1. Zeno's Paradoxes - Wikipedia, The Free Encyclopedia The Archimedean solution is intended only to show that the simple model where distance and time are modelled by real numbers resolves Zeno's paradox, not that this model is http://en.wikipedia.org/wiki/Zeno's_paradoxes

Zeno's paradoxes From Wikipedia, the free encyclopedia Jump to: navigation search "Achilles and the Tortoise" redirects here. For other uses, see Achilles and the Tortoise (disambiguation) "Arrow paradox" redirects here. For other uses, see Arrow paradox (disambiguation) File:Espiral no end.jpg This file is a candidate for speedy deletion . It may be deleted after Friday, October 22, 2010. Zeno's paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion . It is usually assumed, based on Plato's Parmenides 128c-d, that Zeno took on the project of creating these paradoxes because other philosophers had created paradoxes against Parmenides's view. Thus Zeno can be interpreted as saying that to assume there is plurality is even more absurd than assuming there is only "the One" ( Parmenides 128d). Plato makes

2. Zeno's_paradox Synonyms, Zeno's_paradox Antonyms | Thesaurus.com No results found for zeno's_paradox Please try spelling the word differently, searching another resource, or typing a new word. http://thesaurus.com/browse/Zeno's_paradox

3. Zeno's Paradox - Conservapedia Zeno's paradox, formulated by the polytheist Zeno the Greek, is a philosophical paradox about the number . It states that a person can never traverse from one point to another point http://www.conservapedia.com/Zeno's_paradox

Zeno's paradox From Conservapedia Jump to: navigation search Zeno's paradox , formulated by the polytheist Zeno the Greek , is a philosophical paradox about the number . It states that a person can never traverse from one point to another point because he would first go half the distance, then half of what remains, then half of what remains next, and then half of that half. This process keeps continuing indefinitely by halving subsequent distances repeatedly. This argument seems to suggest no one can make this trip in finite time, but this is obviously not true. Mathematically, Zeno's paradox asks if has a value (notice each successive term is half of its predecessor). Using an infinite series mathematicians can express this value symbolically as: which numerically attains the value: Retrieved from " http://www.conservapedia.com/Zeno%27s_paradox Categories Philosophy Mathematics Views Page talk page View source History Personal tools Log in Search Popular Links Main Page Educational Index Debate Topics Recent changes ... Random page Help Help Index Statistics Conservapedia Commandments World History World History Lectures World History Homework Edit Console What links here Related changes Special pages Printable version ... Permanent link This page was last modified on 11 August 2008, at 19:31.

4. Zeno's_paradox Zeno's Paradox(es) As everyone knows, it is impossible to ever get anywhere. If you are currently at point A and wish to move to a different point, B you must first traverse half http://faculty.salisbury.edu/~kmshannon/zeno.htm

Zeno's Paradox(es) As everyone knows, it is impossible to ever get anywhere. If you are currently at point A and wish to move to a different point, B you must first traverse half the distance from A to B then half the remaining distance, then half the still remaining distance, ad infinitum. No matter what you do, you will always have half the remaining distance left, right? This version of Zeno's paradox has even made it to Hollywood, featured in the 1994 film, IQ, where Meg Ryan's character uses the paradox in an attempt to fend off the charismatic mechanic played by Tim Robbins. Of course you can debunk this one as easily as he did. Simply walk across the room and out the door. You know you get there. So what was wrong with Zeno? Another version of Zeno's paradox involves a race between Achilles and a Tortoise. Achilles can run 10 times as fast as the tortoise and therefore gives the tortoise a ten meter head start. However, if the tortoise has a ten meter head start how can Achilles ever catch him? By the time Achilles reaches the 10 meter mark, the tortoise will be at 11 meters. By the time Achilles gets there the tortoise will be at 11.1 meters and so on. This process of looking at where the tortoise will be when Achilles catches up to where he WAS can be repeated indefinitely creating an infinite sequence of snapshots all showing the tortoise still ahead. Therefore, Achilles, even though he runs ten times as fast as the tortoise, will never catch up. Next Page Outline Home K.M.Shannon

