the supposed imperialism of the Euro-American tradition as enshrined in artistic perspective, formal gardens, and city design, the more notable irony that is not recognized is that the Europeans were by no means the developers of these connections, for among the first ever appearances of geometry comes from India, where geometry was viewed as a pivotal part of the art of making religious altars properly, and from India a great deal of mathematical knowledge spread to Europe through the Middle East, a connection that the author barely acknowledges in a perfunctory way.
This particular book is a bit more than 250 pages long and it is divided into three parts and seven long chapters. The book begins with an introduction. The first part of the book then explores the author’s view on how and when it was that the world became geometrical in the sense that the author focuses on, namely the Italian renaissance (I), with chapters on the importance of the mirror image (1), and the mathematical code that was related to the art that followed the revolutionary discovery of the focal point (2). After that the author discusses Euclid’s Kingdom (II) and pays attention to the attempts of the late Valois kings to utilize royal geometries developed in Italy (3) that were found when these French kings repeatedly invaded Italy (4) to build their own fancy royal gardens in various palazzi in France upon their return, culminating in Versailles (5). Finally, the author closes with a discussion of the enormous influence of Louis XIV’s design of Versailles (III), looking first beyond Versailles to the gardens and civic architecture of other European empires (6), and then looking to Washington DC and its importance as a Euclidian and imperial Republic (7), after which the book ends with a conclusion about non-Euclidian geometry as well as notes, acknowledgements, and an index.
In a sense, it is not that the world suddenly became geometrical during the renaissance and early modern periods, only to become more chaotic during the postmodern period as different geometries were discovered. It is that the world itself has always been geometrical and mathematical, and different aspects of this have been chosen for different reasons at different times. Specifically, the development of artistic perspective was easy to exploit by absolutist early modern royals because they wanted to be viewed and to view themselves as the focus of the state and the larger society, with everyone revolving around them. Once such a technique was discovered its obvious political importance could not fail to be utilized by rulers. And it should not surprise us that these insecure monarchs (like the French rulers the author emphasizes in his study) should be so intensely aware of the symbolism of orderly gardens and focusing, and how it is that such designs can endure in cities like Washington DC and New Dehli long after the original designers of those places are dead and gone, giving a symbolic meaning that casts a heavy weight in the world.