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Assignment 2

What is Zeno's paradox?

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Zeno's paradox

Posted by dhruv at Feb 04, 2009 02:27 AM
Zeno's paradoxes were introduced to illustrate that motion was an illusion. here are 3 paradoxes.
1. In a race, the quickest runner can never overtake the slowest,(if initially the slowest is ahead of the quickest), as the quickest will always have to run a finite distance to catch the slowest. & by the time he reaches that point, the slowest would have gone even further ahead.
2. To cover a certain distance, one has to cover half the distance first. & before covering that 1/2 distance, he has to cover 1/4 of the total distance, & so on. as a result, one could neither cover the given distance, nor even start.
3. All stationary objects occupy a fixed space. if v consider a flying arrow, it can't move where it is not present, as it is at the same instant. the arrow can also not move to where it is, b'coz it is there. as a result, it is not moving at all.

explanation to zeno's paradox......

Posted by praneet_cbscients at Feb 04, 2009 04:23 AM
as i have read from wike. there are three main paradoxes of zeno...i will try to give suitable explanation for it:
1.achilles and tortoise.
suppose tortoise is 10m ahead from achilles and speed of achilles is 2m/s and that of tortoise is 1m/s...now just see at initial and final state,so after 10 sec.tortoise and achilles are at same position and just after 10sec. achilles is ahead of tortoise....
2.the dichotomy paradox.
suppose i have to cover a dist. of 1m now according to zeno's this dist. is breaked in to infinite distances,if i cover .25m in one step then i am covering[....1/64,1/32,1/16,1/8,1/4] this much steps in only on shot and therefore by walking further three steps i will cover the whole 1m........
3.the arrow paradox.
according to zeno's at each particular instant the arrow is at rest i fully agree with his statement but if we will take the succesive snapshots of each instant then we can clearly say that though it is at rest at each instant but the position of the arrow is changing at every instant.........

explanation to zeno's paradox......

Posted by praneet_cbscients at Feb 04, 2009 04:23 AM
as i have read from wike. there are three main paradoxes of zeno...i will try to give suitable explanation for it:
1.achilles and tortoise.
suppose tortoise is 10m ahead from achilles and speed of achilles is 2m/s and that of tortoise is 1m/s...now just see at initial and final state,so after 10 sec.tortoise and achilles are at same position and just after 10sec. achilles is ahead of tortoise....
2.the dichotomy paradox.
suppose i have to cover a dist. of 1m now according to zeno's this dist. is breaked in to infinite distances,if i cover .25m in one step then i am covering[....1/64,1/32,1/16,1/8,1/4] this much steps in only on shot and therefore by walking further three steps i will cover the whole 1m........
3.the arrow paradox.
according to zeno's at each particular instant the arrow is at rest i fully agree with his statement but if we will take the succesive snapshots of each instant then we can clearly say that though it is at rest at each instant but the position of the arrow is changing at every instant.........

assignment no.2

Posted by sniranjan at Feb 04, 2009 05:40 AM
Zeno's paradoxes were introduced to illustrate that motion was an illusion.
1. In a race, the quickest runner can never overtake the slowest,(if initially the slowest is ahead of the quickest), as the quickest will always have to run a finite distance to catch the slowest. & by the time he reaches that point, the slowest would have gone even further ahead. In this paradox he did not considered velocity. suppose tortoise is 10m ahead from achilles and speed of achilles is 2m/s and that of tortoise is 1m/s...now just see at initial and final state,so after 10 sec.tortoise and achilles are at same position and just after 10sec. achilles is ahead of tortoise.... .i think all the zenos paradox can be explained by calculus.actually this gave birth to limits and completeness property of realnumbers

assignment no.2

Posted by nsingh at Feb 04, 2009 07:45 AM
basically zeno promoted the permenides's idea of "oneness",to say that there is nothing like motion or plurality.in this context he made statements called zeno's paradox. they r as follows
*if a man is running to reach a point(let it be P), he will first cover half the distance i.e. P/2,then he covers the next P/4, then he covers the next P/8 and so on, so in this way he could never reach the point P.
*a man and a tortoise are having a race, so as the tortoise is slow he starts the race first. now zeno says that the man can never overtake the tortoise, as when tortoise starts from a point(let A), then when the man starts at A, the tortoise is at some point ahead, in this way the will reach the same pointafter the tortoise has passed. so fest runner can never overtake a slow runner
*at any particular instant of time an object occupy a space, at that instant it can either move to another place or it can move to its own place.it cannot move to another place because it is at a particular point of time(not a time interval)and also it cannot move where it is at that point because it is already there. so similarly at every instant it cannot move anywhere. so ther is no motion
*if anything covers a place it requires a space,that space also requires space
so if zeno's paradox were true there would be no motion

