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  1. Zeno's Paradoxes
  2. Zeno's Paradox by F. Gordon Robinson, 2007-10-25
  3. Zeno's Paradox: Unraveling the Ancient Mystery Behind the Science of Space and Time by Joseph Mazur, 2008-03-25
  4. Why mathematical solutions of Zeno's paradoxes miss the point: Zeno's one and many relation and Parmenides' prohibition.: An article from: The Review of Metaphysics by Alba Papa-Grimaldi, 1996-12-01
  5. The Paradoxes of Zeno (Avebury Series in Philosophy) by J. A. Faris, 1996-10
  6. Key Contemporary Concepts: From Abjection to Zeno's Paradox (Sage Key Concepts) by John Lechte, 2003-02-24
  7. Zeno's paradox and the problem of free will.: An article from: Skeptic (Altadena, CA) by Phil Mole, 2004-01-01
  8. Modern Science and Zeno's Paradoxes by Adolf Grunbaum, 1967
  9. Zeno's Paradoxes
  10. The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes by David J. Darling, 2007-02-28
  11. Towards a definitive solution of Zeno's paradoxes by Fazal Ahmad Shamsi, 1973
  12. Modern science and Zeno's paradoxes by Adolf Grunbaum, 1968
  13. MODERN SCIENCE AND ZENO'S PARADOXES. by Adolf. Grunbaum, 1968

41. Talk:Stephenson:Neal:Quicksilver:165:Zeno's Paradox (Matt Zwolinski) - Metaweb
TalkStephensonNealQuicksilver165Zeno s paradox (Matt Zwolinski). From the QuicksilverMetaweb. Talk for Xeno or Zeno From a Lay Person s Point of View.
http://www.metaweb.com/wiki/wiki.phtml?title=Talk:Stephenson:Neal:Quicksilver:16

42. Zeno's Paradox - People Mentioned
UsabilityViews.com Home Page, Zeno s paradox Site Mentions, UsabilityViews.comHome Page. Name, Mentions on Zeno s paradox. Ron Zeno, 37. Jakob Nielsen, 4.
http://www.usabilityviews.com/userati_zeno.html
Zeno's Paradox - Site Mentions home timeline recent popular ... about this site Name Mentions on
Zeno's Paradox Ron Zeno Jakob Nielsen ... Angeles none Timo Arnall none Ricardo Baeza-Yates none Bob Baxley none Dan Beauchamp none Scott Berkun none Mark Bernstein none Nigel Bevan none Peter Bogaards none Danah Boyd none Owen Briggs none Fred Brooks none Bill Buxton none Catriona Campbell none Stuart Card none John Carroll none Steve Champeon none Kevin Cheng none Tom Chi none Tom Coates none Larry Constantine none Alan Cooper none Kara Pernice Coyne none David Crow none Mary Czerwinski none Michael Dertouzos none Dan Diaper none Andrew Dillon none Paul Dourish none Allison Druin none Doug Engelbart none Tom Erickson none Meryl Evans none Xristine Faulker none Louise Ferguson none Nick Finck none Geraldine Fitzpatrick none BJ Fogg none Anne Galloway none Jesse James Garret none Adele Goldberg none Saul Greenberg none Adam Greenfield none Eszter Hargittai none Marti Hearst none Challis Hodge none Adrian Holovaty none Karen Holtzblatt none Molly Holzschlag none William Hudson none Mark Hurst none Keith Instone none Scott Isensee none Matt Jones none Joshua Kaufman none Alan Kay none Steve Krug none Brenda Laurel none Bruce Lawson none Ann Light none Gitte Lindgaard none Lucy Lockwood none Victor Lombardi none Chad Lundgren none Erin Malone none Deborah Mayhew none Beth Mazur none Gerry McGovern none Madhu Menon none Eric Meyer none Lucian Millis none Peter Morville none Joy Mountford none Brad Myers none Carl Myhill none Elizabeth Mynatt none Bonnie Nardi none Ted Nelson none George Olsen none Henrik Olsen none Andrew Otwell none Christine Perfetti none Gary Perlman none

