We provide a conceptual framework for understanding similarities and differences among various schemes of compositional representation, using examples from natural language, traditional AI and connectionism. Nine abstract dimensions specify a vast space of possible compositional schemes. Temporality turns out to play a key role in defining several of these dimensions. From studying how schemes fall into this space, it is apparent that there is no single crucial difference between AI and connectionist approaches to compositionality; that connectionist approaches differ widely among themselves; that neither traditional AI schemes, nor most connectionist schemes, can claim to be closer to the form of human speech. In addition, large regions of the space of compositional schemes remain unexplored, such as the entire class of active, dynamic models that do composition in time.