Guest Essayist: Paul Lake
In one of his most memorable pronouncements, written in 1917 at a time when he was championing free verse, Ezra Pound made a classic statement about the shape of poetry:
I think there is a 'fluid' as well as a 'solid' content, that some poems may have form as a tree has form, some as water poured into a vase. That most symmetrical forms have certain uses. That a vast number of subjects cannot be precisely, and therefore not properly rendered in symmetrical forms.
Written at a time when free verse was a relatively new and exciting development in English language poetry, Pound's metaphor was a brilliant piece of polemic. While allowing that "symmetrical forms" such as sonnets and villanelles and rhymed quatrains had "certain uses," it suggested that a modern poet would be wise to render most of his subjects in the more flexible, organic form of free verse. A vase might possess a pure, if somewhat abstract and fragile, beauty; but it is, after all, a human artifact--cold and unliving, a relic from the dusty museum of the past. Water poured into it must necessarily conform to its pre-existent shape.
Though Pound's water and vase metaphor was an elegant attempt to resolve the form-content dilemma in formal poetry, it still suggests that the distinction between them is absolute. However perfectly liquid contents and vase seem to meld, water and clay remain distinct, separated by an uncrossable boundary. A tree, by contrast, is a living organism in which form and content are one and the same. The implications of Pound's metaphor are therefore welcomed by poets who write free verse and regarded suspiciously by those who write in traditional forms.
Pound's metaphor has other implications for "symmetrical form" as well, almost all of them negative. For instance, didn't Keats write in a letter to John Taylor, "That if Poetry comes not as naturally as the Leaves to a tree it had better not come at all"? Leaves are the natural outgrowths of trees, but can a leaf grow from a vase?
Looked at that way, Pound's metaphor seems a classic illustration of Coleridge's definition of organic form in his Lectures on Shakespeare, where he corrected those critics who confounded "mechanical regularity with organic form":
The form is mechanic when on any given material we impress a predetermined form, not necessarily arising out of the properties of the material, as when to a mass of wet clay we give whatever shape we wish it to retain when hardened. The organic form, on the other hand, is innate; it shapes as it develops itself from within, and the fulness of its development is one and the same with the perfection of its outward form.
To a modern poet, the act of pouring poetic content into a vase-like "predetermined form" seems every bit as mechanical, and even less original, than pressing clay into a vase. Even considering the sacramental, mystical qualities attributed to water, one can't help thinking of the parable of the wine skins. As a result, writers of free verse from Pound to the present have argued that for poetry to be organic, it must be unbound by the mechanical regularity of meter and the formal rules and strictures of traditional poetry.
Merely looking at the two types of verse on the page seems to confirm Pound's intuition. A passage of the late Cantos, or a poem by Charles Olson or A. R. Ammons, sprawls down the page with the scraggly branchiness of an oak tree, or zig-zags from margin to margin like tide and shore. The shape of formal verse, on the other hand, is suggestive of lines, planes, squares, and stacked boxes. Its kinship to Pound's vase seems obvious.
A half century after Pound published his notes on form in "A Retrospect," A. R. Ammons published "Corson's Inlet," a now-classic poetic manifesto, which makes a similar distinction between the organic shapes of nature--and by analogy of free verse--and the more regular symmetries of traditional poetry. In Ammons' poem, the speaker walks among the sand dunes and along the shoreline of Corson's Inlet, watching sand and ocean intermingle, and musing suggestively in words that echo Pound:
. . . I was released from forms, from the perpendiculars straight lines, blocks, boxes, binds of thought into the hues, shadings, rises, flowing bends and blends of sight . . .
A few lines later, he makes similar observations:
. . . in nature there are few sharp lines: there are areas of primrose more or less dispersed; disorderly orders of bayberry; between the rows of dunes, irregular swamps of reeds . . .
