There are many references to it in public discussions, but trying to learn about it from Wikipedia is like reading in a new foreign language.
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To put it simply, early computers could only perform a single function. Imagine the early code breaking machines used during the 2nd Word War. Really advanced machines, but could only do a single job (or algorithm).
Turing machines are closer to modern computers that can be reprogrammed to perform any algorithm as required.
True Turing machines are more abstract that this, but this is a very simple example.
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