Can Calculus Prove I Will Reach the End of a Room If I Start Walking?

  • Context: Undergrad 
  • Thread starter Thread starter wunderkind
  • Start date Start date
  • Tags Tags
    Calculus Interesting
Click For Summary

Discussion Overview

The discussion revolves around the mathematical proof of whether a person starting to walk from one end of a room will eventually reach the other side. The scope includes theoretical considerations, assumptions about motion, and the implications of mathematical models.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant requests a mathematical proof that walking from one end of a room guarantees reaching the other side, emphasizing the need for formulas and theorems.
  • Another participant argues that the initial conditions are insufficient, suggesting that if walking speed decreases significantly over time, it may prevent reaching the other side even with infinite time.
  • A different perspective proposes that if space is discrete, there may be a finite number of steps required to reach the other side, assuming no infinite time between steps.
  • One participant challenges the premise, stating that the problem lacks a true proof due to missing critical elements such as direction, velocity, and the nature of motion over time.
  • A humorous anecdote is shared by a participant who claims they have never reached the end of their backyard despite multiple attempts.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of proving the statement, with some arguing that the conditions are not adequately defined while others explore theoretical implications. No consensus is reached on the validity of the original claim.

Contextual Notes

Limitations include the lack of clarity on initial conditions such as direction and velocity, as well as the assumptions regarding the nature of space and motion. The discussion remains open-ended without resolving these issues.

wunderkind
Messages
12
Reaction score
0
Prove to me mathematically that if I start walking from one end of a room that I will eventually reach the other side. Be sure to include all your formulas!(hint:remember theorems!)
 
Physics news on Phys.org
The conditions you've provided aren't strong enough. If the speed you're walking at decreases over time fast enough, then it's possible that not even an infinite amount of time would be long enough for you to reach the other side.
 
On the other hand, it may be that space is discrete, and that a continuous approximation does eventually break down and stop being useful. (And alas, pragmatic sanction really is the only justification we are left with for our mathematical creations.) There may exist a minimum length scale, below which it is not possible to take steps. In which event, assuming you walk along a "straight line path" from one end of the room to the other, there are only a finite number of steps needed. Then, you will always reach the other side of the room as long as there is not an "infinite" amount of time between any two steps.
 
prooving wrong

There is nothing to proove. This problem, at least how it is stated at present, has no true proof.

The problem statement lacks at least the following:

1) Direction in which you are walking.
if you walk along[/color] the wall you will never reach the opposite wall.[/color]
2) Velocity
velocity that equals zero is also velocity, isn't it? :)[/color]
3) the law of changing of the velocity in time.
4) velocity of the opposite wall :)
Consider a train on a railway station! You start walking from the back end to the cockpit ("opposite wall")... in the way, a policeman asks you to leave the train because you have no ticket. The result - you are on the station, train is half a way to [sensored] city... on the way to that city, because of the malfunction in engines the train explodes... there is no train any more... no cockpit... no "opposite wall"... you will never reach it...[/color]

:)

i just wonder, what theorems were we supposed to use, to proove your problem as is?
 
Last edited by a moderator:
in fact i have never made it to the end of my back yard but have started in that direction many times.
 

Similar threads

  • · Replies 0 ·
Replies
0
Views
3K
  • · Replies 0 ·
Replies
0
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 21 ·
Replies
21
Views
7K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 20 ·
Replies
20
Views
3K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 18 ·
Replies
18
Views
4K