assignment no.2

Posted by nsingh at Feb 04, 2009 07:48 AM
there's also 1 more paradox i read that is half a given time is equal to double of it , i didnt understood the explanation for this

What is Zeno's paradox?

Posted by amits at Feb 04, 2009 08:55 PM
As searched from Wikipedia, Zeno was a great supporter of Permenides's doctrine of “all is one”, according to which the belief in plurality and change is mistaken and that motion is nothing but illusion. In support of Permenides, Zeno created eight paradoxes.
 One of the most popular paradox is-
 “Achilles and the tortoise” . It states, “In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.”
 This paradox can be understood in simpler words as, suppose in a race, achilles allows the tortoise a head start of 100 feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 feet, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, for example 10 feet. It will then take Achilles some further time to run that distance, in which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been--he can never overtake the tortoise.
 This paradox may be solved quite easily now by applying the concept of relative velocity, but in past this had created a lot of debate and confusion amongst philosophers. Suppose the actual velocity of tortoise (u) is 10 feet per second, while that of Achilles (v) is 100 feet per minute. The relative velocity of Achilles to the tortoise (v1) is then 100 – 10 =90 feet per second or 90/60 = 2/3 feet per second. So with this relative velocity the time taken by Achilles to catch the tortoise is 100 feet/2/3 feet per second = 66.66second or 1 minute and 6.66 seconds.
Now, to calculate the distance at which both the Achilles and the tortoise will meet, we can divide the actual velocity (v) with the time of meeting i.e. 100feet per minute / 1 minute 6.66 seconds or, 5/3 feet per second / 66.66 seconds =111.11 feet.
Thus, we find that the Achilles will catch the tortoise at a distance of 111.11 feet from the start point at 66.66 seconds.







zeno's paradoxe's

Posted by piousanya123 at Feb 05, 2009 11:34 PM
   first paradox: in a race the quicker runner can never win the race because he can never overtake the slower runner, if the the slower one has started earlier. that is because the faster one has to reach a point where the slower one is, and by the time he will do that the slower runner will go ahead, thus the fast runner would never be able to reach the slow runner.
   second paradox: to cover a distance x ,one has to cover a distance x/2 first, and x/4 before that and x/8 even before that and so on. thus the person will never cover any distance and would not start from the point.
   third paradox:for motion to be occurring, an object must change the position which it occupies. in any one instant of time, for an arrow to be moving it must either move to where it is, or it must move to where it is not. It cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible. This paradox is also known as the fletcher's paradox

Zeno's Paradox

Posted by VIVEK126 at Feb 11, 2009 01:49 AM
Well I think I don't need to rewrite the paradoxes ( as many of my friends have did ) , it is easily available on net (and right now I am on it !!!!) .
The thing is that I have read it , basically it arises because Zeno had thought of processes ( almost all his paradoxes) in a very discrete way (quantising) , due to which in each of his paradox , the processes he considered were not appearing to attain the state of end , moreover he also not concluded the concept of velocity (rate of progress of process) and therefore ended everytime in infinite series .

