We all know what it means to be homogeneous in a "hand waving" sort of way. And, of course, there are abstract mathematical definitions for a homogeneous space. I have been unable to find a physical measure of homogeneity which could be applied to a ensemble of particles, box of rocks, or the observable universe. The measure should depend on the distribution of particles and the scale at which we do the averaging. I find it hard to believe that this has not been studied by someone. Any leads? “When you can measure what you are speaking about, and express it in numbers, you know something about it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarely, in your thoughts advanced to the stage of science.” William Thomson, Lord Kelvin PS to Moderators: I am posting this in the Cosmology forum. Please feel free to move it to a better spot if you feel it is appropriate.