The shape (but not the essence) of the entropic cone.

According to the Buddhist doctrine all things have no essence, but only shape. In this talk I will discuss the shape of the entropic cone. Entropic cone is the closure of the set of values of entropies of n finitely-valued random variables and their joints. For n=0,1,2,3 the entropic cone is easy to evaluate. Starting with n=4 things become more complicated and interesting. I will discuss what is (un)known and present some new results.