Drop it. It never hit the ground -Philosophy-

[Laura]

I understand your reasoning, but what I don't understand is why you divide by two each time. There is never an exactly even distance between two static objects. Energy is not limited to equal halves of distances.

[Rebdragon]

I've argued this many times with various teachers and adults, and many of them disagree with me, although two of my science teachers and my physics teacher agreed, which gave me more confidence in them as teachers.

 

 

 

For most intents and purposes, the object hit the floor and bounced back, but I believe it's true that no two objects are ever touching, but are separated by a thin layer of..err..something..can't remember, but I read it somewhere.

 

An EMF?

[assassin_696]

It's also possible that all measurements are discrete (not continuous) at the Planck scale, so things really do have to 'touch' simply because you can't keep dividing ad infinatum.

[Mischlings]

and regarding that the two objects can never really "touch"...

 

they touch in the sense how everything else touches.

 

 

 

if your going to hold by this definition, nothing actually touches except for subatomic particles in the nucleus. I forget if they're strong or weak atomic forces.

 

 

 

Precisely, I made that point earlier in a post that it doesn't seem anyone noticed.

 

 

 

The way it works is this: the pencil falls until the electromagnetic force between the pencil and the floor is greater than the gravitational force, causing the pencil to accelerate upwards. It continues until the gravitational force is stronger than the electromagnetic force again, causing the pencil to fall, meaning the pencil would (ever so slightly) osciallate up and down due to gravity and electromagnetic forces unless the net force is 0 where its velocity is 0.

 

 

 

Is there something I missed that means that idea is nonsense? Because that sounds right to me, but I might have missed something.

[ThurinEthir]

I guess it's already been established, but here's my way of seeing it...(Might already have been posted, I read the thread a while ago, only got around to posting now)

 

Instead of dividing by 2, you divide by 10, and go 9/10 of the way each time. So you get 9/10+9/100+9/1000... = .999... = 1

 

1...So they hit. Apparently. Well, fine, I agree that they technically don't hit, but close enough for the purposes of this thread.

[Woodcut Lvr]

I guess it's already been established, but here's my way of seeing it...(Might already have been posted, I read the thread a while ago, only got around to posting now)

 

Instead of dividing by 2, you divide by 10, and go 9/10 of the way each time. So you get 9/10+9/100+9/1000... = .999... = 1

 

1...So they hit. Apparently. Well, fine, I agree that they technically don't hit, but close enough for the purposes of this thread.

 

 

 

But you see, because there are an infinite amount of numbers between 0 and .999... that you can never reach that number by any means of dividing... Sorry, but that idea, while puts up a challange to the idea, does not work in this case.

[Rebdragon]

I guess it's already been established, but here's my way of seeing it...(Might already have been posted, I read the thread a while ago, only got around to posting now)

 

Instead of dividing by 2, you divide by 10, and go 9/10 of the way each time. So you get 9/10+9/100+9/1000... = .999... = 1

 

1...So they hit. Apparently. Well, fine, I agree that they technically don't hit, but close enough for the purposes of this thread.

 

 

 

But you see, because there are an infinite amount of numbers between 0 and .999... that you can never reach that number by any means of dividing... Sorry, but that idea, while puts up a challange to the idea, does not work in this case.

 

What?

 

 

 

There are an infinte amount of numbers between 1 and 2, are we now assuming you can't divide them?

 

 

 

Or, am I reading you wrong, and are you seriously saying that .999... doesn't equal one? [which is a road I honestly don't want to go down again]

[Woodcut Lvr]

I guess it's already been established, but here's my way of seeing it...(Might already have been posted, I read the thread a while ago, only got around to posting now)

 

Instead of dividing by 2, you divide by 10, and go 9/10 of the way each time. So you get 9/10+9/100+9/1000... = .999... = 1

 

1...So they hit. Apparently. Well, fine, I agree that they technically don't hit, but close enough for the purposes of this thread.

 

 

 

But you see, because there are an infinite amount of numbers between 0 and .999... that you can never reach that number by any means of dividing... Sorry, but that idea, while puts up a challange to the idea, does not work in this case.

 

What?

 

 

 

There are an infinte amount of numbers between 1 and 2, are we now assuming you can't divide them?

 

 

 

Or, am I reading you wrong, and are you seriously saying that .999... doesn't equal one? [which is a road I honestly don't want to go down again]

 

 

 

No no no. I wasn't clear sorry. If there are an infinite number of numbers between 0 and 1 (The numbers I used in my examples) then there are an infinite number of numbers between 0 and .999... right? That means, no matter how many times you divide using my method, you cannot reach .999... or 1. Whichever you'd like to call it.

