The Paradox of Zeno: An Analysis of the 2000-Year-Old Puzzle

[Egap]

"The Paradox of Zeno"

"The Paradox of Zeno"

The Paradox of Zeno is 2000 years old and its apparent ability to prove
that all motion is impossible was not resolved until the mathematical
techniques of Calculus became available, even though that technique is not
required. One form of the paradox describes the flight of an arrow which has
been shot at a target. The arrow is shot at a constant velocity, V, to a
target at a distance, L, and the time of flight is divided into intervals.
In the first interval, the arrow covers half of the distance to the target
and, in each succeeding interval of time, it covers half of the remaining
distance. Under the line of reasoning presented, the arrow never reaches the
target because, after each successive interval of time, one half of the
distance to the target that existed at the beginning of the interval
remains.

The author finds it incredible that this paradox has been taken
seriously by intelligent men for over two millennia and has not been
recognized as a form of trickery. If one accepts that in each successive
interval of time the arrow traveled half of the remaining distance to the
target, he must also accept that each of those successive intervals of time
is half of the duration of the interval which preceded it. As a result,
under the Paradox of Zeno, not only does the arrow never reach the target,
the elapsed time of its flight never reaches the time, T, when the arrow
would reach the target.

There is no paradox in the Paradox of the Zeno. As long as one allows a
cheap trick to fool him into considering only those events which occur prior
to the arrival of the arrow at the target, he most certainly will believe
that the arrow never reaches the target. The reality is that THE PASSAGE OF
TIME DOES NOT SLOW AS THE ARROW APPROACHES THE TARGET AND THE ARROW REACHES
THE TARGET WHEN IT SHOULD.

To find the Paradox of Zeno be seriously considered as a topic which
requires a level of mathematics beyond simple arithmetic for its resolution
should lead a reasonable man to have serious doubts as to the mental
capacity of the individuals who are engaged in the teaching process.

The source material for this posting may be found in
http://einsteinhoax.com/hoax.htm/ (1997);
http://einsteinhoax.com/gravity.htm (1987); and
http://einsteinhoax.com/relcor.htm (1997). EVERYTHING WHICH WE ACCEPT AS
TRUE MUST BE CONSISTENT WITH EVERYTHING ELSE WE HAVE ACCEPTED AS TRUE, IT
MUST BE CONSISTENT WITH ALL OBSERVATIONS, AND IT MUST BE MATHEMATICALLY
VIABLE. PRESENT TEACHINGS DO NOT ALWAYS MEET THIS REQUIREMENT. THE WORLD IS
ENTITLED TO A HIGHER STANDARD OF WORKMANSHIP FROM THOSE IT HAS GRANTED WORLD
CLASS STATUS.

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E-mail:- einsteinhoax@isp.com. If you wish a reply, be sure that your
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The material at the Website has been posted continuously for over 8
years. In that time THERE HAVE BEEN NO OBJECTIVE REBUTTALS OF ANY OF THE
MATERIAL PRESENTED. There have only been hand waving arguments by
individuals who have mindlessly accepted the prevailing wisdom without
questioning it. If anyone provides a significant rebuttal that cannot be
objectively answered, the material at the Website will be withdrawn.
Challenges to date have revealed only the responder's inadequacy with one
exception for which a correction was provided...

 

[FSC729@yahoo.com]

Aristotle solved the problem of motion along with the paradox of Zeno,
using his own philosophical concepts. Zeno was a student of Parmenides,
Parmenides believed that motion is impossible because it would imply
that "the entity", the thing in itself aside from all sensory
phenomena, would have to change. The only problem is that the only
quality that the entity can have is "being" so any type of change would
necessarily imply non-being of the entity, which is contradictory since
the only defining quality of the entity is being or existence. Also the
entity is always present, the sensory perception can be near or far or
not at all, but the entity is always present, another problem with
motion.

So according to Parmenides motion is impossible on two fronts, a
traveling arrow going from point A to point B would have to cease to
exist at point A and begin to exist at point B, otherwise if it exists
at every point on its path we run into Zeno's paradox. So, we have the
problem of existence and the problem of sensory perception.

Aristotle solved the problem by making motion "a thing in itself",
stating that motion cannot be broken down into parts, movement must be
seen as a whole. Aristotle's solution is a little more complicated than
that, but that is the essence of it. All calculus did was give us the
tools to break movement down in a special way as to allow mathematical
analysis and avoid Zeno's paradox.

John G.

