How to debunk Zeno's paradox of Achilles and the tortoise.

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Marius Dejess

Senior member
Sep 7, 2015
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I guess every school boy knows the idea of Zeno that Achilles cannot catch up with the tortoise in a race if he gives the tortoise any head start, because as Achilles takes the first step to catch up with the tortoise, he has to first cover 1/2 of the first step, but before he can cover this first 1/2 of the first step, he must first cover 1/2 of 1/2 of the first step, and on and on, so that Achilles will never catch up with the tortoise, for there is always another 1/2 distance of the preceding 1/2 distance.

Now, I will make up some kind of fiction narrative on how Aesop enables any school boy with a good brain to solve the socalled paradox of Zeno.

"Aesop tells us that when a naughty boy kicked the butt of Zeno, Zeno complained to his parents, but the boy told his parents: 'Zeno tried to convince his listeners that I could never reach his butt'."

What do you guys here say about my first message to start the present thread?
 
PowerEngineer

PowerEngineer

Diamond Member
Oct 22, 2001
3,597
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The trick is to understand that the time that passes between each halving step is also halving, and so the description of the situation made by the paradox is only valid for the period of time up to the sum of the infinite series of those halving time periods. Spoiler alert! The sum of the infinite series turns out to be the time it takes for Achilles to catch the tortoise.
 
DigDog

DigDog

Lifer
Jun 3, 2011
14,368
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the "paradox" explains a fallacy in reasoning - it does not actually model the movement of two bodies.
if we have to do the homework for you, just ask "why does the unit of measure change after the first measurement?".
whatever they reply then say "obviously achilles cannot overtake the turtle prior to overtaking the turtle. events cannot occur prior to themselves."
then go on mentioning vectors, how velocity calculation remain constant regardless of the time sample size, etc..
 
M

Marius Dejess

Senior member
Sep 7, 2015
320
34
101
PowerEngineer said:
The trick is to understand that the time that passes between each halving step is also halving, and so the description of the situation made by the paradox is only valid for the period of time up to the sum of the infinite series of those halving time periods. Spoiler alert! The sum of the infinite series turns out to be the time it takes for Achilles to catch the tortoise.
Click to expand...

Dear Power, what is this "Spoiler alert!" about? I feel that you mean that I am going to give my own explanation why paradoxes don't really exist except inside our mind.

If that is what you are saying, I tell you, You are correct.

Paradoxes are due to abstract thinking in man's mind, which kind of thinking is missing all the circumstances that are not factored into the thinking of man, that is why Zeno sees a paradox inside his mind.

But if he factors in the circumstances of an event in his thinking, then there is no paradox at all.

Zeno divides distance which he can do in his mind forever and ever were he living forever, but he neglects to factor in time, and thus he sees the paradox that Achilles cannot catch up with the tortoise, because there is always a shorter and shorter distance between Achilles and the tortoise, no matter how short the distance between him and the tortoise.

If he factors in time, he will see that in the same time that covers both Achilles and the tortoise, the distance between them will get shorter and shorter in time, and sooner than later, Achilles catches up with the tortoise and then overtakes the tortoise.

That is why in concrete reality the naughty boy can kick the butt of Zeno, even though Zeno in his mind sees that there will be always some distance between himself and the tortoise or the naughty boy, as he divides the distance into halves on and on and on... and failing to factor in time.
 
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