Is movement impossible?

Posted By: ISG

Is movement impossible? - 09/14/07 16:50

Zeno, a famous philosopher back in the days, had a theory that movement was actually impossible for us humans to achieve. For example, you getting up from your chair and going to the door is impossible.

His claim was this:

Before being able to reach the door (our goal), we must be able to stand up and reach our halfway point - correct?

Well before we can reach our halfway point, we're going to have to be able to get 1/4 of the way to the door (or halfway between our starting point and our halfway point).

Yet again, before reaching our 1/4 mark, we'll have to reach our 1/8 point. However, this goes on forever BECAUSE numbers are infinite (right?). So without being able to tell when numbers stop we are unable to begin the actual process of movement.

Anyone have any ideas on how to rebute this? After hearing it myself and going over it a few times, in a philosophical way I believe it.
Posted By: PHeMoX

Re: Is movement impossible? - 09/14/07 19:08

Before trying to really thoroughly comprehend movement, we should simply accept that it's measurement is relative to the scale we choose.

It's a strange claim by the way, because everytime we reach the door we have proven to be able to cover all these infinite halfway points all the way up to the door, regardless of the scale you choose before you start.

The actual movement is still happening, the trouble Zeno seems to have had with it, was accepting 1 scale-size on which you base your measurements of distance and movement. Infinity doesn't matter when it comes to reaching the destination, it does matter for comprehending distance covered,

Cheers
Posted By: AlbertoT

Re: Is movement impossible? - 09/14/07 20:57

Quote:

. However, this goes on forever BECAUSE numbers are infinite (right?). .



No, the number are infinite but their sum can be a finite number

n = 1\2 + 1\4 + 1\8 + 1\16...... = 2
Posted By: PHeMoX

Re: Is movement impossible? - 09/14/07 21:04

Huh, are 1/2 and 1/4 and such infinite? I think they are finite, unlike pi for example.

Besides, if you have an infinite amount of numbers in between two (finite or infinite) numbers, then wouldn't adding them all together result in an infinite number as well? edit: answer to this would be "yes they would be infinite", but with this paradox each new number is half the amount of the last one.

Cheers
Posted By: AlbertoT

Re: Is movement impossible? - 09/14/07 21:08

Do you mean the number of addendum in the sum ?
Yes the number is infinite but the sum is finite
This is the solution of the Zeno's paradx
Not mine , of course some one smarter than me
Posted By: PHeMoX

Re: Is movement impossible? - 09/14/07 21:25

Aah, I see, with the Zeno problem in mind I do understand it, because you have a finite distance to cover, yet an infinite amount of smaller distances in between ... the more you count in between the smaller they get individually, hence the fact that they can never 'outgrow' the finite total distance when you add them all together.

Cheers
Posted By: AlbertoT

Re: Is movement impossible? - 09/14/07 21:32

exactlty
An other version of Zeno's paradox is the following
To cover 1/2 way, you need a finite time
The same to cover 1/4 way, you need a shorter time but still finite and so on
The mistake is to assume that the sum of infinite small time intervals must be infinite but it is not
Posted By: PHeMoX

Re: Is movement impossible? - 09/14/07 21:45

Actually, if each next number is half of the last one and this goes on forever, ultimately it will never be a finite number, but still infinite. It will get EXTREMELY VERY CLOSE to a finite number, but will never reach it, right?

Cheers
Posted By: AlbertoT

Re: Is movement impossible? - 09/14/07 21:54

no ,you will reach it the combination of Infinite (bigger than you can imagine) and infinitesim (smaller than you can imagine ) being finite
Posted By: Helghast

Re: Is movement impossible? - 09/14/07 22:22

i know the solution!!

out brain has a INT instruction build in, so it cuts of the decimals and thus we reached our goal

regards,
Posted By: achaziel

Re: Is movement impossible? - 09/14/07 22:40

Quote:

It's a strange claim by the way, because everytime we reach the door we have proven to be able to cover all these infinite halfway points all the way up to the door, regardless of the scale you choose before you start.



/signed.
Posted By: fastlane69

Re: Is movement impossible? - 09/14/07 23:41

Consider that you take steps that are 1/4 the length of the room.
In two steps you've reached the halfway mark... so far tracking with Zeno.
In three steps you've reached half of what was left in two steps... Zeno is feeling awefully smug!
In four steps you've reached the destination... Zeno is quite confused at this point.

