Achilles and the turtle

Achilles and the turtle

Welcome back to our new philosophy lesson!

Do you like turtles? Have you ever seen one close to you? You surely know that there are some of them who live and swim in the waters of the sea or of a lake and that there are others who spend their life on the mainland.


Eccone una di terra! Osservate il suo sguardo attento e consapevole. fonte:

sea turtle

Guardate: qui c’è una bella tartaruga di mare che nuota circondata da due pesciolini. Chissà dove sta andando? fonte:

Surely now you’re wondering why I’m talking about this animal and its habitats. The reason is very simple: the movement or better its slow moving.

Now I ask you a question: in a race on the mainland, between you and a turtle, who would win? You? Are you sure?

I am sorry but the philosopher Zeno of Elea who lived around 450 a.C. will surprise you with his answer.

Zeno was a careful and acute thinker and a pupil of another important philosopher, Parmenides. He said that there is no movement and that each of our acts is only an illusion. In short, for Parmenides, although we are moving, we are actually static.

Now look at the picture:

Achille and turtle

fonte: Di Daniele Pugliesi – Opera propria, CC BY-SA 3.0,

The photo shows the “paradox of Achilles”, the most famous argument of our friend Zeno. Achilles, Greek hero and among the characters of the Iliad of Homer, one day  decided to compete in a racespeed with a turtle giving a few meters of advantage to the animal.

“Achilles runs […] ten meters and the tortoise runs a meter; Achilles runs that meter, the turtle runs a decimeter; Achilles runs that decimeter, the tortoise runs a centimeter; Achilles runs that centimeter, the tortoise runs a millimeter; Achilles runs that millimeter, the tortoise runs a tenth of a millimeter, and so on to infinity; so that Achilles can run forever without reaching it “. (from

As fast as he can run, the turtle will always keep its little advantageand so, even if Achilles runs faster than the turtle, he will never reach it. The space is divisible to infinity and Achilles, in his finitude, will never be able to cover the infinite of the finite space.

So my little philosphers, in a race not everything is as obvious as you might think. Expect always surprises!

At the next lesson and good philosophy!

Maria Domenica Depalo


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