5. Zeno's Paradox - Uncyclopedia, The Content-free Encyclopedia Zeno claimed to be a great philosopher and mathemagician, but everyone knows that's not true. He was formally known as Zeno of Elea, but he was the only Zeno living from 490 to http://uncyclopedia.wikia.com/wiki/Zeno's_Paradox

6. Zeno's Paradox - Joseph Mazur - Penguin Group (USA) Find Zeno's Paradox by Joseph Mazur and other Science books online from Penguin Group (USA)'s online bookstore. Read more with Penguin Group (USA). http://us.penguingroup.com/nf/Book/BookDisplay/0,,9780452289178,00.html?Zeno's_P

7. Zeno's Paradox - Discussion And Encyclopedia Article. Who Is Zeno's Paradox? Wha Zeno's paradox. Discussion about Zeno's paradox. Ecyclopedia or dictionary article about Zeno's paradox. http://www.knowledgerush.com/kr/encyclopedia/Zeno's_paradox/

8. Zeno's Paradox Of The Tortoise And Achilles (PRIME) Zeno's classic paradox, from the Platonic Realms Interactive Math Encyclopedia. http://www.mathacademy.com/pr/prime/articles/zeno_tort/index.asp

BROWSE ALPHABETICALLY LEVEL: Elementary Advanced Both INCLUDE TOPICS: Basic Math Algebra Analysis Biography Calculus Comp Sci Discrete Economics Foundations Geometry Graph Thry History Number Thry Physics Statistics Topology Trigonometry eno 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 Iliad .) It has inspired many writers and thinkers through the ages, notably Lewis Carroll and Douglas Hofstadter, who also wrote dialogues involving the Tortoise and Achilles. The original goes something like this: The 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. Achilles said nothing. Zeno's Paradox may be rephrased as follows. Suppose I wish to cross the room. First, of course, I must cover half the distance. Then, I must cover half the remaining distance. Then, I must cover half the remaining distance. Then I must cover half the remaining distance . . . and so on forever. The consequence is that I can never get to the other side of the room.

9. Math Forum: Zeno's Paradox The great Greek philosopher Zeno of Elea (born sometime between 495 and 480 B.C.) proposed four paradoxes in an effort to challenge the accepted notions of space and time that he http://mathforum.org/isaac/problems/zeno1.html

Zeno's Paradox A Math Forum Project Table of Contents: Famous Problems Home The Bridges of Konigsberg The Value of Pi Prime Numbers ... Links The great Greek philosopher Zeno of Elea (born sometime between 495 and 480 B.C.) proposed four paradoxes in an effort to challenge the accepted notions of space and time that he encountered in various philosophical circles. His paradoxes confounded mathematicians for centuries, and it wasn't until Cantor's development (in the 1860's and 1870's) of the theory of infinite sets that the paradoxes could be fully resolved. Zeno's paradoxes focus on the relation of the discrete to the continuous, an issue that is at the very heart of mathematics. Here we will present the first of his famous four paradoxes. Zeno's first paradox attacks the notion held by many philosophers of his day that space was infinitely divisible, and that motion was therefore continuous. Paradox 1: The Motionless Runner A runner wants to run a certain distance - let us say 100 meters - in a finite time. But to reach the 100-meter mark, the runner must first reach the 50-meter mark, and to reach that, the runner must first run 25 meters. But to do that, he or she must first run 12.5 meters. Since space is infinitely divisible, we can repeat these 'requirements' forever. Thus the runner has to reach an infinite number of 'midpoints' in a finite time. This is impossible, so the runner can never reach his goal. In general, anyone who wants to move from one point to another must meet these requirements, and so motion is impossible, and what we perceive as motion is merely an illusion.

