Abstract

Namespaces are commonly used in Computer Science, with namespace problems as a leading cause of very difficult to identify programming errors. While namespaces have not been extensively used in mathematics, they can be used to describe the variables, identifiers, and components associated with mathematical functions and matrices. Namespace Analysis can be used to evaluate the validity of mathematical derivations that involve functions and matrices; can help identify the source of variable naming problems in complex derivations, and can provide insight on how the problems can be corrected. Here we use namespace analysis to evaluate multiple derivations of the Einstein-Lorentz transformation equations, revealing mathematical problems in each. We show that, in his 1905 paper, Einstein overloads the ?t? variable between his global and function namespaces, while Lorentz, in his 1904 paper, overloads the ?x? variable between his function and matrix namespaces. This overloaded variable problem enabled them to each produce incorrect time transformation equations. This finding of a mathematical problem in each significant Einstein-Lorentz derivation will require that the Einstein-Lorentz equations be modified and that the continued validity of Special Relativity be reexamined.