Zero is central, an important and celebrated number. Like one and two it has meanings that extend far beyond the mathematical. It’s an ideal title for a poem, for a poetry collection.
In the final (of three) sections in Brian McCabe’s Zero, the title poem stands alone, a three-page collage in whose fragments the poet explores the history of the cipher and its multiplicity of meanings. Although 0 is a commonplace today, in the intellectual history of humankind it was not an easy achievement. How, indeed, may we make something of nothing?
McCabe opens Zero with “Counters”—a section named after its initial poem which builds from the childhood game of TiddlyWinks to a comment on the progress of life and number from simple beginnings to complexity and chaos. This introductory poem also shows us what to expect as we move through the sequence of poems: a loss of simplicity. A poem entitled “Throur” celebrates the invention of a new counting number between three and four and ends with a wry comment on the bureaucratic cost of such an innovation. In “Two Quadrilaterals”, a square and a parallelogram appear with social status and personality, a reminder of Edwin Abbott’s Flatland or Guillevic’s Euclidiennes/Geometries:
|He went to bed alone as usual|
dreamt of concentric circles
of cubic curves of elegant ellipses
of shapes unbounded by edges
Integers, especially those we use commonly—the four seasons, the five senses, the seven (or six?) days of creation, unlucky thirteen—give rise to a host of poetic lists, quirkily assembled to delight and confound as, for example, this opening stanza of “Nine”:
|I was John Lennon’s favorite number.|
The number nine. Number nine. Nine.
I’m a stitch in time. A cat’s lives.
McCabe ventures into the vocabulary of theorems and proofs, of unsolved conjectures, and undecidability. A mathematician may be unendingly haunted by an unsolved problem. (S)he may spend hours—or even years—striving to prove or disprove a conjecture, being successful or, more likely, unsuccessful. The long life of an open question is dramatized in these closing lines of “The Undecidables”:
|We are not proven not proven we have never|
been shown to be provable / non-provable
as the case may be we are not included
not included in such admirable certainties.
As we grow older our doubting faces
are stamped with the same question mark
but then we never die we never die
Digging into the history of mathematics has led McCabe to haunting stories of eminent mathematicians, rendered poetically in “Perspectives”, the second major section of Zero. “Monsieur Probability” features Abraham de Moivre (1667–1754), including his role in the Newton-Leibniz controversy concerning credit for the invention of calculus, and ends with these lines telling of de Moivre’s remarkable prediction concerning his death:
|He could always tell the outcome of anything,|
even foretold the day of his own death:
said he slept a quarter hour more every day
so he worked out that when he slept for twenty-four
that would be the day—and he was right.
And what, sir, are the chances of that?
While I applaud McCabe for bringing obscure stories in the history of mathematics to poetic life, I am not totally pleased by his selections. As a mathematician, I am tired of the literary traditions that offer mention of my kind only to spotlight our assumed oddity (as with DeMoivre above) or incompetence as teachers. In rare contrast to this is Susan Case’s The Scottish Café, a collection of poems about mathematicians at work.
McCabe’s portrait of Mary Somerville (1780-1822) reminds us of the long history of equity struggles that continue today; here are the opening and closing lines of that poem, “Perspectives”:
|The strain of abstract thought, her father feared,|
might injure her tender female frame. It did not.
It was more the needlework, the pianoforte
at Miss Primose’s Boarding School for Girls
in dreary Musselburgh which fettered her spirit.
[…] How difficult it was to be a young lady
and midwife to the birth of Neptune.
Mathematics in McCabe’s stanzas is more decorative than substantive; his mathematical imagery is ornamental and without deep meaning. In “Throur”, for example, he names real and complex number sets and uses the powerful word “isomorphic” as if it does not matter what the terms mean. His use of “number” as if it meant only “integer”—occurring in the first of his Notes, where he defines “twin primes”—may be an error noticed only by those who have studied higher mathematics, but do we not also expect accuracy and precision from poets as well as mathematicians!
On the other hand, McCabe’s inventiveness is perhaps elevated by his distance from the rigors practiced by a mathematician. He finds delight in things I might take for granted. Indeed, even I smiled while reading “The Romans”—in which a Mafia boss forces introduction of the Roman numerals, a loathsome crime against all thinking persons. I also much enjoyed a poem dedicated to Ludolf van Ceulen (1540-1610) whose title begins, “Three Point One Four One Five Nine Two …” This poem about the computation of Π imagines an auction with each newly calculated digit raising the bid. Indeed, working out Π continues in 2011 as a worldwide contest; a recent record was set with more than 5 trillion digits.
In my life I play many roles—mathematician, poet, parent, teacher, blogger—and it is from within the blogger role that I make my final comments on Brian McCabe’s Zero. This collection is a rich source of poems that I would (if McCabe and Polygon granted permission) delightedly post on my blog, “Intersections: Poetry with Mathematics”,—and my readers would comment with praise for such postings. These poems fit together nicely to build a collection; moreover, each stands well alone and singly offers readers a savory morsel. McCabe’s poems are accessible and interesting. Enjoy them!