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Achilles and the Tortoise (Zeno's paradoxes)

Is one of the most famous adventure in thought.

The basic question is: How can a turtle beat a human in a race?

According to Zenon the answer is simple: Just give the turtle a headstart.

To overtake the turtle Achilles has to first move to the point where the turtle started.

While Achilles has to catch up the gap between Achilles and the Tortoise will become smaller and smaller. 



Here is what happens: Step by step:

Achilles and the Tortoise (Start)

First the turtle is given a headstart of 100 m.

Achilles and the Tortoise (shortly after start)

Since Achilles was the son of a god he can run the first 100 m in 8s. Lets say that the turtle is runs in these 8 s 50 m. So the gap between the turtle and Achilles is now only 50 m.


When Achilles has run the next 50 m the turtle has run 25 m. However Achilles needs just 4 s for the 50 m.


Achilles runs the next 25 m in just 2 s. The turtle is still leading.


Achilles and the Tortoise (End)

However, after 16 s Achilles has overtaken the turtle. Since the gap (and the time to close the gap) became at this point infinitive small. 

What we can learn from this story is that something finite can be devided in something infinete small.

Here the headstart as well as the time to catch up is devided in infinite small parts.