'First Find a Thinking Being. Lots of Luck'

As a non-mathematician, I’m more interested in the history of mathematics than in math itself. That’s a confession of inadequacy, though I’m not one of those people who says, “I don’t have a head for math,” when what they really mean is arithmetic. Because of my job I’ve learned to ask a lot of questions of the math people, and then fake it. But I have read biographies of Euler, Ramanujan and Erdös. 

I first learned of the French mathematician and polymath Henri Poincaré (1854-1912) in 1974 from a book I’m almost embarrassed to admit having read – Zen and the Art of Motorcycle Maintenance by Robert Pirsig, who paraphrases Poincaré as saying that mathematics “isn’t merely a question of applying rules, any more than science.”

 

At the time of his death in 2009, Turner Cassity left several manuscripts of poems unpublished. Thanks to the poet R.L. Barth, Cassity’s literary executor, I have a copy of Hitler’s Weather. One of its thirty-seven poems is “Reality Check” (Cassity loved playing with clichés), which is preceded by an epigraph from Poincaré’s The Value of Science (1905; trans. George Bruce Halsted, 1907): “What we call objective reality is, in the last analysis, what is common to many thinking beings, and could be common to all . . .” The poem:                                      

 “First find a thinking being. Lots of luck.

Reality is for the nonce in hock

 

“Not to the common but the commonplace:

The knee-jerk psyche and the clear-cut case.

 

“It may be ambiguity is real

In ways its either and its or conceal;

 

“That doubt and certainty are most alike

As credos, in that their excesses spike

 

“In the vicinity of all last things:

Eastern religions and their vaporings,

 

“Doom-sayings of the astrophysicists.

Objective cites the object that exists,

 

“Delimits it. Idolatry makes sense

In ways that animism gives offense.

 

“Come, Thinkers, let us raise, of wood and stone,

A pantheon of the entirely known.

 

“Not Faust, we do not need all knowledge. Some,

And even that may do us grievous harm.”

 

This smacks of a funnier, more cynical John Keats, with his notion of “negative capability,” a thinker’s capacity for being “capable of being in uncertainties, Mysteries, doubts, without any irritable reaching after fact and reason.” Consider the rest of Poincaré’s passage:

 

“. . . this common part, we shall see, can only be the harmony expressed by mathematical laws. It is this harmony then which is the sole objective reality, the only truth we can attain; and when I add that the universal harmony of the world is the source of all beauty, it will be understood what price we should attach to the slow and difficult progress which little by little enables us to know it better.”

 

The Keatsian echoes continue. The poet and scholar J.V. Cunningham, like Cassity a student of Yvor Winters at Stanford, taught mathematics to pilots at the Seventh Army Air base in California, during World War II. 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’ Georg Cantor: His Mathematics and Philosophy of the Infinite (Princeton University Press, 1979). This overlap (or Venn diagram) of poetry and mathematics shouldn’t surprise us. At the risk of oversimplifying things, here’s an equation: Math = Music = Poetry. Paul Erdös was fond of saying: “If numbers aren’t beautiful, I don’t know what is.”