Zeno's Paradox

Further proof that our material world has some major flaws.

Main thesis: Movement is impossible, it's all a construct of our mind.

This greek philosopher, Zeno of Elea, gave a mathematical proof that Achilles can never catch the turtle, even if he's exponentially faster.

Achilles always needs to run half the distance to catch the turtle. Let's say there's a mile between the two.
1)Achilles successfully runs half a mile. So there's another half left.
2)Then he runs half of the distance left. The remaining distance is now 1/4
3)Only a quarter mile left. So he now runs half the distance left. a Half of 1/4 = 1/8.
4)For the remaining distance, he's able to run half of an 1/8.
5)Now only 1/16 of the distance is left, could he catch the fucking turtle? Naah, he has to run half of the distance first. Which makes the remaining distance 1/32 now. After that there's only 1/64...........1/128...........1/256

And on, and on... Achill can NEVER catch the turtle simply because he's always condemned to run half of the remaining distance (1/infinity), before actually running the whole mile.

In other words, this is a strong, very rational (albeit hard to believe by physical standards) argument that movement is impossible.



Discuss. :yumdumdoodledum:

I would need a real life example of Zeno's Paradox to discuss, since I dont see how a myth applies to us :bowdown:

Not really.
It's not even a paradox, only a deceiving manipulation of words.
Each successive increment of distance is covered is done so in half the time as the last, so you're going to hit a limit where each successive increment takes zero time.
In layman's terms:
If you watch a film of Achilles chasing the turtle, slowing it down so that each increment of half the distance takes one second of film, you will find that what you're actually doing is eventually slowing the movie to a halt.
So it's really just a matter of perspective.
Yeah, if you stop time, you'll never get where you're going.

Quote:

---

Originally Posted by juroara

I would need a real life example of Zeno's Paradox to discuss, since I dont see how a myth applies to us [/b]

---

Same thing applies for you and a real life turtle, or we can extrapolate to any other possible movement.

Quote:

---

Originally Posted by juroara

Not really.
It's not even a paradox, only a deceiving manipulation of words.[/b]

---

What manipulation of words?

why would the same thing apply to me? youre not making a whole lot of sense. how is zeno's paradox evidence that movement is a construct of our minds?

I'm with Tsen on this

[edit] anyhow, you are assuming movements can be infinitly small

Lamp paradox

Their is a lamp that get switched of evey half in a minaute. It start on and at 30sec it off then at 15secs it on then at 7.5secs it off e.t.c.

Would it be turned off or on at the end of the minaute.

Quote:

---

What manipulation of words?[/b]

---

Simple--it makes it seem as if Achilles will never catch the turtle because he always has half the distance to go. The catch is, according to calculus, the time it takes him to reach the half way point decreases until it finally reaches zero (albeit at infinity).
So it's not really that he can never reach the turtle, it's that you keep measuring shorter and shorter distances, which he covers faster and faster.
You can easily map out how long it will take him to catch the turtle.
Here, we'll map it out.
Achilles is a pretty fit guy, let's assume he can run 12 miles per hour.
As in your original post, the turtle is one mile away.
The turtle moves at half a mile per hour.
You can map them each out using the equations:
y=12x for Achilles
y=0.5x+1 for the turtle.
Find their intercept, which happens to be at ~0.0869 hours, or 5.22 minutes after they start.
All the paradox is doing is making it seem impossible when it isn't--by measuring increasingly short distances, and simultaneously measuring shorter periods of time. The whole paradox is lost if you simply view time as progressing at a uniform rate, rather than clipping it into infinitely small pieces.

One could surmise that just like there's a unit of Planck Time that appears to be indivisible into smaller increments of time, there might actually also be some cosmic measurement of space beyond which you can move no shorter a distance. In which case movement isn't infinitely divisible into smaller chunks and the paradox could resolve.

Not that I know if this is at all true... perhaps the reality of planck time as I understand it (not very well) alone makes the argument moot - eventually you say Achilles will be goes X a distance for every unit of indivisible time, and then you have to stop and say, oh, alright. No more division, that's how fast he's going.

Quote:

---

Originally Posted by Spamtek

One could surmise that just like there's a unit of Planck Time that appears to be indivisible into smaller increments of time, there might actually also be some cosmic measurement of space beyond which you can move no shorter a distance. In which case movement isn't infinitely divisible into smaller chunks and the paradox could resolve.

