The Motion Paradox(es)

[antimatter]

According to the ancient Greek philospher Zeno, you can never reach a pre-specified destination because you must travel half-way, then half of that, and half of that, down to infinitely small values.

http://en.wikipedia.org/wiki/Zeno%27s_paradoxes#The_dichotomy_paradox

 

As Aristotle said:

That which is in locomotion must arrive at the half-way stage before it arrives at the goal.

 

Here is the equation that "proves" it:

 

Essentially there are two standpoints, one philosophic; that you can easily reach your destination, seeing as it happens all the time,

or the scientific, which I already explained.

[ydoaPs]

Zeno's paradoxes are crap. If you apply how we actually move to the situations, they fall apart. We move with a nearly constant gait. Zeno was an idiot.

[Daecon]

The time taken to travel halfway doubles in speed each time until that, too, reaches infinity.

 

Or something.

 

Paradox solved.

[antimatter]

How exactly does that work?

[timo]

Here is the equation that "proves" it: {..., 1/16, 1/8, 1/4, 1/2, 1}

That's not even an equation, less a proof for something. It's merely a set of rational numbers without further explanation.

 

Essentially there are two standpoints, one philosophic[...], or the scientific, which I already explained.

I didn't understand your explanation. In fact, I fail to see any explanation at all. Please repeat it, possibly a bit more detailed.

[swansont]

Zeno didn't have the concept of infinitesimals available to him, and didn't know that an infinite series can converge.

[Tariq Jamal]

Zeno's paradox: An illusion of motion in physics and infinite Phenomena in mathematics.

A man stood in front of a wall, according to zeno's paradox in mathematics the man can never reach the wall. Because if suppose distance between the man and the wall is 12 feet, then first he has to cover the half of the 12 feet which is 6, then half of the 6 is 3, then 3/2, 3/4, 3/8 and....

[Sayonara]

They key word being "illusion".

[5614]

Why on earth has one person voted for "Yes, travel over a distance cannot be completed, or begun" when that's clearly a load of rubbish based purely on the fact they moved their mouse to click the option and then 'Vote'.

[Riogho]

Thanks to Galileo, this paradox can be proven not to be a paradox, but a confusion in physical properties of motion.

 

The page turns past the first half distance, half way across the book. Let us say it has moved with a constant speed.

 

Now, we use the same speed as it crosses the second half.

 

Now as we continually do this, what is occurring with time?

 

Time is being halved with a constant speed, because the distance is being halved. Since, the remainder of time to fully turn the page is being continually being halved, there will never be enough time to cross the full distance.

 

Zeno conveniently cuts the very last moment in two, halving time and distance, making it seem impossible to pass the very last distance. Ironically, Zeno uses the common sense premise that the page does pass the first half of prior distances to base his argument. But, why would it not pass another equal half successfully, as his argument is based upon?

 

It would. Even if the nonsense scenario that the last smallest half point is nothing, it would take no time to pass it, because it is not a distance at that point. It is not a paradox in terms of the basic formula that Galileo pointed out: speed = distance over time.

 

Besides, distance is quanticized, so you cannot continue to cut space in half anyway.

 

Also, simply calculus will prove it wrong. As an infinite sequence of numbers can add up to a finite answer.

[thedarkshade]

But remember that Aristotle and was a philosopher, and philosophers really know how to screw up a lot of things making them over-complicated when there is actually no need to do so. This is a typical example.

 

"Yes, travel over a distance cannot be completed, or begun." I am a bit ashamed to say but this sentence has no meaning to me. What does this mean? That I don't really get back home from school when I get back home from school?

[a Clown]

Why on earth has one person voted for "Yes, travel over a distance cannot be completed, or begun" when that's clearly a load of rubbish based purely on the fact they moved their mouse to click the option and then 'Vote'.

 

That was me, I am a believer in teh motion paradoxes

[5614]

That was me, I am a believer in teh motion paradoxes

...

 

No comment.

[Klaynos]

The fact it requires belief says it all really...

 

So, if something can never reach it's destination how do photon detectors work?

[antimatter]

...

 

No comment.

 

hehe

[Quartile]

I don't know if its just me, but I see the paradox being heavily grounded in the nature of the observer (namely, the amount of things the observer observes/considers simultaneously). I know this sounds weird.

 

When Zeno developed this paradox he somehow came to the conclusion that an object's position when it comes to rest is impossible to observe. How could this be possible, unless you were to consider that an object in motion will stay in motion until it is acted upon by an outside force? Could it be that Zeno was considering only the mathematically instantaneous reference frames that are accumulated as an object moves, instead of also including its position when it comes to rest? As some posters here have mentioned, if Zeno had opened his eyes he would have seen that an object always finds its destination because it goes where it goes to stop where it stops. In more physical terms, its position when it comes to rest is used to describe its motion in the time directly previous to stopping. But are we doing Zeno an injustice by assuming that he didn't see this obvious blunder?

