Interestingness is an important criterion by which we judge knowledge discovery. But, interestingness has escaped all attempts to capture its intuitive meaning into a concise and comprehensive form. A unifying paradigm is formulated by function composition. We claim that composition is bipolar, i.e. composition of exactly two functions, whose two semantic poles are relevance and unexpectedness. The paradigm generality is demonstrated by case studies of new interestingness functions, examples of known functions that fit the framework, and counter-examples for which the paradigm points out to the lacking pole.