Why Does the Arrow Ever Reach the Target?

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The discussion revolves around Zeno's paradox, specifically the scenario of an arrow approaching a target. Participants explore the idea that as the arrow travels, it covers half the remaining distance repeatedly, leading to confusion about how it can ever reach the target. Some suggest that the concept of quantized space might explain why the arrow "makes the leap" to the target, while others argue against this notion, stating there is no empirical evidence for quantized space and that the problem can be understood through the lens of infinite series. The conversation highlights the relationship between distance, time, and motion, emphasizing that despite dividing the distance into infinite segments, the total distance remains finite. Participants are encouraged to research Zeno's paradox further to grasp the mathematical principles involved. The discussion concludes with a recognition that current theories, including quantum gravity, may eventually address these concepts, but as of now, there is no consensus on the quantization of space or time.
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This was in a maths textbook.

An arrow approaches its mark, (where its supposed to hit) but as it approaches closer and closer, it will approach half the distance it was at some time ago away from the target, and so on and so on and so on..

So I am asking: Why does the arrow ever reach the target?
 
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Ask yourself this first: why wouldn't the arrow ever reach the target?
 
Hurkyl said:
Ask yourself this first: why wouldn't the arrow ever reach the target?

Huh..? confused.. :confused:

I don't understand what you mean. Forgive me if i am being an idiot of somewhat flavour..

To answer your question in a ridiculous, ambiguous, and idiotic way: the distance between the arrow is somewhat infinite..?

I've heard it reaches the target because it depends on dimentions..but i wasn't quite satisfied with that answer, so I am asking here..
 
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The arrow is one object,how do you define:"the distance between the arrow"...?

What dimensions are involved here...?:confused:

Daniel.
 
dextercioby said:
The arrow is one object,how do you define:"the distance between the arrow"...?

What dimensions are involved here...?:confused:

Daniel.

I honestly don't know. I've just heard of answers of that kind, but by no means am i saying those are true.
 
Well,then do some recherche on the problem and then come with a "sound" version to us...:wink:

Da
 
dextercioby said:
Well,then do some recherche on the problem and then come with a "sound" version to us...:wink:

Da

I presume you'll have to see evidence that I've put some effort into it? :wink:

Fair enough. I will try and reword the question, and put down my 'hypothesis'.
 
I mean to be stated very clear,just like a maths problem,not to leave room for interpretations or missunderstandings.

Daniel.
 
Space is quantized so eventually it gets to the point where it can't go halfway any more and has to "make the leap"
 
  • #11
Yes,my guess is that is sounds very much like one of them.Anyway,let there be noted,that,up until now,the OP is not clear what he is trying to ask...

Daniel.
 
  • #12
Icebreaker said:
Are you trying to tell us one of the Zeno's paradoxes?

http://mathworld.wolfram.com/ZenosParadoxes.html

I didn't know it was Zeno's paradoxes. It was just in my mathematics textbook and interested me a lot.

Space is quantized so eventually it gets to the point where it can't go halfway any more and has to "make the leap"

Thats the kind of answer i wanted, since (well now i know) the mathematics behind it seems complicated..

Let me try and make the question more accurate. (although it has already been answered)

Consider a archer firing his arrow to a target at a certain distance away, E. When he fires the arrow, the arrow will travel towards the target, until it reaches a distance of E/2, then E/4, then E/8 and so on.

Looking at this, the arrow shouldn't hit the target at all. However, we know this is not true, as we do actually see the arrow hitting the target.

So, what causes the arrow to hit the target?
 
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  • #13
This is an ancient paradox, and one that was not satisfactorily resolved till the theory of limits was formalised.

Ask yourself :

Can the sum of an infinite series be finite ? Under what circumstances ?

What does a constant velocity of the arrow mean ? What is the relationship of the distance traveled to the time taken to travel that distance ?

Hence what is the time taken to travel each smaller "division" of the distance ? What is the total time taken ?

I think you can answer your own question here.
 
  • #14
Space is quantized so eventually it gets to the point where it can't go halfway any more and has to "make the leap"

*sigh* There is absolutely no empirical evidence space is quantized. Not only is there no working model of the universe that includes quantized space, none of the popular alternatives (e.g. String Theory and Loop Quantum Gravity) feature quantized space.


Looking at this, the arrow shouldn't hit thea target at all, since the distance is infinite.

You said the distance is E. Why do you now think it's infinite?

It is true that you have divided the problem into an infinite number of subtasks, the distance is still finite.
 
  • #15
Hurkyl said:
*sigh* There is absolutely no empirical evidence space is quantized. Not only is there no working model of the universe that includes quantized space, none of the popular alternatives (e.g. String Theory and Loop Quantum Gravity) feature quantized space.




You said the distance is E. Why do you now think it's infinite?

It is true that you have divided the problem into an infinite number of subtasks, the distance is still finite.

Forgive my idiocy. I'm not as familiar as you are on QM.

EDIT: 'infinite' removed.
 
  • #16
Bladibla said:
Forgive my idiocy. I'm not as familiar as you are on QM.

Forget QM, this has nothing to do with QM (Quantum Mechanics). The poster who talked about spatial quantisation is wrong.

Just think of it as an infinite series problem. What conclusions can you draw ?
 
  • #17
You can look at this another way too. If you are marking off the milestones then why should it even ever leave the starting point? It is never halfway to anything before it leaves the starting gate.
 
  • #18
Hurkyl said:
*sigh* There is absolutely no empirical evidence space is quantized. Not only is there no working model of the universe that includes quantized space, none of the popular alternatives (e.g. String Theory and Loop Quantum Gravity) feature quantized space.

Should there be?
 
  • #19
I would presume there should, before one goes off spouting quantized space as if it was a fact.
 
  • #20
  • #22
Yes there is no current evidence that space or time are quantized. We don't currently know how to test it even I don't think. But when someone finally invents a theory of quantum gravity it seems to me space-time will have to be quantized. If space-time isn't quantized then all these people working for the unified theory aren't going to succeed, right?
 

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