large extent, the legacy of the romantic movement that began at the end of the eighteenth century. It followed on the heels of the Enlightenment, when the intellectual world focused on applying scientific methods to understanding human behavior. The French and American Revolutions, for example, were Enlightenment byproducts, and one can see in them the shift from political order based on tradition to political order based on rational principles, such as the rule of the majority. As with most intellectual movements, romanticism is marked by its movement in the direction opposite from the movement that came before— in this case, from intellectualism to physicality. The romantic response to the Enlightenment was to focus attention on humanity’s relationship to nature. If logic is a set of ideas that can be transferred from one situation to another, the romantics turned away from shared knowledge to focus on the subjective experience of the individual writer; if logic is used to find ways to channel water, build bridges, and traverse mountains, romanticism focused on appreciating but not controlling the natural world. The common use of the word “romantic,” referring to love within a personal relationship, offers insight into the nature of romanticism; romance emphasizes personal experience and is generally accepted to be beyond of the rules of logic. To apply geometric theorems to romantic love would strike most people as heartless and cynical. In its extreme, romanticism would reject the intrusion of any and all such mental designs.

The age of romanticism has long since faded, but its most enduring legacy is the bond forged between poetry and nature. Poetry is, of course, a cerebral event, built of words, not of flesh or earth. Though some poetry can be instructive or contemplative, most poetry offers straight, unexplained description, or at least relies heavily on the physical evidence that humans know from their five senses. There is a basic distrust, in modern poetry, of ideas that the poet spoon-feeds to the reader, and so poetry instead moves to capture the physical experience with words. Some poets have extended their distrust of theorizing to a deep resentment and suspicion of all logic. From Whitman to Eliot to Neruda, there is a clear path of poets who have been resistant to order, with an assumption that logic and creativity cannot exist at the same time and that one must therefore give way to the other. Since this has been the prevailing trend for the past century or two, it is understandable that readers might assume “Geometry” to be an attack on the insufficiency of words.

In fact, the imagery Dove uses in the poem does lend itself to be interpreted as being antilogical. Though the first stanza presents the proof of a theorem as an uplifting experience, with the windows and ceiling floating up as if all of the weight of the physical world had been rendered irrelevant, the second is clouded with hints of the theorem’s unintended side effects. Walls are cleared of paint, paper, or anything else that may have adorned them; flowers lose their fragrance. The second stanza ends with “I am out in the open.” Proving a theorem should provide a sense of completeness, but in this line there is less a sense of liberation than of vulnerability. Readers who see this poem as another example of art rejecting science will focus on the second stanza, with the implication of the danger it carries.

It does not help that the poem’s stance toward geometry is not cleared up in the final stanza, which is, if anything, more ambiguous than the previous two. The physical room that the speaker describes does experience an uplifting sense of freedom from the same proof that took the walls away. Does this mean that finding the proof is a good thing because it has liberated the physical world (giving manmade windows the independence and beauty of natural butterflies, for example) or that the proof is bad because life is only tolerable in the places that have escaped the deadening confines of geometry? The poem does not explicitly say, but it does have several aspects that should lead readers to accept intellectualism and not treat it, as so many poets have, as the enemy.

One clue is that this final stanza, though open to interpretation in several ways, clearly is meant to evoke a mood of hope and optimism. The dominant images are of sunlight and truth, and the poem does not say that either has suffered from the proving of the theorem. If reality is escaping from geometry here, it isn’t being aggressively pursued, indicating that its escape is part of the overall plan. In fact, the final word, “unproven,” loops the process back to the opening salvo, “I prove a theorem,” indicating that even something as intellectual as a geometric proof is a part of the cycle of nature.

A minor point, but one still worth mentioning, is the poem’s structure. It does not follow any strict rhythm or rhyme scheme, but it does have a geometric symmetry, with three stanzas of three lines each. Such a structure could be meant to parody the rigors of geometry, but if this were the case, Dove could have made the case better by using a sing-song pattern to mock the lack of inspiration in formal thought. Instead, the limited use of regular structure implies that order can, in a limited way, be of some good.

It is too simple to say that logic and instinct are mutually exclusive, that the world only has room for nature or rationality, but not both. Obviously, both can come together: The combination of reason with physicality is what defines humanity. Readers who have become accustomed to seeing poets and other writers take sides in this conflict are used to reading the works of extremists, who either warn that humans might become unfeeling machines if mathematical order prevails or that barbaric destruction will rule if mathematical precision is forgotten. Usually, poets tend to favor instinct over reason. It is the self-expressive thing to do. Rita Dove is too intelligent to deal in halftruths, however, and “Geometry,” a poem that seems simple and light, refuses to take the easy way out. This poem is too intelligent either to embrace or to reject logic blindly but instead establishes its place in the vast strangeness of the universe.

