You've read a pot. You've driven a servo. Connecting them — knob turns, arm follows — is the smallest closed-loop control system you can build. It looks trivial. It's actually the foundational pattern for every kind of teleoperated machine.
The sketch is six lines
The full program: in loop(), read the pot with analogRead, scale 0–1023 to 0–180 with map, write that angle to the servo. The servo holds its position; the pot's value is sampled hundreds of times per second; the arm tracks the knob with no perceptible lag.
This is teleoperation in its simplest form. The same pattern with a thumbstick → servo is how RC cars steer. With a joystick → flight surface, how 1980s remote-control aircraft worked. With a wheel → angular motor, you have a steering column. The composition is just read → transform → write.
The transform is where you live
For a one-to-one map, map() is enough. But once you're composing inputs and outputs, the transformation is where interesting behaviour goes. Add a deadzone in the middle so the servo doesn't twitch from pot noise. Smooth the transitions so the servo doesn't snap. Apply a curve (square the input) so fine control is at the middle and gross control is at the edges. Every real control system has a custom transform; the read and the write are the boring parts.