Proof! By Amir Alexander
This book is supposed to be about “How the World Became Geometrical”. That sounded cool! Unfortunately, the bulk of the book is actually about how the royal gardens of Renaissance France became geometrical. It is interesting enough, but that’s not even close to the whole world.
His main point is that Renaissance scholars rediscovered Euclidean geometry, and found that, contrary to Aristotle and humanist traditions, there is logical, geometric order in the world. Alexander shows how Italian vanishing point perspective painters showed the geometry of optics that enabled extremely representational painting. At the same time, astronomers were finding geometric order in the skys.
These developments were significant because they seem to show that there are geometric laws governing the layout of the universe. These Euclidean laws can be proved, step-by-unarguable-step. They are not only natural, they are logically necessary.
Alexander shows how these geometric ideas were applied to create formal gardens, culminating in Versailles. He argues that this wasn’t just a clever or convenient template. He believes that visiting and viewing such a garden communicates the underlying geometric order, and, in particular, convinces the spectator of the unalterable, necessity, of the design. He makes a decent case that the designers and their sponsors believed this, but I don’t really buy it.
This approach to gardens was enthusiastically picked up by the Kings of France, who built a series of geometric gardens and palaces, culminating in the paradigmatic Versailles. Alexander’s claim is that the Kings perceived these gardens to be a visual argument, indeed, proof, of their absolutist ideology. The layout of Versailles is hierarchical, with the King at the center/top. Every element has a place and only one place. It isn’t possible, Alexander says, to change even a single element.
At least, that’s what the Kings of France thought, and wanted everybody to think (or else!)
Alexander carries this (dubious) argument forward, noting similar geometric plans for cities throughout Europe, and in colonial empires. In all these cases, the garden or streets supposedly “prove” the absolutist, hierarchical political ideology of the builders.
“In the early 1400s geometry came down to Earth, bringing the promise of a rational and irrevocable universal order that reaches to all corners of creation. It made note only modern physical science possible, but also the modern state in all its variations—from kingdoms to republics to empires. Geometry made the modern world possible.” (p. 22)
Alexander discusses one additional case; L’Enfant’s design for Washington city. The US was definitely not seeking to express a god-given, divine monarchical ideology in its capital.
But, Alexander says, L’Enfant sought (at the cost of his career) to express the divinely inspired, immutable order of the Constitutional federal republic. This was the ideology of the Washingtonian Federalist party, but there were plenty of dissenters who viewed the constitutional order as contingent and changeable. This was the ideology of the Jefferesonian anti-Federalists.
While the tension between precedent and popular will continues to our day, the notion that the geometric design of L’Enfant’s streets somehow expresses such ideas is far fetched. The notion that, for example, the US Capital building and White House could not be relocated is pure and utter nonsense. Nobody even notices the street plan, let alone is influenced by it. (We Americans are too busy loathing each other for such thoughtful observation!)
Overall, what Alexander calls ‘how the world became geometrical’ might better be called “geometric conceits of autocrats”. And, by the way, with the exception of the US government, all the political regimes he describes are gone now. And the US itself has transformed far beyond anything L’Enfant could have envisioned.
“Unalterable geometric truth”? Hardly.
OK, Alexander makes a decent case that the rising monarchies and colonial empires embraced fantasies of divine design, and imagined that their power hierarchies somehow expressed mathematically truths. These same elites created fantasies of religious, racial, and cultural hierarchies that justified their privilege and violent domination.
By the nineteenth century, the descendants of these ideologs deployed other alleged scientific “proof” to support the political order, including bogus biological and historical “laws”. And others deployed alternative “historical science” to prove the inevitable logic of Communist revolution. And so on.
None of this means that geometry (or any science) actually had much influence, except as symbols of “undeniable truth” in ideological argument. The alleged geometric symbolism of Versailles is, frankly, opaque–to the degree it even exists. (For one thing, the geometry only exists at certain scales and certain viewpoints–in the eyes of the King and his toadies, but not to others, and certainly not to an all seeing god.)
For those of use who neither know nor care about the Bourbon monarchy, the gardens are just obsessive compulsive extravagances. They aren’t even interesting.
Finally, Alexander does briefly touch on the catastrophe that befell geometry in the nineteenth century. Euclidean geometry was proved to not be divine, or even necessarily “correct”. In its place arose an infinite number of alternative geometries. And, as he correctly notes, different geometries describe parts of the universe, and there conceivably are alternative universes with different geometries.
So much for the one-true-way absolutism of kings and empires. Even if you bought the supposed geometric proof of autocracy, you now have to face the notion that there are an infinite number of different possible geometries, all equally valid. No one, not even the beepin’ King of France, is special.
- Amir Alexander, Proof! How the World Became Geometrical, New York, Scientific American, 2019.
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