Literary Criticism: Form

The project:

The first part of my essay, "The Uses of Periodicity in English Verse" (first published in the Hudson Review, Vol. 58 / 2 (Summer 2005), pp. 259-274) expresses many of the considerations of form (poetic, painterly, musical, mathematical) that I explore in my literary essays.

Natural systems, like molecules, cells, organisms, solar systems, stars and galaxies, exhibit stability that persists for awhile, and then disperses. Their stability is manifest in geometric forms that are often highly symmetrical, and that express a "low" energetic state in contrast to other more highly excited, unstable possible states of the same system. It is also manifest in the successful accomplishment of functions that allow the system to interact with its environment while maintaining its own integrity. Integrity is once again linked to shape, as well as to periodicity, which – as Bas van Fraassen observes – is symmetry in time. It would be a philosophical mistake to conclude either that the stability of natural systems is an illusion (with Heracleitus) or that their dispersal is an illusion (with Parmenides). The things of the world inhabit the middle kingdom between being and becoming; in fact, they constitute that middle kingdom.


Natural systems organize themselves. In our Newtonian world, the schema for self-organization is the deflection of a corpuscle in inertial motion (straight-line motion at a constant velocity) out of its endless, aimless path into an elliptical orbit around a center of force that obeys the inverse square law: the force of gravity falls off quickly, proportional to the square of the distance. This circling, which becomes a circle back, induces a periodicity: the corpuscle now in one sense always comes back to the same place at regular intervals. Our earth brings us back to the winter solstice every year, then to the vernal equinox, and so forth. We have a home in space (near the sun) and in time (our year); the periodicity itself provides the auspicious circumstances in which we can grow. Of course, in another sense our solar system and our galaxy wander through space, so our home near the sun is more like the tents of Bedouins than the apartments of Parisians.

In our Euclidean world, the schema for self-organization is geometrical form, the circles, triangles, and squares (or spheres, tetragons, and cubes) that articulate the infinite, homogenous, hole-less, bump-less, edge-less plane (or 3-space) so that it can be understood. In our Cartesian world, geometrical form is overlaid by numbers. Finite geometrical figures, the periodic notation of Arabic numerals, the fancy footwork of decimal notation, group theory and set theory, all induce periodicity on the plane, making one everywhere a little room, to reverse Donne's metaphor of love. The shape of a planetary orbit is an ellipse; stars and planets are spheres; molecules array themselves as hexagons and pyramids, and crystals as cubes and tetragons. Soap bubbles and cell membranes are often catenoids, and molecules may knit together to form helicoid surfaces, emblems of stable energy states. No wonder we find these figures beautiful: they allow us to inhabit the world.

And so with our houses (or tents) whose doors and windows frame the open sky, roads that lead always away, rivers and mountains without end. Our little rooms define and organize outside by opposing to it the shapes of inside, circles or squares, and elsewhere by the lived reality of home. A home is somewhere we depart from and return to, in the periodicity of every day. So with our stories, bending the aimless, endless line of temporality into purposeful actions with a beginning, middle, and end, as Aristotle taught; actions once told can always be told again. Stories are inherently periodic; we organize and constitute our lives by telling stories about ourselves and others, retelling the stories we love and fighting with others over whose versions of the beloved stories are true. So too arguments, whose premises close the gate on the infinite regress of reasons, murmuring "let us assume," and "let us reason downwards from this point." Arguments are also meant to be revisited, like the garden paths of the Academy or University, as terms and propositions are analyzed and rules of inference are quarreled over. Shall we go along with the purely formal return of Reductio ad Absurdum, shall we trust the detachment of Modus Ponens, shall we step sideways into the flowerbeds of analysis?

But I have moved too abruptly here, and must bridge my leap between nature and culture. A solar system organizes itself by establishing periodicities; but not being conscious it does not see its displacements as departing from and returning to the "same place." Aristotle in his physics and celestial mechanics attributed striving and fleeing to bits of matter; but the periodic self-maintenance of physical systems is mindful only in a very rudimentary way. People, however, know their periodicities and name them, love them and fear them, and recognize that they articulate space and time: the warmth of our arm-chair-planet near the sun, the vigil of our evening-meal-winter solstice. We read organizing symmetries in space and periodicities in time as repetition: sameness with difference as the rationalists would have it, or difference with sameness, as the deconstructionists contend. A planet doesn't know it is repeating the same orbit every year, but we use its orbiting to discursively assign places within and beyond our solar system and indeed to see our solar system as a place. This Christmas is the same as last Christmas, but the children are a bit older, or one of them has gone away to college. The slant of sunlight as we carve the turkey is the same as it was last year, for we have come back to the same house on the face of the earth, in the same orientation to the sun, which changes all year long because the axis of our planet is inclined at a certain angle to the ecliptic, the plane of the solar system as it traces out a great circle on the night sky along which the constellations cluster, and the moon and the sun rise and set, and the other planets wander.

