61. Analysis WebNotes: Chapter 01, Class 01 Zeno s paradox. Suppose an arrow is flying through the air. Before it can reachits target, it first has to cross at least half the distance between the http://www.math.unl.edu/~webnotes/classes/class01/Zeno.htm

Zeno's Paradox: Suppose an arrow is flying through the air. Before it can reach its target, it first has to cross at least half the distance between the archer and the target. But after it has reached the midway point, it still has to cross half the remaining distance. And after crossing that, it must cross half of the yet remaining distance. In fact, this process goes on for ever, because the distance between the arrow and its target can always be halved, and the first half always stands between the arrow and its destination. So, there are infinitely many states the arrow must pass through before it can hit the target, and only a finite amount of time to do it in. The arrow can't possibly do infinitely many things in finite time, and so it can never reach the target. (in fact the same argument, applied to the journey from the bow to any point on its path, shows that any motion at all is impossible for it!) What's wrong with the argument? If your answer involves adding up infinitely many things, ask yourself how you can do infinitely many things (additions in this case) in finite time-a computer couldn't! What about a bouncing ball? If at every bounce it only reached half as high up as at the last bounce, does it ever completely stop bouncing?

62. Art Museum Network News Robert Arnold Zeno s paradox to Show at DeCordova Saturday, September 10, 2005 —Sunday, January 8, 2006. DeCordova Museum and Sculpture Park http://www.amnnews.com/press.jsp?id=2729

63. Geocaching: Zeno's Paradox Out) Main Greetings from California 1 ». December 26, 2004. Zeno s paradox.Is this one coming back? Posted by jeff at December 26, 2004 0100 PM. http://boulter.com/geocaching/archives/013118.html

Geocaching boulter's geocaching logs Main December 26, 2004 Zeno's Paradox Is this one coming back? Posted by jeff at December 26, 2004 01:00 PM

64. Geocaching: Zeno's Paradox Zeno s paradox. 850 am DNF 3. I spent a good half-hour looking, but came upempty-handed. My coordinates were confirmed with mmp who confirmed them with http://boulter.com/geocaching/archives/013216.html

Geocaching boulter's geocaching logs Main January 31, 2005 Zeno's Paradox 8:50 am - DNF #3. I spent a good half-hour looking, but came up empty-handed. My coordinates were confirmed with mmp who confirmed them with the owners. There's quite a few places to look for a micro in this area within reasonable GPS accuracy, even excluding the ivy. If the difficulty of this cache is supposed to be in solving the puzzle and not in locating the micro, then a descriptive hint would be helpful. I did find a secret walkway though which at least made the trip in shorter. Posted by jeff at January 31, 2005 08:50 AM

65. Zeno's Paradox Non Archimedean version of Zeno s paradox. Recall the usual version has Achilleschasing a turtle, where the turtle is given a ten cubit head start and http://www.lix.polytechnique.fr/Labo/Ilan.Vardi/zeno.html

Non Archimedean version of Zeno's paradox. Recall the usual version has Achilles chasing a turtle, where the turtle is given a ten cubit head start and Achilles runs ten times faster than the turtle. When Achilles runs 10 cubits, the turtle goes 1 cubit. When Achilles runs 1 cubit, the turtle goes 1/10 of a cubit. It follows that Achilles catches the turtle in 10 + 1 + 1/10 + ... cubits. In modern notation, one can write these numbers as decimals yielding It follows that Achilles catches the turtle in 11 1/9 cubits. The non Archimedean case has the turtle trying to catch Achilles who is now given a ten cubit head start. When the turtle goes 10 cubits, Achilles will have run 100 cubits. When the turtle goes 100 cubits then Achilles will have run 1000 cubits, and so on. It follows that the turtle goes 10 + 100 + 1000 + .... Ordinarily, this would be considered as meaningless or ``infinity''. However, one can consider this purely formally, in other words, without caring too much about the actual meaning of the numbers and just using algebraic manipulations. So let x = 10 + 100 + 1000+ ..., then 9(x + 1) = 9 + 90 + 900 + 9000 + ... = ... 9999.

66. ChuckJerry.com: Home D has stumbled upon Zeno s paradox. It appears to have blown his mind. Now fora little philosophy. I ve read something very interesting lately, http://www.chuckjerry.com/thoughts/zeno.shtml

ChuckJerry.com : Haven't you ever wondered? home about me my wedding great stories ... email me last update: 8/16/04 My Thoughts Fruition Thoughts From the Last Update Just Rambling Life Was Better Politics of Fruit Pain and Suffering ... Road Signs Other People's Thoughts Mini Thoughts Vanilla vs. Chocolate Objective Deep Thought Russians ... Road Signs Thoughts About Religion Mini Thoughts on Religion Why D Believes In God Religion Sucks Religion Doesn't ... Blind vs. Limited Zeno's Paradox D has stumbled upon Zeno's Paradox . It appears to have blown his mind.

