Shared aspects of intrinsic dimension and differential entropy estimators are studied in this paper, thus yielding a pragmatic approach for joint estimation of these two fundamental measures of random observations. Numerical simulations are performed to highlight the steps in common on both estimators, mainly when quadratic (or collision) entropy is considered, and their useful consequences to data analysis. It is shown that both estimators are complementary parts of a single approach, and that the simultaneous estimation of differential entropy and intrinsic dimensionality give meaning to each other. Experiments with synthetic and real datasets are presented to illustrate how to extract meaning from visual inspections of resulting graphs, and how to compensate for biases due to finiteness of experimental observations.