Tomasch (1954) and Aboitiz et al. (1992) found the majority of the fibers of the human corpus callosum are under 1 micron in diameter. Electron microscopic studies of Swadlow et al. (1980) and the detailed study of LaMantia and Rakic (1990a) on macaques show the average size of the myelinated callosal axons also to be less than 1 micron. In man, the average-sized myelinated fiber interconnecting the temporal lobes would have a one-way, interhemispheric delay of over 25 msec. Thus, finely detailed, time-critical neuronal computations (i.e., tasks that strain the capacity of the callosum and hence could not be handled by just the larger fibers) would be performed more quickly via shorter and faster intrahemispheric circuits. While one transit across the commissural system might yield tolerable delays, multiple passes as in a system involving "setting" would seem prohibitively slow. We suggest that these temporal limits will be avoided if the neural apparatus necessary to perform each high-resolution, time-critical task is gathered in one hemisphere. If the, presumably overlapping, neural assemblies needed to handle overlapping tasks are clustered together, this would lead to hemispheric specialization. The prediction follows that the large brains of mammals such as elephants and cetaceans will also manifest a high degree of hemispheric specialization.