Running 3 Miles: The Staggering Implications

  • Context: High School 
  • Thread starter Thread starter Namloh2000
  • Start date Start date
  • Tags Tags
    Frames
Click For Summary

Discussion Overview

The discussion revolves around the concept of motion and Zeno's Paradox, specifically in the context of running a distance of 3 miles. Participants explore the implications of dividing distances into infinite halves and the resulting paradoxes related to motion and time.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant questions how it is possible to run 3 miles if one must exist at all halfway points, suggesting that this leads to the conclusion of running forever.
  • Another participant identifies the issue as Zeno's Paradox, noting that the sum of an infinite series can still be finite.
  • A different participant attempts to clarify the paradox by referencing the finite sum of the series ½ + ¼ + 1/8 + ..., indicating that the total time taken is finite because each step takes half as much time as the previous one.
  • One participant expresses skepticism about the mathematical explanations provided and suggests further exploration in a different forum section.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the understanding of Zeno's Paradox and its implications for motion. There are differing levels of confidence in the mathematical explanations provided.

Contextual Notes

Some assumptions about the nature of motion and the interpretation of infinite series are not fully explored, leading to unresolved questions about the relationship between distance, time, and the concept of infinity.

Namloh2000
Messages
28
Reaction score
0
Moving in Frames??

okay, so let's say I ran 3 miles. At one point, I must have been halfway between start and finish right? From the halfway point, I must have existed halfway from there and the remaining 1.5 miles also. And halfway between THAT point and the finish. Then halfway from THAT point and the finish. I must have existed at all these halfway points, but if motion was fluid, couldn't this not be accomplished, being that I can divide my new remaining distance in half from here to infinity, meaning that I would have to be running forever? The implications are staggering!

seriously though, what's up - how come I can run 3 miles?
 
Physics news on Phys.org
This is known as Zeno's Paradox. The sum of an infinite series is still finite. Google it. Much has been said about it.
 
okay so i read up a bit and the solution seems to be something in that because the sum of the series ½ + ¼ + 1/8 + ... is equal to 1. The total time is finite because each step is done in half as much time as the previous step.

But I still don't understand.
 
OK, I see that you don't have much faith in mathematics. Anyway, go visit here if you are interested: https://www.physicsforums.com/showthread.php?t=22419

You can open a new thread in the General Math section if you still don't believe in Zeno's Paradox. You will get more replies there, and most of them will be harsh. So good luck! :)
 

Similar threads

High School How Far is Mile Start Line from Finish Line at end of Lane 8
  • · Replies 9 ·
Replies
9
Views
5K
High School Using energy principles to find equilibrium depth of floating object
  • · Replies 8 ·
Replies
8
Views
1K
Undergrad Using reference frames for derivation of Lagrangian
  • · Replies 25 ·
Replies
25
Views
3K
High School How does running in a moving train affect race times?
  • · Replies 27 ·
Replies
27
Views
3K
High School Understanding Spacetime Diagrams from "Reality is not What it Seems
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Universal stationary frame of reference for speed, d and t
  • · Replies 7 ·
Replies
7
Views
2K
High School Sign conventions in torque and non-uniform circular motion
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Comparing Clock Rates in Accelerated vs Constant Velocity Frames
  • · Replies 14 ·
Replies
14
Views
2K
High School Am I understanding the concept of proper frame of reference?
  • · Replies 33 ·
2
Replies
33
Views
4K
High School Questions about momentum and force as well as normal force/friction
  • · Replies 35 ·
2
Replies
35
Views
6K