81. Re: O.K., Dick, Forget 'Zeno's Paradox', But Re OK, Dick, forget Zeno s paradox , but. In Reply to Re OK, Dick, forget Zeno s paradox , but posted by DickT on February 25, 2003 at 065024 http://superstringtheory.com/forum/extraboard/messages10/148.html

String Theory Discussion Forum String Theory Home Forum Index Re: O.K., Dick, forget 'Zeno's Paradox', but Follow Ups Post Followup Extra Dimensions X FAQ Posted by StephenZ on February 26, 2003 at 10:15:19: In Reply to: Re: O.K., Dick, forget 'Zeno's Paradox', but posted by DickT on February 25, 2003 at 06:50:24: Zeno never really intended to dethrone rational thinking but how we limit our thought should we follow only logical processes. The arrow does not accupy the total duration between the start and finish - the duration is a reference to the arrow's movement not the movement itself. The arrow in motion does not actually hold a position (that would lead to a logical paradox on the assumptions of a discrete world known at the time) but a trajectory. All movement follows a temporal direction based upon the initiation point and ends at the termination point - it does not occupy both points. The same applies to other paradox's of Zeno - the race of the tortoise and Achilles where distance is considered much the same way duration was with the arrow. Regards (Report this post to the moderator) Follow Ups: (Reload page to see most recent) Re: O.K., Dick, forget 'Zeno's Paradox', but

82. Re: O.K., Dick, Forget 'Zeno's Paradox', But Re OK, Dick, forget Zeno s paradox , but. In Reply to Re OK, Dick, forget Zeno s paradox , but posted by StephenZ on February 26, 2003 at 101519 http://superstringtheory.com/forum/extraboard/messages10/152.html

String Theory Discussion Forum String Theory Home Forum Index Re: O.K., Dick, forget 'Zeno's Paradox', but Follow Ups Post Followup Extra Dimensions X FAQ Posted by DickT on February 26, 2003 at 16:52:53: In Reply to: Re: O.K., Dick, forget 'Zeno's Paradox', but posted by StephenZ on February 26, 2003 at 10:15:19: StephenZ, Fraid I can't reduce your explanation to clear thoughts in my head. It sounds like you're saying "There is a mapping from a closed interval of time ("duration") to an open set of space such that maps into the particle's initial position and d maps into its final position". If this is what you were saying, how does it meet Zeno's objections? It appears to me you are just denying them. Regards, Dick (Report this post to the moderator) Follow Ups: (Reload page to see most recent) Post a Followup Follow Ups Post Followup Extra Dimensions X FAQ

83. Wu :: Forums - Zeno's Paradox wu forums « wu forums Zeno s paradox » Welcome, Guest. PleaseLogin or Register. May 19 th , 2004, 157am. ZENO S paradox. http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action

84. Zeno Zeno s paradox and the Creationist Demand for Transitional Forms. This certainlywould evade Zeno s paradox if distance were infinitely divisible. http://home.entouch.net/dmd/zeno.htm

Zeno's Paradox and the Creationist Demand for Transitional Forms By Glenn R. Morton This may be freely distributed so long as no chances are made and no monetary charge is assessed. http://home.entouch.net/zeno.htm var go_mem="glennmorton"; free hit counter Visitors to these pages since 12-29-97 One might not think of modern anti-evolutionary apologists as having much in common with ancient Greek philosophers, but they do. What this paper will suggest is that they, like Zeno, argued for a particular viewpoint by creating an absurdity. Zeno believed his teacher Parmenides. Parmenides taught that sense data was an illusion. What you see isn't real. He taught that there was no change in the world, no multiplicity of objects. Being was one and all being was unchanging. Now it is not difficult to see that Zeno's paradox doesn't apply to real life. Why? Because the mathematical laws which are used in Zeno's paradoxinfinite divisibility of spacedoes not happen. It is clear from the fact that Zeno's demonstration that infinite divisibility requires no motion combined with the observation that athletes actually finish races that there comes a point in the division process in which the distance to the finish line is so small that it can no longer be divided. Thus, this paradox hints at the quantization of space, the famous del X of Heisenberg's uncertainty principle. While Zeno didn't come to that obvious conclusion, it is one mathematical way out of the paradox. Similarly, Zeno presented a paradox that said that our athlete could not beat a tortoise. Give the tortoise a head start on our swift athlete. In order to pass the tortoise, the runner must first reach the point where the tortoise started from. But by the time our muscle-bound but inept hero has gotten there, the tortoise isn't there anymore. He has moved a bit. So in order to pass the tortoise, the muscleman must now run to the place where the tortoise is now, but once again, the tortoise has already moved and the athlete can continue this forever and never catch up with the tortoise. Both of these paradoxes show that the continuum doesn't exist. Space is not equally divisible.