The easier resolution lies in realizing that just because you cross 1/2 the distance you are not restricted to only that or put another way the discreteness of steps resolves the paradox.

By this I mean that Zeno's paradox is completely true: if you took a step that was EACH TIME half the distance to the end of the room, (in other words if you shortened your step each time) you would never reach it (or rather asymptotically reach it which means it will take an infinte amount of time to cover the final infinitely small distance).


But this doesn't mean that ALL movement is impossible. When the paradox states that you have to move half the distance, that is true... but at the point where you reach the 1/2 way mark you don't stop... you actually go further than half way. So if you take steps that are a third the distance to the end, after the first step you have covered the 1/2 way mark (Zeno Smiles), after the second step you have covered half the remaining distance (Zeno Laughs), but after the third step you are at the end (Zeno Crys).


So the paradox is no paradox at all: if you follow it exactly, shortening your step by half, then it's true; if you take same sized steps the whole time, then it isn't.
Posted By: ISG

Re: Is movement impossible? - 09/15/07 02:36

You all are going in the wrong direction with this. Are YOU moving to the door, or is the door moving to you? Are these imaginations in your head and not reality? Can you prove the door is actually real?
Posted By: AlbertoT

Re: Is movement impossible? - 09/15/07 10:26

Quote:

if you shortened your step each time you would never reach it or rather asymptotically reach it which means it will take an infinte amount of time to cover the final infinitely small distance.




Nope , I dont agree
It will not take an infinite amount of time
If you shorten your step each time , the number of steps tend to "infinite " that's true , but the lenght to "zero" thus also the interval of time to cover each step tends to zero
This is the tricky part of the Zeno's paradox
We focus on the term "infinite" , ignoring the term " infinitesim" but both terms must be considered simultanuosly
If so you get a finite result

Zero*infinite = finite ( in some cases)


If the distance if "d" and the speed is "v" the time "t" to reach the target is, according the common sense

t = d / v

A finite value
But you can get the same result also via the Zeno's paradox
Cosider the time t as sum of the partial time : t1,t2,...tn
Where

tn= 1/ 2^n d/v

for n = 1,2,3.....infinite

you have t = d/v( 1/2 + 1/4 + 1/8 + 1/16 + ....)

The number of addendum between the brakets is infinite, nevertheless their sum is : 1

so, again, you get t = d / v

same as common sense would suggest

Obviously I ma talking in principle ,in practice if you try to cover a certain distance using the Zeno's method you will actually take a long time , if not an infinite time, but this has nothing to do with the paradox itself
Posted By: AlbertoT

Re: Is movement impossible? - 09/15/07 11:33

Quote:

You all are going in the wrong direction with this. Are YOU moving to the door, or is the door moving to you? Are these imaginations in your head and not reality? Can you prove the door is actually real?



This has nothing to do with Zeno's paradox
Everybody was of course convinced that Zeno's pardox was false but it is also a matter of fact that humanity took some thousand years to provide a reasonable explanation
The Zeno's pardadox is therefore a serious issue
What are you saying know is just one of the absurd theories generated by the twisted mind of some phylosopher
Is universe a reality or just a dream ?
A claim without any serious foundation and consequently no serious answer can be provised
Typical of phylosophy
Posted By: PHeMoX

Re: Is movement impossible? - 09/15/07 11:48

Quote:

Obviously I ma talking in principle ,in practice if you try to cover a certain distance using the Zeno's method you will actually take a long time , if not an infinite time, but this has nothing to do with the paradox itself



This is where you lost me. That's exactly the prove I had in mind about why these particular infinites are not finite when all added together.

On the other hand I now do understand why in theory it must be finite, after all you're talking about áll numbers in between two numbers which all together make up the difference between those numbers, not less and not more. The numbers in between are infinite in amount, so if added up altogether they must be finite. BUT in this paradox each subsequent number is half of the last, so even when infinite, it can never consist of every number inbetween and thus can not become a finite number.

Code:


you have t = d/v( 1/2 + 1/4 + 1/8 + 1/16 + ....)

The number of addendum between the brakets is infinite, nevertheless their sum is : 1


You're actually missing a lot of numbers in between each step because of the step size (half of each old step size), so isn't it not infinite and therefore not every number between those two points? The finite number 1 in this case simply means 0 to 1 and the infinite amount of numbers in between, but what if you're skipping a lot of those infinite numbers? Isn't it smaller than the 'other' infinite?

