"[Penrose] explained that his interest in consciousness goes back to his discovery of Gödel’s incompleteness theorem while he was a graduate student at Cambridge. Gödel’s theorem, you may recall, shows that certain claims in mathematics are true but cannot be proven. “This, to me, was an absolutely stunning revelation,” he said. “It told me that whatever is going on in our understanding is not computational.”"

Penrose starts from a specific conclusion, that formal systems are limited in ways that he clearly is not, and then searched for some way to explain the difference.