I just read about this in Dawkin's God Delusion and thought it was an interesting thought exercise. It's no plane on a treadmill but interesting to think about. Reproduced sans permission from planetmath.org (don't click this link if you don't want to read the maths answer):

Imagine the great Greek hero Achilles starting a race with a turtle. Achilles is a fast runner, running 10 metres per second, while the turtle is slow and runs at one metre per second. Therefore Achilles agrees to give the turtle some advantage and the turtle starts 10 metres in front of Achilles. The ancient Greek philosopher Zeno found the following “paradox”.

If Achilles wants to get in front of the turtle he first has to run to where the turtle started. But in that time the turtle has bridged some distance, which Achilles now has to run in order to take up. But in this time again the turtle has gone for some distance and Achilles is still in behind of the turtle. This process continues forever and apparently Achilles cannot pass the turtle.

That's silly, of course if you keep taking infinitely small slices of time the universe will end before you take enough of those slices to prove that the tortoise will be overtaken, but take a huge slice of time.. i.e. 100 seconds and you can see Achilles wins. (or you can just look at the math proof)

lol, not this again :)

I'm sure everyone has seen this, pretty cool.

hm. im about to start the god delusion myself.

dont spoil the ending!

Spoiler:
jesus comes back and you all go to hell

Freewheelin this is the ending

PRIME Minister John Howard has made a strong pitch for the Christian and family vote with a $189 million package to provide a free internet filter for every Australian family in a bid to fight pornography and foul language online.

That's the result of the God delusion.

I think the question could have been worded slightly differently so it seemed much less intuitive.

It's no plane on a treadmill

Well them my care cup is empty.

Obviously Achilles takes an arrow to the heel and the tortoise wins.

lolz... turtle. No big deal.

My life has no tortoise.

What kind of a race is it where one entrant seeks only to catch up with another? No, Achilles is only aiming for the finish line, not the tortoise.

I like turtles!

this seems kinda dumb to me?

after 1 second, achilles is on the 10metre mark, turtle is on 11metre mark, after 2 seconds achilles is on 20metre mark, turtle on 12metre mark.

am i missing something here?

I'm with the cock

yes le cock you are

is the turtle on a treadmill?

The plane takes off

yes le cock you are

He forgot to pre-empt s***kickers responding with their wild ramblings.

dont spoil the ending!

The 'ending' is you then go out and buy "Letter to a Christian Nation" by Sam Harris, "Six Impossible Things Before Breakfast - The Evolutionary Origins of Belief" by Lewis Wolpert, and then, most importantly, "God is Not Great - how Religion Poisons Everything" by Christopher Hitchens.

Hitchens is far more convincing than Dawkins, but also far more agressive and scathing.

If it was Chuck Norris, he'd win.

zeno was a noob

What kind of a race is it where one entrant seeks only to catch up with another? No, Achilles is only aiming for the finish line, not the tortoise.

you missed the point. Achilles is aiming for the finish line. what he is doing is taking screenshots of time at an increasing rate.

basically:

turtle at 10m at 0 sec
Achilles at 0m at 0 sec

turtle at 11m at 1 sec
Achilles at 10m at 1 sec

turtle at 11.1m at 1.1 sec
Achilles at 11m at 1.1 sec

turtle at 11.11m at 1.11 sec
Achilles at 11.1m at 1.11 sec.

this gives the appearance that Achilles will never catch up. however if we increase the time to say 1.2 sec, we will see that Achilles will indeed over take (as logic dictates).

Thats f***ing stupid.

It's like this little idea I read about ages ago.

It's like halving a distance over and over to reach a stationary point, you will never reach it no matter how many times you add that halved distance.


Say you start 10m away from a stationary object, you need to half that distance every time to move back closer to it. So you move 5m closer the first time, 2.5 the second time etc etc. You will never get back to that 10m distance, sort of the same idea I spose but opposite.

|__________

|_____

|__

if that makes sense.

We covered this in Maths C in high school (along with other 'cool' things like proof that 0.9999~ = 1 etc).

Trog - did you read the whole book? I watched his 2 part doco (Roof of Evil) on youtube & then bought the book. Since then I bought & read several other of his books.

^ that's just a simpler version of the same "paradox".

you missed the point. Achilles is aiming for the finish line. what he is doing is taking screenshots of time at an increasing rate.

I know what the point is, I just think it's stupid. People always fall into the same mindset trap, why not think a bit laterally for a change? If the finish line is 100 metres away, and Achilles is running at 10 metres a second (and the tortoise is "running" at 1 metre per second), it'll take Achilles 10 seconds to reach the goal, and the tortoise 100 seconds. The rest isn't relevant.

last edited by icewyrm at 12:29:03 12/Aug/07

that's why it's a paradox

I know what the point is, I just think it's stupid. People always fall into the same mindset trap, why not think a bit laterally for a change? If the finish line is 100 metres away, and Achilles is running at 10 metres a second (and the tortoise is "running" at 1 metre per second), it'll take Achilles 10 seconds to reach the goal, and the tortoise 100 seconds. The rest isn't relevant.

If everyone thought like you and didn't bother thinking of mathematical proofs of stuff that just sounds "common sense", then we wouldn't have stuff like Calculus (or even discrete maths).

Without calculus ... let's just say we'd still be in the bronze age.

last edited by parabol at 15:15:35 12/Aug/07

^ that's just a simpler version of the same "paradox"

I agree it too is a paradox, but not really along the same lines? ie,

Let x = 0.9999~
then 10x = 9.99999~

10x - x = 9.99999~ - 0.999999~ = 9
hence x = 1

uh i meant the post above yours...

People always fall into the same mindset trap, why not think a bit laterally for a change?

Yes, you need to think pretty laterally to wonder if a running human is going to beat a turtle in a foot race

Fine

PRIME Minister John Howard has made a strong pitch for the Christian and family vote with a $189 million package to provide a free internet filter for every Australian family in a bid to fight pornography and foul language online.

That cocksucking motherf***er

pfft, straight in the bin or a big fat RETURN TO SENDER.

See, the thing is, this paradox is a boring one that defies common sense (sence?). We need challenging ones, like planes and snakes........and treadmills.

I dunno if this is a paradox or not.....i have never actively researched the finer points of such things......that one about an all powerful god, went something like could god create a rock so heavy it was unliftable, followed by could the god then create an army of ants strong enough to lift the rock.....eh? eh? Yeah probably a common boring one, but when i heard it years ago, i thought it was neat. Again, on the surface i reckon it pwns christian noobs.......now, carry on

comon seriously. if Achilles is on the treadmill and and tortoise has wind coming over his shell then clearly we would be be in a parallel universe

ITS SCIENCE DO SOME RESEARCH MORANS

This is why I prefer Physics... Pure Math just gets so whacky with stuff that sometimes defines a common sense.