85. Zeno's Paradox FHTW Berlin, FHTW Berlin Fachbereich 4 Internationale Medieninformatik MMA II AktuelleThemen multimedialer Anwendungen Wintersemester 2003/2004. Zeno s paradox. http://www.f4.fhtw-berlin.de/~weberwu/didaktics/zeno.shtml

FHTW Berlin Fachbereich 4 Internationale Medieninformatik MMA II: Aktuelle Themen multimedialer Anwendungen Wintersemester 2003/2004 Zeno's Paradox Zeno of Elea (circa 450 b.c.) is credited with creating several famous paradoxes, but by far the best known is the paradox of the Tortoise and Achilles. (Achilles was the great Greek hero of Homer's The Illiad.) It has inspired many writers and thinkers through the ages, notably Lewis Carroll and Douglas Hofstadter, who wrote their own dialogues involving the Tortoise and Achilles. The original goes something like this: T he Tortoise challenged Achilles to a race, claiming that he would win as long as Achilles gave him a small head start. Achilles laughed at this, for of course he was a mighty warrior and swift of foot, whereas the Tortoise was heavy and slow. “How big a head start do you need?” he asked the Tortoise with a smile. “Ten meters,” the latter replied. Achilles laughed louder than ever. “You will surely lose, my friend, in that case,” he told the Tortoise, “but let us race, if you wish it.” “On the contrary,” said the Tortoise, “I will win, and I can prove it to you by a simple argument.”

86. Philosophy Forums - Zeno's Paradox zeno s paradox. Can anybody explain his paradox in mathematical terms? Zeno sparadox, Guddy, Philosophy of Science and Math, 27, 0623-03 0923 AM. http://forums.philosophyforums.com/showthread.php?goto=lastpost&t=7558

87. Zeno's Paradox This maze is a variation of one of the paradoxes proposed by Zeno. Zenostates that to travel a distance d, you need to cover d/2 first. http://www.sfu.ca/~dkeller/TOUCH_PC/TEXT/FAREWEL.HTM

Farewell , welfare (Literary note) Borges, when finishing his short story Death and the Compass, makes reference to an infinite labyrinth: a straight line. This maze is a variation of one of the paradoxes proposed by Zeno. Zeno states that to travel a distance d, you need to cover d/2 first. To get to d/2, you need to reach d/4. To. . . well, the story goes on. In other words, why ever move if we won't ever get anywhere?

88. Archive Of Astronomy Questions And Answers How do you reconcile Zeno s paradox with modern physics? You reconcile itby refuting Zeno s presumption that nature is infinitely divisible. http://www.astronomycafe.net/qadir/q520.html

How do you reconcile Zeno's paradox with modern physics? You reconcile it by refuting Zeno's presumption that nature is infinitely divisible. We know that at the atomic domain, particles are defined in terms of wave functions which connect all points in spacetime by a 'probability' that a particle will be found there. We also suspect that space-time itself cannot be subdivided below a scale of 10**-33 centimeters at which point space-time becomes a quantum mechanical 'thing' lacking a definite shape. Both of these things differ from Zeno's assumption that space and motion were subdividable infinitely, and it is in the TRUE character of space, time, and motion that the mathematical paradox is resolved once and for all. We do not live in an abstract mathematical universe, but one with lots of 'dirt' and things that go bump in the night!!! Return to Ask the Astronomer

89. Archive Of Astronomy Questions And Answers How is Zeno s paradox resolved in physics? See a previous question about this. Ithink that this goes a long way towards fuzzing out Zeno s paradox. http://www.astronomycafe.net/qadir/q1267.html

How is Zeno's Paradox resolved in physics? See a previous question about this. The basic idea is that the physical world is probably not infinitely divisible in time and space. Also ordinary quantum mechanics predicts that all particles have a built-in uncertainty in their position and velocity that makes their 'wave functions' be spread out in space and time, and not permanently defined at a specific point. I think that this goes a long way towards 'fuzzing out' Zeno's Paradox. Return to Ask the Astronomer

