Master of Science

This thesis studies connections between disorder type in tree polymers and the branching random walk and presents an application to swarm site-selection. Chapter two extends results on tree polymers in the infinite volume limit to critical strong disorder. Almost sure (a.s.) convergence in the infinite volume limit is obtained for weak disorder by standard theory on multiplicative cascades or the branching random walk. Chapter three establishes results for a simple branching random walk in connection with a related tree polymer. A central limit theorem (CLT) is shown to hold regardless of polymer disorder type, and a.s. connectivity of the support is established in the asymmetric case. Chapter four contains a model for site-selection in honeybee swarms. Simulations demonstrate a trade-off between speed and accuracy, and strongly suggest that increasing the quorum threshold at which the process terminates usually improves decision performance. / Graduation date: 2013

Writers of early American texts frequently express astonishment at the abundance of swarming things found in nature, from rustling clouds of insects to ponds teeming with fish to forests of countless trees. They report feeling overwhelmed, fascinated, and threatened by the dynamic, formless grouping of the swarm, in which the distinction between part and whole is lost in a blur of motion. In this dissertation, I trace these experiences of swarming across religious tracts, natural histories, philosophy texts, and historical fiction to argue that the swarm is crucial for understanding early American ways of relating to the environment. Scholars of the colonial period have long maintained that settlers viewed the American continent as a vast and empty land, available for settlement and resource extraction, and that the settler mind sought to manage the perceived chaos of their new surroundings through the application of European systems of thought and order. I argue, however, that the experience of the swarm indicates another kind of environmental relation, one in which the viewer and the natural world become ecologically entangled. In this entanglement, settlers found their preconceived ideas challenged, forcing them to revise or generate anew their theories of the world. While these ecological experiences of the natural world appear in texts by the settler writers Jonathan Edwards, Hector St. John Crèvecoeur, William Bartram, and James Fenimore Cooper, the ideas that develop through the swarm are influenced by or overlap with the epistemologies of the Native American peoples who inhabited the lands these settlers occupied. The project also addresses Indigenous modes of environmental relation and philosophies through Haudenosaunee cosmologies, Maskoke origins stories, and the work of the Tuscarora writer David Cusick. Overall, this dissertation offers an epistemological history of the colonial period that not only revises long- accepted characterizations of the settler mindset but that also takes seriously the histories of Indigenous philosophies as early American intellectual movements. In detailing experiences in which the mind and the natural world are not in fact separate entities, my work presents alternative modes of environmental relation and offers suggestions to today’s urgent need to rethink our orientation toward the natural world.