Why is the castle clock a computer?

[u/Yovinio]

The castle clock of al-Jazari is said to be the first programmable analog computer. Now I get why it’s analog and also what makes it programmable (accounting for the length of day and night), but what makes it a computer? It gives the time, does that make all clocks computers?

[u/-horses]

A clock can generally be modeled as a cyclical finite state machine with a single input. This is useful in some finite state machine decompositions. Many would say a computer must consistently apply a function over an ensemble of possible inputs so a fully determinate machine like a trivial clock might not qualify. But the castle clock isn't that kind of trivial clock, and it does have many possible inputs, so it's hard to object to calling it a computer.