Source: David Kelly, Critical Essay on “Geometry,” in Poetry for Students, The Gale Group, 2002. Kelly is an adjunct professor of creative writing and literature at Oakton Community College and an associate professor of literature and creative writing at College of Lake County and has written extensively for academic publishers.

The poem “Geometry,” by Rita Dove, is a poem about ideas and space and the way in which ideas and space represent possibility and liberation. A mathematical science, the discipline of geometry revolves around precision and around measurements that add up to an organic whole to prove a scientific truth. The human mind has the capability to create such precision and order, to make sense of what would otherwise be chaos.

By titling the poem “Geometry,” Dove alerts the reader as to the subject of the poem. Unlike a “riddle poem” (such as Emily Dickinson’s “A Narrow Fellow in the Grass”), this poem makes its metaphor explicit—in this case, the comparison of geometry and poetry. The reader then begins reading this poem thinking about the science of geometry and brings with him- or herself ideas about geometry and what it means. Simply defined, geometry is the branch of mathematics that deals with the relations and measurements of lines, angles, surfaces, and solids. Most students study geometry at some point in their schooling and, as part of their learning, have to memorize theorems, proofs, and formulas. Geometry is exact; a measurement is what it is; an angle is what it is—there are no grey areas. Whether the reader likes or dislikes geometry, these are some of the perceptions he or she may bring to this poem upon glancing at the title.

If, by chance, the reader has forgotten his or her high school geometry, the first line brings it all back: “I prove a theorem and the house expands.” The word “theorem” is very much associated with geometry, and proving theorems is a main tenet. The speaker immediately takes ownership of the poem, as well as the action of doing geometry. The first line highlights the setting of the poem nicely as well. The reader can imagine a school-age girl, inside of her house, working on her geometry problems. Dove is deliberate in her choice of verbs for the first line. She doesn’t equivocate or say “I study” or “I grasp”; instead, she says, “I prove”— a strong statement. The speaker is clearly both confident and competent in her geometry skills.

The second part of the first line is even more interesting: “the house expands.” There is a causal connection; the house expands because the speaker proved a theorem. The house even takes on human characteristics. The last two lines of the first stanza showcase this personification: “the windows jerk free to hover near the ceiling, / the ceiling floats away with a sigh.” The mood is one of lightness. The softness of “hover” and “with a sigh” suggests this is a peaceful transformation. The house is expanding beyond its walls. The walls are, in fact, ceasing to exist. And the liberating force is the theorem, which the speaker has proven to be true.

There is a way in which the house in this poem stands in for the mind, especially in the way that it expands. Literary critic Therese Steffen writes in her book Crossing Color: Transcultural Space and Place in Rita Dove’s Poetry, Fiction and Drama:

Two slightly different readings are imaginable: Either the house metaphorically portrays the mind, or the mind-blowing expansion blasts the house apart.” In any case, it is the mental powers at work that cause the shift from solid to soft. What was once a stable structure is drifting apart. In the same way, what was once a stable knowledge base is drifting too— expanding outwards and upwards.

The reader might think about childhood drawings of a house—very angular, consisting of a box with a triangle roof, a rectangle door and two box windows, usually crisscrossed with a “t.” As a physical space, the house is very much a center of geometrical shapes—walls, doors, windows, floors, ceilings, and furniture. But it is also a center of ideas; in other words, of cultural space. Therese Steffen reads the difference between physical space and cultural space in this way: “Cultural space, as distinguished from place and location, is a space that has been seized upon and transmuted by imagination, knowledge, or experience.” This is a useful distinction because it helps us separate the metaphorical from the actual. If we speak in literal terms, we know the actual house isn’t actually expanding; rather, the cultural space the house represents is expanding—namely the mind of the speaker.

As the poem progresses to the second stanza, the structure of the house continues to destabilize. “As the walls clear themselves of everything / but transparency, the scent of carnations / leaves with them. I am out in the open.” That last line of the second stanza is very powerful—why is the speaker “out in the open”? Why has this geometry caused her to lose her grounding? Even sensory perception has faded away with the carnations. Critic Helen Vendler, in her book The Given and the Made, reads this as an experience of “pure mentality”: “As the windows jerk free and the ceiling floats away, sense experience is suspended; during pure mentality, even the immaterial scent of carnations departs.” The speaker is one with her mind—outside forces do not seem to matter. Her surroundings have become “transparent,” leaving nowhere to hide. One way to read “openness” is that the speaker’s foundation of knowledge has been so altered, the “walls” around her mind so shaken, that all of the limits of imagination and understanding that previously held her back have now vanished. There is great liberation in the transparency because it allows her to see beyond what she previously thought were the limits.