Periodicity is symmetry in time. When people take up periodicity mindfully, and turn it into departure and return, regret and anticipation, the representations they use often turn periodicity back to spatial symmetry. We do this on the round faces of our clocks that superimpose midnight on midday, and the square arrays of our calendars that show how stormy Monday always abandons the weekend, how January must introduce the rest of the year. We picture periodicity symmetrically in the ceinture of constellation emblems that decorate mechanical models of the "celestial sphere" as well as the columns of horoscope advice in the daily paper. We express it in the bilateral symmetry of our cathedrals with respect to their east-west axis, which sets the towers of the portal against darkness in the west while orienting the windows of the apse to the rising sun. Symmetry that stands for periodicity is also depicted on the printed page in the lineation of a poem, the left-rectification or centering of its lines, the array presented by the stanzas of a sonnet, the visual repetition – perhaps in italics – of a refrain.

Of course, people who read periodicity as repetition cannot ever forget the difference that nuances their sameness. Natural systems are not aware of their own dissolution; the solar system does not rue the day when the sun will grow large and red, devour its children-planets, and then sink into darkness. We are able to use periodicities to make ourselves at home in the world, but only because we know and represent them; and the shadow side of knowledge and representation is death. The circles of periodicity are really spirals, stretched out along the arrow of time that flies only in one direction, and sooner or later brings down every creature. When we assert the identity and existence of something in discourse, we write "A = A," and thus introduce difference into the heart of A. This is just as true when we say, "cogito, sum," or when God roars out of the cloud of the Old Testament, "I am that I am." Even our organizing arguments and stories are linear in their internal structure: the beginning comes before the middle and end, and the premises before the conclusion. We finish the novel in a shower of tears, we are convinced by the argument and turn away: it's over. We read our child's first poem, and understand its plaint or praise.  We can re-visit the story or argument, it's true, and even the story of our own life over a glass of beer in a bar or on the analyst's couch; but we cannot revisit our life.

Great poetic traditions are characterized by line and stanza; stanze are rooms. The dactylic hexameter, the alexandrine, the iambic pentameter, the n-beat alliterative Anglo-Saxon line, the doubled line of classical Persian poetry, each defines the poetry it organizes. What constitutes a line is conventional, and the convention may be given in terms of foot, stress, number of syllables, rhyming end-words, typographical convention, and so forth; but the convention is essential because it establishes a primary periodicity. Here is an analogy: the natural numbers can be represented in terms of strokes:

/  //  ///  ////  /////  //////  ///////  //////// . . .

But this notation just goes on and on, like inertial motion, like the writing of English word-strings by underpaid, non-Anglophone typists who generate documents in order to eat. The genius of Arabic notation is the re-organization of the whole numbers by the multiple superposition of periodicities in powers of ten, an organization so familiar to all of us who learned the addition and multiplication tables in first grade that we no longer recognize its genius. In fact, that organization gives us finite addition and multiplication tables; without it, we would have an infinite number of addition and multiplication facts to memorize. It establishes a primary periodicity in terms of ten; and even though that fiat is a convention, probably related to our twice-five fingers on two hands, we must have some sort of convention to get arithmetic and then number theory going as enterprises. The iterated periodicities that number theorists use to build their discipline (borrowed from group theory and ring theory, analysis, algebraic geometry, and so forth) must have a place to start.

So too with any great tradition of poetry: we must have a place to start, the conventions of lineation, and along with them conventions of stanza, poetic form, and (sometimes) chapter. The effects of lineation are both direct and indirect. Some direct effects are that the first and last words of each line have special weight; we see them and hear them more distinctly than other words in the line, generally speaking, and so pay more attention to their meanings. The poet also tends to choose grammatical units and units of thought that "fit" into the line; so the line both organizes and limits, opening up some possibilities while suppressing others. Poets interested in exploiting ambiguity will choose lines as well as terms that lend themselves to more than one meaning, where the meanings are mutually ampliative, coherent without being consistent. Each line has its own beginning, middle, and end; it may describe an act, but it is itself also an act of the fashioning of language, with the miniature drama, the building and resolution, such an act entails.

