The mapping problems are solved through cultural conventions, or constraints. It is a worldwide convention that the left faucet should be hot; the right, cold. It is also a universal convention that screw threads are made to tighten with clockwise turning, loosen with counterclockwise. You turn off a faucet by tightening a screw thread (tightening a washer against its seat), thereby shutting off the flow of water. So clockwise turning shuts off the water, counterclockwise turns it on.
