Moreover, a direct connection can be made between the two. If the probabilities in question are the thermodynamic probabilities "pi": the (reduced) Gibbs entropy σ can then be seen as simply the amount of Shannon information needed to define the detailed microscopic state of the system, given its macroscopic description. Or, in the words of G. N. Lewis writing about chemical entropy in 1930, "Gain in entropy always means loss of information, and nothing more". To be more concrete, in the discrete case using base two logarithms, the reduced Gibbs entropy is equal to the average of the minimum number of yes–no questions needed to be answered in order to fully specify the microstate, given that we know the macrostate.