Achilles and the tortoise - one of the aporias of the ancient Greek philosopher Zeno .
The fast-footed Achilles will never catch up with a leisurely turtle if at the beginning of the movement the turtle is in front of Achilles.
Suppose Achilles runs ten times faster than a turtle and is a thousand steps behind her. During the time that Achilles runs this distance, the turtle crawls a hundred steps in the same direction. When Achilles runs a hundred steps, the turtle will crawl another ten steps, and so on. The process will continue indefinitely, Achilles will never catch up with the turtle.
Diogenes Laertius considered the author of this famous aporia Parmenides , teacher Zeno  . The tortoise as a character was inserted by a later commentator, in the text of the aporia cited in Aristotle 's Physics, the swift-footed Achilles catches up with another runner.
The image of Achilles (Achilles) in the aporia is taken from the Iliad , where the hero of Achilles is repeatedly referred to as "swift." The plot of the aporia resembles the unsuccessful pursuit of Achilles after Hector ( chapter 22 ):
188. Hector, in pursuit of flight, drove Achilles unceasingly.
It’s like a dog driving a young deer in the mountains. <...>
199. As if in a dream a person cannot catch a person,
This one to run away, and the other to catch tense in vain, -
So the heroes, neither this will not catch up, neither that leaves.
One of the possible explanations of the paradox: the falsity of the idea of the infinite divisibility of distance and time.
Aporia in Literature and Art
- Lewis Carroll wrote a dialogue with logical riddles called "What did the Turtle say to Achilles?"  .
- Leo Tolstoy in the third volume of the epic “ War and Peace ” (beginning of the 3rd part) retells the paradox about Achilles and the tortoise and offers his own interpretation: you cannot divide continuous movement into “separate units” (probably, points are meant). Then Tolstoy, by analogy, discusses the role of the individual in history.
- Paul Valerie in the poem “Cemetery by the Sea” ( Le Cimetière Marin , 1920) wrote  :
Zeno of Elea, smashing thought,
He pierced me through a trembling arrow
Though he neglected her flight.
I was born by sound, struck by an arrow.
Will the turtle’s shadow really cover me
Real Achilles fast run!
- Aporia about Achilles is repeatedly mentioned in the works of Borges .
- Takeshi Kitano made the film Achilles and the Turtle in 2008.
- These characters are found in the Dialogues of the book by Douglas Hofstadter " Godel , Escher , Bach - this endless garland."
- In 2003, the poet, essayist and journalist Linor Goralik wrote the work “Achilles speaks to the tortoise”, later published in Max Frey's Book of Solitude  .
The paradoxical situation described in the aporia is reflected in humorous verses and even in anecdotes  .
And where did you climb
He said: "There that garbage?
I'll catch up! ”
No one's mother,
—— Eugene Lukin 
Achilles fled while the tortoise
Drew him to the edge of the earth.
The hero thought, not without fear:
“I’m not catching up with something here!”
—— Konstantin Efetov 
- Makovelsky A.O. Dosocracy. In 3 volumes. Chapter 15 - Minsk: Harvest, 1999 .-- 784 p. - (Classical philosophical thought). .
- Knowledge-Power, No. 9 (1991), “What did the Turtle say to Achilles?”
- Paul Valerie. Cemetery by the sea.
- BABYLON: Magazines. AUTHORNIK, issue 11: Linor GORALIK
- Zeno, Achilles and the tortoise
- Aporia of Zeno
- Aphorisms in the Literary Newspaper
- Achilles task // Brockhaus and Efron Encyclopedic Dictionary : in 86 volumes (82 volumes and 4 additional). - SPb. , 1890-1907.