An alternating unity

The corpus callosum links the two hemispheres through 

"300-800 million fibres connecting topologically similar areas in either hemisphere. Yet only 2 per cent of cortical neurones are connected by this tract. What is more, the main purpose of a large number of these connections is actually to inhibit – in other words to stop the other hemisphere interfering." (The Master and His Emissary, Iain McGilchrist, 2009; page 17). 

The Aharonic kehuna differs from the first-born kehuna in this bi-directional, inhibitory function. 

Inhibition at the neuronal level does not necessarily lead to functional inhibition. You can take your foot off the gas pedal and the car still moves forward in a functionally permissive fashion. 

The corpus callosum however seems to operate in order for one hemisphere to inhibit the other. Both sides can't be working at the same time. After an initial arousal in the contralateral hemisphere, excitation on one side of the brain is accompanied by a subsequent inhibition of the corresponding regions on the other side of the brain. The connecting channel stays open all the time but it serves alternately to shut down one or the other side of the redundancy. 

The function of the corpus callosum is to render the hemispheres not into a single unity but into an alternating unity. Like covenantal partners who are so dissimilar they can consume each other's wastes, the unity of the two hemispheres is based on an alternation rather than on an integration. 

For any dialogue to be possible the other person must be quiet while the first person is speaking. The difference between war and sport is that in war both sides go on the offense at the same time while in sport the offensive and defensive teams alternate under the rules of the game and under the referee's signal. Who will give and who will receive is something the referee settles at the beginning of the game and then the rules determine the order from then on. 

Gift receiving is as much a sign of affection as gift giving, if not sometimes more. 

Self-inhibition so that the other can come forth and take charge is a sign of diplomacy and a courtesy that bespeaks a certain decorum.