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•Eight Greatest Computer Innovations that Actually Make Life Easier 77

Turing went on to work as the mathematical genius of Bletchley Park, where he
did more than anyone to make possible the breaking of the Enigma codes and give
the allies certain information of the strategy and tactics of the axis powers in World
War II.

A colleague at Bletchley Park, Donald Michie, a classics scholar from Balliol
College, Oxford, and subsequently an expert on computers and the Professor of
machine intelligence at Edinburgh University, spoke thus of Turing.

‘Alan Turing is one of the figures of the century. His consequences are everywhere
and nobody knows now where it is going to take us. The world of computing and
now the world of the Internet stems from Alan Turing’s fundamental ideas. There
were other great men in Bletchley Park, but in the long long wall of history I think
Turing’s name will probably be the number one in terms of consequences for man-
kind.’

Idea 45 – Getting the answer through trial and error

A combination of a human feel for the solution to a problem, usually mathematical,
and the power of a computer has enabled many new insights into equations. The
process is called iteration. Taking as an example the formula to find the square root
of a number. The iterative process is

where a is the number whose square root is required, we will gradually get to a
better and better approximation to the answer. Suppose we wanted to use iteration
to find the square root of 2. If we start with

X =1
1