67. Zeno's Paradox Of The Arrow Go to next lecture on Empedocles. Go to previous lecture on the Zeno s Paradoxof the Race Course, part 2. Return to the PHIL 320 Home Page http://www.aarweb.org/syllabus/syllabi/c/cohen/phil320/ZenoArrow.htm

A reconstruction of the argument (following Aristotle, Physics 239b5-7 = RAGP 10): 2. At every moment of its flight, the arrow is in a place just its own size. 3. Therefore, at every moment of its flight, the arrow is at rest. The argument falsely assumes that time is composed of "nows" (i.e., indivisible instants). There is no such thing as motion (or rest) "in the now" (i.e., at an instant). The velocity of x at instant t can be defined as the limit of the sequence of x t x is in a place just the size of x at instant i " entails neither that x is resting at i nor that x is moving at i Perhaps instants and intervals are being confused: "When?" can mean either "at what instant?" (as in "When did the concert begin?") or "during what interval?" (as in "When did you read War and Peace 1a. At every instant false 2a. At every instant during its flight, the arrow is in a place just its own size. ( true 1b. During every interval true 2b. During every interval of time within its flight, the arrow occupies a place just its own size. (

68. Minding The Planet: Zeno's Paradox, Finally Solved? Listed below are links to weblogs that reference Zeno s paradox, Finally Solved? Zeno s paradox is flawed logic. So it s no wonder that this amateur http://novaspivack.typepad.com/nova_spivacks_weblog/2003/08/zenos_paradox_f.html

Minding the Planet About Subscribe to Minding The Planet... Click this button: Radar Networks Photo Albums Nova's Trip to Edge of Space Recent Posts Katrina Disaster: Where is the Military? DUH - Design by Unintelligent Hand Remote Control Humans Idea for Safer Submarines ... Fascinating Article Surviving a Nuclear Attack on Washington DC Categories Alternative Medicine Alternative Science Artificial Intelligence Biology ... Wireless Technology Recent Comments fanglong on I'm Learning Tibetan chip jones on I Want Wireless Power Kara on DuPont Chemical Found in Blood of 96% of People in USA Andy Schindler on I Want Wireless Power jamie ferguson on I Want Wireless Power Sarah on Humans Should Intentionally Seed Life on Mars. Why We Must Start Now. Starry on Walking Libraries Storing Messages in DNA... Main August 06, 2003 Zeno's Paradox, Finally Solved? This article claims that a 20 year old amateur scientist in New Zealand has solved the age-old paradox of Zeno, which states that you can never travel to any point in space since you have to travel half the distance, and then half of half the distance, etc. August 06, 2003 in

69. DC.pm Paul Ceruzzi Zeno s paradox and the History of Computing. Pages 1 2 3. Pages1 2 3. Date March 5, 2002. (Photos by Larry Hixson) http://dc.pm.org/cgi-bin/gallery?gallery_num=1

70. Zeno Zeno s paradox and the Creationist Demand for Transitional Forms Now it isnot difficult to see that Zeno s paradox doesn t apply to real life. Why? 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 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.

71. The 2+2 Forums: Zeno's Paradox (continued) Zeno s paradox boils down to saying (staying with this specific example) that ifyou re moving at a constant rate of 1.0 mph, you won t cover 1.0 mile http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=2929946&page=0&vi

72. The 2+2 Forums: Zeno's Paradox (continued) Zeno s paradox boils down to saying (staying with this specific example) that ifyou re moving at a Re Zeno s paradox (continued) new Re BobFeduniak http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=2937641&Main=2929946

73. Science Blog -- Zeno's Quantum Paradox Reversed: Watching A Flying Arrow Increas Zeno s quantum paradox reversed Watching a flying arrow increase its speed.Is motion an illusion? Can glimpses freeze radioactive decay? http://www.scienceblog.com/community/older/2000/F/200005451.html

From: Weizmann Institute Zeno's quantum paradox reversed: Watching a flying arrow increase its speed 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 every line is composed of an infinite number of points). One of these paradoxes is known as the arrow paradox: if the motion of a flying arrow is divided ad infinitum, then during each of these infinitesimal moments, the arrow is at rest. The sum of an infinity of zeroes remains zero, and therefore the arrow cannot move. One can imagine how someone giving a flying arrow quick, repeated glimpses, can actually freeze it in place. Zeno inferred from this that movement cannot happen. Indeed, he was a true follower of Parmenides, his teacher and mentor, who advocated that any change in nature is but an illusion.

