Zeno's paradox.

[NotATool]

In order to move a distance x, you have to move x/2.
In order to move a distance x/2, you need to move x/4.
And so on.

This is the sum of (1/t)^n from t = 0 -> infinity, which has no finite answer.

Is movement impossible?
My physics proffessor was unable to give me any proper explanation.

 

[Que-Ever]

typing..typing...typing...
moving? yes, I believe so. Maybe not mathematically possible, but measurements are so innaccurate I don't believe in them anyway.

*does a dance*

 

[NotATool]

typing..typing...typing...
moving? yes, I believe so. Maybe not mathematically possible, but measurements are so innaccurate I don't believe in them anyway.

Measurments?

This has nothing to do with measurements.

 

[Ikerous]

The infinite series ∑(x)^n is always convergent if |x| < 1

In the case of ∑(1/t)^n from 1->inf, |1/t| < 1 for all values of t greater than 1
So it definitely converges

As to the actual paradox, ::Shrugs::
I think calculus itself is proof that infite divisions in something can be finite

 

[Que-Ever]

Measurments?

This has nothing to do with measurements.

yeah, well... I'm dumb, so don't pay me any attention.
*continues dance*

 

[Ikerous]

More people should post in math threads

 

[madog]

madog's solution: in order to move 1 foot, you don't move .5 foot, you move 1 foot. So I declare this paradox stupid and void.

 

[Ikerous]

madog's solution: in order to move 1 foot, you don't move .5 foot, you move 1 foot. So I declare this paradox stupid and void.

How do you manage to move one foot without first moving half a foot?
I wish i could teleport too

 

[JellyWorld]

An infinite sum of finite numbers is not necessarily infinite.


1 + 0.1 + 0.01 + 0.001 .... is an infinite sum of finite numbers, but it adds up (or tends to, rather) to 10/9, which is hardly close to infinity.

This is the sum of (1/t)^n from t = 0 -> infinity, which has no finite answer.

It's sum[(1/2)^n] from n = 0 -> infinity, actually.

 

[NotATool]

An infinite sum of finite numbers is not necessarily finite.


1 + 0.1 + 0.01 + 0.001 .... is an infinite sum of finite numbers, but it adds uo (or tends to, rather) to 10/9, which is hardly close to infinity.

I know, but not this particular sum I don't think.

 

[JellyWorld]

I know, but not this particular sum I don't think.

It's the same principle, except you're using 1/10 instead of 1/2.

You're trying to find a geometric sum, and the formula for doing so is

In this case, a = 1/2, r = 1/2, and n is infinity (hence r^n = 0).

So you get (1*1/2)/(1-1/2) = 1, hence you move 1 foot.

 

[JellyWorld]

Another way of doing it is consider the

1 + 0.1 + 0.01... example in binary.

(binary) 1 = 1 (base 10)
(binary) 0.1 = 1/2 (base 10)
(binary) 0.01 = 1/4 (base 10)

So 1/2 + 1/4 + 1/8 etc. = 0.111111111111111...... in binary, which is finite.

 

[xcellerate]

42?

Man, i feel stupid, i don't even see the problem. So to move 1 foot, i have to first move .5 feet, but to move .5 feet i must first move .25 feet, and to move .25 feet i must first move .125 feet, etc?

That can't be what you're saying though, because i don't see a paradox. Of course movement is possible. We do it everyday.

 

[Ikerous]

Of course movement is possible. We do it everyday.

Maybe you do Me, i never leave this computer.

 

[JellyWorld]

Actually, the original Zeno's paradox was that it was impossible for an athlete to catch up with a turtle, because by the time the athelte had gotten to where the turtle last was, the turtle had already moved forward a bit.

 

[xcellerate]

Actually, the original Zeno's paradox was that it was impossible for an athlete to catch up with a turtle, because by the time the athlete had gotten to where the turtle last was, the turtle had already moved forward a bit.

what the hell, how does this make any sense?

This is like the airplane joke all over again...[over my head]

How can that be a paradox when i can take a turtle and an athlete go outside and PROVE, 100 times over that an athlete can in fact catch up to, and pass, a turtle.

-------------------------------------------------

Oh that is stupid! I just read the article, and it goes something like this:

Turtle and guy start a race
Turtle gets 10 meter head start

--race starts--
ten meters between them
guy covers ten meters
turtle covers 2 meters
Two meters between them
---
guy covers 2 meters
Turtle covers 1 meter
One meter between them
---
rinse and repeat



That is THE dumbest 'paradox' i have EVER heard of. I can't even believe he's famous for that garbage. Where would this 'paradox' ever be used that you could prove it's a paradox?? That' not how races work, if the guy covers 5m/s and the turtle covers 1m/s then after 3 seconds, the guy would be in front!

Turtle - 10
Guy - 0
---1 second---
Turtle - 11
Guy - 5
---2 seconds---
Turtle - 12
Guy - 10
---3 Seconds---
Turtle - 13
Guy - 15

Wow...I'm gonna make up some stupid 'paradox' now and be remembered for the next 2000 years.

 

[_Z_Ryuken]

The infinite half-distances are made up and do not have to exist.

 

[15357]

I've heard of this, and why its wrong is in the thinking of this paradox.

 

[JellyWorld]

How can that be a paradox when i can take a turtle and an athlete go outside and PROVE, 100 times over that an athlete can in fact catch up to, and pass, a turtle.

Actually, that's what supposedly makes it a paradox, because one can easily observe that the athelete can catch up in the real world, whereas the mathematical reasoning allegedly states that it can't. Of course, the logic behind it is faulty.

 

[clarky003]

I think Jellyworld should randomly write some mathmatical equation that explains his avatar.

 

[Alexferris]

I think Jellyworld should randomly write some mathmatical equation that explains his avatar.

1/2log3.5^(1/3log3.9^x)

1 + 1.

 

[Codcommando]

In order to move a distance x, you have to move x/2.
In order to move a distance x/2, you need to move x/4.
And so on.

This is the sum of (1/t)^n from t = 0 -> infinity, which has no finite answer.

Is movement impossible?
My physics proffessor was unable to give me any proper explanation.

uuuuuum.....

 

[NotATool]

Wow...I'm gonna make up some stupid 'paradox' now and be remembered for the next 2000 years.

Yeah go for it, we'll wait.

 

[The Brick]

If you want to move 1 feet, then try to move 2 feet, cause then the first step will take you 1 feet further. Done.