 

Upon consideration of Zeno's paradox in relation to Netwon's laws of motion, it becomes apparent that Zeno's reason didn't provide him with the realization that more than one object does exist. That is, the object being scrutinized is not the only object worth considering. However, as Zeno pointed out, if we focus the reasoning power of mathematics on only one moving object (excluding even gravitational effects from other objects), we see that its position when it comes to rest cannot be described by calculus. When you pretend that the object in question is the only object in existence, Newton's first law allows for Zeno's paradox to become scientifically rational. Perhaps Zeno was actually highlighting the relativistic nature of observation by pointing out this paradox.

 

I added paragraphs in a desperate attempt to help this make sense lol. Please feel free to re-read it? If anyone thinks I'm making even the slightest philosophical or pseudo-scientific sense please give me a hoo-rah.

[DrP]

But remember that Aristotle and was a philosopher, and philosophers really know how to screw up a lot of things making them over-complicated when there is actually no need to do so. This is a typical example.

 

 

Yes - it brings me back to the stupid question of "if a tree falls in the woods........ etc.. BS, BS... would it still make a sound?" Ans: Of course it would you plonker!

 

Aren't some of these 'philosophical' type questions made up just to stir debate, to practice argument, and to annoy the hell out of scientists??

 

 

QUOTE: OP

As Aristotle said:

That which is in locomotion must arrive at the half-way stage before it arrives at the goal.

 

- What about an electron going from n=1 to n=2. No halfway there - just one quantised leap the WHOLE way.

[thedarkshade]

Aren't some of these 'philosophical' type questions made up just to stir debate, to practice argument, and to annoy the hell out of scientists??

I don't think so. Scientists are reasonable people and only spend time doing reasonable things.

[iNow]

I don't think so. Scientists are reasonable people and only spend time doing reasonable things.

 

Hmmm... That might be a bit of a stretch, shade. Scientists are first people, and people, regardless of vocation and/or training tend to do all manner of unreasonable things...

[antimatter]

iNow brings up a good point, as usual; scientists, are just people, and what people do, varies of course on the person we're talking about...which I think is me...or Zeno...

 

Just an explanation, I wasn't trying to stir up an argument, just to hear some opinions, and using those, somehow formulate my own.

My apologies to all the rest, including DrP, if this was a waste of time.

[Quartile]

Yes - it brings me back to the stupid question of "if a tree falls in the woods........ etc.. BS, BS... would it still make a sound?" Ans: Of course it would you plonker!

 

What is the sound it would make and how would it be measured? Scientific answers to these questions exist today, but thousands of years ago when philosophical ideas like "would it make a sound?" were being developed and communicated for the first time they were no doubt understood mostly as descriptions of the concept of relativity, the relationship between observer and observed. Science would not be where it is today unless these questions were asked when they were. The knowledge base at the fingertips of modern man is absolutely massive - there have been many generations of people contributing to it throughout time.

 

The answer science gives is something along the lines of: sounds are compression waves that travel through matter and vary in frequency based on the elastic modulus and the.. BS BS etc.. but at its heart, what is sound? Kinetic energy (mostly, I think) transferred between objects of various mass. Living creatures obtain the ability to perceive/interpret sounds through evolution. Perhaps the scientific answers to these philosophical type questions are philosophical answers as well. Maybe the existence of energy-transfer phenomena is what allows for evolution to occur and for life to exist at all. The long-term plasticity of various elements/compounds comes to mind.

 

I was mentioning that Zeno's paradox is true if you consider only the object in motion while excluding all outside forces. Its motion would never end and its stopping point would be infinitely indeterminable. This is the problem with Zeno's paradox, again as people have pointed out: objects do not come to rest on their own. There always seem to be outside forces.

[Donut.Hole]

Zeno's paradoxes are crap. If you apply how we actually move to the situations, they fall apart. We move with a nearly constant gait. Zeno was an idiot.

Hear, hear! But they're entertaining:D.

 

That was me, I am a believer in teh motion paradoxes

 

The motion paradox states that you may move toward a point, but you will never reach it. If you do indeed approach something, you have already moved from one point to another.

 

Plus, your destination is the halfway point to some other destination.

 

I can't believe the paradox.

 

Last I checked, you have some aquaintance with antimatter.

But about the subject, I not really at the liberty to say.

[DrP]

iNow brings up a good point, as usual; scientists, are just people, and what people do, varies of course on the person we're talking about...which I think is me...or Zeno...

 

Just an explanation, I wasn't trying to stir up an argument, just to hear some opinions, and using those, somehow formulate my own.

My apologies to all the rest, including DrP, if this was a waste of time.

 

....certainly no need to appologise to me.. .

 

Here's one.. 'if a bear poos in the woods and there is no-one else around - does it still make a smell'?

[hermanntrude]

... to hear some opinions, and using those, somehow formulate my own...

 

the trouble with opinions is that they're like arseholes. everyone's got one.

[iNow]

the trouble with opinions is that they're like arseholes. everyone's got one.

 

... and they usually stink.