Egap wrote:
> "The Paradox of Zeno"
>
> The Paradox of Zeno is 2000 years old and its apparent ability to prove
> that all motion is impossible was not resolved until the mathematical
> techniques of Calculus became available, even though that technique is not
> required. One form of the paradox describes the flight of an arrow which has
> been shot at a target. The arrow is shot at a constant velocity, V, to a
> target at a distance, L, and the time of flight is divided into intervals.
> In the first interval, the arrow covers half of the distance to the target
> and, in each succeeding interval of time, it covers half of the remaining
> distance. Under the line of reasoning presented, the arrow never reaches the
> target because, after each successive interval of time, one half of the
> distance to the target that existed at the beginning of the interval
> remains.
>
> The author finds it incredible that this paradox has been taken
> seriously by intelligent men for over two millennia and has not been
> recognized as a form of trickery. If one accepts that in each successive
> interval of time the arrow traveled half of the remaining distance to the
> target, he must also accept that each of those successive intervals of time
> is half of the duration of the interval which preceded it. As a result,
> under the Paradox of Zeno, not only does the arrow never reach the target,
> the elapsed time of its flight never reaches the time, T, when the arrow
> would reach the target.
>
> There is no paradox in the Paradox of the Zeno. As long as one allows a
> cheap trick to fool him into considering only those events which occur prior
> to the arrival of the arrow at the target, he most certainly will believe
> that the arrow never reaches the target. The reality is that THE PASSAGE OF
> TIME DOES NOT SLOW AS THE ARROW APPROACHES THE TARGET AND THE ARROW REACHES
> THE TARGET WHEN IT SHOULD.
>
> To find the Paradox of Zeno be seriously considered as a topic which
> requires a level of mathematics beyond simple arithmetic for its resolution
> should lead a reasonable man to have serious doubts as to the mental
> capacity of the individuals who are engaged in the teaching process.
>
> The source material for this posting may be found in
> http://einsteinhoax.com/hoax.htm/ (1997);
> http://einsteinhoax.com/gravity.htm (1987); and
> http://einsteinhoax.com/relcor.htm (1997). EVERYTHING WHICH WE ACCEPT AS
> TRUE MUST BE CONSISTENT WITH EVERYTHING ELSE WE HAVE ACCEPTED AS TRUE, IT
> MUST BE CONSISTENT WITH ALL OBSERVATIONS, AND IT MUST BE MATHEMATICALLY
> VIABLE. PRESENT TEACHINGS DO NOT ALWAYS MEET THIS REQUIREMENT. THE WORLD IS
> ENTITLED TO A HIGHER STANDARD OF WORKMANSHIP FROM THOSE IT HAS GRANTED WORLD
> CLASS STATUS.
>
> All of the Newsposts made by this site may be viewed at
> http://einsteinhoax.com/postinglog.htm.
>
> Please make any response via E-mail as Newsgroups are not monitored on
> a regular basis. Objective responses will be treated with the same courtesy
> as they are presented. To prevent the wastage of time on both of our parts,
> please do not raise objections that are not related to material that you
> have read at the Website. This posting is merely a summary.
>
> E-mail:- einsteinhoax@isp.com. If you wish a reply, be sure that your
> mail reception is not blocked.
>
> The material at the Website has been posted continuously for over 8
> years. In that time THERE HAVE BEEN NO OBJECTIVE REBUTTALS OF ANY OF THE
> MATERIAL PRESENTED. There have only been hand waving arguments by
> individuals who have mindlessly accepted the prevailing wisdom without
> questioning it. If anyone provides a significant rebuttal that cannot be
> objectively answered, the material at the Website will be withdrawn.
> Challenges to date have revealed only the responder's inadequacy with one
> exception for which a correction was provided.
>
>
> .

 

[Entropia]

I find the Paradox of Zeno to be a fascinating and thought-provoking puzzle. While it may seem like a simple trick at first glance, the concept of infinite divisions of time and space raises interesting questions about the nature of motion and our understanding of the physical world.

However, I also agree with the author's point that this paradox should not be taken as a serious challenge to our current understanding of physics. The development of Calculus and other mathematical techniques has allowed us to better understand and explain the concept of motion, and we now have a much more sophisticated understanding of how objects move through space and time.

It is important to remember that science is a constantly evolving field, and our current understanding of the physical world may be refined or even completely overturned in the future. But as scientists, it is our responsibility to approach these challenges with open minds and rigorous analysis, rather than dismissing them as mere trickery.

In conclusion, the Paradox of Zeno serves as a reminder of the complexities and mysteries that still exist in our world, and it should continue to be studied and analyzed by scientists and philosophers alike.