`An Instrument of Thought'

An online search at my office for something in applied mathematics, a set I assumed was disjoint with literature, turned up an interesting essay by Philip J. Davis, professor emeritus of applied mathematics at Brown University. Collected in his Unity and Disunity, and Other Mathematical Essays (American Mathematical Society, 2015) is “Four Literary Men Comment on Mathematics: Henry James, George Santayana, Paul Valéry, and Isaiah Berlin.” Valéry came as no surprise. As Joseph Epstein reminds us, “The only standard of truth that Valéry was able to invoke was that of science, especially mathematics. The man who when young was unable to set out on a naval career for want of mathematical ability later developed a passionate fascination for the beauty of mathematics and an intense interest in neuroscience.” Valéry’s Cahiers/Notebooks, Vol 4. (Peter Lang, 2010) includes a section devoted to mathematics. If you know Valéry’s poems and prose, this passage from his Notebooks (trans. Rima Joseph and Norma Rinsler) will not surprise you:

“The importance and the beauty of geometry is that (because of its purity) it is an instrument of thought—a method of processing—a way of seeing and extending and not an alien object -- Everything that allows us to discern clearly and to establish operations of the mind is geometrical in nature – And all true geometrical definitions are constructions or operations – We do nothing beyond that.”

Davis wonders if Valéry was merely a hobbyist, a dilettante of recreational mathematics, or if he formulated substantial insights into the discipline. Were his notes “simply mathematical graffiti?” Davis never condescends to the poet who dares to speculate in a seemingly foreign realm. He admires Valéry’s audacious intelligence, and devotes more space to him than to the other three writers. Davis writes:

“The aspects of mathematics that he admired so much are today simply part of the working knowledge and attitudes of today’s mathematicians. He did not contribute anything either to mathematics or physics or to their philosophy. But what is absolutely remarkable in this story is that a person so devoted to language and literature should have immersed himself deeply and knowingly and arrived at individual insights into questions of mathematics and physics.”

Not surprisingly, the briefest portion of Davis’ essay is devoted to Henry James. The mathematician says he read The Turn of the Screw as a university freshman and “didn’t understand it then and still don’t.” [The Turn of the Screw is the most over-assigned and overrated of James’ works, probably because of the heavy dose of Freudian mystification inflicted on it by critics.] Davis quotes reputedly math-related passages from four works by James, including this from Washington Square: “Dr. Sloper’s opposition was the unknown quantity in the problem he had to work out.” We can conclude James and math is a null set.

Davis says he got the idea for his essay while browsing in Santayana’s sole novel, The Last Puritan (1936), where he found this passage devoted to the book’s hero, Oliver Alden:

“It was in school though that Oliver came to a realization that would stick with him until manhood: that there was a sunny and shady side to knowledge. The sunny side was to be found in nature, geography, mathematics, and anything left untainted by the crude passions of humanity. For him only non-human subjects were fit for the human mind.”

Davis dismisses the observation as “mathematical Platonism, pure and simple,” which he defines as “the idea that mathematics exists and always has existed in its full scope and glory independently of human beings.” Davis suspects Santayana knew less than what the average math major in the late nineteenth century would have known. Davis confesses that, while admiring The Last Puritan, he finds Santayana’s philosophical work “totally bewildering.” He cites this passage from The Realm of Truth (1938):

“Undoubtedly, if reality were confined to spiritual being, mathematics would be useless, and the study of it an idle pastime, if not a vice; and if any spiritual man, like Pascal, got too deeply entangled in mathematics, the sad effects might be seen in his self-torture and desperation.”

About Isaiah Berlin, I know little. Davis knew him socially and found him companionable. Berlin’s understanding of mathematics, he says, was “a bit naïve, and occasionally misinformed.” Davis writes: “He thought of mathematics as presented via the Euclidian paradigmatic sequence: definition, theorem, proof.” In other words, what a lot of us think we know. Davis approves of Berlin’s interest in Vico. Berlin’s Vico and Herder (1976) “pleased me greatly and strengthened my own Vicovian tendencies.”

Here’s Davis’ tote board: 4^th place, James; 3^rd place, Berlin; 2^nd place, Santayana; 1^st place, by x³ lengths, Valéry. For the others, mathematics was at most a metaphor; for Valéry, it was one more essential tool of thought. The poet Ron Mash in “Graph Paper” (Buyer’s Remorse, 2014) would agree:

“Once the truth was gooey thunder. A wad

of spirits glommed on every tree and rock.

Rainbows gauzed their signatures. Green wonder

knelt before the omens. Rapt, agog. Me,

“I love these acred cubbyholes, the lace

they leave on sea and sky, on stone, on bush;

this wickerwork of our Cartesian souls,

these lucid rooms and numbered pairs. This skin.

“Keep your smug romantics who idolize

the blur, the smudge, the gush, the night. Give me

this plane of sanity where blue semantics

rules the earth, and every angle is right.”