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Here's one resolution to the Arrow paradox: Zeno imagines that the state of the arrow must be represented by a single number--its position. But if its state in

Here's one resolution to the Arrow paradox: 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.

pontifier 12y ago
Another way that does not require any changes is if the arrow is made of multiple particles (which they are). Then some portion of the particles may move from step to step. These particles then interact with others which are stationary, passing their motion to them for the next step. Thus the total speed of any composite object would be the ratio of how many of the particles are "moving", to how many are "stationary" at that step.
- MildlySerious 12y ago
  Wouldn't that imply that the size of objects influences the way they could possibly move?