How Is Motion Even Possible?

[lexmark]

How is it possible to have infinite space in a finite area? If you have to travel an infinite distance to get from one point of a line to the other, how is motion even possible if there is always an infinite distance to travel between the two locations?

having infinity in a finite area sounds contradictory...

 

[CycloWizard]

Originally posted by: lexmark
How is it possible to have infinite space in a finite area? If you have to travel an infinite distance to get from one point of a line to the other, how is motion even possible if there is always an infinite distance to travel between the two locations?

Huh?

having infinity in a finite area sounds contradictory...

Because it is contradictory. Where did you get the idea that the distance from one point to another is always infinite? It's not.

 

[lexmark]

lets say you were trying to travel from 0ft to 5ft.

there are an infinite amount of points between the two points right (4.98, 4.998, 4.99999999998, etc.)?wouldnt you have to pass through an infinite amount of points to reach to 5ft? how would you reach 5 if there is always a small distance to travel? (4.9999999999999999999999 ft?)

 

[jakalsucks]

Read up on Zeno's paradox, and please don't post while high.

 

[everman]

You could fit an infinite amount of points between two points which are 5 feet apart, because you can make the points smaller, but they are still only 5 feet apart.

 

[Special K]

You cannot control your movement with that much accuracy. It would not be possible to take a step that was, say, 1/1000th of an inch.

 

[RyanVM]

Zeno's Paradoxes
http://en.wikipedia.org/wiki/Xeno%27s_paradox

 

[DrPizza]

Just in case lexmark is starting to get a decent grasp on infinity, I'll toss this one out:

It's possible for a curve to have two endpoints, have a box (with finite area) be drawn around the curve with those two points, yet the length of the curve between those two points is infinite. And, the curve never crosses itself.

 

[bobsmith1492]

^How?^ I want one... what kind of space are you working in would be the question, I suppose?

 

[Born2bwire]

Originally posted by: DrPizza
Just in case lexmark is starting to get a decent grasp on infinity, I'll toss this one out:

It's possible for a curve to have two endpoints, have a box (with finite area) be drawn around the curve with those two points, yet the length of the curve between those two points is infinite. And, the curve never crosses itself.

You mean like a circle?

 

[TuxDave]

Originally posted by: Born2bwire

Originally posted by: DrPizza
Just in case lexmark is starting to get a decent grasp on infinity, I'll toss this one out:

It's possible for a curve to have two endpoints, have a box (with finite area) be drawn around the curve with those two points, yet the length of the curve between those two points is infinite. And, the curve never crosses itself.

You mean like a circle?

Or more like an infinite spiral

 

[forrestroche]

Originally posted by: lexmark
lets say you were trying to travel from 0ft to 5ft.

there are an infinite amount of points between the two points right (4.98, 4.998, 4.99999999998, etc.)?wouldnt you have to pass through an infinite amount of points to reach to 5ft? how would you reach 5 if there is always a small distance to travel? (4.9999999999999999999999 ft?)

A point has zero dimensions (therefore it has no LENGTH) - points are theoretical mathmatical constructs that do not occupy physical space. There are infinite points on any line, not infinite length. It's that simple. I don't know why people are complicating it.

 

[imported_Seer]

Originally posted by: forrestroche

Originally posted by: lexmark
lets say you were trying to travel from 0ft to 5ft.

there are an infinite amount of points between the two points right (4.98, 4.998, 4.99999999998, etc.)?wouldnt you have to pass through an infinite amount of points to reach to 5ft? how would you reach 5 if there is always a small distance to travel? (4.9999999999999999999999 ft?)

A point has zero dimensions (therefore it has no LENGTH) - points are theoretical mathmatical constructs that do not occupy physical space. There are infinite points on any line, not infinite length. It's that simple. I don't know why people are complicating it.

It's not that simple. Did you even read the links posted? His question is actually an ancient "problem" that took calculus to solve.

 

[Aisengard]

You're right Seer.

So say you have seemingly 'infinite' points to traverse. The distance between each point would then be infinitely small, and so would the time to traverse each. Now, your thinking could diverge at this point, but thankfully calculus was invented so that the solution converged.

