The World of Null-A

Gilbert Gosseyn, a man living in an apparent utopia where those with superior understanding and mental control rule the rest of humanity, wants to be tested by the giant Machine that determines such superiority. However, he finds that his memories are false. In his search for his real identity, he discovers that he has extra bodies that are activated when he dies (so that, in a sense, he cannot be killed), that a galactic society of humans exists outside the Solar system, a large interstellar empire wishes to conquer both the Earth and Venus (inhabited by masters of non-Aristotelian logic), and he has extra brain matter that, when properly trained, can allow him to move matter with his mind.