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 "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.

Deloated10 wrote:

The Paradox of Zeno

There is no paradox. Trasnfinite numbers cleaned things up in the
late 1960s.
[snip]

Psychotic ineducable boring retic (Ernest Wittke),
http://w0rli.home.att.net/youare.swf
http://www.mazepath.com/uncleal/sunshine.jpg
http://www.you-moron.com/
http://groups.google.com/groups?q=gr...uthor%3Awittke

http://www.apa.org/journals/psp/psp7761121.html
http://insti.physics.sunysb.edu/~siegel/quack.html
http://www.firehead.org/~jessh/film/kubrick/Kubrick-Psycho.html
http://www.naturalchild.com/elliott_barker/prisons.html

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)
[snip]

Hey, stooopid Ernest Wittke - Do you want EVIDENCE? Each of the 24
GPS satellites carries either four cesium atomic clocks or three
rubidum atomic clocks in orbit, with full relativistic corrections
being applied.

http://arXiv.org/abs/hep-th/0307140
GR structure, especially Part 4/p. 7
http://rattler.cameron.edu/EMIS/journals/LRG/Articles/Volume4/2001-4will/index.html
Experimental constraints on General Relativity.
http://rattler.cameron.edu/EMIS/journals/LRG/Articles/Volume6/2003-1ashby/index.html
http://www.eftaylor.com/pub/projecta.pdf
Relativity in the GPS system

http://fourmilab.to/etexts/einstein/specrel/specrel.pdf
http://www.physics.gatech.edu/people/faculty/finkelstein/relativity.pdf
http://users.powernet.co.uk/bearsoft/Paper6.pdf
http://users.powernet.co.uk/bearsoft/LPHrel.html
Longitudinal and transverse mass

http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf
http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm
http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm
http://www.trimble.com/gps/index.html
http://sirius.chinalake.navy.mil/satpred/
http://www.phys.lsu.edu/mog/mog9/node9.html
http://egtphysics.net/GPS/RelGPS.htm
http://www.schriever.af.mil/gps/Current/current.oa1
http://edu-observatory.org/gps/gps_books.html
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

If anyone
provides a significant rebuttal that cannot be objectively answered, the
material at the Website will be withdrawn.

Right, like your head has ever been withdrawn from your ass - even
when you ****.


--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

Deloated10 wrote:

The Paradox of Zeno

The Paradox of Zeno is 2000 years old and its apparent ability
snipped


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.

Your solution has been around for a couple hundred years already. The
problem is that it doesn't address the real paradox, which is that if
time is a succession of 'instants' (zero time intervals), then motion
cannot occur. A thoughtful resolution to the paradox is simply that the
premise is incorrect, i.e. that time is not a succession of instants,
but rather it is a succession of infinitesimal intervals which are
always constrained to be greater than zero. Thus enters a seeming link
to quantum processes, and even to quantum geometry. Stay that thought,
because there is another thoughtful resolution that is a bit more
correct:

Motion, in mathematical form, invokes the concept of speed, and speed in
turn requires a non-zero time interval in order to define it, hence
motion truly doesn't exist in any given instant, by shear definition of
speed (speed = ds/dt), and thus we have an alternate resolution to the
paradox, i.e. that the statement 'motion cannot exist if time is a
succession of instants' turns out to be precisely valid and correct and
we can therefore allow for the reality that that time is indeed a
succession of instants, without the least contradiction to the motions
of objects. And thus explains the success of the Calculus in dealing
with true continuums, that is, it is perfectly ok to let the interval
shrink to exactly zero when summations of sequences are not involved in
the calculations, but rather are shortcut by some other law of Calculus
such as differential equations. It is our notion that a continuum can be
segmented into discrete non zero elements that is incorrect, thus the
reason that approach always gives only approximations rather than exact
solutions.

JMTCW

Richard Perrry

(Deloated10) 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.


Delo, perhaps Zeno was half right. Not all arrows reach their target.

Peter Riedt