When model neural networks are used to gain insight into how the brain might carry out its computations, comparisons between features of the network and those of the brain form an important basis for drawing conclusions about the network's relevance to brain function. The most significant features to be compared, of course, relate to behavior of the units. Another network property that would be useful to consider, however, is the extent to which units are interconnected and the law by which unit-unit connections scale as the network is made larger. The goal of this paper is to consider these questions for neocortex. The conclusion will be that neocortical neurons are rather sparsely interconnected — each neuron receives direct synaptic input from fewer than 3% of its neighbors underlying the surrounding square millimeter of cortex — and the extent of connectedness hardly changes for brains that range in size over about four orders of magnitude. These conclusions support the currently popular notion that the brain's circuits are highly modular and suggest that increased cortex size is mainly achieved by adding more modules.