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Alan Turing made a seminal contribution to logic, computation, computer science, artificial intelligence, cryptography and theoretical biology. The articles here, by outstanding writers and thinkers, reflect on these contributions, how the subjects have developed since then, and how they might develop still further. Five themes are explored: language, universality and computation; computing and the brain; computing life and morphogenesis; quantum computing; and the challenge of incomputability. These essays will provoke and engross the reader who wishes to understand better the lasting significance of one of the twentieth century's deepest thinkers.