In each of the five sections, certain elements of the scene--"chocolate," "umbrellas," "green," "machine," "blooms," and "clouds"--oriented with respect to "the deck"--are held as invariants in a changing light, first a "morning summer" hue, next a "streaked" "breakfast jelly yellow," next a "patterned" "pale silver," then a "mallow morning," and, finally, "The day . . . bowing and voluble." Each "light" projects a different atmosphere. Or, rather, each set of terms introducing the "light" determines another set of terms which, in turn, determines the distinctive ambience of each section, each "scene" an ambience which, though believable, is conspicuously synthetic in much the same way that Eliot, in "Tradition and the Individual Talent," suggests, with his metaphor drawn from chemistry, that "art-emotion" is synthetic. When terms such as "rosy chocolate," "gilt umbrellas," "Paradisal green," "suavity," "perplexed," and "machine" are put together, they so mutually react, so color one another, that they form something new, a combination in which none of them retains its original properties: they form not a mixture but a new compound. Eliot's metaphor is more than satisfactory. It implicitly portrays the poet as a word-scientist conducting, in the laboratory of the poem, an experiment. We know, too, that behind Eliot's metaphor lies the symboliste enthrallment with the synthetic and with the ideal, Mallarmé’s professed intent to synthesize the "flower absent from all bouquets." But if we make the short leap from a chemical metaphor to a mathematical one, we find an analogue which may be as satisfying as Eliot's; we find, in fact, that Eliot's analogy, for all its virtues, has obscured some other illuminating connections. We might think of the invariant structure of "chocolate," "umbrellas," "green," "machine," "blooms," and "clouds" as akin to coefficients in a polynomial, f(x), of the form* anxn + an-1xn-1 + . . . + a1x + ao* in which the variable, x, the deck, can assume a different value or "light" in each section, so that each section rather playfully, as if in demonstration, yields a different value for f(x) as each new "light" is substituted for x. In this poem, the "value," instead of being numerical, is aesthetic--a mood, a flavor, a feeling-tone, an intimation of something impalpable yet recognizable; for just as number is a specialized language that has evolved to express quantifiable values, poetry is the specialized language that has evolved to express synthetically otherwise inexpressible aesthetic values and experiences.

We might entertain a different mathematical analogy: the "deck" in each section is analogous to the Cartesian coordinate system in two dimensions; "chocolate," "umbrellas," "green," "machine," "blooms," and "clouds" are points--the vertices of some hexagonal geometrical figure composed of vectors mapped onto the plane. This hexagonal figure seems to change in each section, as the "deck," the axes in each section, are translated or rotated or altered in scale. But actually the polygon remains invariant: only the axes with respect to which the polygon is oriented and scaled are transformed. The poem, like a mathematical demonstration, escorts us through a sequence of linear transformations. Moreover, like a mathematical demonstration, in each of its steps it succeeds through its specialized language, in expressing "something" which, without this language, would have remained inexpressible and, because it was inexpressible, scarcely perceptible at all. It is this issue of "inexpressibility" which should enable us to appreciate fully the analogy between poetry and mathematics and how serious this analogy might be. Without mathematics, how would we describe the orbit of a planet? As "round"? As an "oval" path? How close to looking like a circle? How "eccentric"? Without the quadratic equations that graph an ellipse, we are reduced to clumsy guesses, incredibly crude linguistic approximations. The mathematical formula for the ellipse, on the other hand, can yield us the precise shape. It is the only way to express that shape. Similarly, without mathematics, how would we express the behavior of a falling object? All we could say was that it goes "'faster and faster and faster." But how "fast" does it go "faster"? Only a differential equation can express this precisely and meaningfully. "Acceleration" can be measured only in mathematical terms. Indeed, the entire concept of "acceleration" is meaningful only in mathematical terms.

Is there an analogous "something" that can be expressed precisely--be measured--only by means of the specialized terms of poetry? I think so. And I think that the mysteriously impalpable moods and changes of light synthesized in each section of "Sea Surface Full of Clouds"--moods which, though seemingly ineffable, we recognize through the language of the poem--demonstrate the specialized capacity of poetic language, like mathematical language, to measure accurately and thereby to find names for areas of experience which would otherwise have eluded us. But even as I suggest this, I am poignantly aware that I cannot prove it. The poem must serve as its own demonstration. Either the reader is overcome with recognition of what had hitherto seemed insufficiently expressed, or the reader is left cold. Auden puts rather neatly this "inexpressibility" theorem of poetry, linking it with the very function of poetry itself, in the prologue to The Sea and the Mirror:

Well, who in his own backyard
Has not opened his heart to the smiling

Secret he cannot quote?

Which goes to show that the Bard

Was sober when he wrote

Pope put a similar idea into somewhat more modest terms: "True wit is Nature to advantage dressed, / What oft was thought, but ne'er so well expressed." One can attempt to explicate each section of "Sea Surface Full of Clouds," to apply "interpretation" as a means of convincing the skeptical reader that there is "something" recognizable being measured and named by each section, "something" which might be mutually acknowledged with a nod or perhaps a sharp intake of breath or a bristling of the pores--by a frisson. But if the poem cannot accomplish this by itself--if it cannot be its own demonstration--extrinsic attempts at demonstration will never suffice, but will remain prime targets, ludicrous sitting ducks, to be coolly picked off by the poststructuralist critics. And so I will leave "Sea Surface Full of Clouds" undisturbed, trusting that it is its own sufficient testimony.