Though some readers may love geometry and see unlimited possibilities in mathematical science, to claim that theorems and geometry problems are inherently beautiful and liberating is still a hard sell for many math-fearing readers. Dove isn’t speaking strictly of geometry, though. Just as the house can be read as a metaphor for the mind, geometry itself has a metaphorical quality, especially as it relates to Dove’s true love: poetry. Vendler understands the poem “Geometry” in this way:

It is a poem of perfect wonder, showing Dove as a young girl in her parents’ house doing her lessons, mastering geometry, seeing for the first time the coherence and beauty of the logical principals of spatial form. The poem ‘Geometry’ is really about what geometry and poetic form have in common.

Both geometry and poetry concern space. Simply speaking, geometry takes a logical approach and studies the relationship of objects to the space around them. Poetry takes a more fluid, less tangible approach in that it “studies” the inner space of the mind and the mind’s relationship to thoughts and ideas. Poetry and geometry are alike in that they both seek truth. Geometry is guided by logical principles: If x and y are true, then we can make a statement about z, and it must be true as well. While this is a mathematical way of thinking, it is also highly poetic. There is poetry in the thought process and in the belief that the truth is important in that it helps us to organize our world and understand our place in it. Theorems are as much about shapes and angles as they are about human beings. The speaker in the poem “Geometry” is swept away by these thoughts and connections, and her world is altered as a result.

The experience of “pure mentality” continues through the third and final stanza. There is a sense of a great transformation in the final lines: “and above the windows have hinged into butterflies, / sunlight glinting where they’ve intersected. / They are going to some point true and unproven.” Butterflies are often symbolic of beauty, wonder, and freedom. Here, the windows have actually transformed into butterflies. Solid materials like wood, brick, and glass have changed into brightly colored, delicate wings. Steffen remarks: “This liberating move from the initial “prove” to the final unproven . . . metamorphoses the wallbound windowframes like earthbound caterpillars into butterflies.”

The windows of the house, which provide only a limited view on the world, are exchanged for a more expansive view through the eyes of butterflies. They are flying away, as the speaker says, “to some point true and unproven.” The last line of the poem suggests that there is much more still to be discovered. The speaker be- gins the poem by “proving” a theorem. This sets the initial outward movement into action. This new knowledge leaves the speaker left out in the open, without solid walls to shield and limit her. Her entire relationship to the world has shifted by the last stanza. The solid windows have “intersected” with the liberated butterflies—an intersection of an old way of thinking and the new way of thinking and looking at the world. Another way to read the line “sunlight glinting where they’ve intersected,” is to understand it as the intersection of geometry and poetry—the meeting point of mathematical science and emotional introspection. In that intersection is true liberation, which causes the curious, wellrounded mind to continue searching for truth in the world.

This is a poem about poetry and about the beauty of ideas and human thought processes. But it does not exist in a vacuum. Thinking about the larger social implications for this poem enriches the reading of it. The speaker in “Geometry” experiences a liberation brought on by learning something new about herself and the world around her. The saying “knowledge is power” comes to mind. There is great power in the implications of this poem— the sense of wonderment increases with each stanza, as boundaries disappear and possibilities loom. By proving the theorem, a whole new world opens up to the speaker, and it is a world where windows can transform into butterflies.

In short, education is the real stimulus behind the speaker’s transformation. And Dove, a highly educated woman, not to mention former poet laureate of the United States, certainly knows the value of education. Much of Dove’s poetry speaks to the African-American experience. This poem does not so much speak to that experience as it does to the value of education, which is certainly relevant to the African-American experience. Education is wonderful in that it brings about personal enlightenment, but it is also the way out of poverty and despair. Poetry and abstract ideas about space and people’s relationship to the world may seem far removed from the social and cultural realities of everyday working people, particularly poor people who are more concerned with basic needs. However, as the final lines of “Geometry” suggest, there is a key intersection—whether it be the intersection of rational thought and emotion, of thought and action, or of old and new—that can lead to liberation.

Source: Judi Ketteler, Critical Essay on “Geometry,” in Poetry for Students, The Gale Group, 2002. Ketteler has taught literature and composition.