Achilles and the Tortoise
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Achilles and the Tortoise
Achilles and the Tortoise is similar. Suppose that the swift Achilles is having a race with a tortoise. Since the tortoise is much slower, she gets a head start. When the tortoise has reached a given point a, Achilles starts. But by the time Achilles reaches a, the tortoise has already moved beyond point a, to point b. And by the time Achilles reaches b the tortoise has already moved a little bit farther along, to point c. Since this process goes on indefinitely, Achilles can never catch up to the tortoise. -
HUH?
I dun understand wad u saying. -
so the faster guy runs, stops and runs, stops and run?
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rephrase
A 100 metre race has been arranged between Achilles and the tortoise. Of course Achilles can run much faster than the tortoise, so Achilles feels pretty confident of an easy victory. He therefore decides to make the race a little more interesting by giving the tortoise a 10 metre head start. Most of the spectators are sure that Achilles can easily make up the 10 metre deficit and they place bets on Achilles to win. The wise old Zeno, however, decides to bet on the tortoise. Zeno reasons as follows: The first thing Achilles must do is to run to the tortoise's starting position. But while Achilles is doing that, the tortoise, although slow, will move on to a new position. Next, Achilles must run to the tortoise's new position, but once again, while Achilles is doing that, the tortoise will move on a little further and so on and so on. No matter how small the gap between them is, while Achilles is closing the gap the tortoise is able to make a new gap. Zeno concludes that no matter how fast Achilles runs, he can never catch, let alone pass, the tortoise. Since Achilles can't pass the tortoise, so long as the tortoise keeps moving, the tortoise will win the race.
What do think about Zeno's reasoning? -
nt beri smart. if it's a say 100km race. the rabbit sure catch up in the end.Originally posted by unclebutcher:rephrase
What do think about Zeno's reasoning? -
WHERE GOT RABBITOriginally posted by motoway:nt beri smart. if it's a say 100km race. the rabbit sure catch up in the end.
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aiya, in reality, i think achilles wun lose la.
unless achilles is the name of another similar tortoise.
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hahahahaOriginally posted by ChoCoChips:aiya, in reality, i think achilles wun lose la.
unless achilles is the name of another similar tortoise. -
ok i tot achilies is rabbit. my bad.Originally posted by unclebutcher:WHERE GOT RABBIT
beri chim. but i still standyby zeno is lame. -
zeno is an old greek fartOriginally posted by motoway:ok i tot achilies is rabbit. my bad.
beri chim. but i still standyby zeno is lame. -
ROFLMAO!!Originally posted by unclebutcher:WHERE GOT RABBIT -
my money is on the SPARTANS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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i thought someone solved this before? go dig around for the answers
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just overtake the !@%$%$#% Tortoise!
no point just moving to its prior position...
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yeah i saw this before.
like the tortoise will always be infront of achilies by abit even if achilles speed is 10x faster.
i think the question goes sth like
if the tortoise speed is 1m/s and achilles is 10x faster which means 10m/s. achillies will never be able to catch up with the tortoise because
when achillies has ran a the 10m, the tortise willl be 1m infront.
then achilles run the 1m, the tortoise will be 0.1m infront and so and on and so for. -
the ans is clear. in this context Achilles lost, maybe, but in real life, sooner or later he'll catch up. the sorta 'new' gap that the slow dude makes each time is getting smaller and smaller. like duh?Originally posted by Xtrider:i thought someone solved this before? go dig around for the answers -
The problem is that the ancient Greeks did not know about calculus yet.
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basically the tortoise will always be 10% farthur than archilles
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lol...depends on whether u believe space is quantized?
heres another version i heard of sometime back:
suppose i shoot an arrow, the arrow must travel x distance to reach the tree. but before it travels x distance it must travel x/2 distance, and before that it must travel x/4 distance...neverending -
=/ if it's 100m race, achilles completes it in 10s and the tortoise completes it in 100s.Originally posted by stellazio:yeah i saw this before.
like the tortoise will always be infront of achilies by abit even if achilles speed is 10x faster.
i think the question goes sth like
if the tortoise speed is 1m/s and achilles is 10x faster which means 10m/s. achillies will never be able to catch up with the tortoise because
when achillies has ran a the 10m, the tortise willl be 1m infront.
then achilles run the 1m, the tortoise will be 0.1m infront and so and on and so for.
tortoise wins as he is given 91s headstart.
if achilles move another metre, the tortoise would move 0.1m or 1.1m? 1m can defnitely take over 0.1m -
Achilles run to the finish point, not to the tortoise's position.Originally posted by unclebutcher:rephrase
A 100 metre race has been arranged between Achilles and the tortoise. Of course Achilles can run much faster than the tortoise, so Achilles feels pretty confident of an easy victory. He therefore decides to make the race a little more interesting by giving the tortoise a 10 metre head start. Most of the spectators are sure that Achilles can easily make up the 10 metre deficit and they place bets on Achilles to win. The wise old Zeno, however, decides to bet on the tortoise. Zeno reasons as follows: The first thing Achilles must do is to run to the tortoise's starting position. But while Achilles is doing that, the tortoise, although slow, will move on to a new position. Next, Achilles must run to the tortoise's new position, but once again, while Achilles is doing that, the tortoise will move on a little further and so on and so on. No matter how small the gap between them is, while Achilles is closing the gap the tortoise is able to make a new gap. Zeno concludes that no matter how fast Achilles runs, he can never catch, let alone pass, the tortoise. Since Achilles can't pass the tortoise, so long as the tortoise keeps moving, the tortoise will win the race.
What do think about Zeno's reasoning?
Calculating distance over speed = time.
Speed of a 100m sprinter is 10m/s
Speed of a tortoise 0.133m/s
Time for achilles to finish race 100/10 = 10s
Time for tortoise to finish race 90/0.133=676.69s
if it is not a race, but chasing the tortoise, sure the gap will minimize until approximately zero. Then Achilles reach out his hands. -
Originally posted by SilverRevo:if it is not a race, but chasing the tortoise, sure the gap will minimize until approximately zero.
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like i said. just with a lot more explanation.Originally posted by SilverRevo:Achilles run to the finish point, not to the tortoise's position.
Calculating distance over speed = time.
Speed of a 100m sprinter is 10m/s
Speed of a tortoise 0.133m/s
Time for achilles to finish race 100/10 = 10s
Time for tortoise to finish race 90/0.133=676.69s
if it is not a race, but chasing the tortoise, sure the gap will minimize until approximately zero. Then Achilles reach out his hands.