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Birkhoff's interest in aesthetics began early. As an undergraduate at Harvard, he was intrigued by the structure of western music and pondered the riddle of what makes something melodious.
In the early 1930s, Birkhoff spent a year traveling around the world studying art, music, and poetry in various countries. He came up with a formula that encapsulated his insights into aesthetic value and described his theory in a 1933 book, Aesthetic Measure, published by Harvard University Press.
At the core of his theory was a formula: M = O/C, where M is aesthetic measure or value, O is aesthetic order, and C is complexity. In other words, Birkhoff put a high aesthetic value on orderliness and a low one on complexity. In his view, beauty increases as complexity decreases.
Birkhoff's formula and its potential applications—to such creations as vases, architectural designs, melodies, and even poetry—were intriguing enough to be the subject of an article in the March 17, 1934, issue of Science News Letter (now known as Science News). Indeed, the same article was also distributed to newspapers for use in their illustrated Sunday magazines.
The article described the application of Birkhoff's measure of aesthetic value not just to polygons but also to paintings.
It quoted Birkhoff: "The 'complexity' of paintings is usually so considerable that they are analogous to ornamental patterns whose constituent ornaments must be appreciated one by one. However, it is decidedly interesting to remark in this connection how a fine composition is always arranged so as to be easily comprehensible."
In any work of art, Birkhoff claimed, imaginary lines can be drawn across from point to point, following the principal lines of the composition. These lines define geometric areas that generally have a comprehensible form. Similarly, light and dark areas have a certain order or pattern.
"There should be a natural primary center of interest in the painting and also suitable secondary centers," Birkhoff explained. "Such a primary center of interest is often taken in the central vertical line of the painting or at least near to it. The elements of order are of course taken to be the same as in the three-dimensional object represented. Finally there are the connotative elements which play a decisive part; a good painting requires a suitable subject just as much as a poem requires a poetical idea."
Much of the Science News Letter article is about poetry. In Birkhoff's formula for poetry, O = aa + 2r + 2m – 2ae – 2ce, where aa stands for alliteration and assonance, r for rhyme, m for musical sounds, ae for alliterative excess, and ce for excess of consonant sounds.