74. Lines Of Embarkation, Stan Rogal: Zeno's Paradox ZENO S paradox The first letter of any poem is always a . Comfort (even) for anold Greek. Zeno, for instance, would applaud. Such immutability. http://www.chbooks.com/online/lines_of_embarkation/18.html

ZENO'S PARADOX The first letter of any poem is always 'a'. Comfort (even) for an old Greek. Zeno, for instance, would applaud. Such immutability. Such endless non-progression. Never reaching halfway until half-way to halfway Achilles lost at the starting line where a fleet forward step would boil any distanced turtle to plodding soup. Puzzled by the shortness of his own mean feat to disentangle from this literal knot. Or: Held fast between Scylla and Charybdis rearranges itself to mean web scented, can hardly sail by. Not hardly, Achilles, but unable. The same general rule applies. 'The ampersand sign' is 'met reshaping "ands"' 'a poem' also begins with '"a"'

75. Zeno's Paradox Essay Unique collection—our essays appear nowhere else online. Zeno s paradox Essay Pass.• $6.99 for this one essay • Access available for 30 days http://www.bookrags.com/essays/story/2004/10/27/02348/753

Search BookRags.com English History Other Subjects Essays Biographies Research Topics eBooks Register Login Help Literature Study Guides ... Games Welcome, Guest Why not Login or Register Essays Navigation Submit an Essay for Points View My Essays Explain Points and Status Home Essays › Zeno's Paradox Help/FAQ Category: All Categories Literature Art Business History Humanities Social Sciences Sciences Grade Level: All Grade Levels Elementary School Middle School Junior High School High School College - Undergrad College - Graduate Search Terms: as Phrase Match All Zeno's Paradox Grade Level: High School , Section: Mathematics , Rating: Summary: Provides a discussion of Zeno's Paradoxes and a description of how they work. Gives biographical detail on the life of Zeno of Elea. 4.4 pages / 1322 words Read Essay What if someone told you that motion was not real and had a way to prove it? That is just what Zeno of Elea did in his studies during the 400s BC. I chose this topic in hopes to learn something new, and I did. I also chose this topic because it not only involved mathematics, but philosophical thinking as well. When I first read about how someone had a way to argue that motion and some of the physics of motion were not true, I was rather intrigued. I know now, however, that these theories are not true and can be proved false. I will get more in depth into each paradox that Zeno proposed and then show how using modern day mathematics they are false. Zeno of Elea was born in a small ....

76. Essay On Zeno's Paradox, Irresistible Forces, Immovable Objects, The Universe, B Have you ever heard of Zeno s paradox? Well, it goes something like this. Zeno s paradox was put forth, back over 2000 thousand years ago when it was http://www.allnerdsandgeeks.com/index.Paradox.html

Essay on Zeno's Paradox, irresistible forces, immovable objects, the universe, black holes, the human brain, reptiles, and the war on terrorism Have you ever heard of Zeno's Paradox? Well, it goes something like this. . . . . . . What happens when an irresistible force meets an immovable object? There is no answer to this question, and any physics professor will tell you that the question is invalid. If there is an irresistible force, then there can be no immovable objects, and if there are immovable objects, then there can be no irresistible forces. It is quit obvious that we do not live in a universe of immovable objects. That's obvious since everything in the universe is in motion. Zeno's Paradox was put forth, back over 2000 thousand years ago when it was assumed that the Earth was in the center of the cosmos, and therefore it was believed to be immovable, while the sun and planets was thought to revolve around the Earth. Now we can theorize about two different kinds of universes, each one with it's own set of physical laws that are self consistant with one universe in which there are immovable objects, and another universe where there are irresistible forces. Each universe would operate by it's own set of laws that are consistent within itself, but the laws of one would be different from the laws of the other. So, in a universe of immovable objects, there can be no irresistible forces. That would violate the physical laws of such a universe, and in the other universe of irresistible forces, there can be no immovable objects because that would violate the physicals laws of that universe. Therefore no universe can exist that has both immovable objects and irresistible forces. That would be a contradiction.

