Amplified intelligence, or what makes a computer a computer?

I actually cut two chunks out of What would superhuman intelligence even mean?.  I think the one that turned into this post is the more interesting of the two, but this one's short and I didn't want to discard it entirely.

Two very clear cases of amplified human intelligence are thousands of years old: writing and the abacus.  Both of them amplify human memory, long-term for writing and short-term for the abacus.  Is a person reading a clay tablet or calculating with an abacus some sort of superhuman combination of human and technology?  No?  Why not?

Calculating machines and pieces of writing are passive.  They don't do anything on their own.  They need a human, or something like a human, to have any effect.  Fair enough.  To qualify as superhuman by itself, a machine needs some degree of autonomy.

Autonomous machines are more recent than computing and memory aids.  The first water clocks were probably built two or three thousand years ago, and there is a long tradition in several parts of the world of building things that, given some source of power, will perform a sequence of actions on their own without any external guidance.

But automata like clocks and music boxes are built to perform a particular sequence of actions from start to finish, though some provide a way to change the program between performances.  Many music boxes use some sort of drum that encodes the notes of the tune and can be swapped out to play a different tune, for example.  Nevertheless, once the automaton starts its performance, it's going to perform whatever it's been set up to perform.

There's one more missing piece: The ability to react to the external world, to do one thing based on one stimulus and a different thing based on a different stimulus, that is, to perform conditional actions.  Combine this with some sort of updatable memory and you have the ability to perform different behavior based on something that happened in the past, or even multiple things that happened at different points in the past.

My guess is that both of those pieces are also older than we might think, but the particular combination of  conditional logic and memory that they use is the real difference between the modern computers that first appeared in the mid twentieth century and the automata of the centuries before.