 This suggests several possible strategies for defining a notion of naturalness for classes. One could take into account facts about the “shape” of a class: for example, whether it is spherical (such that for some \(x\) and \(y\), \(z\) belongs to it just in case \(d(x,z)\le d(x,y)\)), or convex (such that whenever \(x\) and \(z\) belong to it and \(d(x,z)=d(x,y)+d(y,z)\), \(y\) belongs to  it).[11]  One could also consider facts about its “size”, e.g. the maximum degree of dissimilarity between any two of its  members.[12]  Or one could consider the extent of the gulf between a class and its complement: the minimum degree of dissimilarity between any member and any non-member.