How tall is a mountain, exactly?

A mountain's height is measured from sea level, and sea level is not level. The sea is pulled about by the moon, pushed by the wind, and sits higher where the Earth's gravity is slightly stronger. Two survey teams using two definitions of 'sea' can disagree about a summit by several metres, and both are right.

Modern surveys use a mathematical sea, a smooth surface that the real ocean would settle to if it were calm and continuous under the continents. Even that moves a little as the models improve. The world's tallest peak has been re-measured several times, each time with better instruments, each time with a slightly different answer.

None of this makes the mountain shorter or taller. It makes the number on the sign a decision rather than a fact, which is true of more numbers than we like to admit. The mountain, for its part, does not mind.