Not that I know if this is at all true... perhaps the reality of planck time as I understand it (not very well) alone makes the argument moot - eventually you say Achilles will be goes X a distance for every unit of indivisible time, and then you have to stop and say, oh, alright. No more division, that's how fast he's going.[/b]

---

Theres a Plank distance too, IIRC its related to the Plank time by the speed of light.

But the Plank has nothing to do with it. If you calculate the sum to infinity of the series and halvings, it works out right. Its a geometric series.

S(infinity) = a / (1 - r), |r| < 1

for u_1 = a, u_n = a.r^(n-1)

Here r = 0.5, so

u_1 = a
u_n = u_1 / (2 ^ (n - 1))

and S(infinity) = a / (1-0.5) = 2.a

Yay for A-level math.

EDIT: IOW if your first step takes you a feet, and each subsequent step takes you half the distance of your previous one, and you continue for all eternity, you will eventually have travelled double the distance taken by your first step. Which makes sense if you think about it.

What kind of turtle is it? :bigteeth:

The turtle is a figmant of Achille&#39;s imagination, that is why he can never catch it.

Case solved.


But really: if such movements are possible, he could never catch the turtle it because his movement would travel less distance every time, for eternity.

Use the Cake paradox. Follow two rules:
1. You must eat all the cake.
2. You can only have half of the total cake left.
In the end (even though it&#39;s not possible) you could never eat the whole cake. EVER&#33; :shock:

Like Tsen said, it is just word-play.

Also, "movement doesn&#39;t exist, it is created by our mind." or something like that, the topic-starter said. Seriously, how silly does it get. Movement does exist, things collide all the time without our conscious having to do anything with it. Just because the conscious only interperates the world around us so we can&#39;t really put an absolute/objective certainty on things we register doesn&#39;t falsify the normal &#39;movement-hypothesis&#39; we all embrace in normal life.

If movement doesn&#39;t exist, go stand in front of a (non-)moving train. :wink:

I have read this paradox in my Philosophy class earlier, and it doesn&#39;t make much sense to me.

Quote:

---

1. You must eat all the cake.
2. You can only have half of the total cake left.
In the end (even though it&#39;s not possible) you could never eat the whole cake. EVER&#33;[/b]

---

What if putting the cake in a protective bubble that ensures not a single piece of the cake can come out, then swallowing the bubble, thus the cake aswell and eating it.

By starting this thread, i thought i&#39;d have some more open-minded replies, you know, being in a dream community and all... :roll: I mean, who am i to argue that movement is impossible? I was just presenting a theoretical point that is rationally valid. Now, i must admit my original post was unclear, so don&#39;t judge the theory by the way i presented it&#33;

Basically, i was just trying to talk about the limits of our senses. Movement can be a construct of our minds, and not only a consequence of a more objective physical motion. When you&#39;re running in an dream, aren&#39;t you lying on your bed, completely paralyzed?

Quote:

---

Originally Posted by Neruo

If movement doesn&#39;t exist, go stand in front of a (non-)moving train. :wink:[/b]

---

Ok, i&#39;ll report back&#33;

Quote:

---

Originally Posted by Unicorn

Basically, i was just trying to talk about the limits of our senses. Movement can be a construct of our minds, and not only a consequence of a more objective physical motion. When you&#39;re running in an dream, aren&#39;t you lying on your bed, completely paralyzed?
Ok, i&#39;ll report back&#33;[/b]

---

Do report back, I always wondered how 100 mph feels like.

Also, how is it rationally that movement does not exist? Even if we are all dreaming / in the matrix, there is movement. It might be &#39;fake&#39; movement, but since it is so extremely reliable, one can certainly say that it is extremely likely that movement exists within our reality.

I mean, if you take the "if you dream and run you don&#39;t really run" to another level you get "if you *insert anything* in a dream you don&#39;t really do that". *insert anything* <-- can include existance, or at least personal existance. Point being: We CAN be all in the matrix or in some extremely &#39;solid&#39; dream with a kind of logic not present in the dreams we know. However, even if we are, the movement within our reality is as real as everything (within our reality).

Since there is no certainty, or even any reason to believe our reality is all a big illusion, Movement is real. Just maybe not objectively real. But that doesn&#39;t matter.