Can Calculus Prove that Walking in a Room Will Eventually Reach the Other Side?

[wunderkind]

Prove to me mathematically that if I start walking form one end of a room that I will eventually reach the other side. Be sure to include formulas!

(hint: use calculus)

 

[selfAdjoint]

If you start walking how do I know you'll continue walking? You might slip and fall, or be snatched up by ET's, or who knows what! You might never reach the other side of the room.

 

[dreemcacher2002]

walking

to save time, we will say that it is a known that you are in a room. and that a room as we know it has six sides,there fore we know there is a wall at the other end of the room ,your destination,which we will presume to be your destination,and we will also presume your path of movement to be a straight line. also we will presume you are governed by the known existing laws of physics of this and present day Earth and gravity, you will eventually reach the opposite wall no matter your speed, also we will presume that you can walk.

ps. i failed calculus. your on your own.

 

[arivero]

Actually it is easier to use quantum mechanics instead of calculus. In this way, even if you do not start walking, you will eventually reach the other side.

Now if you take the *unphysical* calculus limit, ie h->0, you must to assume that a non-null linear momenta is obtained, directed towards the other side. With this assumption, you will get a *mathematical* proof.
Still, the mathematical proof uses an unphysical limit.

 

[modmans2ndcoming]

use infinite serise

that will get you what you are looking for.

 

[[ infinite ]]

...so what's the answer (the one using calculus, I mean)?

I'd love to see how this works out.

 

[nine6]

hey, i got a fun way to get to the other side of the room.

first, turn off all inertia and simlutaneously jump up into the air.

the turn of the Earth will smash you into the other wall at about two thousand miles per hour.

and we can all stare at the blood stain and try to figure out what it looks like to us.



i never took calc.

i'm an artist. i would do a lot better trying to interpret the stain.

 

[Vodka]

i did this one before, i'll try to see if i can find it... all i remember is that it has to do with limits [duh] because a finite distance when broken into an infine number of parts is still finite when added back together.

 

[masonium]

Assume that you are moving at some distance v(t), where v(t) > 0 for all t >= 0. Then you will reach the end of the finite room at time t1 when the distance from the room is equal to the integral of v(t) from 0 to t1. Of course, this can easily be proved if v(t) is increasing monotonely (correct word?). The integral of a monotonely increasing function from 0 to n as n approcahes inifinity will diverge. This also is true if v(t) is constant. However, some functions for v(t) will converge to a specific value. For example, if your speed at any given moment was inversely proportional to the elapsed time + 1 second [ v(t) = 1/(t+1)^2 ], then the integral of v(t) from 0 to n as n -> infinity would actually converge at 1. So, if you were trying to walk a greater distance, then you would be out of luck.

Please feel free to point out any flaw in my logic, for if it exists I don't see it.

 

[DeadWolfe]

Originally posted by Vodka
i did this one before, i'll try to see if i can find it... all i remember is that it has to do with limits [duh] because a finite distance when broken into an infine number of parts is still finite when added back together.

I *think* that depends on your views regarding the axiom of choice.

Ever heard of the Banach-Tarski paradox?

 

[selfAdjoint]

Originally posted by DeadWolfe
I *think* that depends on your views regarding the axiom of choice.

Ever heard of the Banach-Tarski paradox?

Heh! That deserves a thread all to itself!

 

[DeadWolfe]

Originally posted by selfAdjoint
Heh! That deserves a thread all to itself!

Good point. I'll go make one.

 

[Terry Giblin]

There is a simply solution to your question.

Turn the light off in the room and put the light switch on the opposite wall.

Now that I know you are confined in the room, I therefore know your position and momentum, which may or may not be complementary.

If I wait long enough applying calculus and Schrödinger equation, you will either reach the far wall and turn the light on or simply leave the room, like a good electron.

