physics

Poincaré's doctrine of geometric conventionalism presents observers of space with a difficult quandary: how to know that space is Euclidean or non-Euclidean. He begins his discussion with some definitions and clarifications. He distinguishes between two types of phenomena, external and internal.

This essay will look at two parts of astronomical history; general relativity and the research into the phenomena of black holes. First will be a history of general relativity (GR) and a discussion of its impacts on scientific thought, then the history of black hole research and the specific interactions between GR theory and black holes.

This essay will show that non-Euclidean geometries arose as a direct consequence of a weakness in one of Euclid's own axiomatic postulates, specifically Postulate Five. Further, that should Euclid have omitted this contentious Fifth Postulate, the very possibility of non-Euclidean geometries would be challenged.