Mike W

Midlands UK

Developer

Surely the point of a Turing machine is not that it is 'powerful', but that it is simple enough for its basic operations and sequences thereof to be completely analysed in a mathematical way, but with enough expressive power that it can compute any required algorithm (eventually !!).

One can then apply transformations to demonstrate that various 'real' (or conceptual) computing devices are computationally equivalent to a TM, and therefore any theorem proved for a TM is true for any 'real' device.

In this way, one can make proofs within a very restricted environment, but have them shown more generally valid by dint of the proven equivalence.