  The cerebrum of mammals spans a vast range of sizes and yet has a very
regular structure. The amount of folding of the cortical surface and the
proportion of white matter gradually increase with size, but the underlying
mechanisms remain elusive. Here, two laws are derived to fully explain these
cerebral scaling relations. The first law holds that the long-range information
flow in the cerebrum is determined by the total cortical surface (i.e., the
number of neurons) and the increasing information resistance of long-range
connections. Despite having just one free parameter, the first law fits the
mammalian cerebrum better than any existing function, both across species and
within humans. According to the second law, the white matter volume scales,
with a few minor corrections, to the cortical surface area. It follows from the
first law that large cerebrums have much local processing and little global
information flow. Moreover, paradoxically, a further increase in long-range
connections would decrease the efficiency of information flow.
