Cutting the Gordian Knot...Literary Geometry

It is a great thing to be able to discuss two of my favorite subjects in one article. Math and literature may not seem to coincide, but in actuality, the two areas share a lot of common ground. I love math, and I love literature, so I especially love reading books in which authors use mathematical truths (especially in the area of geometry) to enhance their stories. There are rare times in which an author will write directly about math, as in “Euclid Alone Hath Looked on Beauty Bare,” Edna St. Vincent Millay’s sonnet in praise of geometry. However, math makes most if its literary appearances in the form of metaphor. Authors often use shapes (the line, the angle, the circle) as metaphors to develop their descriptions of characters and events.

Biblical authors, including Solomon and Paul, used the line as a metaphor to discuss goodness and evil. Typically, a straight line is representative of goodness and obedience, while a crooked one symbolizes departure from righteousness. Solomon’s famous proverb is one example: “Trust in the Lord with all your heart and lean not on your own understanding; in all your ways acknowledge him, and he will make your paths straight.” In contrast, Solomon writes in Ecclesiastes 7:29, “This only have I found: God made mankind upright – but men have gone in search of many schemes.” These two verses show that God makes one’s path, or life, straight and righteous, while rebellious men scorn uprightness and seek an alternate, crooked path.

Paul makes a similar point in Philippians 2:14-15: “Do everything without complaining or arguing, so that you may become blameless and pure, children of God without fault in a crooked and depraved world.” Here, crookedness and depravity are synonymous. Both the New and Old Testaments employ mathematical metaphors to discuss goodness and evil, obedience and rebellion.

Another mathematical metaphor is that of the angle. In some of Robert Frost’s most famous lines, an angle represents a choice.

“Two roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;

I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I –
I took the one less traveled by,
And that has made all the difference.”

This entire poem is metaphorical, for the idea of two roads converging represents different choices to be made in life. Central to the theme of the poem is the angle. The fact that two roads diverge is what forces the author to choose between them. The same mathematical metaphor in this poem is commonly used in everyday conversations about choices; people regularly speak about being at a “crossroads” and having to make a decision about which road to take. In elevated poetical language, as well as in metaphorical clichés, angles represent the need to choose between to options.

A third mathematical element that appears in literature is the circle. Circles indicate the passage of time, cycles, and repetition. Alfred Knoyles once wrote a poem entitled “Unity,” in which he asked the question “What should we doubt of the years that roll?” This poem makes the pantheistic claim that all Nature is one, and in addition, advocates the cyclical view of history that is typical of pantheism. The idea that years “roll,” that they come and go, each different, yet each the same, is at the heart of pantheism, and when authors attempt to communicate this idea, they often use the circle metaphor to emphasize their point.

Like Knoyles, William Wordsworth employed the circle metaphor in his pantheistic ode “Intimations of Mortality.”

“Our birth is but a sleep and a forgetting
The soul that rises with us, our life’s Star,
Hath had elsewhere its setting,
And cometh from afar:
Not in entire forgetfulness,
And not in utter nakedness,
But trailing clouds of glory do we come
From God, who is our home…”

According to Wordsworth, the human soul rises and sets like the sun: it comes from God, and returns at the end of its “life.” Then, it is born once again, in an endless cycle of rising and setting, or of circling from life to death to life.

Artists use shapes to build their pictures, and mathematicians use them and study them for enjoyment and for practical reasons. We also find shapes in literature, in poems, in the Bible, and in common figures of speech. Lines, angles, and circles are powerful metaphors because all humans understand them. We all experience these shapes in our lives, so when we encounter them in literature, they can speak to us as metaphors. Many great authors and teachers have recognized this truth and used it to better communicate with their various audiences. Because so many different authors – Americans like Robert Frost, Englishman like William Wordsworth, ancient kings like Solomon, and Jewish teachers like Paul – have used shapes as metaphors with great success, we can conclude that they are universal metaphors. Shapes can impact readers from all cultures and times, and are not limited to specific peoples and regions. When math and literature intersect, the result is powerful indeed!