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Oriel Humes
Undergraduate, GPS

A sestina is a poetic form consisting of six stanzas with six lines each. Each line ends in one of six chosen words, each stanza containing an instance of each of the six chosen terminal words exactly once. The order in which the terminal words appear in each stanza is determined algorithmically through a permutation. Given the nth terminal word in one stanza, its position in the next stanza is given by 2n if n is between 1 and 3, and 1 + 2(6 - n) if n is between 4 and 6. This piece represents a visual interpretation of the permutation pattern of a sestina, inspired by the technical drawings used to depict braid theory and knot theory in mathematics. This representation also illustrates how a particular permutation can be decomposed into a series of transpositions, i.e. reshufflings that only swap two elements at a time. Since it takes six permutations to return to the original word ordering, the sestina braid represents a six-link knot, or a cyclic group of order six.

ohumes@caltech.edu

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