90. Perplexus.info :: Forums Sam. 200309-24 002438, New answer to Zeno s paradox He has written twosrticles on it and one of them deals directly with Zeno s paradox. http://perplexus.info/forum.php?fid=3&tid=271

91. ZenosParadox Zeno s paradox (English). Search for Zeno s paradox in NRICH PLUS maths.org Google. Definition level 2. If Achilles and a http://thesaurus.maths.org/mmkb/entry.html?action=entryById&id=1178

92. Zeno's Lag Ladder Zeno s paradox In the Athens of 5th Century BC, Zeno of Elea was a philosopher whobelieved that all motion and change was illusory, and reality was actually http://puttingzone.com/MyTips/ladder.html

Home Intro News Tips ... Geoff Zeno's Lag Ladder by Geoff Mangum http://www.puttingzone.com geoff@puttingzone.com The Artist ZipTip: Touch: Zeno's Lag Ladder Long putts that cause concern about coming up too short often cause the golfer to blow the ball too far past the hole, and a useful approach is to take a practice stroke to a target merely halfway to the hole, then take another practice stroke to a second target halfway between the first target and the hole, and then make the real stroke not shorter than the second practice stroke and with the same size increase in the stroke one big step halfway there, then two halfsize steps the rest of the way. Dr Dialtone Quarry Ridge, Portland CT Big Moss long-putt mat at the PGA Merchandise Show The Problem : Monster putts have you three-jacking? When facing a long putt that seems outside the comfort level for distance control, the typical golfer reaction is to dwell on the negative of leaving the putt too short for a two-putt. This anxiety causes the golfer then to "gas" the putt by adding force that he would not ordinarily add, in an effort to make sure the force of the putt is sufficient to overcome the anticipated shortfall. These "gassed" putts are the most common cause of three-putting. The ball almost always blows past the hole too far, and the golfer watches helplessly as the putt just won't stop rolling on the far side of the hole.

93. Zeno's Quantum Paradox Reversed: Watching A Flying Arrow Increase Its Speed More recently, scientists believed that the counterpart of this paradox, known asthe quantum Zeno paradox, is realizable in the microscopic world governed by http://www.globaltechnoscan.com/7june-13june/Zeno.htm

Please register here to Search or Submit B usiness O pportunities REGISTER HERE LOGIN Zeno's quantum paradox reversed: Watching a flying arrow increase its speed For Business Opportunities in Engineering Industry please click here Is motion an illusion? Can"glimpses" freeze radioactive decay? For over 2,500 years, scientists and philosophers have been grappling with Zeno of Elea's famous paradox. More recently, scientists believed that the counterpart of this paradox, known as the quantum Zeno paradox, is realizable in the microscopic world governed by quantum physics. Now, scientists from the Weizmann Institute of Science have shown that in most cases, the quantum Zeno paradox should not take place. An article describing the calculations that lead to this surprising conclusion appears in today's Nature. The article is also surveyed in the journal's News and Views section. The Greek philosopher Zeno, who lived in the 5th Century B.C., decades before Socrates, dedicated his life's work to showing the logical paradoxes inherent to the idea of indefinite divisibility in space and time (i.e., that

94. 03Motion01.nb § 12 Patterns of Motion Zeno s paradox, Achilles and the Tortoise, andInfinite Series Motion is movement through space, and through time. http://info.citruscollege.com/ff/RCarter/MA160/Notes/03Motion01/03Motion01.html

Patterns of Motion: Zeno's Paradox, Achilles and the Tortoise, and Infinite Series Motion is movement through space, and through time. Is motion continuous, or, discrete? Is it not true that a body in motion, at any particular instant, is really at rest in a particular space at that very moment? So how can the body move? The ancient Greeks concentrated their attentions mainly on geometry, and through the Renaissance, most analysis went towards static situations. Not until the invention of calculus by Isaac Newton and Gottlieb Liebniz were complete desriptions of motion possible . The Paradox of Motion Zeno's Paradox of the Arrow from http://faculty.washington.edu/smcohen/320/ZenoArrow.html Zeno"s Paradox from http://www.deltalink.com/dodson/html/puzzle.html Zeno Paradox from http://www.shu.edu/projects/reals/numser/answers/zeno.html Zeno's Paradox Achilles and the Tortoise Achilles races the Tortoise for, say, 100 meters. Tortoise is given a 10 meter start. By the time Achilles has reached the 10 meter mark, Tortoise has covered exactly 1 meter, and is therefore, 1 meter ahead. By the time Achilles has covered that 1 meter, Tortoise is now 1/10 meter ahead.

