Is Motion Really Impossible Due to the Infinite Divisibility of Space?

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SUMMARY

The discussion centers on the philosophical paradox of motion, specifically referencing Zeno's paradoxes. It argues that due to the infinite divisibility of space, a runner attempting to cover 100 meters must first reach an infinite number of midpoints, making motion seemingly impossible. However, counterarguments highlight the importance of time in this equation, suggesting that an infinite series can indeed sum to a finite distance, thus allowing for motion. This debate illustrates the complexities of motion and perception in physics and philosophy.

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A runner wants to run a certain distance - let us say 100 meters - in a finite time. But to reach the 100-meter mark, the runner must first reach the 50-meter mark, and to reach that, the runner must first run 25 meters. But to do that, he or she must first run 12.5 meters.

Since space is infinitely divisible, we can repeat these 'requirements' forever. Thus the runner has to reach an infinite number of 'midpoints' in a finite time. This is impossible, so the runner can never reach his goal. In general, anyone who wants to move from one point to another must meet these requirements, and so motion is impossible, and what we perceive as motion is merely an illusion.


Motion is impossible; doesn’t this just defy all logic? I think it’s a hoax.
 
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Zeno already did this. What he and you are forgetting is that time is involved, not just distance.
 
And, if I understand correctly, that an infinite series can sum to a finite number.
 

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