Quote:

Is universe a reality or just a dream ?



Ever had a dream inside a dream waking up in your dream but not in reality just yet? Or ever had a serious déjà vu?
Pure theoretically the question is about another possibility.

Problems with all this, and that's where most people stop thinking about this, are our definitions of 'real', 'reality' and 'dream'. It's the good all Matrix movie question "how do you know something is real?". Well, actually we don't know, but by definition it must be... I think there's plenty of room for philosophers to seriously think about this, question reality and so on. The thing about philosophy is that some parts of it are rather hard to prove once you've made up your mind about something like 'reality', you'll either need to prove it somehow or convince people...

Cheers
Posted By: Damocles

Re: Is movement impossible? - 09/15/07 12:38

There is no such thing as an infinitly small distance.
At the atomic level, there is still the law of quantum uncertainty.
So there is at a certain point no senseful determination of a smaller distance.

So there is a limited amount of steps to reach the goal, and not
an infinit.

----

We can state that the worl we see is real:

-> the world is so complex, we can interact with it, and the
reactions are even more complex.
Simulating such a complex world would be almost imposible.
And even if: there is no economical reason for someone to
make such a complex simulation, just to observe our primitive (for them) reactions.

Would be cool though to be able to change the simulation.
I would assign me free money, and pretty girls and a big boat.
And call me: "Big Daddy", or "Luder Horst".

Posted By: PHeMoX

Re: Is movement impossible? - 09/15/07 13:33

Quote:



-> the world is so complex, we can interact with it, and the
reactions are even more complex.
Simulating such a complex world would be almost imposible.
And even if: there is no economical reason for someone to
make such a complex simulation, just to observe our primitive (for them) reactions.



Perhaps from where we are standing and in our perspective this is true, but perhaps the reason behind the simulation was something other than just personal gain, scientific insight, economic benefit or other such very human things. We can't quite tell.

Perhaps the world ís a dream, only created by giving the real us some chemicals that causes us to dream? In such a case it wouldn't necessarily be about any benefits except that we're not moving in the real reality.

Personally I don't think complexity is a boundary, why would it be? If you look at us 3000 years ago and now there's a massive and back then unimaginable difference in level of technology. Why would super complex things be impossible?

Cheers
Posted By: AlbertoT

Re: Is movement impossible? - 09/15/07 14:05

Quote:

you are actually missing a lot of numbers in between each step because of the step size (half of each old step size), so isn't it not infinite and therefore not every number between those two points? The finite number 1 in this case simply means 0 to 1 and the infinite amount of numbers in between, but what if you're skipping a lot of those infinite numbers? Isn't it smaller than the 'other' infinite?








The number of addendum between the bracket is infinite it is not just a long number, while the result is 1 , it is not just something between 0 and 1 , it is 1 (one)
Modern maths treats infinite same as an ordinary number
I skipped the numbers in_between because this is the Zeno's paradox
You must grasp the key concept
The series of infinite numbers can be divided into two classes : converging and diverging
The former tend to a finite number the latter to infinite

You can re_formulate this paradox whatever you want but you will alwayes get a converging series of infinite numbers which tend to d/v
Posted By: PHeMoX

Re: Is movement impossible? - 09/15/07 14:59

Quote:

The number of addendum between the bracket is infinite it is not just a long number, while the result is 1 , it is not just something between 0 and 1 , it is 1 (one)
Modern maths treats infinite same as an ordinary number



That's exactly what I've said actually, but perhaps I simply drew the wrong conclusion. I do understand that if all those numbers are added that it will come close to 1.

Anyways, here an image to show what I mean:



Still it bothers me that it wíll reach the full 100% when added, that doesn't make much sense if the next number, eventhough infinite, will always be half of the last one. Even when an infinite sequence, the numbers will always be divided by two each time. Why would it still reach the full 100%?