95. Jef's Web Files | Empathy, Energy, Efficiency, Extropy Zeno s paradox. Place to discuss Zeno s paradox. paradox Rationality.» Jef Allbright s blog login or register to post comments. http://www.jefallbright.net/node/view/1078

@import url(misc/drupal.css); @import url(themes/xtemplate/xtemplate.css); home misc about empathy ... extropy Home Subcategories: Empathy Energy Efficiency Extropy ... Zeno's paradox Place to discuss Zeno's paradox Paradox Rationality Jef Allbright's blog login or register to post comments Never express yourself more clearly than you think. - Niels Bohr User login Username: Password: Remember me Create new account Request new password Navigation recent posts Blogs China to crack supercomputer top 10 list Study: Self-Replicating Nanomachines Feasible Love really is blind... Quoth the raven ... more

96. [Z] Top Of HyperLex. Z. ZEPELLIN TUBE A source of immense power, possessedby the Sumatran RATs in an adventure of HEMLOCK STONES. ZENO S paradox http://home.earthlink.net/~ritter/firesign/lexicon/Z.html

Top Of HyperLex [Z] ZEPELLIN TUBE: A source of immense power, possessed by the Sumatran RAT s in an adventure of HEMLOCK STONES ZENO'S PARADOX: A paradox devised by the Greek philosopher Zeno, which seems to prove that motion as such is impossible; Reason: Consider an arrow flying towards a target. Before it gets to the target it must first get halfway there, but before it gets to that point it must first get 1/4 the way there, but before that (etc..) Since an infinite number of things must be done first, the arrow could never get *anywhere*; ergo, motion is impossible. This paradox is referred to indirectly in the TWO PLACES album, where BABE falls asleep in his car, while the talking freeway signs read off: "Antelope Freeway, one mile" "Antelope Freeway, one half mile" "Antelope Freeway, one quarter mile" "Antelope Freeway, one eighth mile" "Antelope Freeway, one sixteenth mile" "Antelope Freeway, one thirtysecondth mile" "Antelope Freeway, one sixty-fourth mile" "Antelope Freeway, one one-hundred-and-twenty-eighth mile" ... ZIPS: As in "I'm hip like a zip, let's take a trip". One of the

97. Zeno S Paradoxes objects is 0. The power of Zeno s paradox is that this solution requires thenotion of a limit and an understanding of how to compute infinite sums. http://chandra.bgsu.edu/~gcd/Zeno.paradoxes.html

Back to the course home page. Zeno's Paradoxes I. The Dichotomy (1) If anything moves from one place to another, then it performs infinitely many tasks. (2) Nothing can perform infinitely many tasks. Therefore, (3) Nothing moves. Is the argument valid? Is it sound (i. e., are all the premises true)? Aristotle rejects premise (2) on the grounds that Zeno has failed to distinguish between infinite divisibility and infinite extension. How might one justify (2)? Aristotle suggests the following argument: (A1) To complete an infinite number of tasks would require an infinite amount of time. (A2) Nothing can do anything which requires an infinite amount of time. Therefore, (A4) Nothing can perform infinitely many tasks. Aristotle rejects this argument in terms of the distinction between infinite divisibility and infinite extension. What then, he asks, is the justification for (2)? But, Aristotle's argument is not quite right, since the infinite divisibility of the motion is reduced to the infinite divisibility of the temporal interval of the motion. If this interval is infinitely divisible then it has an infinite number of parts and to get from one moment to the next requires an infinite series of steps. Aristotle introduces a new distinction between potential and actual infinities. Infinitely divisible intervals are only potentially infinite. But, the fact remains that the interval (either of motion or time or space) contains an infinite sequence of non-zero intervals.

98. FirstMatter Sidebar: Zeno's Paradox Zeno s paradox. An excerpt from the Reality Inspector by John Cariswith links. Go there Return to What I ve Learned About Visioning. http://www.firstmatter.com/newsletter/sidebar.asp?key=162&art=39

99. DC.pm YAPC 19100 June 2000 (Photos by Henry Hartley). Paul Ceruzzi Zeno s Paradoxand the History of Computing Pages 1 2 3. Pages 1 2 3. Date March 5, 2002. http://dc.pm.org/cgi-bin/gallery?gallery_num=1

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