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Paradoxical fall

8 November 2019

Walking quietly on the streets of our beautiful city, with its walls adorned by the colorful graffiti of a fellow citizen who shows his disagreement with the system; It is the movement of a drop that falls on my face that announces the second downpour of the day. Without wasting time I seek shelter under some roof, because experience has taught me that it will not take long for fear of the one who has put to dry his freshly washed clothes.

When placed under the protection of the marquee of a store, which by bad luck is closed; the rain falls that forces the unsuspecting to run randomly, in search of the most convenient place to spend the next few minutes in the company of strangers. During this time interval, I see someone running who, in his attempt to avoid getting wet, slips, and before falling he walks the amazing two meters.

The movement from the point of view of Zeno?

The displacement is perceived so slowly that you can see the succession of images that completes the journey to its fateful end. Each of these images corresponds to a precise moment in the total time it takes for the unfortunate to reach the ground. As well as in the paradox of the philosopher of ancient Greece Zeno of Elea (c. 490-430 a. C.). https://es.wikipedia.org/wiki/Paradojas_de_Zen%C3%B3n

For the unfortunate to reach the ground, he must first travel half of the total distance, it is at this moment that an image corresponds to him; then it travels half of the remaining segment, that is, a quarter of the total distance, to which another image corresponds, possibly very different from the first; on the eighth part there is another different image, on the sixteenth part there is another image, on the thirtieth part there is another image, and so on. In this way all the action has been divided indefinitely into images that are placed at the proportion of a medium; that is, they are always placed in the middle of the remaining segment.

An infinite movement

If Zeno was right, and the movement was nothing more than an illusion of our senses, our unfortunate friend would keep falling paradoxically forever without knowing the pain caused by the fall. However, as Aristotle thought, it would not be possible to divide this trajectory indefinitely, which has as an end the unfortunate "splash" of the shock of a body with a body of water.

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