Zeno's Paradox and Planck Units

Zeno imagines that the state of the arrow must be represented by a single number--its position. But if its state includes a second number, velocity, the paradox goes away.

Imagine the arrow's life is a game played on a checkerboard. Its column represents its position in space, and its row represents its velocity. On each turn, if the arrow is in the first row, it moves one column to the right; if it is in the second row, it moves two columns to the right; in the third row three columns, and so on.

This game is easy enough to imagine, and represents both time (turns) and space (columns) discretely. No paradox here. No quantum mechanics either.