A sharp observer of natural detail, Ammons does note that nature has a few symmetrical, vase-like shapes close to hand, but he quickly dismisses their significance, contrasting their small, tight organization with the more sprawling, dynamic forms all around him:
. . . in the smaller view, order tight with shape: blue tiny flowers on a leafless weed: carapace of crab: snail shell: pulsations of order in the bellies of minnows: orders swallowed, broken down, transferred through membranes to strengthen larger orders: but in the large view, no lines or changeless shapes: the working in and out, together and against, of millions of events: this, so that I make no form formlessness . . .
Trained in biology, with a bachelor's degree in science from Wake Forest College, Ammons uses the vocabulary of science to elaborate his ideas. For instance, while looking over the sand dunes and clumps of bayberry, he describes the flocking behavior of a group of swallows, using scientific terms such as chaos and entropy:
. . . thousands of tree swallows gathering for flight: an order held in constant change: a congregation rich with entropy: nevertheless, separable, noticeable as one event, not chaos . . .
Then while still musing on the birds and other "disorderly orders" he's observed around him, Ammons considers "the possibility of rule" in nature "as the sum of rulelessness."
Thirty years have passed since Ammons published "Corson's Inlet," and in that time, discoveries in science and mathematics have shed new light on the problems discussed in his poem--discoveries with immense significance for our understanding of form and content, nature and art, organic and mechanical form. In retrospect, Ammons' use of the phrase "not chaos" in his description of the swallows' behavior is startlingly prescient because, in fact, a whole new science of chaos--or "anti-chaos," as it's sometimes called--has come into being precisely to explain such phenomena. Surprisingly, though, what the new sciences of chaos and complexity have shown is that Ammons is wrong in his conclusions about art and nature: that the "rule" of nature is not the sum of "rulelessness," as he proposes, but is clearly derived from formal rules and principles, which can be described and even imitated by a new form of mathematics called fractal geometry. Thanks to these new discoveries, we now know that the "order tight with shape" he observes in a tiny snail shell is the same order seen in "the large view": in coastlines, weather systems, sand dunes, mountain ranges, and galaxies. That the laws governing the growth of trees--as well as of leaves, ferns, pine cones, and sunflowers--is the same law that governs the growth of human organs, snowflakes, tornadoes, bird wings--and, I will argue, the elegant, broken symmetries of formal verse.
It turns out that writing formal poetry is not at all like pouring water into a vase, but, rather, like the growth of a tree--far more so than writing free verse, which, except in special cases, is too ruleless, arbitrary, and mechanical to produce the organic integrity of a good sonnet.
Let's begin by considering those flocking swallows. In his book Complexity: The Emerging Science at the Edge of Order and Chaos, M. Mitchell Waldrop describes a presentation by Craig Reynolds at the Santa Fe Institute on the flocking behavior of birds. As Waldrop explains it, Reynolds placed a number of "autonomous, bird-like agents," which he called "boids," into an artificial environment filled with obstacles on a computer screen. Then to see if flocking behavior could be generated by applying a few simple rules, each boid was programmed to behave in the following ways:
1. . . . to maintain a minimum distance from other objects in the environment, including other boids. 2. . . . to match velocities with boids in its neighborhood. 3. . . . to move toward a perceived center of mass of boids in its neighborhood.
Waldrop describes the results of this computer simulation as follows:
What was striking about these rules was that none of them said, "Form a flock." Quite the opposite: the rules were entirely local, referring only to what an individual boid could see and do in its own vicinity. If a flock was going to form at all, it would have to do so from the bottom up, as an emergent phenomenon. And yet flocks did form, every time. Reynolds could start his simulation with boids scattered around the computer screen completely at random, and they could spontaneously collect themselves into a flock that could fly around obstacles in a very fluid and natural manner. Sometimes the flock would even break into subflocks that flowed around both sides of an obstacle, rejoining on the other side as if the boids had planned it all along. . .
One of the most interesting aspects of the emergent behavior of the flock of "boids" noted by Waldrop was that there was no top-down rule telling the boids to form flocks: "Instead of writing global, top-down specifications for how the flock should behave or telling his creature to follow the lead of a Boss Boid, Reynolds had used only the three simple rules of local, boid-to-boid interaction."
