Gary Lee Stonum
English Department, Case Western Reserve University
Cleveland, OH 44106
gary.stonum@case.edu
Marcia Birken and Anne C. Coon, Discovering Patterns in Mathematics and Poetry,
Amsterdam and New York: Rodopi, 2008. Internationale Forschungen zur Allgemeinen
und Vergleichenden Literaturwissenschaft, vol 116. 213 pp.
Professors of mathematics and of literature respectively, Marcia Birken and Anne
C. Coon emphasize the overlap of their fields in Discovering Patterns in Mathematics
and Poetry, They aim to allay the wariness that each side of the disciplinary divide has
sometimes held for the other. And although ultimately conceding that the “works of
mathematicians and poets are fundamentally different, as are the ways we approach
and study those works,” for the most part Birken and Coon delight in identifying what
they see as the similarities between theorems and poems.
The chief similarity is pattern itself. Poems and mathematical concepts are both
obviously structured objects, and both have at least some claim to having been found
by their creators as much as invented by them.
Moreover, in mathematics structures
and patterns are often the content of the object as well as its form. Birken and Coon
accordingly introduce several branches of mathematics that exemplify structure most
clearly: number theory, fractal geometry, and transformation symmetries. Although
they pay some attention to how these branches were invented and how mathematicians
have developed them, they focus on the amateur’s learning of and about what
professional mathematicians have previously established.
If in mathematics structure is a clear, often rigorously defined and demonstrable
property, on the literary side things are a bit softer. Birken and Coon understandably
downplay theme and meaning in order to emphasize rhyme, meter and stanza form,
and they attend most enthusiastically to relatively uncommon but highly patterned
forms: villanelles, sestinas, and visually shaped poetry.
Noticing verbal, visual, and
aural patterns can be an important aspect of poetry’s pleasures, but such structures
manifestly do not occupy so central a place in poetry as their counterparts do in
mathematics, and only in special cases are a poem’s structural properties its content as
well as its form.
Furthermore, although patterns can be discovered in poetry and mathematics, so
can they be in most endeavors. Consider dog breeding, where patterns of canine
behavior and appearance are of the essence. Is mere pattern sufficient grounds for
linking otherwise distinct enterprises?
It would be if the two influenced one another significantly or if, as Poe’s M. Dupin
claims, the linkage revealed something neither poets nor mathematicians knew without
the other. Birken and Coon do not make such strong claims, however, and they do not
quote Poe. Their accounts of the interaction between mathematics and poetry
consistently flow downhill from the latter to the former.
As a goal and a value pattern
belongs first and foremost to the mathematicians. Indeed, the strongest links cited
between mathematics and arts are not to poetry but to M.C. Escher, every math geek’s
favorite artist.
Birken and Coon do cite numerous poems explicitly about mathematics and note
a number of authors influenced by math: Emily Dickinson, Alice Fulton, Ron Silliman,
Inger Christensen, et al.
More strikingly, they offhandedly suggest a distinctive take on
the mechanisms of literary production. Diane Der-Hovanessian’s “Fractals,” draws
explicitly on Edna St. Vincent Millay’s “Euclid alone has looked on Beauty bare,”
installing for kudos Benoit Mandelbrot where Millay had praised Euclid.
Such use of
an older text by a newer one is hardly unfamiliar, of course, but Birken and Coon
interestingly propose thinking of the later poem as an iteration of the earlier one.
Iteration, the use of recursive formulas to produce new objects out of old, differs from
influence, allusion, and similar ideas in emphasizing the systemic properties of the
literary corpus rather than the acts and intentions of authors. A new structuralism?
They apply the same notion to the development of metaphor in Shakespeare’s sonnet
73.
Such matters of advanced literary criticism are otherwise foreign to Discovering
Patterns, which despite the publication circumstances is not addressed to research in
comparative literature or any of its usual tributaries. For one thing, although some
attention is paid to non-anglophone writers, all of them are quoted in English translation,
and nearly all the other poets mentioned are 20th-century Americans.
More important,
at heart and in rhetoric the book is addressed not to scholars but to undergraduates
(and common readers) who are largely unfamiliar with either poetry or mathematics and
who are fearful of either or both. One indication of this is that the authors consistently
address their readers in the second person pedagogical: “If you enjoy the challenge of
thinking creatively within a complicated framework, you might like to try your hand at
writing a sestina.”
Indeed, the book originates in a course that the authors have taught for several
years at the Rochester Institute of Technology. The course and hence the book would
seem to have be meant for those (engineers? pre-meds?) who had stereotypically had
read little verse, who were competent enough with the drill-and-fill mathematics of
lower-division calculus, but who neither appreciated poetry nor had encountered the
sort of imaginative activity real math majors cherish.
For scholars in comparative literature and interdisciplinary studies the book’s
contribution is thus limited. As an introduction to poetic form for those unfamiliar with
verse, Discovering Patterns is accurate but painfully elementary by comparison to most
textbooks on the subject. As an introduction to mathematical ideas for those who fear
math, it fares better.
Although considerably less challenging than such popularizers as
Martin Gardner or Douglas Hofstadter, Birken and Coon do admirably introduce some
basic ideas and, more important, the excitement and the aesthetic pleasure that
discovering these ideas can elicit.