Egap

2006-07-15 10:53:17 UTC

"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:- ***@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.

.

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:- ***@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.

.