This should alleviate the fears of those poets who, like Ammons, think that by writing in traditional forms they are submitting their work to the arbitrary rule of authority, to the top-down rules and "Boss Boids" of the past. In "Corson's Inlet," Ammons explicitly rejects such authority, arguing that in poetry, as in nature, there is, or should be,
no arranged terror: no forcing of image, plan or thought: no propaganda, no humbling of reality to precept . . .
Ironically, though, by rejecting the rules of formal poetry, Ammons is not, as he declares in the poem, leaving "all possibilities / of escape open," but rather cutting himself off from the possibility of achieving the types of rule-governed behavior that produce nature's emergent forms. Once we look at how poems actually take shape, it becomes clear that Ammons and Pound are wrong: The rules of formal poetry generate not static objects like vases, but the same kind of bottom-up, self-organizing processes seen in complex natural systems such as flocking birds, shifting sand dunes, and living trees.
Richard Wilbur, perhaps the foremost living practitioner of traditional verse in America, described in a recent interview (The Formalist) what happens when he starts to write:
. . . my practice is absolutely the reverse of saying, well let's write a sestina now, let's see if I can write a roundeau. I've never, never found myself doing that kind of thing. It's always a matter of sensing that something wants to be said, something of which, as yet, I have a very imperfect knowledge, and letting it start to talk, and finding what rhythm it wants to come out in, what phrasing seems natural to it. When I've discovered those things for a couple of lines, I begin to have the stanza of my poem, if I'm going to have a stanzaic poem. In any case, the line lengths declare themselves organically as they do, I suppose, for a free verse poet. The difference between me and a free verse poet is simply that I commit myself to the metrical precedents which my first lines set. I have found that though I don't know how a poem is going to end, I always have a pretty good advance awareness of how long the poem is going to be, what its tone is going to be, and thus can initially arrive at rhythms and line lengths which are going to be capable of repetition without troubling the flow of thought as it emerges.
The process Wilbur describes will, I'm sure, sound familiar to other writers of formal poetry. It also echoes what scientists who work with chaotic and complex systems describe as happening in nature. John Briggs, for instance, in his book Fractals: The Patterns of Chaos, describes what happens when silicon oil is heated to a boil in a container. At first, as the heat is applied, the oil merely roils and bubbles chaotically in random turbulence; then suddenly, a startlingly complex and intricate pattern emerges:
As soon as the temperature difference between the bottom and the top of the container reaches a critical point, the convection cells bubbling chaotically from the boundaries of the container self-organize themselves so that a symmetry hidden in the chaos asserts itself.
The photograph accompanying his description shows a beautiful pattern of hexagonal convection cells, packed together like the beeswax cells of a honeycomb. The sudden appearance of this beautiful geometrical arrangement is completely unpredictable and results from nature's surprising ability to self-organize holistically, through a complex and sensitive system of feedback, into an emergent new form. As Wilbur describes it, the way a mass of bubbling chaotic thoughts and scattered phrases turns into a sonnet or villanelle is very similar to the seemingly magical transformation that occurs in heated silicon oil. Writing a sonnet, it turns out, is less like pouring water into a dead clay mold than like heating water and watching it suddenly self-organize into a vase.
The term scientists now use to describe the complex, elegant patterns that emerge from nonlinear dynamic systems is "strange attractor." The honeycomb pattern emerging from heated silicon oil is one; a tornado organizing itself from random atmospheric turbulence is another. Completely unpredictable from the behavior of its constituent parts, a strange attractor is a higher-order, emergent phenomenon. Like the flocking behavior of real birds and computer "boids," it somehow spontaneously happens when a simple set of rules, interacting in a holistic way throughout a complex system, produces a dynamic new form of order.
There's a deep paradox here, and one that poets should pause to consider. On the one hand, a poem in its early stages resembles the chaotic random activity of a storm, organizing itself through a rule-governed process of self-adjustment and feedback to produce the strange attractor: the poem. On the other hand, as its name suggests, the attractor--the finished poem--somehow draws the turbulence into its final shape. It's both a top-down and a bottom-up phenomena--what Douglas Hofstadter calls a "strange loop" or "tangled hierarchy."
