Arrow Paradox
Paradox
At any particular instant, a moving arrow is either at rest or in motion.
If the instant is indivisible, the arrow cannot move, because if it did, the instant would immediately be divided.
But time is made up of instants.
As the arrow cannot move in any one instant, it cannot move in time.
Hence the arrow remains at rest.
Resolution
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This is an example of how an incorrect model of reality (time is made up of instants) leads to incorrect predictions (movement is impossible).
Might be able to invoke set theoretical results concerning the notion that time is a continuum and therefore composed of an uncountable number of instants, then deduce the existence of a time interval by invoking something from measure theory. Parp.
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Historical Note
The Arrow Paradox is one of Zeno's Paradoxes, as famously raised by Zeno of Elea.
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{II}$: Modern Minds in Ancient Bodies
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Entry: Zeno's paradoxes
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: Zeno of Elea (5th century bc)