David Hockney is possibly the world's most popular living painter, but he is also something else: an incisive and original thinker on art. Here are the fruits of his lifelong meditations on the problems and paradoxes of representing a three-dimensional world on a flat surface. How does drawing make one 'see things clearer, and clearer, and clearer still', as Hockney suggests? What significance do different media - from a Lascaux cave wall to an iPad - have for the way we see? What is the relationship between the images we make and the reality around us? How have changes in technology affected the way artists depict the world? The conversations are punctuated by wise and witty observations from both parties on numerous other artists - Van Gogh or Vermeer, Caravaggio, Monet, Picasso - and enlivened by shrewd insights into the contrasting social and physical landscapes of California, where Hockney lives, and Yorkshire, his birthplace. Some of the people he has encountered along the way - from Henri Cartier-Bresson to Billy Wilder - make entertaining appearances in the dialogue.