This talk will investigate the geometric nature of infinity. It will unfold, like a David Lynch film, in a sequence of increasingly surreal episodes populated by characters in split algebraic and geometric roles, filled with abstract symbols whose veiled meanings might at once confound and intrigue, and conveyed through graphic imagery and strong language which might at times discomfort. (Rest assured however that every effort will be made to make the talk broadly accessible.) The story begins with the disappearance of a point from a small Euclidean neighborhood. Tracing the point’s steps leads to a twisted reality at the outskirts of town where parallel lines meet and ultimately to a shadowy algebraic underworld where one plus one equals zero.