Order and Disorder
Geometry is the branch of mathematics devoted to understanding physical space in terms of logical theorems. In Rita Dove’s poem “Geometry” human beings’ ability to understand the world in terms of logic is viewed as a mixed blessing. In the first stanza, the expansion of a house can be taken as a symbol that the intellect has conquered the limitations of the physical world, making what is there bigger and better. The poem’s speaker seems to control the dimensions of the house by understanding them. Up to this point, humanity’s ability to understand the principles of order that already exist in nature is presented as a marvelous skill because it has not only made the house possible but has also improved beyond its original sense of order, creating this expansion.

By the second stanza, however, the poem raises doubts about the overall worth of geometric order. It shows the things that are lost when there is too much importance placed on logical understanding. The walls “clear themselves,” presumably of art works that have been hung on them, which relies on a sense of disorder that has no place in logical theorems. Flowers then lose their scent because their fragrance does not fit into geometric equations. The joys of life are the disorderly and illogical ones, which cannot be appreciated when humans focus strictly on their ability to create order.

In the end, the poem finds a peaceful compromise between order and disorder by observing that the untidy elements that give life pleasure can never be completely deadened by theorems but will always be able to escape them. The windows, made by humans with the help of geometry, have some element to them that makes them as natural and free as butterflies, with the sunlight shining off them in a way that is aesthetically pleasing but not measurable by geometry. The last line refers to “some point true and unproven,” expressing the confidence that the natural world has its own order that exists independently of the geometric sense of order.

Beginning and Ending
In a world that thinks that logic is the only really important thing, the proof of a geometric theorem might be considered an end unto itself. The proof may be the start of a different road of scientific inquiry, as scientists and mathematicians apply the information from the theorem to some practical use, but that one particular theorem has been proven, marking an end to a line of inquiry. In this poem, though, Dove presents the proof of the theorem as the beginning of the physical world’s independence. Abstract thought, such as geometry, has been seen as confining the essence of nature in the past, but this poem shows that nature’s essence can never be captured in a theorem. It is a neverending resource. As many times as humans can create logical models of the physical world, the world has even more mysteries that go beyond all logic. Just when it might seem that geometry has made the pleasures of art and flowers vanish, as depicted in the poem, the physical world asserts itself again.

In this poem, man-made windows are no more contained by logic than are butterflies. Both have “unproven” qualities about them that go beyond their mathematical qualities, which is why the poem presents them, in the end, as escaping. As Dove presents it, no one logical proof can offer complete understanding of the physical world, but instead it represents the start of a new line of inquiry in the quest for knowledge about reality, which is constantly elusive.

Absurdity
This poem presents a struggle against the constraints of logic. It is a warning that the clearly defined view of the world that is sought by mathematics is too limited, because it only presents a small segment of reality. To make her readers think about reality in ways that go beyond logic, Dove presents them with a sense of reality that is unfamiliar and unexpected. By weaving absurd notions throughout the poem, she is able to counter the human predisposition for logic with the equally strong tendency toward imagination.

Of course, it is absurd to state that a mental act like proving a theorem can cause a physical result like making a room expand, but it is exactly the absurdity of such a statement that forces readers to reconsider the situation being described. Describing a natural and predictable physical reaction would not pique readers’ curiosity: when Dove describes things that could not happen, she challenges her readers’ assumptions about what they do and do not know. Mathematical equations do not make windows float or walls turn transparent, but the poem does raise the issue of how these imaginary consequences resemble the actual goals of geometric proofs.