Monday, March 26, 2012

`The Poetry of Mathematics'

Up there with other heroes of the intellect, sharing a bench with Dr. Johnson, Pasteur and Yvor Winters, is Paul Erdős, the Hungarian mathematician who was born in Budapest on this date in 1913. His sui generis personality made “eccentric” too flaccid a word, and like many inarguable geniuses, his manner was childlike, at once innocent and cunning. He discovered negative numbers at age three and was already multiplying three-digit numbers in his head. He owned nothing but a change of clothes, never married or had children, and lived nomadically until his death in 1996. Like Lester Young, Erdős devised an idiolect. The United States and the Soviet Union were “Sam” and “Joe,” respectively, and children were “epsilons” (in math, an arbitrarily small quantity is represented as ε).

Two good popular biographies were published within two years of the mathematician’s death – The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth by Paul Hoffman, and My Brain Is Open: The Mathematical Journeys of Paul Erdős by Bruce Schechter. Chief among Erdős’ mathematical heroes was Georg Cantor (1845-1918), the founder of set theory who hypothesized “an infinity of infinities.” Erdős signed some of his correspondence “C[antor]. be with you.” Schechter writes:

“Cantor showed that not only does the concept of infinity make mathematical sense, but infinities exist in a never-ending hierarchy of increasing size. This may sound like a Blakean fantasy, but the genius of Cantor was to prove that towering infinities follow from the sober, irrefutable mathematics of set theory.”

For those of us with mathematically mundane minds, this sounds like pot-fueled paradox. For Erdős and other mathematical theorists, it changed everything. The poet and scholar J.V. Cunningham also taught mathematics. Among his later epigrams is “Cantor’s Theorem: In an Infinite Class the Whole Is No Greater Than Some of Its Parts”:

“Euclid, alone, who looked in beauty’s heart,
Assumed the whole was greater than the part;
But Cantor, with the infinite in control,
Proved that the part was equal to the whole.”

In his two-paragraph note in The Poems of J.V. Cunningham (Swallow Press/Ohio University Press, 1997), Timothy Steele succinctly explains the math – “…infinite sets may simultaneously correspond and differ.” – and helpfully refers us to Joseph Warren Daubens’s Georg Cantor: His Mathematics and Philosophy of the Infinite (Princeton University Press, 1979). This overlap (or Venn diagram) of poetry and math shouldn’t surprise us. At the risk of oversimplifying things: Math = Music = Poetry. Schechter tells us Erdős was fond of saying: “If numbers aren’t beautiful, I don’t know what is.” Thoreau, an unlikely collaborator in this effort, writes in A Week on the Concord and Merrimack Rivers:

We have heard much about the poetry of mathematics, but very little of it has as yet been sung. The ancients had a juster notion of their poetic value than we. The most distinct and beautiful statements of any truth must take at last the mathematical form. We might so simplify the rules of moral philosophy, as well as of arithmetic, that one formula would express them both.


WAS said...

I died for poetry, but scarce
Adjusted in the tomb,
When one dead for mathematics spread
In an adjoining room...

I remember, age 14 or so, the excitement of being handed a book, by my older cousin, the first in our family to be published. Unfortunately, there were few words in it – it consisted almost entirely of the stochastic formulas of a mathematics professor, indecipherable to his proud family. I suppose the way I felt then is the way most people feel now when they’re handed a book of poetry: the sublime promise, kept secret in an occult code.

Metaphors, grammar and phonetics (not to mention complex rhyme and metric poetic schemes) all have mathematical consonances, and the beauty of both poetry and mathematics is in expressing the most that can be said in the most concise possible way, with nothing left over. Many have tried to combine math and poetry, but the result is usually not multiplication but division, not non-Euclidean decadents and topological surrealists but mathematicians who wrote poetry (Roubard, Masheroni, Barbu) or poets who practiced mathematics (Goethe, Empson, Parra). The one notable exception to this of course is the Iranian Omar Khayyam, who in addition to explaining the principles of algebra, solving cubic equations, inventing Pascal’s triangle, and inspiring non-Euclidean geometry, formulated the famous poetic equation “A loaf of bread+ a jug of wine+ thou =x” (where x is the unnamable).

There’s a whole fascinating blog devoted to the intersections between poetry and mathematics". In one post, the reader is given a variety of quotes and asked to select poetry or mathematics to fill in the blank (condensed here):

1. A thorough advocate in a just cause, a penetrating ______ facing the starry heavens, both alike bear the semblance of divinity.

2. When you read and understand ______, comprehending its reach and formal meanings, then you master chaos a little.

3. All ______ [is] putting the infinite within the finite.

4. _________ is pure play, with pre-suppositions

Answers: 1 – mathematician (Goethe); 2 – poetry (Stephen Spender); 3 – poetry (Robert Browning); mathematics (George Santayana)

The blog owner, Joanne Growney, selects Carl Sandburg’s “Number Man” as her favorite poem about mathematics, a judgment with which I concur:

“…He knew love numbers, luck numbers,
how the sea and the stars
are made and held by numbers.

“He died from the wonder of numbering.
He said good-by as if good-by is a number.”

Anonymous said...

Johann Sebastian Bach created the most sublimely beautiful Infinite Class of math and music and poetry.


George said...

On encountering Cantor's proof of the "nondenumerability of the continuum" in a college math course, I felt a certain vindication, for at some point in middle or high school I had been told that No, real numbers are not more infinite than the integers. (I think that I may have suggested that they were "thicker.") However, I must say that I wasn't entirely vindicated, for I would not have dreamed of Cantor's demonstration of the denumerability of the rationals (ratios of two integers.) The book Journey Through Genius gives a good treatment of Cantor's two famous results.