 

 

 

And by the way, I know .999... = 1.

[Rebdragon]

You're contradicting yourself.

[Darksavior69]

Your math is just plain wrong. You're arguing that this infinite series isn't convergent when in fact it is. If that is your definition for touching there is no room for debate or philosophy, the math is just wrong.

[StrOwez]

as the halves become smaller, so does the time to reach those halves becomes smaller. Hence when the halves become infinity small so does the time to cross those halves and therefore the pencil hits the floor :mrgreen:

[ThurinEthir]

 

But you see, because there are an infinite amount of numbers between 0 and .999... that you can never reach that number by any means of dividing... Sorry, but that idea, while puts up a challange to the idea, does not work in this case.

 

What?

 

 

 

There are an infinte amount of numbers between 1 and 2, are we now assuming you can't divide them?

 

 

 

Or, am I reading you wrong, and are you seriously saying that .999... doesn't equal one? [which is a road I honestly don't want to go down again]

 

 

 

No no no. I wasn't clear sorry. If there are an infinite number of numbers between 0 and 1 (The numbers I used in my examples) then there are an infinite number of numbers between 0 and .999... right? That means, no matter how many times you divide using my method, you cannot reach .999... or 1. Whichever you'd like to call it.

 

 

 

And by the way, I know .999... = 1.

 

...What's your point? I don't understand what you're saying...I did the exact same thing you did, except I divided by 10, rather than 2. How does that make a difference? I don't know if I made myself clear, I was ADDING the numbers I got from dividing together, not just taking the numbers I got from dividing.

[re4p3r1]

i have no idea what your saying makes no sense to me

 

who made this philosophy?

[meol]

i have no idea what your saying makes no sense to me

 

who made this philosophy?

 

An ancient Greek philosopher called Zeno.

 

 

 

I personally think (am sure) that the problem has a nice and simple mathematical solution, but I probably won't be able to convince anybody.

[Oy_the_Great]

I understand what you're saying, but the moment the pencil touches the ground isn't just a moment, it takes a while. That's where I think your problem lies: it's not like it touches the ground and immediately bounces back up. A better example to show what I mean:

 

 

 

 

 

 

The bounce may seem like a miniscule moment, but in fact it's like this:

 

 

 

 

 

 

The moment the ball hits, does not last 0.000...001 sec, it lasts a while, which means that the scale you used to prove that a moment something happens can be reduced to 0 ends at a certain number. The impact (also of that pencil) lasts a couple of milliseconds, so in the end you will not reach infinity, or 0.

 

 

 

You could argue about it by saying that 'the' moment is just a series of different moments, which are all 1 divided by infinity, which is 0, and that would make more sense. But that is exactely why I do not think 1 divided by infinity really implies 0, it's just the number closest to 0 next to 0 itself. Mathematicians of course realise that, but to make working with such numbers easier, they simply round it to 0, much like we commoners round numbers like 98.45999% to 98.46%.

[Furah]

I don't see why people are arguing. It's a good-on-paper-not-practice thing, like Operation Iraqi Freedom. Obviously the objects hit, but it would appear through this that they don't.

 

 

 

yes I agree, both ARE good-on-paper-not-practice, now lets take this to the goverment! they just waste too much money on it -.-

[Randox]

The point of my tortise dtory was simple. Both problems are based on the same operation of continualy dividing an interval of distance into infinatly smaller intervals of distance. Because you know the runner will pass the tortise, you can safely assume the pencil hits the ground.

 

 

 

Another non calculus way to do this would be to change the eqation slightly, so that you messure from dropping to some point after the pencil bounces. Of course, thats a fundamental change to the problem so it would be better to just lern calculus.

 

 

 

This is really a form of zeno's paradox (or one of them, theres a few). Theres another one that can 'prove' thatnothing can move by only looking at instances/points in time. Essentialy a snapshot if you will, and we know that nothing moves in a snapshot. This paradox goes on the fact that since without timeflow, nothing can move (because time is needed to move from point A to point B) in any one given instance of time, nothing can move in any instance of time, and if nothing can move in any instance of time, then nothing can move at all. The thing is, hes right, nothing can move in any single instance of time, but it does not apply to real life anyways. Just like when I type, my fingers divide the distance from fingertip to key into incresing smaller fractions infinate time, yet even as they do that, my fingers will actualy complete that infinite series, hit the keys, and rebound many times per second.