There are plenty of formulas that come close to 0 with a nice curve but will never reach it, even if it goes on forever simply because of the nature of the formula (divides the next number by two for example). Honestly I don't see why this Zeno problem is any different from that,

Cheers
Posted By: AlbertoT

Re: Is movement impossible? - 09/15/07 18:48

The point is that you consider " infinite " same as a " potential " number rather than an " actual " number
This was the ancient Greeks' idea of infinite
In the modern math infinite is considered as an ordinary number which can be manipulated same as any other number
You must not consider the series : 1/2 + 1/4 + ...
same as some thing unfinished
You must consider it same as any other normal math expression which supplies one and only one result
It is somewhat similar to the irrational number issue
The diagonal of a square having side 1 is : square(2)
Try to write this number
You can not , the number of figures after the decimal point being infinite
Does it mean that the diagonal of a square is infinite ?
Dont students use irrational numbers along with integer numbers ?
This is the logic explanation
As far as the Physical explanation is concerned, well actually it would not deserve even an explanation being evident that movement does exist regardless of the phylosophers' nonsenses
However
You claim that you have reached your goal when the ditance is : 0
But you must also measure such distance so you have to do with the measuring errors due to measuring istruments
Halving and halving your distance , sooner or later your super sophisticated istruments will tell you : hey you have reached your goal
Posted By: fastlane69

Re: Is movement impossible? - 09/15/07 19:52

Quote:

Nope , I dont agree
It will not take an infinite amount of time
If you shorten your step each time , the number of steps tend to "infinite " that's true , but the lenght to "zero" thus also the interval of time to cover each step tends to zero





Keyword: "tends to". Tends to in math means a limit or in this case, as n->inf....
...but how long does it take to get to infinity? If you start counting the infinite 1/2 numbers, whether this is time or distance, it will still take you an infinite amount of time. Don't forget that the nature of Zeno's paradox is the disconnect between mathematical models and physical reality. And that is what I'm saying: that it "tends to" but doesn't ever "acheive" is the basic definition of asymptotically approaching.

Using a series limiting process to "solve" the paradox does nothing of the sort for it assumes you can actually physically carry out that infinite sum... which is exactly what causes the problem to be paradoxical in the first place!!!

Or in the words of Wikipedia:

Quote:

Indeed, the problem with the calculus and other series-based solutions is that these kinds of solutions beg the question. They assume that one can finish a limiting process, but this is exactly what Zeno questioned.


Posted By: AlbertoT

Re: Is movement impossible? - 09/15/07 20:17

Quote:

....
...but how long does it take to get to infinity? If you start counting the infinite 1/2 numbers, whether this is time or distance, it will still take you an infinite amount of time. Don't forget that the nature of Zeno's paradox is the disconnect between mathematical models and physical reality.




No sorry, it is not like that
You must disconnect between the mathematical models and the physical reality
Of course it will take a long time if you try to implement he Zeno's paradox in practice but the Zeno's paradox is a logic paradox and it must be solved in the domain of logic
You can not introduce in a logic discussion partical elements which have nothing to do with the logic
The Zeno's paradox is nothing else that one version of the ancient greeks' nightmare for the " infinite ", the most famous being the irrational numbers
The great Pitagora became almost crazy being not able to explain why a so evident definite entity such as the diagonal of a square can not be measured by an integer number
take the number ;
square(2) = 1.41421.....
This number has an infinite sequence of figures after the decimal point , you will never reach the end of it, nevertheless it is the measure of a well defined segment

This is the "key point" of the Zeno's paradox

The solution has been found two thousand years later thanks to the modern analysis and the theory of numbers
Posted By: Matt_Aufderheide

Re: Is movement impossible? - 09/16/07 14:44

I think however its also valuable to take this paradox as an illustration of how the vagaries of language can affect logical argument...Zeno of course knows his argument and conclusion is absurd; he is warning you to be careful how you construct arguments, and not to rely too much on pure logic over common sense and observation.
Posted By: AlbertoT

Re: Is movement impossible? - 09/16/07 17:25

I quote fro Wikipedia

" Status of the paradoxes today
Mathematicians thought they had done away with Zeno's paradoxes with the invention of the calculus and methods of handling infinite sequences by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century, and then again when certain problems with their methods were resolved by the reformulation of the calculus and infinite series methods in the 19th century. Most philosophers, and certainly scientists, generally agree with the mathematical results.

Zeno's paradoxes are still hotly debated by philosophers in academic circles. Infinite processes have remained theoretically troublesome. L. E. J. Brouwer, a Dutch mathematician of the 19th and 20th century, and founder of the Intuitionist school, was the most prominent of those who rejected arguments, including proofs, involving infinities. In this, he followed Leopold Kronecker, an earlier 19th century mathematician. Some claim that a rigorous formulation of the calculus (as the epsilon-delta version of Weierstrass and Cauchy in the 19th century or the equivalent and equally rigorous differential/infinitesimal version by Abraham Robinson in the 20th) has not resolved all problems involving infinities, including Zeno's."

