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==The Turing Machine==

==The Turing Machine==

In the 1930s Turing proposed the concept of a "[[turing machine|Universal Turing Machine]]".  Turing had, first, proposed that the operations needed to calculate any formula could be broken down into a base set of instructions (or primitive [[Recursion|recursive functions]]) that could in principle be followed by a machine: the "Turing Machine".  Once fully formalized the calculations needed to derive the instructions themselves were capable of being run by a Turing Machine.  The looped [[logic]] allowed the conception of a Turing Machine that could create its own instruction and, in principle, run a huge variety of calculations. Turing then used the concept of Universal Turing Machine to prove the undecidability of the [[halting problem]].

In the 1930s Turing proposed the concept of a "[[turing machine|Universal Turing Machine]]".  Turing had, first, proposed that the operations needed to calculate any formula could be broken down into a base set of instructions (or primitive [[Recursion|recursive functions]]) that could in principle be followed by a machine: the "Turing Machine".  Once fully formalized the calculations needed to derive the instructions themselves were capable of being run by a Turing Machine.  The looped logic allowed the conception of a Turing Machine that could create its own instruction and, in principle, run a huge variety of calculations. Turing then used the concept of Universal Turing Machine to prove the undecidability of the [[halting problem]].

==Code breaking==

==Code breaking==