Indirect effects have to do with the superposition of periodicities. One obvious example of this is the difference between end-stopped lines, and lines that exhibit weaker and stronger kinds of enjambment. The lineation of poems establishes a formal periodicity; but grammar has its own periodicity, signaled by the completion of a sentence when a noun and a verb are coupled properly, and in Western languages by a capital letter at the beginning, a period at the end, and a space before the next sentence. These two kinds of periodicity may coincide, as in carefully end-stopped lines, or in the formulae chosen over centuries by the bards of oral traditions. However, they may not. The grammatical structure of enjambed lines overflows and violates the boundaries set by the poetic line, setting up a tension between the thought expressed and the form, like a river articulated and deflected by boulders but still rushing over them. Conversely, the boundaries set by the poetic line may interrupt the grammatical structure in ways that reinforce and emphasize words or phrases, or ironically undermine and analyze them.

One frequent consequence of the fluent conflict between grammatical organization and lineation is the creation of caesuras mid-line. In a rhymed poem with strong caesuras, the sound has a period created by the lineation and end-rhymes, while the thought articulated in grammatical units set off by caesuras has a period that begins and end mid-line, and may in fact run for two or more lines. (I am of course overstating the opposition, because lines are always units of meaning as well as aural units no matter how extreme the enjambment – one might say a poetic line insists upon its own formal integrity and hence its own meaning no matter what one puts into it grammatically – and caesuras are marked aurally by a pause.) This creates an interesting counterpoint, at once aural and conceptual; the best example I know (without the rhymes) is Milton's Paradise Lost.

Poetic superpositions are many. We produce the effect of counterpoint by juxtaposing lineal periods with grammatical periods. But grammar is a more formal mode of organization than thought, having less to do with content, and doesn't always coincide with it. An argument, whose premises and conclusion are a good example of a completed thought, often runs over a number of sentences, and certainly a number of phrases. Small thoughts, like "I do" or "I am" or "Alas" often form only part of grammatical sentences or phrases. And in a narrative a continuous thought can be grammatically very broken up, and indeed strung out along many pages. Thus the counterpoint between lineation and grammar in a poem may itself be subject to a further articulation, thought, which as its own periods are superimposed introduces new patterns of reduction and amplification.

Aural counterpoint is also possible in poems. End-rhymed poems may still include a great deal of alliteration, slant rhyme, and even full rhyme in the middle of lines. Then our ears register not only the linear period and alternation of the end rhymes (for example, ABAB) but also the chime that complicates it: three occurrences of sibilance in one line, for example, or a glottal stop in the middle of a line echoing another in the middle of the next. And poems that have no end-rhyme are often knit together aurally by frequent alliteration, slant rhyme, and full rhyme set internally in the lines, often before caesuras; in which case we hear their submerged periods, in connection with the interplay of line and caesura-unit. Another aural effect created by caesuras in highly enjambed poems is a counterpoint of the pauses expected at the end of lines with the pauses that occur mid-line as they frame a completed thought or grammatical unit. Note that highly enjambed poems often rush over the end of a line like rapids, so that what remains is only the ghost of a pause, a pause not taken, which we none the less register.

A similar effect is the counterpoint created between the regular metric pattern of a line and the ordinary patterns of speech. Ordinary speech may demand an emphasis or temporal extension just where the regular metric pattern demands a brief light syllable; every poet knows that this juxtaposition of expectations can produce extraordinary effects, which when successfully accomplished make the reader hear two, or even perhaps three things at once. We hear the speech pattern (that we know well from our everyday life) and the metrical pattern (that the poet has successfully established in the foregoing lines) virtually as aural ghosts behind the resultant outcome, which is a combination of both and what we "really" hear. Actors interpreting Shakespeare's iambic pentameter invent their own characteristic mixture of the formal and conversational to produce what we hear onstage.