As you can see the explanation which I provided in my previous post is normally accepted by all scientits

"Zeno's paradoxes are still hotly debated by philosophers in academic circles"
Well actaully I have not so much respect of Phylosophy
Posted By: Damocles

Re: Is movement impossible? - 09/17/07 09:52

Its not a paradox!
The explanation bases on real motion in the real world.
The error of mathematicians is to think the real world is like the
mathematical world. In the mathematical world there are infinitely small distances,
in the real world there are not!.
The laws of quantum mechanics make distances below a certain scale senseless.
Therefore there is a practical bottom level to distances, and the solution
results in a limited amount of steps to follow (to move to a point)

Mathematicians think that their mathematical laws are the only truth, and applicable
to the real world.

For example: there can be -5 Apples in one room mathematically.
But never practically!

Even Democritus in ancient Greece knew that there is a smallest
unbreakable unit "atomos". And not "half an atomos"

There is also no practically infinitely small time-duration.
To measure time you need a referrence basis, like the movement of an
atom or quantum. But there is a bottom limit to determine the position
of a quantum moving between points A and B, where you can not differentiate
animore if it is at A or B now.
Posted By: PHeMoX

Re: Is movement impossible? - 09/18/07 01:34

Quote:

asymptotically reach it which means it will take an infinte amount of time to cover the final infinitely small distance



Which in practice means you'll never reach your goal.

Quote:

Nope , I dont agree
It will not take an infinite amount of time
If you shorten your step each time , the number of steps tend to "infinite " that's true , but the lenght to "zero" thus also the interval of time to cover each step tends to zero
This is the tricky part of the Zeno's paradox



Uhm, regardless, when each next step becomes half the step size of the previous then how on earth can you EVER reach your goal, especially when you go on for infinity dividing your next step by 2? It's impossible.

By the way, there's no such thing as a 'final' step when something really is infinite, even when the difference between infinite and (infinite+1 step more) becomes 'irrelevant' in terms of usage of our language.

Anyways, as fastlane said, you really can only reach your goal this way when your very first step practically gets you there (for example when the whole journey only takes 2 steps in total), since your next step will be half of your last in distance.

Cheers
Posted By: AlbertoT

Re: Is movement impossible? - 09/21/07 17:41

Quote:


The error of mathematicians is to think the real world is like the
mathematical world.




This is the error of many common people not of mathematicians
No professional mathematician will never claim that math has to do with real world
At the very beginning math have been created to solve concrete problems, ok, but very soon mathematicians, realized that the only way to get rid of paradoxes was the sharp separation of math and reality
If a mathematician claims that a certain theorem is "true" it means that it is "consistent"

Read the book "The infinite" by John D. Barrow

The author clearly explains the difference between the concept of infinite in math and in Physics

Posted By: AlbertoT

Re: Is movement impossible? - 09/21/07 20:49

Quote:


you really can only reach your goal this way when your very first step practically gets you there (for example when the whole journey only takes 2 steps in total), since your next step will be half of your last in distance.

Cheers



You are simply playing with words, same as many phylosopher normally do
What does it mean ?
If you claim : It is not possible to move from A to B , you must be aware, first of all, that B does actually exist
How do you know it ?
You should at least receive a signal from B, maybe just some photons of light
So something must be able to move , anyway
Not only
The paradox claims that you will never reach the goal
Ok , suppose that such claim is true
Howeve it admit that you can get closer to your goal
Isnt' a movement ?
As you see if you get out of the domain of math and logic , Zeno's paradox is simply a nonsense
Posted By: PHeMoX

Re: Is movement impossible? - 09/21/07 21:20

There is movement, but it's not possible to reach your goal if each next step is half of your last step ánd when the first step doesn't cover more than half of the total distance you want to move. If you keep dividing a cake by two forever, you'll only get smaller and smaller crumbles, but never the full cake. There will always be a next crumble (infinitely small and beyond) that gets divided by two. I tends to zero, but never reaches it.

I do understand that in practice you should not think in terms of distance dividing by two, however íf you would do so... basically the 'formula' you would use to move is one of slowing down for infinity dividing your distance by two.

