Zeno's Paradox can be expressed by considering turning a page in a book half way the distance from being fully turned. Then, turning it half the remaining distance. Then, half the remaining distance, ad infinitude. Another premise is added that there are an infinite number of points between each halved distance. Finally, the question is posed: How can the page ever fully turn, since it would take eternity to pass an infinite amount of points?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks to Galileo, this paradox can be proven not to be a paradox, but a confusion in physical properties of motion.

The page turns past the first half distance, half way across the book. Let us say it has moved with a constant speed.

Now, we use the same speed as it crosses the second half.

Now as we continually do this, what is occurring with time?

Time is being halved with a constant speed, because the distance is being halved. Since, the remainder of time to fully turn the page is being continually being halved, there will never be enough time to cross the full distance.

Zeno conveniently cuts the very last moment in two, halving time and distance, making it seem impossible to pass the very last distance. Ironically, Zeno uses the common sense premise that the page does pass the first half of prior distances to base his argument. But, why would it not pass another equal half successfully, as his argument is based upon?

It would. Even if the nonsense scenario that the last smallest half point is nothing, it would take no time to pass it, because it is not a distance at that point. It is not a paradox in terms of the basic formula that Galileo pointed out: speed = distance over time.

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# Debunking Zeno's Paradox with Galileo's Speed

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