From the testimony of Richard Wilbur and other poets, it appears that a poem begins with a "something that wants to be said" that generates random phrases and rhythms that organize themselves into lines, then shapely stanzas, then poems. Wilbur says he doesn't decide ahead of time what the line lengths will be, but, rather, that they "declare themselves organically." Yet, paradoxically, these initial lines declare themselves into the right lengths because of his dim initial awareness of "how long" and of what the overall "tone" of the poem is going to be. The initial lines determine the shape of the finished poem, yet the overall shape and tone of the finished poem is what draws the initial lines into being.
Donald Hall in a recent interview (Poets & Writers) gives a similar description of the way poems evolve, declaring that he begins with "a notion of a subject area, maybe a tone of feeling in connection with a phrase, maybe an image with a compelling cadence." He adds that he doesn't know where he's heading with the poem, but simply jots down phrases, often over a period of years, till a sufficient number have accumulated. "The scattered words that accumulate before I start to write," he concludes, "are the first draft of the poem. Along with them I have something like an impetus toward a poem, a shadow that hulks toward the page."
Hall's description almost exactly echoes Wilbur's: a poem begins with a mysterious "impetus," a chaotic scattering of rhythms and phrases, and a sense of the poem's overall tone. All of these disparate elements then somehow coalesce into the poem's final form, which also somehow already existed as a strange attractor: "a shadow that hulks toward the page."
The great Argentinean poet Jorge Luis Borges in his poem "A Poet of the Thirteenth Century" offers a further parallel to the descriptions of Wilbur and Hall. Borges describes how an unnamed thirteenth century Italian poet (possibly Guittone D'Arezzo) invented the sonnet form in words that suggest the theories of complexity science. As translated by William Ferguson, the poem reads as follows:
Think of him laboring in the Tuscan halls On the first sonnet (that word still unsaid), The undistinguished pages, filled with sad Triplets and quatrains, without heads or tails. Slowly he shapes it; yet the impulse fails. He stops, perhaps at a strange slight music shed >From time coming and its holy dread, A murmuring of far-off nightingales. Did he sense that others were to follow, That the arcane, incredible Apollo Had revealed an archetypal thing, A whirlpool mirror that would draw and hold All that night could hide or day unfold: Daedalus, labyrinth, riddle, Oedipus King?
Borges suggests that the sonnet was an "archetypal thing," a strange attractor that somehow caused those first quatrains and triplets to self-organize by reaching back through time: ". . . a strange slight music shed / From time coming and its holy dread / A murmuring of far-off nightingales." Borges' final image of an "avid crystal"-- or "whirlpool mirror" in Ferguson's translation--is another apt description of the "strange attractor" that pulled myth, riddle, paradox, and labyrinth into the sonnet's equally tangled form.
Still, I know that while some people can accept that the free-flowing forms of leaves and trees are produced by rule-governed natural processes, they can not believe there's anything natural about poems being coaxed into existence by metrical rules and formal procedures. Coleridge, however, in the same essay quoted above, has already answered those skeptics:
The spirit of poetry, like all other living powers, must of necessity circumscribe itself by rules, were it only to unite power with beauty. It must embody in order to reveal itself; but a living body is of necessity an organized one--and what is organization but the connection of parts to a whole, so that each part is at once end and means! This is no discovery of criticism; it is a necessity of the human mind--and all nations have felt and obeyed it, in the invention of meter and measured sounds as the vehicle and involucrum of poetry, itself a fellow growth from the same life, even as the bark is to the tree.
As with the poem by Borges, this passage remarkably evokes the discoveries of chaos science. In it, Coleridge declares that as with a living body, "the spirit of poetry" must operate through "rules," which allow a new type of organization incorporating a bottom-up and top-down connection between whole and parts--the way the root system, leaves, bark, and other subsystems of a plant emerge into the thing we call an oak tree. Far from being a dead "received form," meter is, in Coleridge's words, nothing less than the "vehicle and involucrum of poetry," an"involucrum" being the outer covering of part of a plant. The relationship, therefore, of the "spirit" of poetry to "meter and measured sounds" is not that of water poured into a vase, but, in the words of Coleridge again, "a fellow growth from the same life, even as the bark is to the tree."