10. Zeno's Race Course, Part 1 Thoughtful lecture notes for discussing this paradox, presented by S. Marc Cohen . http://faculty.washington.edu/smcohen/320/zeno1.htm

The Paradox Zeno argues that it is impossible for a runner to traverse a race course. His reason is that Physics Why is this a problem? Because the same argument can be made about half of the race course: it can be divided in half in the same way that the entire race course can be divided in half. And so can the half of the half of the half, and so on, ad infinitum So a crucial assumption that Zeno makes is that of infinite divisibility : the distance from the starting point ( S ) to the goal ( G ) can be divided into an infinite number of parts. Progressive vs. Regressive versions How did Zeno mean to divide the race course? That is, which half of the race course Zeno mean to be dividing in half? Was he saying (a) that before you reach G , you must reach the point halfway from the halfway point to G ? This is the progressive version of the argument: the subdivisions are made on the right-hand side, the goal side, of the race-course. Or was he saying (b) that before you reach the halfway point, you must reach the point halfway from S to the halfway point? This is the

11. Zeno's Paradoxes (Stanford Encyclopedia Of Philosophy) Almost everything that we know about Zeno of Elea is to be found in the opening pages of Plato's Parmenides. There we learn that Zeno was nearly 40 years old when Socrates was a http://plato.stanford.edu/entries/paradox-zeno/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free Zeno's Paradoxes First published Tue Apr 30, 2002; substantive revision Fri Oct 15, 2010 Almost everything that we know about Zeno of Elea is to be found in the opening pages of Plato's Parmenides 1. Background 2. The Paradoxes of Plurality 2.1 The Argument from Denseness 2.2 The Argument from Finite Size ... Related Entries 1. Background is As we read the arguments it is crucial to keep this method in mind. They are always directed towards a more-or-less specific target: the views of some person or school. We must bear in mind that the arguments are ad hominem reductio ad absurdum So whose views do Zeno's arguments attack? There is a huge literature debating Zeno's exact historical target. As we shall discuss briefly below, some say that the target was a technical doctrine of the Pythagoreans, but most today see Zeno as opposing common-sense notions of plurality and motion. I will approach the paradoxes in this spirit, and refer the reader to the literature concerning the interpretive debate. 2. The Paradoxes of Plurality

12. Zeno S Paradoxes - Wikipedia, The Free Encyclopedia Zeno s paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides s doctrine that all is one and that, http://en.wikipedia.org/wiki/Zeno's_paradoxes

13. Zeno's Paradox - Joseph Mazur - Penguin Group (USA) Find Zeno's Paradox by Joseph Mazur and other Science books online from Penguin Group (USA)'s online bookstore. Read more with Penguin Group (USA). http://us.penguingroup.com/nf/Book/BookDisplay/0,,9780452289178,00.html?sym=REV

14. Zeno S Paradoxes - Simple English Wikipedia, The Free Encyclopedia Zeno s Paradoxes are a famous set of thoughtprovoking stories or puzzles http://simple.wikipedia.org/wiki/Zeno's_paradoxes

15. Zeno’s Paradox – Floating Sun I first read about Zeno's paradox in GEB. Amazing guy, this Zeno. I mean, until GEB, I had never really appreciated paradoxes like 'this sentence is false'. http://floatingsun.net/2005/01/19/zenos-paradox/

16. Zeno's Paradox Zeno's Paradox While critical thinking may not make up for a lack of knowledge, it is essential for gaining knowledge. http://ronz.blogspot.com/

Zeno's Paradox While critical thinking may not make up for a lack of knowledge, it is essential for gaining knowledge. Friday, December 14, 2007: Critical Thinking, Humor: ED The Future (EDTF) External delivery refers to a scientific research program as well as a community of older kids, teachers, and other adults who seek evidence of external sources of Christmas presents. The theory of external delivery holds that certain features of how Christmas presents are delivered each year are best explained by an external source, not an internal source such as your parents. Yes, Virginia, there is evidence for External Delivery, and it's all tongue-in-cheek. - Ron 10:58 AM Tuesday, December 11, 2007: Influence: The Christmas Campaign In recent years some media pundits and "culture warriors" have waged a vocal campaign against a so-called "War on Christmas." Targeting department stores, local governments and school systems for replacing Christmas with "Happy Holidays" or "Seasons Greetings," Bill O'Reilly and John Gibson of Fox News have led the charge against what they call a "secular progressive agenda" determined to drive religion out of the public square. William Donohue of the Catholic League for Religious and Civil Rights warns of "cultural fascists" bent on destroying Christmas. The real assault on Christmas, however, is an excessive consumer culture that has turned a holy season into a celebration of commercialism and materialism. By focusing our attention on shopping malls and the consumerism that accompanies Christmas, this misguided campaign further distracts us from the real message of the holiday.

