Zeno's Paradoxs

[NikonL]

These are irritating the crap out of me.

Most of you have probably heard of Zeno, he's the guy who said you couldn't hit a tortoise with an arrow, and that movement is impossible etc.

Now obviously these are wrong, but i can't work out how you disprove them >.< and the internet is not helping currently. Anyone able to put into idiot-speak for me exactly where these paradoxs fall down?

 

[megadave]

heh. just read up to see what the hell your talking about and it basically just pissed me off, what a laod of crap ;/

 

[kivik]

I remember one, I think.

Zeno claimed if Hercules and a toroise would race, and the tortoise started 10m ahead of Hercules, Hercules would never reach and pass the tortoise.

Since Hercules runs half of the distance to the tortoise in X seconds he would after the first X seconds have 5m to reach the tortoise, after another X seconds 2,5m and after another X seconds 1,25m. So Zeno's conclusion was that Hercules would never reach and pass the tortoise.

The disproval is obvious, if Hercules runs 10/2 metres in X seconds, it means he runs 10m after 2X seconds and is 5m ahead of the tortoise after 3X seconds.

Think that's the simpliest though, haven't seen any others.

 

[Bugz]

I remember one, I think.

Zeno claimed if Hercules and a toroise would race, and the tortoise started 10m ahead of Hercules, Hercules would never reach and pass the tortoise.

Since Hercules runs half of the distance to the tortoise in X seconds he would after the first X seconds have 5m to reach the tortoise, after another X seconds 2,5m and after another X seconds 1,25m. So Zeno's conclusion was that Hercules would never reach and pass the tortoise.

The disproval is obvious, if Hercules runs 10/2 metres in X seconds, it means he runs 10m after 2X seconds and is 5m ahead of the tortoise after 3X seconds.

Think that's the simpliest though, haven't seen any others.

Depends how the question is worded tbh.

 

[kivik]

Checked it up on teh internet and found it was Achilles and not Hercules, and the paradox wasn't exactly like i retold it but it was something like that...

Here's from wiki.

Achilles and the tortoise
"You can never catch up."

"In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead." (Aristotle Physics VI:9, 239b15)

In the paradox of Achilles and the Tortoise, we imagine the Greek hero Achilles in a footrace with the plodding reptile. Because he is such a fast runner, Achilles graciously allows the tortoise a head start of a hundred feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run a hundred feet, bringing him to the tortoise's starting point; during this time, the tortoise has "run" a (much shorter) distance, say one foot. It will then take Achilles some further period of time to run that distance, in which said period the tortoise will advance farther; and then another period of time to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, Zeno says, swift Achilles can never overtake the tortoise. Thus, while common sense and common experience would hold that one runner can catch another, according to the above argument, he cannot; this is the
paradox.

Achilles runspeed isn't depending on the length between him and the tortoise.

then after some finite time, Achilles will have run a hundred feet, bringing him to the tortoise's starting point; during this time, the tortoise has "run" a (much shorter) distance

After another some finite time Achilles still will have run a hundred feet while tortoise has only moved a short distance.

 

[NikonL]

"A thought experiment used against the calculus-based solution is as follows. Imagine that Achilles notes the position occupied by the tortoise, and calls it first; after reaching that position, he once again notes the position the turtle has moved to, calling it second, and so on. If he catches up with the turtle in finite time, the counting process will be complete, and we could ask Achilles what the greatest number he counted to was. Here we encounter another paradox: while there is no "largest" number in the sequence, as for every finite number the turtle is still ahead of Achilles, there must be such a number because Achilles did stop counting."

It just gets more mind boggling :/

 

[Darzil]

However, the infinite series of finite numbers, in this case, sums to a finite number. Hence, no paradox.

Darzil

 

[crispy]

I like this paradox better:

Could god microwave a burrito so hot he couldnt eat it?

(Paradox since god can do everything.. or so we are to believe!!!)

 

[tris-]

Most of you have probably heard of Zeno, he's the guy who said you couldn't hit a tortoise with an arrow, and that movement is impossible etc.

absolutley not, but sounds like hes talking bullshit.

i can see no physical reason why you couldnt hit a tortoise with an arrow.

and as far as movement being impossible, i could only class that as a "bull shit statement" as i, personally, am free to move when ever i like