# A sign records direction

Choose right as positive and left as negative. Opposite displacements can cancel without either particle staying still.

Written for this edition, not translated from Einstein.

## How can movement add up to zero?

On the ruler below, the starting point is zero. A final mark three units to the right has displacement +3; one three units to the left has displacement −3. Adding the signed displacements gives zero. Adding the distances from the start gives six.

Displacement compares where something ends with where it started, whatever it did in between. A walker who goes three units right and comes back has displacement zero after walking six, which is the lower pair of arrows in the drawing.

## Worked example: Two walkers, opposite directions, average zero

Two walkers both finish one unit from their start, one at −1 and the other at +1. The signed average is zero. The average distance is one.

## Where this lesson stops

The sign names a direction relative to a chosen axis; it does not mean a negative distance.

## This lesson builds on

- [Adding and averaging](/foundations/bridge-sum-average/)