Why Does the Arrow Ever Reach the Target?

  • Thread starter Thread starter Bladibla
  • Start date Start date
  • Tags Tags
    Brain
Click For Summary

Discussion Overview

The discussion revolves around the philosophical and mathematical implications of Zeno's paradox, specifically the scenario of an arrow approaching a target. Participants explore why the arrow, despite seemingly never reaching the target due to infinite subdivisions of distance, does indeed hit it. The conversation touches on concepts from mathematics, physics, and the nature of space and time.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the definition of distance in relation to the arrow and the target, expressing confusion over the concept of the arrow reaching the target.
  • Another participant suggests that space is quantized, implying that at some point the arrow must "make the leap" to reach the target.
  • Some participants reference Zeno's paradoxes, discussing the implications of infinite series and the conditions under which such series can sum to a finite value.
  • A participant challenges the idea of quantized space, stating there is no empirical evidence supporting this notion and questioning the validity of such claims.
  • There is mention of the relationship between constant velocity, distance traveled, and time taken, suggesting that these factors are crucial to understanding the paradox.
  • Some participants express uncertainty about the mathematical underpinnings of the problem and the implications of quantum mechanics on the discussion.
  • Several links to external resources are shared to provide further context on Zeno's paradoxes and related mathematical concepts.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the nature of space or the validity of quantized space. There are competing views on the interpretation of Zeno's paradox and the mathematical reasoning behind the arrow reaching the target.

Contextual Notes

Limitations include the ambiguity in the original question posed by the OP and the varying interpretations of the paradox. The discussion also reflects differing levels of familiarity with quantum mechanics and mathematical concepts among participants.

Bladibla
Messages
362
Reaction score
1
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?
 
Physics news on Phys.org
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..
 
Last edited:
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?
 
Last edited:
  • #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?
 

Similar threads

Undergrad How Do ICBMs Accurately Reach Their Targets?
  • · Replies 13 ·
Replies
13
Views
8K
Undergrad Why does laser beam hit the same target when fired?
  • · Replies 90 ·
4
Replies
90
Views
5K
Arrow strike, Avg force, Conservation of energy
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Why do gamblers go broke even when the odds favour them at every step?
  • · Replies 7 ·
Replies
7
Views
3K
High School How Does Entropy Relate to the Arrow of Time in the Early Universe?
  • · Replies 14 ·
Replies
14
Views
4K
Projectile Motion on an Incline
  • · Replies 6 ·
Replies
6
Views
3K
Special relativity and simultaneity: Spacecraft and Target
  • · Replies 2 ·
Replies
2
Views
1K
Projectile motion - determining initial velocity and angle
  • · Replies 8 ·
Replies
8
Views
2K
Arrow Pitching during the Power Stroke
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How often on average - shooting arrows into 2 targets
  • · Replies 7 ·
Replies
7
Views
2K