  The last century saw dramatic challenges to the Laplacian predictability
which had underpinned scientific research for around 300 years. Basic to this
was Alan Turing's 1936 discovery (along with Alonzo Church) of the existence of
unsolvable problems. This paper focuses on incomputability as a powerful theme
in Turing's work and personal life, and examines its role in his evolving
concept of machine intelligence. It also traces some of the ways in which
important new developments are anticipated by Turing's ideas in logic.