17. Zeno S Paradox - Uncyclopedia, The Content-free Encyclopedia Aug 12, 2010 Zeno claimed to be a great philosopher and mathemagician, but everyone knows that s not true. He was formally known as Zeno of Elea, http://uncyclopedia.wikia.com/wiki/Zeno's_Paradox

18. The Interpretation Of Zeno S Paradox And The Theory Of Forms Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://muse.jhu.edu/journals/journal_of_the_history_of_philosophy/v002/2.2allen.

19. Zeno's Paradoxes Zeno's Paradoxes Copyright 1997, Jim Loy. Among the most famous of Zeno's paradoxes involves Achilles and the tortoise, who are going to run a race. http://www.jimloy.com/physics/zeno.htm

Return to my Physics pages Go to my home page Zeno's Paradoxes Among the most famous of Zeno's "paradoxes" involves Achilles and the tortoise, who are going to run a race. Achilles, being confident of victory, gives the tortoise a head start. Zeno supposedly proves that Achilles can never overtake the tortoise. Here, I paraphrase Zeno's argument: Before Achilles can overtake the tortoise, he must first run to point A, where the tortoise started. But then the tortoise has crawled to point B. Now Achilles must run to point B. But the tortoise has gone to point C, etc. Achilles is stuck in a situation in which he gets closer and closer to the tortoise, but never catches him. What Zeno is doing here, and in one of his other paradoxes, is to divide Achilles' journey into an infinite number of pieces. This is certainly permissible, as any line segment can be divided into an infinite number of points or line segments. This, in effect, divides Achilles' run into an infinite number of tasks. He must pass point A, then B, then C, etc. And what Zeno is arguing is that you can't do an infinite number of tasks in a finite amount of time. Why not? Zeno says that you can divide a line into an infinite number of pieces. And then he says that you cannot divide a time interval into an infinite number of pieces. This is inconsistent.

20. Zeno's Paradox... - Platforms - National Theatre Plays and performances at all three theatres at the National Theatre. Information on what's on and calendar of performances and events and activities, locations, history, behind http://www.nationaltheatre.org.uk/4737/platforms/zenos-paradox.html

Skip to Content Login Register View basket ... Zeno's paradox... Zeno's paradox... Learn more about some of the mathematical, scientific and philosophical conundrums in Tom Stoppard's Jumpers Mathematician Helen Joyce and philosopher Tim LeBon talk about Zeno's paradoxes, infinitesimals, the limit of polygons, logical positivism, space travel, the existence of God and other themes from the play. The paradoxes of the philosopher Zeno, born approximately 490 BC in southern Italy, have puzzled mathematicians, scientists and philosophers for millennia. The most famous of Zeno's arguments is the Achilles: 'The slower when running will never be overtaken by the quicker; for that which is pursuing must first reach the point from which that which is fleeing started, so that the slower must necessarily always be some distance ahead.' This is usually put in the context of a race between Achilles and the Tortoise. Achilles gives the Tortoise a head start of, say 10 m, since he runs at 10 ms-1 and the Tortoise moves at only 1 ms-1. Then by the time Achilles has reached the point where the Tortoise started (T0 = 10 m), the slow but steady individual will have moved on 1 m to T1 = 11 m. When Achilles reaches T1, the labouring Tortoise will have moved on 0.1 m (to T2 = 11.1 m). When Achilles reaches T2, the Tortoise will still be ahead by 0.01 m, and so on. Each time Achilles reaches the point where the Tortoise was, the cunning reptile will always have moved a little way ahead. This seems very peculiar. We know that Achilles should pass the Tortoise after 1.11 seconds when they have both run just over 11 m, so Achilles will win any race longer than 11.11m. But why in Zeno's argument does it seem that Achilles will never catch the tortoise…?

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