The talk will consider to what extent machines operating under Newton's
laws can compute more than a Turing machine. Various examples will be given, and
their advantages and drawbacks discussed. The examples will be studied using a
methodology to analyse and classify the physical sub-theories allowing the
computations and hyper-computations. The work is part of our programme to
discover just what pieces of classical mechanics are necessary ensure that
machines can only compute what a Turing machine can compute.