In 1933, Harvard mathematician George Birkhoff quantified beauty. The basic idea, he said, is that M = O/C, where M is the “aesthetic measure,” O is order, and C is complexity. By elaborating this principle into specific formulas, he decided that the square is the most pleasing polygon and the major triad the most pleasing diatonic chord. Of eight vases he considered, a Ming jar ranked highest, with M = 0.80, and in poetry the opening of Coleridge’s “Kubla Khan” received an M rating of 0.83. The same principles can be applied to painting, sculpture, and architecture.

This kind of use of the formula leads at once to certain well known aesthetic maxims:

1. Unify as far as possible without loss of variety (that is, diminish the complexity C without decrease of the order O).
2. Achieve variety in so far as possible without loss of unity (that is, increase O without increase of C).
3. This ‘unity in variety’ must be found in the several parts as well as in the whole (that is, the order and complexity of the parts enter into the order and complexity of the whole).

“Now it seems to me that the postulation of genius in any mystical sense is unnecessary,” he concluded. “The analytic phase appears as an inevitable part of aesthetic experience. The more extensive this experience is, the more definite becomes the analysis.”

In 1889 Monet was midway through a landscape when a pivotal oak tree sprouted leaves.

He mulled this for a few days and then approached the landowner with an unusual proposition. On May 9 he wrote:

I am overjoyed — permission to remove the leaves of my beautiful oak has been graciously accorded! It was a huge job bringing large enough ladders into this ravine. Enfin, it is done, two men have been busy with it since yesterday. Isn’t it a feat to finish a winter landscape at this time of year?

In The Ultimate Irrelevant Encyclopaedia (1984), Bill Hartston remarks, “Monet makes the leaves go aground.”

Claiming to be haunted by the “spirit of proportion,” German sculptor Franz Xaver Messerschmidt (1736-83) found he could subdue its attacks by pinching himself and pulling a face in a mirror. Pleased with this success, he resolved to sculpt every “canonical” variety of human grimace.

By the time of his death at age 47, he had executed 69 “character heads” in lead, stone, and wood. None had been commissioned, and none were sold during his lifetime; they were the product of a peculiarly personal obsession and a passionate discipline. (A visitor who had observed him in 1781 noted that Messerschmidt “looked into the mirror every half minute and made, with the greatest exactitude, precisely that grimace which he just needed.”)

Interpreting the heads has been equally the province of psychology and art history. Messerschmidt may have been mentally ill, but he was undeniably gifted, and it appears he achieved the goal he had set. “It is utterly strange,” wrote Jonathan Jones of a recent Louvre exhibition. “No other artist of the age worked in a similar way, and you sense a long sickness of compulsive, isolated behaviour in what are nevertheless great works of art.”

Suppose … that a finely wrought object, one whose texture and proportions are highly pleasing in perception, has been believed to be the product of some primitive people. Then there is discovered evidence that proves it to be an accidental natural product. As an external thing, it is now precisely what it was before. Yet at once it ceases to be a work of art and becomes a natural ‘curiosity.’ It now belongs in a museum of natural history, not in a museum of art. And the extraordinary thing is that the difference that is thus made is not one of just intellectual classification. A difference is made in appreciative perception and in a direct way. The esthetic experience — in its limited sense — is thus seen to be inherently connected with the experience of making.

— John Dewey, Art as Experience, 1934

Grant Wood’s American Gothic is a bit ersatz — the artist recruited a Cedar Rapids dentist, B.H. McKeeby, to pose as the farmer, and his sister Nan plays the woman (conceived as the farmer’s spinster daughter, not his wife).

But the setting was inspired by a real cottage in Wood’s native Iowa, and by his admiration for “the kind of people I fancied should live in that house.”

“I tried to characterize them honestly, to make them more like themselves than they are in actual life,” he said. “To me they are basically good and solid people.”