I can't really explain it, but then again, I'm not Aristotle.

EDIT:

Then again, thinking about it, you could say Quantum physics gets called upon, where an object in motion has no set position, which goes against the assumptions of some of Zeno's paradoxes, and renders them moot. I don't know. I'm pretty much talking out of my ass at this point.

 

[Evadman]

Do some research on a 'plank' unit. space can not be broken up into an infintesimal amount of pieces, there really is s 'smallest' unit.

 

[forrestroche]

I must disagree with both Mr. Aisengard and Mr. Seer.

Originally posted by: Seer
It's not that simple. Did you even read the links posted? His question is actually an ancient "problem" that took calculus to solve.

I read them, and rather more carefully than you I would say. Mr. Lexmark's original question (the only one I directed myself to you might note) is phrased, "If you have to travel an infinite distance to get from one point of a line to the other, how is motion even possible if there is always an infinite distance to travel between the two locations?" The underlying assumption (that there is infinite distance between two points on a line) is false.


I am also familiar with the problem to which I believe YOU refer (Achilles and the Tortoise); one which bears no relation to the original question. The paradox is one of infinite division of remaining distances, and one that was, as you state, only solved through Calculus. But your statement, "His question is actually an ancient 'problem'" is incorrect. They are not the same question.

You would be best served by following your own advice and reading Mr. Lexmark's post and question more carefully yourself (and perhaps the paradox to which you equate them) before attempting to start some sort of childish conflict with me.

 

[liquid51]

coming from someone who does not have an indepth eduction regarding such matters (other than what I've read or learned for pleasure), let me try and explain the answer I've deduced:

To have a point A and a point B, you must have a distance set between them. Two connected points make a segment, which cannot be infinite. If you wanted a line with an infinite length, it must be a ray and could only have a point A (because no movement cannot have a start point).

If you attempted to travel from point A on the segment toward point B, you would have to make measurable progress because that distance cannot be infinite.

If you traveled from point A on the ray, you would never reach a destination because there isn't one; there can't be one. However, if you measured your progress from point A (distance traveled, not the distance to be traveled), you will make measurable progress.

The universe as I understand it (doing my best there ) is infinite. You could never measure your progress attempting to cross it. But you'd pass solar systems and planets on the way. Based on those, you could measure progress and thus record movement. This is all relative mind you. I've actually never moved since my conception, ever. Thats because the entire universe revolves around me

 

[1prophet]

Originally posted by: lexmark
lets say you were trying to travel from 0ft to 5ft.

there are an infinite amount of points between the two points right (4.98, 4.998, 4.99999999998, etc.)?wouldnt you have to pass through an infinite amount of points to reach to 5ft? how would you reach 5 if there is always a small distance to travel? (4.9999999999999999999999 ft?)

Eventually your measurements will probably hit this wall if you keep going smaller.

 

[BucsMAN3K]

Aha, the old paradox.

Say you walk towards a wall. Theoretically you have to walk through an inifinite amount of halfway points to get there..but if you keep walking in intervals, how do you get there?

Time...the answer is time. While it may be hard to believe your walking through an infinite amount of points, you must also realize you are doing so in an infinite amount of time intervals.

So basically, motion seems impossible because it implies having an infinite amount of time to reach that wall. Well, good news, you do!

In conclusion: It's best not to think about it.

 

[BucsMAN3K]

Originally posted by: 1prophet

Originally posted by: lexmark
lets say you were trying to travel from 0ft to 5ft.

there are an infinite amount of points between the two points right (4.98, 4.998, 4.99999999998, etc.)?wouldnt you have to pass through an infinite amount of points to reach to 5ft? how would you reach 5 if there is always a small distance to travel? (4.9999999999999999999999 ft?)

Eventually your measurements will probably hit this wall if you keep going smaller.

I don't believe that applies here. That is more of a principle established on thermodynamic probability. Basically, all that is obersved in physics is done so with certainty because we are seeing trillions of actions taking place, which converge on a similar outcome. But the outcome of these actions in reference to an individual particle is not certain.

