A Foundational Mathematical Account of a Specific Complex Social Reality: Conflict in A Midsummer Night's Dream

Mathematics is associated with abstraction, generality, and simplicity, whereas reality is associated with specificity and complexity. Because of this, it might be argued that the humanities disciplines are better than mathematics at providing accounts of the history of societies and the lives of individuals. The aim here is to counter this argument by presenting a mathematical account of a specific complex social reality. This is in accordance with recent appeals to peace scientists to engage with scholars in history and other humanities disciplines. Here, Shakespeare's A Midsummer Night's Dream is studied. The advantage of studying this piece is that the set of events is sufficiently complex to present a challenge to the modeler and yet sufficiently circumscribed to allow a reasonable coverage of the entire reality within the space of a paper.

The play is analyzed in terms of mathematical social science concepts. The analysis considers how people and groups participate in within-group and between-group activities over space and time. The value and power relationships in the activities are analyzed and the following concepts are deployed: roles, rules, hierarchy, anarchy, social divisions, and inequality. Some of the activities involve movement through space-time, and the set of movements can give rise to encounters. These may or may not be planned, and so alternative histories are in play. The analysis then switches to a more detailed level, and dialogic expressions of power relationships are noted. Finally, the logical structure of beliefs and dialogue is analyzed using “dynamic social propositional calculus.”