Well do you? Does one half decide to start healing and the other rot away? Or would both equal halves begin to heal since they would both have half a brain? If one half is completely destroyed, does the other half then get the "signal" to begin rehealing raher than try to reconnect with the missing half? If you were to then split those two halves again down the middle, keeping a quarter of the brain intact with each section, would you end up with four?