The title alludes to
one of Zeno’s paradoxes of motion
, in which Achilles could never overtake the tortoise in a race. In Carroll’s dialogue, the tortoise challenges Achilles to use the force of logic to make him accept the conclusion of a simple deductive argument.
What did the tortoise say to Achilles jstor?
“
So you’ve got to the end of our race-course?
” said the Tortoise. “Even though it does consist of an infinite series of distances ? I thought some wiseacre or other had proved that the thing couldn’t be done ?” ” It can be done,” said Achilles. “It has been done!
What the tortoise said to the hare?
A hare insulted a tortoise on account of his slowness, and vainly boasted of her own great speed in running. “Let us make a match,” replied the tortoise. “
I’ll run you five miles for five pounds, and the
fox yonder shall be umpire of the race.”
Why can Achilles pass the tortoise?
Zeno’s argument rests on the presumption that Achilles must first reach the point where
the tortoise started
, by which time the tortoise will have moved ahead, even if but a small distance, to another point; by the time Achilles traverses the distance to this latter point, the tortoise will have moved ahead to another, …
How many steps did it take the tortoise to get to Achilles?
If the tortoise starts the race
20
Achilles-steps ahead of him, then after 20 steps Achilles reaches where the tortoise was (See diagram below: Tortoise starting point). In the meantime, the tortoise has made 20 of her steps, and she is now one full Achilles-step ahead of him.
What did Achilles say to the tortoise?
“Then I shouldn’t be here,” Achilles modestly replied; “and you would have got several times round the world, by this time!” “You flatter me—flatten, I mean” said the Tortoise; “
for you are a heavy weight, and no mistake!
Why Zeno’s paradox is wrong?
It might seem counterintuitive, but pure mathematics alone cannot provide a satisfactory solution to the paradox. The reason is simple: the paradox isn’t simply about dividing a finite thing up into an infinite number of parts, but
rather about the inherently physical concept of a rate
.
What is the moral of the hare and tortoise?
The hare is very confident of winning, so it stops during the race and falls asleep. The tortoise continues to move very slowly but without stopping and finally it wins the race. The moral lesson of the story is that
you can be more successful by doing things slowly and steadily than by acting quickly and carelessly
.
Why does the tortoise wins the race?
Competing in a race, everyone thought the hare would win, the tortoise had a surprising victory. While he was clearly outclassed in speed, the tortoise focused on the finish line.
Steady and plodding he made consistent motion forward
, ultimately winning the race.
What is the main idea of the tortoise and the hare?
The tortoise wins the race by cunning while the hare fails because he overestimates himself and takes a nap during the race. The moral of the story is
“slow and steady wins the race”
which is incorporated in the game mechanic.
Who is the slowest Achilles or tortoise?
Achilles’ speed is 100 metres per minute and
the tortoise’s
speed is 1 metre per minute (the actual numbers don’t matter). Achilles is 100 times faster than the tortoise, so let’s give the poor animal a very large head start: 100m.
Is Achilles and the tortoise solved?
Although the numbers go on forever, the series converges, and
the solution is 1
. As long as Achilles is making the gaps smaller at a sufficiently fast rate, so that their distances look more or less like this equation, he will complete the series in a measurable amount of time and catch the tortoise.
What did Zeno’s paradoxes attempt to prove?
Learn about Zeno’s Achilles paradox. Paradoxes of Zeno, statements made by the Greek philosopher Zeno of Elea, a 5th-century-bce disciple of Parmenides, a fellow Eleatic, designed to
show that any assertion opposite to the monistic teaching of Parmenides leads to contradiction and absurdity.
How do you solve Achilles and tortoise?
According to Zeno’s argument, Achilles can never overtake a tortoise in a footrace if he gives him a head start. In order to pass the tortoise,
Achilles must first reach the initial position of the tortoise
. But during this time, the tortoise moves ahead. Achilles must then reach the new position.
What is the mistake in Zeno’s logic?
The faulty logic in Zeno’s argument is often seen to be the
assumption that the sum of an infinite number of numbers is always infinite
, when in fact, an infinite sum, for instance, 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +…., can be mathematically shown to be equal to a finite number, or in this case, equal to 2.
Why according to Zeno should it be impossible for Achilles to catch the tortoise?
And so on to infinity: every time that Achilles reaches the place where the tortoise was, the tortoise has had enough time to get a little bit further, and so Achilles has another run to make, and so Achilles has an infinite number of finite catch-ups to do before he can catch the tortoise, and so, Zeno concludes,
he
…
