Tea at Trianon: The Mathematics of Beauty, #1: Harmony, Monotony, and Cacophony

John Wilson Croker on Marie-Antoinette

"We have followed the history of Marie Antoinette with the greatest diligence and scrupulosity. We have lived in those times. We have talked with some of her friends and some of her enemies; we have read, certainly not all, but hundreds of the libels written against her; and we have, in short, examined her life with– if we may be allowed to say so of ourselves– something of the accuracy of contemporaries, the diligence of inquirers, and the impartiality of historians, all combined; and we feel it our duty to declare, in as a solemn a manner as literature admits of, our well-matured opinion that every reproach against the morals of the queen was a gross calumny– that she was, as we have said, one of the purest of human beings."

~from History of the Guillotine by John Wilson Croker, 1844

Edmund Burke on Marie-Antoinette

"It is now sixteen or seventeen years since I saw the queen of France, then dauphiness, at Versailles; and surely there never lighted on this orb, which she hardly seemed to touch, a more delightful vision. I saw her just above the horizon, decorating and cheering the elevated sphere she had just begun to move in, glittering like a morning star full of life and splendor and joy. Oh, what a revolution....Little did I dream that I should have lived to see such disasters fall upon her, in a nation of gallant men, in a nation of men of honor and of cavaliers! I thought ten thousand swords must have leaped from their scabbards, to avenge even a look which threatened her with insult. But the age of chivalry is gone; that of sophisters, economists, and calculators has succeeded...."

~Edmund Burke, October 1790

Thursday, October 8, 2026

The Mathematics of Beauty, #1: Harmony, Monotony, and Cacophony

From The Way of Beauty:

This is the first of six posts on the mathematics of beauty1: the traditional body of knowledge, running from the ancient Greeks through the Church Fathers and into the design of Western art and architecture, which held that beauty has a mathematical structure and that this structure can be studied, learned, and applied. It was a standard part of an artist’s and an architect’s formation for centuries. Today it is virtually unknown, and I think its recovery is essential if we are to build beautifully again.
As six posts devoted to a single subject is a lot to post on consecutive weeks, I will post them on alternate weeks.
In this first post, I want to establish the problem by looking at some buildings, and to say something about how this tradition relates to natural science, which is the other great tradition of describing the world by number. The posts that follow will set out where the tradition came from, what it consists of, how it is used in practice, why it was abandoned, and what its recovery would mean.
If you examine almost any building constructed since the Second World War, the chances are that it will conform to one of two simple guiding principles of architectural design, and in both cases, the results are often bad. These two principles are even spacing and random spacing. The first generates visual monotony; the second generates visual cacophony. I have chosen these terms deliberately to set them against what traditional architecture always sought to achieve instead: harmony. (Read more.)