What is the self? How does the activity of neurons give rise to the sense of being a conscious human being? Even this most ancient of philosophical problems, I believe, will yield to the methods of empirical science. It now seems increasingly likely that the self is not a holistic property of the entire brain; it arises from the activity of specific sets of interlinked brain circuits. But we need to know which circuits are critically involved and what their functions might be. It is the "turning inward" aspect of the self -- its recursiveness -- that gives it its peculiar paradoxical quality.