One thing that I don't quite get though is how you can mathematically go from infinitely small, to zero, to negative numbers. In a logical way this doesn't quite make much sense. Perhaps that's your problem with this "paradox"?

Quote:


You are simply playing with words, same as many phylosopher normally do
What does it mean ?
If you claim : It is not possible to move from A to B , you must be aware, first of all, that B does actually exist



Actually, I didn't say that we aren't aware of A and B, nor did I say that it's impossible to move from A to B. It ís however impossible to reach your goal when you use the method of movement as Zeno said. His conclusion of 'ow then there can't be movement' is ridiculous though,

Cheers
Posted By: Damocles

Re: Is movement impossible? - 09/21/07 21:43

Maybe you should take the "paradox" of
Zeno of Elea (490BC) from a different angle.

It describes the impossibility of movement in a world where
you can take any distance and still devide it by 2, thus a world with
infinitively small distances.
Since movement in such a world is impossible, but obviously possible in the real world,
it can be a proove that the real world has distances / lenghts that can not be
devided / or split up in smaller distances.

Zeno would have thus proovesd 490BC the basic laws of quantum mechanics !
Where there are "resolutions" of the world that can not be measured more accuratly.
(Quanten-unschärfe).
Posted By: AlbertoT

Re: Is movement impossible? - 09/21/07 21:44

Quote:


If you keep dividing a cake by two forever, you'll only get smaller and smaller crumbles, but never the full cake.
....
the 'formula' you would use to move is one of slowing down for infinity dividing your distance by two.





Again you are treating the "infinitesim" and the "infinite " separatly
Try to "blend" them

If you halve and halve , the number of steps get bigger and bigger but the time interval to cover each step get shorter and shorter
Why do you suppose that total time become infinite ?
In practice yes because you must waste time to measure the intervals ,as well as other operations but
Is it logic ?
In my opinion it is not
The total time which is given by the sum of all the time intervals is finite
Anyway, this is the basic of that branch of the modern math called analysis
Posted By: PHeMoX

Re: Is movement impossible? - 09/21/07 22:34

@AlbertoT: Okey, but then explain to me why there is no such thing as infinitely small distances to cover when you keep dividing your stepsize by two? The paradox doesn't say anything about time, except that speed will logically slow down. Like you said, the interval at which the dividing takes place stays the same. But why would the dividing stop at some point? It would require infinity to be infinite instead... infinity has no end,

Cheers
Posted By: AlbertoT

Re: Is movement impossible? - 09/22/07 00:19

Quote:



The paradox doesn't say anything about time, except that speed will logically slow down.





The original paradox speaks of time
Zeno claimed that an arrow will never reach its target because it will take an infinite time to reach the target for the raeson already discussed

This is false also from a logical point of view even though it seems to make sense
The reason being that the sum of infinite terms can be a finite value
It may be not intuitive but it is like that

Why should speed logically slow down ?

Speed is given by : distance / time
Distance gets smaller and smaller but also time does the same , so their ratio can remain constant along the path

In modern math "Infinity" must be understood as a "actual " number
it is not a "potential" number
Infinity in math must not be understood as something that is growing and growing
This is the common idea of infinity

I made the example of the diagonal of the square
It is measured by the irrational number

d = sqrt(2) = 1.4121....

this number never ends
if you trunk it even 1.000.000.000 positions after the decimal point you get a segment that is shorter than the diagonal of the square

Would you claim that the diagonal of a square does not exist, then?

No the diagonal exists same as the infinite number which is its measure
it is not a potentiality it is a reality

These arguments are valid in the domain of the logic and math
In this domain and in this domain only the Zeno's paradox make sense and consequently can be solved
In the domain of physics it simply does not make any sense

How would you define for example the event :

the arrow hits the target

The arrow has a dimension, which part of the arrow should hit the target to trig the event ?
The tip of the arrow , maybe ?
Well , the arrow is made of atoms
Ok , let's say the more external atom of the tip of arrow hits the target
The atom is made of protons and neutrons
Ok the most external proton or neutron of the most external atom of the tip of the arrow hits the target
The proton has a dimension
Ok, the baricenter of the most external atom of the most external proton hit the target
OK that's clear now, but a baricenter is not physical entity , the baricenter is a mathematical entity

You are again back in the domain of logic and math
and you have already got the solution
Posted By: fastlane69

Re: Is movement impossible? - 09/23/07 17:40

Isn't the bottom line to this WHOLE thread what I said a few post back:

Philosophically the paradox exsists because of the semantics on "movement" and "the infinite".
Physically there is no paradox; there is obviously movement and people don't move the way zeno described.
Mathematically there is no paradox; an infinite series can still be summed to one.