 

 

 

Your philosophy proves the pencil never hits the ground, it never gets there. I can prove not only that the pencil never left your hand, but that your hand is incapable of even opening to drop the pencil in the first place.

[RichieMcD]

Common sense shows this a load of theoretical [cabbage] :lol: If it doesn't hit the ground then does it lie on it's side in mid-air?

[Sk4terpunk90]

Without intention to flame this seems, how do I say it nicely...

 

 

 

Stupid?

[Woodcut Lvr]

Common sense shows this a load of theoretical [cabbage] :lol: If it doesn't hit the ground then does it lie on it's side in mid-air?

 

 

 

You really didn't read the thread then :D

[OwnagePie]

It does touch the ground, because you can look closer and closer, dividing and dividing, and you do so infinitely.

 

And at infinity cycles, the distance between the pencil and the ground is an infinitesimal.

 

 

 

As with 0.999... = 1,

 

0.000...001 = 0

 

 

 

Distance between pencil and ground = 0

 

 

 

So you can study something infinitely, but you will just end up with the obvious answer.

 

 

 

noob philosopher got poont... it will eventually go down to .99999999...... which obviously = 1 meaning it hit the ground. or you dont have to be such a [kitty], and just LOOK at it .....

[Topazjewel]

This is slightly different but it's sort of the same concept, kind of. In my Geometry class my sophomore year of high school I had this psycho teacher. We just watched movies like Alice in Wonderland and Monty Python and A Beautiful Mind, because they all had logic or math in them. Anyways, my teacher was a bum. But one day we had a discussion:

 

 

 

Suppose there is a distance of twenty feet. You can cross it in 10 steps, or you can go halfway, then half of the remaining distance, and half of that remaining distance, etc, etc. Some kids thought it would be faster to go the half-way way, but then my teacher said you'd never get there. So long as you were only covering half of the remaining distance, while you'd get closer to your destination faster, you'd never actually get there. Because you were always only going halfway. So you could go 10 feet, then 5, 2.5, 1.25, etc, until you were down to teeny decimals. You'd never get there. But then logic says that so long as you're always moving forward you'd get there eventually. But at the same time, if you always were covering half the remaining distance, you wouldn't.

 

 

 

What do you think?

[Flu]

Atomically, it never hit the floor anyway, because the electromagnetic force holding an atom together will repel another atom before they actually touch... if 2 atoms were to ever touch, usualy it wil end in a big bang and someone has cleverly found a way to create cold fusion.

 

 

 

It does touch the ground, because you can look closer and closer, dividing and dividing, and you do so infinitely.

 

And at infinity cycles, the distance between the pencil and the ground is an infinitesimal.

 

 

 

As with 0.999... = 1,

 

0.000...001 = 0

 

 

 

Distance between pencil and ground = 0

 

 

 

So you can study something infinitely, but you will just end up with the obvious answer.

 

 

 

noob philosopher got poont... it will eventually go down to .99999999...... which obviously = 1 meaning it hit the ground. or you dont have to be such a [kitty], and just LOOK at it .....

 

 

 

It's true. 0.9 Reccuring (0.99999....) does mathmatically equal 1.... there's a maths formulae somewhere that proves it...

 

 

 

EDIT: http://en.wikipedia.org/wiki/Recurring_ ... _0.99999...

 

 

 

EDIT2: http://en.wikipedia.org/wiki/0.999...

 

 

 

also, look at it this way.

 

 

 

0.11111... = 1/9

 

9 X 0.11111..... = 0.999999... = 9/9 = 1

 

 

 

Thus the pencil hit the ground.

[doomy]

Isn't there some fancy infinity [something] that states that it'll hit the ground or something like that, I can't really remember.

 

 

 

EDIT: Tbh it seems that your slowing down time to make this worl, becaus eif the ball travels at a constant rate (even accelerating) then it'd hit the ground, the way your doing it is that each half takes the same time (so 1/2, 1/4, 1/8 all take a sec to do....)

 

What I mean is your saying-

 

0 Sec- 100%

 

1 sec- 50%

 

1.5sec- 25%

 

1.75 sec- 12.5%

 

1.875sec- 6.25%

 

Etc, but if you say 2 sec, the answer is 0. Time is a constant.

[Nenga]

There's a famous quote for this situation: "whatever goes up must come down." So halfway is 50%, half of that is 25%, again half it you have 12.5%, 6.25%, etc, eventually it rounds down to 0%, which is the ground. In this case gravity does the rounding for us.

 

 

 

I hope no one noticed I just copied most of the first post and then said it rounds down to 0.