  Church (1940) repeated this characterisation. Turing neither endorsed it nor said anything to contradict it, leaving the general concept of ‘machine’ itself undefined. The work of Gandy (1980) did more to justify this characterisation, by refining the statement of what is meant by ‘a machine.’ His results support Church's statement; they also argue strongly for the view that natural attempts to extend the notion of computability lead to trivialisation: if Gandy's conditions on a ‘machine’ are significantly weakened then every real number becomes calculable (Gandy 1980, p. 130ff.). (For a different interpretation of Church's statement, see the article on the  Church-Turing Thesis.)