77. Untitled1.html This paradoxical fate of Zeno s paradox deserves most minute attention. For Nabokov s narrative is another miseen-scene of the Zeno s paradox - however http://www.pd.org/topos/perforations/perf6/uncanny_linetski_p6.html

NABOKOV AND SWIFT, ACHILLES AND THE TORTOISE: THE SUBLIME INNOCENCE, OR THE UNCANNY RETURN OF THE REFERENT IN POSTSTRUCTURALIST THEORY ALONG THE LINES OF ZENO'S PARADOX Vadim Linetski The vogue which the Zeno's famous paradox enjoys in poststructuralist theory is not surprising. It is this paradox which provides a point of convergence between the main strands associated with the illustrious names of Deleuze, Lacan and Derrida as well as between the crucial issues of poststructuralist project - those of difference/alterity, identity construction and the "bar games" with the referent (Genosko 1994: 7, 41) - furnishing the framework for the allegedly non-logocentric redefinition of the status of the work of art and aesthetic activity in general. However, as the attempts to attain a critical distance from what has already become a poststructuralist orthodoxy gain in strength and scope, the reasons that of yore have pushed our paradox to the fore become obscured if not obfuscated. This paradoxical fate of Zeno's paradox deserves most minute attention. If the efforts to carve the path beyond deconstruction have thus far so obviously failed to produce anything worthwhile, then precisely because the paradoxicality just mentioned points to the very heart of the problem with which theorists unsuccessfully grapple for the last thirty or so. In most general terms the problem in question is the undoubdtfully honorouble task of surpassing logocentric tradition in all its forms and disguises, the task for which the name of Derrida has become totemic. And yet the very mood characteristic of the current theoretical scene - that of melancholic scepticism - seems to suggest that the deconstructive project, by and large, has fizzled out. Fortunately, as we shall see, the funeral is not fatal, for the deceased has been buried alive. Put otherwise, it is not so easy to kill the mocking-bird of deconstruction, this Phoenix of sorts.

78. [Z] ZENO S paradox. A paradox devised by the Greek philosopher Zeno, which seems toprove that motion as such is impossible; Reason Consider an arrow flying 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

79. Theorized Solution To Zeno's Paradox (Philosophistry) Theorized Solution to Zeno s paradox. Lynd emailed me the other day in responseto my complaint that Why hasn t anybody solved Zeno s paradox. http://www.philosophistry.com/archives/2003/08/000504.html

Philosophistry Theorized Solution to Zeno's Paradox Lynd e-mailed me the other day in response to my complaint that "Why hasn't anybody solved Zeno's Paradox." This is an exerpt of what he had to say... Lynds' solution to the Achilles and the tortoise paradox, submitted to Philosophy of Science, helped explain the work. A tortoise challenges Achilles, the swift Greek warrior, to a race, gets a 10m head start, and says Achilles can never pass him. When Achilles has run 10m, the tortoise has moved a further metre. When Achilles has covered that metre, the tortoise has moved 10cm...and so on. It is impossible for Achilles to pass him. The paradox is that in reality, Achilles would easily do so. A similar paradox, called the Dichotomy, stipulates that you can never reach your goal, as in order to get there, you must firstly travel half of the distance. But once you've done that, you must still traverse half the remaining distance, and half again, and so on. What's more, you can't even get started, as to travel a certain distance, you must firstly travel half of that distance, and so on. According to both ancient and present day physics, objects in motion have determined relative positions. Indeed, the physics of motion from Zeno to Newton and through to today take this assumption as given. Lynds says that the paradoxes arose because people assumed wrongly that objects in motion had determined positions at any instant in time, thus freezing the bodies motion static at that instant and enabling the impossible situation of the paradoxes to be derived. "There's no such thing as an instant in time or present moment in nature. It's something entirely subjective that we project onto the world around us. That is, it's the outcome of brain function and consciousness."

80. Totse.com | A New Quantum- Physics Twist On Zeno's Paradox Of M totse.org A new quantum- physics twist on Zeno s paradox of m - A newquantum-physics twist on Zeno s paradox of motion. http://www.totse.com/en/fringe/fringe_science/zeno.html

Link to totse.com! About Community Bad Ideas Drugs ... ABOUT A new quantum- physics twist on Zeno's paradox of m twist on Zeno's paradox. Can't Get There from Here Two thousand years ago the Greek philosopher Zeno noted that an object moving from one place to another must first reach a halfway point, and before that a point half of the way to the halfway point, and so on. Any movement involves an infinite number of intermediate points, and so any motion must require an infinite amount of time Motion, Zeno concluded, is logically impossible In fact, things do move Zeno did not consider that an endless series could have a finite sum. But in the counter-intuitive realm of quantum physics, something akin to Zeno's paradox can occur: atoms can be paralyzed if they are closely scrutinized. The act of observing prevents the atom from passing a halfway point between two energy levels. In 1977 E. C. George Sudarshan and Baidyanath Misra of the University of Texas at Austin realized that an unstable object, such as a radioactive atom, would never decay if it were observed continuously.

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