It's like flipping a coin. If you flipped the coin an infinite amount of times, you will see your probility converging on a value of 1/2 of getting heads. But if you flip the coin 10 times, you could land on heads 7 times and tails 3 times, giving a probability of 7/10 for that incident.

Basically what this means is, a trillion particles doing trillions of actions will converge on a predictable outcome. But if just observing 10 particles, a totally different outcome can result.

If that makes any sense, and is a bit off topic, but these are things I've had long, boring, time consuming conversations about.

 

[JSFLY]

Originally posted by: BucsMAN3K
Aha, the old paradox.

Say you walk towards a wall. Theoretically you have to walk through an inifinite amount of halfway points to get there..but if you keep walking in intervals, how do you get there?

Time...the answer is time. While it may be hard to believe your walking through an infinite amount of points, you must also realize you are doing so in an infinite amount of time intervals.

So basically, motion seems impossible because it implies having an infinite amount of time to reach that wall. Well, good news, you do!

In conclusion: It's best not to think about it.

QTF GOOD ANSWER!

 

[JSFLY]

Originally posted by: JSFLY

Originally posted by: BucsMAN3K
Aha, the old paradox.

Say you walk towards a wall. Theoretically you have to walk through an inifinite amount of halfway points to get there..but if you keep walking in intervals, how do you get there?

Time...the answer is time. While it may be hard to believe your walking through an infinite amount of points, you must also realize you are doing so in an infinite amount of time intervals.

So basically, motion seems impossible because it implies having an infinite amount of time to reach that wall. Well, good news, you do!

In conclusion: It's best not to think about it.

QTF GOOD ANSWER!

errr QFT

 

[Valrandir]

The concept of the line itself if infinite.
Yet the distance between two fixed points on that said line, is finite.

 

[gabriel87120]

Originally posted by: Evadman
Do some research on a 'plank' unit. space can not be broken up into an infintesimal amount of pieces, there really is s 'smallest' unit.

Take it from me, I am a physicist. The guy I am quoting stated the answer.

Points are not physical, you do not "move along a series of infinite points" because technically they aren't there. You do however move along a series of finite planck lengths during a finite amount time.


To clarify this nonsense further. If you try to solve this problem all the rhetoric in the world will not help you, unless it's mine lol. Read below. Mathmatically, a "series of infinitely small points" implies ONE SINGLE POINT if you are intelligent enough to chew on that. IE, placing infinitely small amounts of a substance into a bucket over an infinite amount of time, you still have a bucket thats empty. All those infinite amounts of little "zero" points next to each other extend over a total distance of zero. A point has NO REAL PHYSICAL EXISTANCE and is only a theoretical pinpoint of a relationship between an independent and dependent variable of a closed system. Calculus and even algebra depends on these "zero distance" points to work. But when did you ever walk to the store on a zidewalk paved with zeroes? So know this, to have independent and dependent variables, one must imply physical separation of the two (because if all variables were the same, all points in the universe are of value = 1, because var A = var B = var C).
If all values were one, then the sky wouldn't be blue if the grass was green. Separation of variables defines a finite nature of the physical characteristics of the universe. if everything were indeed points, then you wouldn't be here to observe the universe anyway (which itself would be curled up in an empty bucket of nothingness. Analyzing this problem incorrectly shows that not only motion is not possible, but neither is space, time, and pretty much everything alltogether.

The measurements of the universe are actually finite in its basic structure. Think of a knitted sweater, the thread being the universe's material, and the holes being the nothingness having diameter equal to one Planck length. If you existed as a theoretical ant with length less than a Planck length, you would fall through the actual fabric of the universe and cease to exist in our observable dimensions. So as you move, finite amounts of molecules in your body move over finite amounts of space. Incorrectly analyzed mathematically: infinite points in your body move over infinite amounts of points in space, so it's infinity over infinity. And we know anything divided by itself equals one... one stupid argument.

so...

Motion = possible

any questions?

 

[BucsMAN3K]

Originally posted by: gabriel87120

Originally posted by: Evadman

so...

Motion = possible

any questions?

LIES!