  In an attempt to understand the origin and robustness of the
Boltzmann/Gibbs/Shannon entropic functional, we adopt a geometric approach and
discuss the implications of the Johnson-Lindenstrauss lemma and of Dvoretzky's
theorem on convex bodies for the choice of this functional form. We contrast
these results with a more recent result on flowers of balls, which may be
interpreted as suggesting the use of power-law entropies for some systems.
