In this talk I will discuss the relationship between some symplectic measurements of convex sets and a classical geometric measurement, the mean width. More precisely, I will describe an inequality between the symplectic capacity of a convex subset and a symplectic refinement of its mean width. This inequality is formally weaker than a much-studied inequality between the capacity and volume of convex sets that was conjectured by Viterbo. It is not yet clear whether it is actually weaker. I will lay out the evidence, state some open questions, and present some new results concerning a linear version of the problem. This is joint work in progress with Jonghyeon Ahn.