assignment 2

Posted by abhishek25490 at Feb 11, 2009 02:28 AM
Zeno's paradox are generally the problems that supports the PARMENIDES idea of "one is all".(As per parmenides the only truth that is existing in this world is "one".the belief osf together i.e.,plurality and senses are all false.generally as per him the motion is abstract(illusion) or not true.)
The zeno's paradox consisted of following :
1->THE PARADOX OF MOTION:as given by the Aristotle.the paradox means that if in a race there is fast runner and a slow runner,and in the starting if the slow runner is ahead of the faster ,let's consider 100ft ahead then the faster will have to cover 100ft to come near the slower one but then till that time time slower one would have moved a certain distance say 20ft.and so this process continues again and again.so one can conclude that the faster will never be able to catch the slower one .(as the faster runner reaches those points where the slower one has moved the slower one would have moved a further distance.so there will be infinite no. of points).
2->THE DICTOMY PARADOX:as per this ,if one has to a cover a certain fixed amount of distance he has to first cover the half of the distance the one has to cover 1/4th of the total distance and in this manner it finally forms a non converging sequence and so one will not be able to even cover the total distance nor even the starting point.so finally due to this the trip might not even begin also.
3-->THE ARROW PARADOX:in this paradox ZENo'S states that any body will be said to be in motion when it's position changes with the time.considering a arrow,the arrow is said to be in motion when its position changes with time.Arrow's position will change only when it is moving towards a directed point or it is moving in the direction where it should not.It cannot move where it is not not because this is a single instant and it cannot move to where it is because it is already present there.so as per this paradox the motion will not be able to take at all.
4-->PARADOX OF PLACE:Everything that is present in the space is having place then place itself is having its own place.

zeno paradox

Posted by alkesh at Feb 11, 2009 02:39 AM
Zeno's paradoxes were introduced to illustrate that motion was an illusion. here are 3 paradoxes.
1. In a race, the quickest runner can never overtake the slowest,(if initially the slowest is ahead of the quickest), as the quickest will always have to run a finite distance to catch the slowest. & by the time he reaches that point, the slowest would have gone even further ahead.
this paradox is due to lack of concept of velocity .now we are having knoeledge of velocity this is no more a paradox.
2. To cover a certain distance, one has to cover half the distance first. & before covering that 1/2 distance, he has to cover 1/4 of the total distance, & so on. as a result, one could neither cover the given distance, nor even start.
a infinite sequence can converge to a finie limit this sequence also converges to a finite limit
suppose i cover 1/2 distance in one step and when i will take the second step i will automatically cover 1/4,1/8,1/12 of the distance and will cover the whole distance
3. All stationary objects occupy a fixed space. if v consider a flying arrow, it can't move where it is not present, as it is at the same instant. the arrow can also not move to where it is, b'coz it is there. as a result, it is not moving at all.

Zeno's paradox

Posted by sandiip at Feb 11, 2009 05:07 AM
Main paradox of Zeno is that it is impossible to cover a finite distance because before covering full distance he has to cover its half distance,then one quarter ,then half of quarter and so on.Then it becomes an infinite series and no end for it.As a consequence it is not possible to start a motion from rest position.Because the same type of statements we can make for half of original distance, one quarter of original distance, half of quarter of original distance.............so on.
               "EVERYTHING THAT IS AT REST,CAN'T DO MOTION"

zeno's paradox

Posted by chandan at Feb 14, 2009 12:57 AM
zeno's paradox are the set of problems that are assumed to be divised by zeno(a pre socratic greek philosopher of southern italy)to support parmenides doctrine that "all is one".
zeno had given eight paradoxes ,i am listing few of them which i find more interesting.
paradox 1 "the motion less runner"
suppose a runner wants to cover 50m in a finite time .According to zeno paradox it is not possible ?
This is because for this he (runner )must cover say 25m ,for this he must cover 12.5m.
Similarlywe can divide a fixed distance into infinite parts and runner had to cover that distance in "finite" time ,which is not possible.As one can't cover infinite distances in finite time.so,motion is not possible and what we see is illusion.
paradox 2nd "the arrow paradox"
zeno states that for motion to be occuring a body must change the position which it is occupying.
he gives an example -for a arrow to be moving it must move to where it is or to where it is not.since both are impossible .soit is at rest.
paradox 3
If every thing has a place then place must also have a place and so on.

          

zeno's paradox

Posted by sarath at Feb 24, 2009 08:56 PM
Zeno's paradoxes illustrates that motion was an illusion.Though there are more paradoxes the most famous is:
 In a race, the quickest runner can never overtake the slowest,(if initially the slowest is ahead of the quickest), as the quickest will always have to run a finite distance to catch the slowest. & by the time he reaches that point, which was initially occupied by the slowest he would have gone even further ahead.
              But thinking properly we see that this is not really a paradox.Our inductive mind tells us that the faster one would overtake the slower one after a time say T.In the paradox we see that we are never reaching that time.we are only talking about some t<T.Actually when lim(t)-T the faster one would overtake.
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