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Achilles and the tortoise

Achilles and the tortoise - one of the aporias of the ancient Greek philosopher Zeno .

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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.

 
Achilles and the tortoise - chase stages

Diogenes Laertius considered the author of this famous aporia Parmenides , teacher Zeno [1] . 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.

Aporia Resolution

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?" [2] .
  • 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 [3] :

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 [4] .

Comic Poems

The paradoxical situation described in the aporia is reflected in humorous verses and even in anecdotes [5] .

And where did you climb
Achilles?
He said: "There that garbage?
I'll catch up! ”
No one's mother,
don't catch
philosophical turtles
in turtles.
—— Eugene Lukin [6]

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 [7]

Notes

  1. ↑ Makovelsky A.O. Dosocracy. In 3 volumes. Chapter 15 - Minsk: Harvest, 1999 .-- 784 p. - (Classical philosophical thought). .
  2. ↑ Knowledge-Power, No. 9 (1991), “What did the Turtle say to Achilles?”
  3. ↑ Paul Valerie. Cemetery by the sea.
  4. ↑ BABYLON: Magazines. AUTHORNIK, issue 11: Linor GORALIK
  5. ↑ Zeno, Achilles and the tortoise
  6. ↑ Aporia of Zeno
  7. ↑ Aphorisms in the Literary Newspaper

Links

  • Achilles task // Brockhaus and Efron Encyclopedic Dictionary : in 86 volumes (82 volumes and 4 additional). - SPb. , 1890-1907.
Source - https://ru.wikipedia.org/w/index.php?title=Achilles_and_ turtle&oldid = 101006149


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Clever Geek | 2019