Information theory inference, better known as the maximum entropy method, is used to infer the lateral density distribution inside the earth. The approach assumes that the earth consists of indistinguishable Maxwell-Boltzmann particles populating infinitesimal volume elements and follows the standard methods of statistical mechanics (maximizing the entropy function). The GEM 10B spherical harmonic gravity field coefficients, complete to degree and order 36, are used as constraints on the lateral density distribution. The spherically symmetric part of the density distribution is assumed to be known. The lateral density variation is assumed to be small in comparison with the spherically symmetric part. The resulting information theory density distribution for the cases of no crust removed, 30 km of compensated crust removed, and 30 km of uncompensated crust removed all give broad density anomalies extending deep into the mantle, but with the density contrasts being the greatest toward the surface (typically ¿0.004 g cm-3 in the first two cases and ¿0.04 g cm-3 in the third). None of the density distributions resemble classical organized convection cells. The information theory approach may have use in choosing standard earth models, but the inclusion of seismic data into the approach appears difficult.