Conversation is one of those everyday, commonsense abilities that we can all do without thinking. But paradoxically, understanding how conversation works is one of the most difficult problems for scientists - for example, even after decades of research, computers are still miserable conversationalists. This text explores this paradox: how can conversation be so difficult, and at the same time come to us so naturally.? The answer to the paradox is found in the creativity of everyday conversation. The author, a psychologist and an expert in the sciences of creativity of everyday conversation, shows that the same basic creativity - improvisational creativity - is found in conversation, jazz, children's play, and theatre.