Am I wrong on any of the above three steps for if not, this thread seems to have reached a "zeno-esque" paradox of it's own: if a thread is allowed to be posted on forever, how can a thread ever reach a concludion?
Posted By: Helghast

Re: Is movement impossible? - 09/23/07 19:22

Quote:

Quote:



The paradox doesn't say anything about time, except that speed will logically slow down.





The original paradox speaks of time
Zeno claimed that an arrow will never reach its target because it will take an infinite time to reach the target for the raeson already discussed




tell that to the hundreds of thousand knights (if not millions) that died because of arrows... yeah, sorry, you didnt die, the arrow never reached it's target.

I agree with fastlane here, if you look at it from a mathematical point of view, it can allways be summed up to 1.
Posted By: ISG

Re: Is movement impossible? - 09/23/07 23:38

@Helghast

Many knights died? To whom did this occur to? Do you believe the sights a schizophrenic may see to be true? So who says who has the proper views in our world? We believe those that are schizo are incorrect with their sights, but it's only because it's socially believed that having chemical imbalance in the mind is wrong - or not normal.

But back to the on topic matter...it's perceived by the individual perceiving it.
Posted By: PHeMoX

Re: Is movement impossible? - 09/23/07 23:50

Quote:


Physically there is no paradox; there is obviously movement and people don't move the way zeno described.



True, couldn't agree more, but isn't this "paradox" about the theoretical situation in which people would move like that? Off course it's no physical paradox, but a theoretical one if you do move like Zeno said,

Quote:


Am I wrong on any of the above three steps for if not, this thread seems to have reached a "zeno-esque" paradox of it's own: if a thread is allowed to be posted on forever, how can a thread ever reach a concludion?



Yes, indeed, but I think it's a matter of miscommunication in a way, although I still do not agree on some points. (For example adding up the infinite time you divide your next step 'reaching' a total of 100%, physically that's impossible, logically it doesn't make much sense to jump from infinite to finite especially when you divide by two never reaching it, but tending towards it..)

Cheers
Posted By: fastlane69

Re: Is movement impossible? - 09/24/07 02:33

Quote:

For example adding up the infinite time you divide your next step 'reaching' a total of 100%, physically that's impossible, logically it doesn't make much sense to jump from infinite to finite especially when you divide by two never reaching it, but tending towards it..)




Exactly... it's not physical nor philosophical... so what your confusion lies in the mathematical description of a finite sum to an infinite series. It's math. It doesn't have to make sense, it just has to be mathematically correct.
Posted By: PHeMoX

Re: Is movement impossible? - 09/24/07 15:02

True and yes, that's my problem indeed. I guess I can't quite understand why 'tend to' will become 'reaches it' when it goes on forever.
Posted By: AlbertoT

Re: Is movement impossible? - 09/28/07 18:17

Quote:

It's math. It doesn't have to make sense, it just has to be mathematically correct.



The term "true" in math stands for "consistent"
You start from some some definitions and you draw some conclusions
The conclusions must be logic but the definitions are neither true nor false
They are definitions, that's it
In case of Zeno's paradox , it is implicit that ZENO speaks of " mathematical points" i.e of a dimensionless entitities
In this case only ,he can exactly define the event

the arrow reaches the target,being equivalent to

the point "A" of the arrow and the point "B" of the target overlaps

If for point you mean a "physical point" i.e something very small but with dimensions than the Zeno's paradox does not make any sense

Obviously the "mathemtical point" does not exist , it is just an abstraction


However I dont agree, if I have correctly understood your opinion, that Zeno's paradox leads to a endless discussion
The Zeno's paradox has been solved about 400 years ago and all the scientific comunity agrees with the solution
Posted By: fastlane69

Re: Is movement impossible? - 09/29/07 23:19

Quote:

that Zeno's paradox leads to a endless discussion



If this was directed at me, I'm saying quite the opposite: that Zeno's is a moot point to discuss because it carries no phyiscal significance, carries theoretical mathematical significance, and is only a paradox when viewed purely as a logical linguistic philosophy. In other words like you said, it's been "solved", but with the solution depending on how you choose to view the problem.
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