Roger Penrose is a guy who has a way of asking good questions and providing controversial answers. On page 20 of his monumental survey of applied mathematics, " The Road To Reality"  he explains an interesting theory about three "worlds": R*:The "real", physical world of "stuff" and phenomena, which he (quite reasonably) takes to exist apart from the other two worlds; M:The world of ideas - what I call the "meme space". In principle, this is all the theories, observations, direct or indirect perceptions that could ever be made by the human mind; F:The world of forms, mathematics and logic. While he contends is that each world "maps" completely to the others. In principle at least, each world can be explained in terms of the other.  But he allows us to imagine that the mapping is incomplete. It is the incompleteness that interests me: There may be aspects of reality that are "illogical" or cannot be described by math...