Finite Automata can add but not multiply.via David Singer's Read This Blog!
Turing Machines can compute any computable function.
Turing machines are incredibly more powerful than Finite Automata.
Yet the only difference between a FA and a TM is that the TM, unlike the FA, has paper and pencil.
Think about it.
It tells you something about the power of writing.
Without writing, you are reduced to a finite automaton.
With writing you have the extraordinary power of a Turing machine.