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 and it does not require the
techiques associated with calculus for its resolution. 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 "Gravity" (1987),
"The Einstein Hoax" (1997), and "Corrections to Residual Errors in Special
Relativity (1999) located at http://www.members.aol.com/einsteinhoax/site.htm .
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.

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.

For a response send E-Mail to

The material at the Website has been posted continuously for over 5 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.

"Niatnoc24" wrote

The material at the Website has been posted continuously for over 5
years.
In that time THERE HAVE BEEN NO OBJECTIVE REBUTTALS OF ANY OF THE MATERIAL
PRESENTED.

This is clearly a lie.

There have only been hand waving arguments by individuals who have
mindlessly accepted the prevailing wisdom without questioning it.

This also is clearly either a lie or just plain ignorance.

Pmb

"Pmb" wrote in message
...

"Niatnoc24" wrote

The material at the Website has been posted continuously for over 5
years.
In that time THERE HAVE BEEN NO OBJECTIVE REBUTTALS OF ANY OF THE
MATERIAL
PRESENTED.

This is clearly a lie.

There have only been hand waving arguments by individuals who have
mindlessly accepted the prevailing wisdom without questioning it.

This also is clearly either a lie or just plain ignorance.

Pmb
Whilst I would generally disagree with you, Pmb, in this case I fully
concur. I have objectively rebutted the arguments, but met with a response
of "you don't know what you are talking about". Plainly the author doesn't
understand objectivity and considers it to mean "agree with me".

Androcles

There is no justification for attributing a time t, save by measurement, and
Zeno was pointing out that measurements concerning motion embody a paradox.

"Niatnoc24" wrote in message
...
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 and it does not
require the
techiques associated with calculus for its resolution. 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 "Gravity"
(1987),
"The Einstein Hoax" (1997), and "Corrections to Residual Errors in Special
Relativity (1999) located at
http://www.members.aol.com/einsteinhoax/site.htm .
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.

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.

For a response send E-Mail to

The material at the Website has been posted continuously for over 5
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.

Tom M-G wrote:

There is no justification for attributing a time t, save by measurement, and
Zeno was pointing out that measurements concerning motion embody a paradox.

But they don't. Achilles beats the turtle, right on schedule.

Bob Kolker