While notions of transposition have emerged in different disciplines and fields of study, there seems to be something particular about how the artistic appropriation of the term articulates the movement of research. Rather than repeating basic definitions of the concept as it is used, for instance, in music, where it refers to a change of the key of a composition, or in linear algebra, where the term denotes the switching of rows and columns in a matrix, the authors of this book speculate what kind of transpositional operations may be implied as research develops. While it is impossible to compare the diverse approaches collected here to find a single new definition of the notion, there seems to be sufficient agreement that the kinds of transposition, which are of interest in the context of artistic research, operate outside registers of representation, resemblance, or mimesis. Since these notions suggest a functional identity between two things, for instance, a score and a performance or a sitter and his or her portrait, the change of position that a transposition affords cannot be so potent that it disturbs this identity. Conversely, if the change of position affects what something is-that is, if an identity does not underlie a difference but may emerge from it-a new non-representational, transpositional logic is required in which something at its previous position is not easily reconciled with what appears at its new position, altered as it is by the move. We may also express this by saying that the logic of representation is singular, remaining the same across different instances, while the logic of transposition is multiple, needing to be transposed from instance to instance. The positional specificity that is part of transpositionality-whether in space, time, or otherwise determined-thus explains why it has been so difficult to approach transpositional operations philosophically, and why artistic research, which is sensitive to the specifics of what is at hand, may present new options not only for a bottom-up rather than top-down approach but also for an approach for which there is no "up," only positions that result from movement.Such transpositional operations require a particular emphasis on the differential aspects of the relationships enacted between positions. To do so, a number of chapters refer to quantum mechanics, for example, through notions of entanglement as discussed by Karen Barad (2007), while others emphasise literary devices, such as analogy or metaphor to show that language has always had the ability to create relationships with the unknown, working with it rather than against it. Hence, a number of the book's authors suggest that transpositional operations may even be fundamental to the formation of meaning despite the difficulty of assessing their epistemic importance. A focus on the Michael Schwab 8 multiple logic of transposition complicates our episteme, allowing more complex phenomena to emerge that cannot be traced formally. The methodologies, epistemologies, and aesthetics that h...