William Empson explained how and why the successful management of ambiguity is so important to poets, and showed in a brilliant series of examples how ambiguity can be exploited by the poet at every grammatical level: term, phrase, sentence, narrative or argument. (I would add, also at the formal level of a poetic line, and the contentful level of a thought, neither of which can be identified with a grammatical unit.) In successfully ambiguous poems, the primary and secondary construals of the words are coherent and not contradictory, without being strictly consistent: they are present at the same time even if one (the primary construal) is more present, and their combination will reinforce, amplify and deepen the meaning of the poem. Thus, the primary dictionary meaning of a term will dance with the secondary meaning, or an archaic meaning almost but not completely forgotten. Writ large, ambiguity in argument is Platonic dialectic, even when Socrates seems more philosophical than everyone else; ambiguity in narrative is an action contested and expressed by many agents, even when Oedipus is the tragic hero.

Here, I argue that the successful management of periodicity is also important to poets, for comparable reasons. Bach's counterpoint combines three or four heard melodies; the poet's counterpoint is even more subtle, because it combines melodies (of rhythm and rhyme) that are heard and also unheard (yet still determinate), as it combines patterns that are aural with patterns that are thoughtful, having to do with grammar and meaning. It always remains true that ambiguity and counterpoint can be mismanaged by a careless or inexperienced poet and will ruin the poem, when the multiple meanings simply cancel each other out, or when the counterpoint becomes unrelieved dissonance. But their successful use is the heart of poetry, and for reasons that have to do, I believe, with the ambiguity and counterpoint of human life. The meaning of a human action is not only what happened, but what brought it about, what we hope it will lead to, and – just as important – what might have happened but did not.

Arthur Danto has argued that human action can only be characterized as a project that collects moments in the present and refers them to the future in view of its aims, so that no physicalist account of human action is possible. But the characterization must go even deeper: the meaning of an action includes reference to the acts it precluded – possibles it rendered impossible – which will never be "there" and may still be quite determinate. What happens is a counterpoint among what might have happened and what did happen as a complex knot of past, present, and future; and we are aware of both the realized and the virtual dimensions of that action. Moreover, whenever we tell or hear stories, we understand them against a cultural background of expectations about the way such a story goes; even if, or especially if, the story doesn't turn out as we expected, we are aware of our disappointed expectation. Keats wrote, "heard melodies are sweet, but those unheard / are sweeter still." I would say that the melodies we hear play against a background of unheard melodies, and that is why we can hear them as melodies at all.

A couple of conclusions can be drawn from my description of the art of poetry as, among other things, the art of making multiple periodicities lend themselves to meaning and music. First, the poetic line is a pure but necessary convention. In oral cultures, it is a heard content: a certain number of accents, a certain number of metrical feet or alliterated words around a caesura. In our print culture, it is the typographic line, even more of a formality. But a poem must be lineated in order to have the basic periodic structure that makes it an ordering, a repetition, and a home-coming, and that stands up to all the other superimposed periodicities, making them audible to the ear and legible to thought. Paul Valéry wrote that while prose is like walking, poetry is like dancing. In the room of the stanza, in the house of the sonnet, to which we return again and again, we are able to dance because of the formal periodicity established by the line.

Second, oddly enough, this argument doesn't prove that traditional, formal verse is better than vers libre. I would argue that the opportunities for playing periodicities off against each other are clearer and more numerous in traditional verse, but in any case the English canon offers plenty of variety in the way one can choose one's line and then dance with it. Free verse, losing the rigid underscoring of fixed meters, often compensates for the loss by piling on other kinds of periodicities at the level of sound and meaning, and those extra layers create a different kind of coherent roominess.  Sometimes this leads the poet to guide the reader's attention to explicitly articulated vertical relations on the printed page, as well as to the horizontal unfolding of a single line. Conversely, it may lead the poet to downplay the vertical thrust of the poem as argument or narrative, the linear progression from beginning to end, and create instead a conceptual stasis or circularity. Both strategies mark the free verse of the late twentieth century.


This work has resulted in the following publications:

  1. "Vibrant Stasis, Childhood, and the Influence of Pushkin in Olga Sedakova's Poetry," for Olga Sedakova: Poems, Philosophies, Points of Contention, eds. S. Sandler, M. Khotimsky, M. Krimmel, O. Novikov, forthcoming in both Russian and English. Supported by a grant from the Moscow Charitable Fund to Support Scholarship in Philosophy. Forthcoming.
  2. "The Discreet Charm of the English Spondee," Special Issue on Rhythm in English Poetry, Texas Studies in Literature and Language, N. Gerber and N. Myklebust, eds., forthcoming.
  3. "Space, Time and Poetic Form: Golden Slippers, Poems by Eleanor Wilner and W. S. Di Piero," special issue of Think Journal, eds. C. Yurick, J. Schreiber, and D. Rothman, in press.
  4. "Great Circles: The Analysis of a Concept in Mathematics and Poetry," Special issue on poetry, ed. S. Glaz, Journal of Mathematics and the Arts, Vol. 8 / 1-2, 2014, pp. 24-30.
  5. "Compacting Time: Anne Stevenson's Poems of Memory," Hudson Review, Vol. LXII, No. 3 (Autumn 2009), pp. 405-416. Reprinted as a revised and expanded version in Voyages over Voices: Critical Essays on Anne Stevenson, A. Leighton, ed., University of Liverpool Press, 2010, pp. 151-163.
  6. "Tree, Lily, Rose, Grape: Object and Thought in the Painting of Farhad Ostovani," Hudson Review, LX, No. 4 (Winter 2008), 621-629.
  7. "On Necklaces," Best American Essays 2008, Adam Gopnik and Robert Atwan, eds., Houghton Mifflin, 2008, pp. 75-89; first published in Prairie Schooner, Summer 2007, Vol. 81, No. 2, pp. 182-195.
  8. "The Uses of Periodicity in English Verse," Hudson Review, Vol. LVIII, No. 2 (Summer 2005), pp. 259-274.
  9. "Poetry and Science in America," The Measured Word: Essays on Poetry and Science, K. Brown, ed., University of Georgia Press, 2001, pp. 69-89. First published in Princeton University Library Chronicle, special issue on American poetry, 1908-1992, Vol. LV, No. 3 (Spring 1994), pp. 532-552.
  10. "Report: Mathematical Poetry at Bridges 2012, Baltimore, MD, July 2012," Journal of Mathematics and the Arts, Vol. 6, No. 4 (December 2012), pp. 219-20.
  11. "Jean Starobinski's History of 'Reaction': The Uses and Dangers of Metaphorical Language," review essay of Jean Starobinski, Action and Reaction: The Life and Adventures of a Couple (Zone Books, 2003), The Hudson Review, Vol. LVI, No. 4 (Winter 2004), pp. 726-732.
  12. "Nicholas de Staël," review of an exhibit of paintings, Hudson Review, Vol. 34, No. 3, Autumn 1981, pp. 397-400.


And I have given the following related presentations:

  1. "Poetry and Science," with Ruth Padel and Lavinia Greenlaw, Upper Wimpole Street Literary Salon, London, March 2015.
  2. "Writing and Drawing in Series: Yves Bonnefy's Snow and Summer Nights and Farhad Ostovani's Horizons and Irises," Signature du Livre Farhad Ostovani, Musée Jenisch, Vevey, Switzerland, March 2014.
  3. "Great Circles: The Analysis of a Concept in Mathematics and Poetry," Workshop on Creative Writing in Mathematics and Science, Banff International Research Station for Mathematical Innovation and Discovery, Banff, Canada, November 2013.
  4. "The Uses of Spondaic Rhythms in the Poetry of Yeats and Pound," Critical Seminar on "Understanding the Expressive Purposes of Rhythm: Meters, Measures, Free Verse," West Chester University Poetry Conference, June 2013.
  5. "Golden Slippers: Space, Time and Poetic Form in the Poetry of Eleanor Wilner and W. S. Di Piero," Third Annual Symposium on Poetry Criticism, Writing the Rockies, Western State College, Gunnison, Colorado, July 2012.
  6. A twelve hour lecture series, in French, on "Forme symbolique et parole efficace: Beauvoir et Colette, Rilke, Yves Bonnefoy, Anne Stevenson," University of Paris Nanterre – Paris 10, May 2010.
  7. "Literary Form and Periodicity," Panel on "Mirror Neurons, Mathematics, Metaphor and Mind: Where Science and Poetic Craft Meet," AWP 2007 Conference, Atlanta, February 2007.
  8. "Poetry, Mathematics, and Science," Workshop on Mathematics and Creative Writing, Banff International Research Station, Banff, September 2003; April 2004.
  9. "Poetry and Science," with Robert Morgan and James Applewhite, Duke University, March 2003.
  10. "Fractals, Bach, and Poetry," with Benoit Mandelbrot and Rosalyn Tureck, Entertaining Science at the Cornelia Street Café, New York, September 2002.