The purpose of this inter-disciplinary study is to propose a theory of culture; what it is, how it arises from the information processing of mind/brains, its noisy turbulence and our consequent collective inability to fully predict, understand and control our thoughts and actions in the unfolding of history. The strategy is to bring together Sperber and Wilson’s (1995) relevance pragmatics and the new sciences of complexity in order to gain insight into the emergence of collective culture from individual acts of communication. It begins by explaining and illustrating the relevance theory of cognition and communication and Sperber’s (1996) epidemiological approach to culture while interpreting both these in terms of cultural emergence. It concludes with an exploratory attempt to re-analyze relevance principles quantitatively in terms of the mathematical concept of algorithmic complexity and hence gain a new information theoretic perspective on cultural emergence. This further develops the cognitive pragmatics of culture in Downes (2011).