 

[modmans2ndcoming]

heh...I guess this is what you expected in a board full of Physics enthusiasts and artists (aparently they like hanging out here)

anyway, it goes somehthing like this

the Limit as x -> infinity of the nth term function of the series:
1/2 + 1/4 + 1/8 + 1/16...

you will find that the limit of this is 1, so you will reach the other side of the room.

 

[DeadWolfe]

Originally posted by modmans2ndcoming
heh...I guess this is what you expected in a board full of Physics enthusiasts and artists (aparently they like hanging out here)

anyway, it goes somehthing like this

the Limit as x -> infinity of the nth term function of the series:
1/2 + 1/4 + 1/8 + 1/16...

you will find that the limit of this is 1, so you will reach the other side of the room.

.


Any particular reason you chose that equation?

 

[modmans2ndcoming]

well, I was using the classic argument that if you continually take half the distance to your location, then you will never get there.

there is another one that my professor used that was even better, but I can not recall it now (2 years ago).

 

[EvilDawg]

How about this?

I will get into the room with you and walk you to the other side. This way I can prove to myself that you made it :)

 

[gazzo]

isn't this one of Zeno's paradoxes ?

aaaahhh the infamous greeks.

 

[Allah]

I have an easier way

Quantum mechanics tells us that there are parallel universes. Therefore in a parallel universe, you have already reached the wall.

 

[selfAdjoint]

Quantum mechanics tells us that there are parallel universes. Therefore in a parallel universe, you have already reached the wall.

Quantum mechanics doesn't tell us that. One interpretation of QM, the many worlds interpretation (MWI) says that. You don't have to believe it to believe in QM.

 

[Allah]

Really

Really, I thought that QM cannot distinguish between the paths that a particle takes. Thereby implying parallel universes.

 

[calculii]

.


Any particular reason you chose that equation?

Yes, I think he chose it because that is known as Zeno's Paradox, which is exactly what the question of "will I ever get to the other end of the room" involves.

 

[Tau_Muon_PlanetEater]

proof

Assumptions: Velocity >0; Room length <infinite; 90 degrees < Velocity direction >270 degrees, where far is 0 degrees; t>0

Therefore, given infinite time (which we have), and a finite room length (which we have), we must eventually reach the far wall, even if it entails bumping into the side walls at a slight angle for a very long time. In other words, because we walk towards the wall (positive direction) at a positive angle, and because the far wall is a finite distance away, and because we have infinite time, we will definitely reach the wall.

Infinite always catches up to finite.

 

[Leonardo Sidis]

Since one can always find half of a number, then would traveling any distance be traveling an infinite amount of finite distances?

 

[Chaos' lil bro Order]

Since you said its a room it must have a finite length other wise it would not be a room. Therefore any motion forward (walking) even if its at an extremely acute angle like 1 degree orthogonal to the wall at your back, means that you are imparting some velocity forward towards the wall that's your destination.

You may argue that the room is infinitely long, but then I would answer it is not a room, but a hallway with one wall at your back.

Forget the math.

 

[Leonardo Sidis]

Since you said its a room it must have a finite length other wise it would not be a room. Therefore any motion forward (walking) even if its at an extremely acute angle like 1 degree orthogonal to the wall at your back, means that you are imparting some velocity forward towards the wall that's your destination.

You may argue that the room is infinitely long, but then I would answer it is not a room, but a hallway with one wall at your back.

Forget the math.

I see what you are saying, but my question is: Is it true that something with a finite total distance has infinite smaller distances? If yes, then it is infinite in its finite capacities. And therefore, to travel a distance is to travel an infinite amount of finite distances; either making the act of traveling infinite distances possible, or making movement impossible.

 

[Chaos' lil bro Order]

I understand your concept of a finite distance being broken into an infinity of parts as you continually halve the previous part. But, no where in the question was the concept of 'approaching but never reaching' a finite distance stated or in my opinion inferred. The question says neither that the room's wall is moving away from the walker, nor does it say that the walker's forward velocity is decreasing.