When, in the primeval sea, creatures first began to crawl, 'right' and 'left' came into being, yielding neuronal nets to control response to the sidedness of stimuli. In the half billion years of moving and sensing, two brains have evolved, the right and the left; and human experience now shows them to be roughly equivalent, potentially independent, conscious entities. This dramatic fact is evidenced by 'split-brain' patients and by numerous cases of therapeutic removal of either hemisphere. Equally dramatic, of course, is that there is not the slightest sign of this duality in everyday experience, the right and left visual fields are seamlessly knit, and cross purpose is absent in the moment to moment operation of the two cerebral hemispheres. This unity is constantly synthesized by the 100,000,000 fibers passing from each hemisphere to the other; the vastness of that interchange emphasized upon comparison with the mere 1,000,000 fibers conveying all the visual world from each eye. With the large distances in the human brain some 100+ ms may commonly transpire for one hemisphere to send to and receive a response from the other. Efficiency thus demands that most neuronal calculation occur within rather than between hemispheres, thereby promoting differences in the characteristic capabilities of each alone, i.e., 'hemispheric specialization'. Despite this there is a bewildering bilaterality of activation revealed by fMRI for most cognitive tasks. In the absence of the forebrain commissures brainstem systems can be shown, in macaques, also to participate in the unification of behavioral result from the actions of the separated hemispheres. The system favors synthesis from congruent (visual) input to the two hemispheres; but in the face of incompatible hemispheric input, the two hemispheres are able to work out an accommodation in their control of subcortical systems.