0000002 degrees, a variation from Euclid's geometry which, for instance, satellite navigation systems nowadays have to take into account. In other situations - such as near black holes - the differences between Euclidean and Einsteinian geometry are so profound that they can no longer be described in terms of 'deviations' of one from the other. Another example of the same mistake was in computer science.
Turing initially set up the theory of computation not for the purpose of building computers, but to investigate the nature of mathematical proof. Hilbert in 1900 had challenged mathematicians to formulate a rigorous theory of what constitutes a proof, and one of his conditions was that proofs must be finite: they must use only a fixed and finite set of rules of inference; they must start with a finite number of finitely expressed axioms, and they must contain only a finite number of elementary steps - where the steps are themselves finite.
Computations, as understood in Turing's theory, are essentially the same thing as proofs: every valid proof can be converted to a computation that computes the conclusion from the premises, and every correctly executed computation is a proof that the output is the outcome of the given operations on the input. Now, a computation can also be thought of as computing a function that takes an arbitrary natural number as its input and delivers an output that depends in a particular way on that input. So, for instance, doubling a number is a function.