The error made by Pound and Ammons is a common one. Like many a contemporary theorist, they saw the shapes that formal poems make on the page, noted their resemblance to Euclidean squares and rectangles, and concluded that they were produced by a different geometry than that which produces the biomorphic shapes of trees and leaves. They mistook the two-dimensional outline of the poem on the page for the shape of the poem itself--which, as Pound said more wisely in another famous aphorism, is a shape cut "in time." In confusing a poem's two-dimensional outline with the four-dimensional shape it creates when spoken or read, poets like Pound and Ammons resemble the citizens of Flatland in the classic novel who see only a two-dimensional cross-section of a multi-dimensional object when it intersects the flat plane of their universe. Like his predecessor Charles Olson, who also composed on a typewriter and thought in spatial terms, Ammons tries to substitute a typewriter's mechanical spacing for the organic coherence produced by rules and "measured sounds." Ammons once even composed an entire book-length poem, Tape for the Turn of the Year, on a roll of adding-machine tape, letting its narrow dimensions mechanically dictate the form and rhythms of his poem.
Now, thanks to a new tool, the computer, and a new type of mathematics, fractal geometry, we know that time plays a role in the evolution of nonlinear dynamic systems. We can express the rules governing complex natural systems such as sand dunes and coastlines and measure their shapes in precise mathematical ways. Using fractal geometry, we can even assign a shape like a coastline a fractal dimension (The coast of England, for example, has a fractal dimension of 1.25). We now know that the shapes of trees and leaves are not the sums of "rulelessness," as Ammons proposed, but the result of a rule-governed process dictated by their DNA and feedback from the environment as they adjust themselves in an endless feedback loop.
Like growing leaves and changing coastlines, the nonlinear equations of fractal geometry need time to enact their iterations. Unlike linear equations, which simply plug numbers in and calculate the answer to a result, nonlinear equations feed the results of each step back into themselves, altering themselves and their outcome through constant feedback, and thus creating a perfect mathematical analog to the processes undergone by living things.
For instance, one of the simplest types of nonlinear equations is the Fibonacci sequence. Starting with the number 1, the sequence then progresses to 1, 2, 3, 5, 8, 13, 21, 34, so that each number is the sum of the two preceding it. The approximate ratio of each number to the preceding one is .618. . . , the number of the golden section. The poet John Frederick Nims in his book Western Wind finds this ratio in the proportions of the Golden Rectangle, and demonstrates how when the Golden Rectangle is subdivided into smaller and smaller versions of itself, and connected by a curving line through corresponding points, it produces the spiral found in a nautilus shell--one of those small forms "tight with shape" Ammons mentioned in "Corson's Inlet." The same golden section ratio can also be found in other natural objects such as the spiral of sunflowers and the curve of mountain goat horns.
Nims has even speculated that the ratio in the Golden Section might lie behind the proportions of the Petrarchan sonnet, giving further support to Borges' suggestion that the sonnet is an "archetypal thing" discovered by a Tuscan poet in the thirteenth century. Interestingly, the Fibonacci sequence was discovered by another thirteenth century Italian, Filius Bonacci.
But the perfect symmetry of the nautilus shell is clearly of a different type than that of leaves and trees, not to mention clouds and coastlines. That's because the nonlinear equation that produces the Fibonacci sequence lacks the element of chance provided by environmental feedback to a tree or a boulder-strewn beach. But as John Briggs and F. David Peat note in their book Turbulent Mirror, ". . . when a random variation in the iterations is allowed so that details vary from scale to scale, it's possible to mimic the actual forms and structures of nature much more closely. This suggests natural growth is produced through a combination of iteration and chance." They go on to show that by "combining an iterative scaling with a random element of choice," the shapes of mountains and coastlines can be generated so realistically on computers that they're now used in movies and videos. A landscape similar to Corson's Inlet can now be generated on a computer screen.