  The beauty of Turing machines is that the model is extremely simple, yet nonetheless, extremely powerful. A Turing machine has potentially infinite work space so that it can process arbitrarily large inputs, e.g., multiply two huge numbers, but it can only read or write a bounded amount of information, i.e., one symbol, per step. Even before Turing machines and all the other mathematical models of computation were proved equivalent, and before any statement of the Church-Turing thesis, Turing argued convincingly that his machines were as powerful as any possible computing device.