The discussion centers on the nature of arguments in exponential and trigonometric functions, questioning whether they can be vectors or must remain scalars. It is noted that while functions expressed as power series can be extended to matrices, the general application to vectors is limited due to the absence of a universal multiplication function yielding vector results. Typically, in physical contexts, arguments are dimensionless, although hypothetical scenarios can create dimensioned arguments. An example involving force and mass illustrates the unusual dimensions that can arise from exponentiating physical quantities. Overall, the consensus suggests that while scalars are standard, there are theoretical allowances for more complex arguments.