Small Worlds, Mathematics, and Humanities Computing

Abstract

Primarily the conversation surrounding humanities computing has been mainly focused on defining the relationship between humanities computing and conventional humanities, while the relationship humanities computing has to computers, and by extension mathematics, has been mainly ignored. The subtle effect computers have on humanist research has not been ignored, but the humanities general illiteracy surrounding computers and technology acts as a barrier that prevents a deeper understanding on these effects. This goal of this thesis is to begin a conversation about the ideas, epistemologies, and philosophies surround computers, mathematics, and computation in order to translate these ideas into their humanist counterparts. This thesis explores mathematical incompleteness, mathematical infinity, and mathematical computation in order to draw parallels between these concepts and similar concepts in the humanities: post-modernism, the romantic sublime and human experience. By drawing these parallels this thesis both provides a general overview of the ideas in mathematics relevant to humanities computing in order to assist digital humanists in correctly translating or interpreting the effects of computers on their own work and a counter argument to the commonly accepted notion that the concepts developed by mathematics are mutually exclusive to those developed in the humanities.