I am working on a story idea where a character in a medieval world develops a rudimentary computer. It is made of simple building blocks similar to the flip-flop and and/nor gates of digital logic. It is built with wood and iron, and operated by a water wheel. I imagine that its computing power is roughly similar to the first machines used in WWII, such as the Turing machine and the Enigma. With it, she can perform computations far beyond the abilities of humans. But I'm stuck on how it could be useful. All I have so far is...
- Predict various astronomical events with greater accuracy
- Encode messages that can't be broken by hand
There must be something else that a conputer, hundreds of years ahead of its time, would enable this character to do. What am I missing?
EDIT: this is different than the suggested duplicate in my opinion. That question asks what it would need to be feasible; this asks what one could do with such technology. Further, it's a different sort of machine than an abacus.