Foundation · Explanatory preview
A sign records direction
Choose right as positive and left as negative. Opposite displacements can cancel without either particle staying still.
Original explanatory text; editorial review pending. This is not a translated source passage.
How can movement add up to zero?
Put the starting point at zero on a ruler. A final mark three units right has displacement +3; one three units left has displacement −3. Adding the signed displacements gives zero. Adding the distances from the start gives six.
Displacement compares the final and initial positions. It is not the length of the path travelled between them.
One worked example
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.
A stopping point: The sign names a direction relative to a chosen axis; it does not mean a negative distance.
Read as Markdown · All foundations · Return to the Brownian argument
Your browser’s Back button returns to the passage that brought you here.