43. Zeno's Paradox - Architecture Forum
Message Zeno s paradox. Responses Re Zeno s paradox Richard Haut 0956571/26/2002 (3) Re Zeno s paradox Jacques Pochoy 101127 1/26/2002 (2)
http://www.designcommunity.com/discussion/13365.html
Design
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Message - Zeno's Paradox Responses Architecture Forum Architecture Students Architecture Scrapbook ... ArchitectureWeek
Posted by Paul Malo on January 26, 2002 at 09:19:06: In Reply to: Re: fractal posted by Jacques Pochoy on January 24, 2002 at 15:16:41: Wasn't it Zeno who formulated the famous conundrum, that if you divide the distance between any two points in half, and when you are haflway to your destination, divide the remaining distance in half, and when 3/4 there, divide the remaining quarter in half (etc.) you can never reach your destination, because the process is infinite? This may descirbe the design process when there is no deadline, but always something more than can be done before we are "ready." Of course, we are never ready, but have to conclude anyway.
ArchitectureWeek Search Buildings Architects ... Library Search GreatBuildings.com by name of Building, Architect, or Place:
Examples: "Fallingwater", "Wright", "Paris" Advanced Search
Responses:

44. Re: Zeno's Paradox - Already There - Architecture Forum
Message Re Zeno s paradox - already there. In Reply to Re Zeno sparadox posted by Jacques Pochoy on January 26, 2002 at 101127
http://www.designcommunity.com/discussion/13408.html
Design
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Message - Re: Zeno's Paradox - already there Responses Architecture Forum Architecture Students Architecture Scrapbook ... ArchitectureWeek
Posted by JWmHarmon on January 27, 2002 at 09:36:53: In Reply to: Re: Zeno's Paradox posted by Jacques Pochoy on January 26, 2002 at 10:11:27: I have always been fascinated by Zeno's paradox. I read somewhere once that we can logically conclude that since we observe ourselves on the other side of the doorway, even though we cannot logically get there (always having to go half the remaining distance first), that we must have been there all the time. Talk about being two places at once! Logically then we must be everywhere we have ever been and everywhere we will ever be, all at the same time. We cannot get to where we are going, but we observe that we in fact do arrive. Again, this proves that we are already there. Time then would be just an illusion. Perhaps Bishop Berkeley (spelling?) was right... we are all just characters in God's dream. In that case we can be omnipresent with the Almighty. What has this to do with architecture? It just goes to "prove" that there are no new ideas. All designs and inventions already exist. We just have to open the right door to see them. Remember that, the next time you specify a door for your building design.

45. Zeno's Paradox
zeno s paradox Time 4 54 Lyrics Andy Wagner First performed November 22,1997 show 4 Appears as track 2 on Pastor of Muppets Tim electric
http://www.losingblueprint.com/hmmobzenos.html
[zeno's paradox]
[Time: 4'54"]
[Lyrics: Andy Wagner]
[First performed November 22, 1997 show #4]
[Appears as track #2 on "Pastor of Muppets"]
[Tim: electric bass, Nevin: violin, Kort: bouzouki, Jamie: percussion, vocals, Andy: guitar, vocals, Thom: guitar, vocals]
This is definitely a math-rock song. It deals with Zeno's Paradox,
which states that you can never get from point A to point B without going half
of the distance, and then half of the remaining distance, and then half of that
remaining distance, etc., thus you have to travel through an
infinite number of half-distances, and can never get there. And imagining yourself at point A, and the object of your enamoration at point B. Instant romance! Viva la math! I proffered my first step toward you And in that advance moved twice as near In calculating a foothold I thought I'd soon be there and you'd be here But the second stretch was not such a stretch And there still lay One quarter between us seamed from the half I'm trying to reach you but I'm thrown off by the math Should throw physics to the dogs And just jump, not crawl, not creep

46. ZENO'S PARADOX: A RESPONSE TO MR. LYNDS (by Eric Engle)
Zeno s paradox A response to Mr. Lynds by Eric Engle. paradoxes existto point out flaws in our reasoning. They are thus heuristic devices.
http://philsci-archive.pitt.edu/archive/00001333/01/ZENO.html
Zeno's Paradox: A response to Mr. Lynds
by Eric Engle
Paradoxes exist to point out flaws in our reasoning. They are thus heuristic devices. A paradox occurs when our presumptions are inadequate to solve a problem. Thus for example, if we believe (erroneously) that all statements must be either true or false we will quickly run into paradoxes. For example, the statement "this statement is false" is a classic paradox with no truth value. The statement is neither true nor false. It is indeterminate. (The tougher paradox of this art is in fact whether statements about unicorns have truth value - clearly unicorns do not exist - but does that mean that a statement about a non-existing entity is false or merely with no truth value?).
Paradoxes such as these exist because people think that all statements must have a truth value, that is that all statements are either true or false. In fact Aristotle in Posterior Analytics (
Zeno's paradoxes all concern motion. Zeno effectively asks "How can motion be possible?" This paradox is arguably of little heuristic value today because we have since Einstein at least recognized that time and matter-energy are convertible elements, the same thing in fact. Thus rather than seeing a solid object, an arrow, existing at definite points in its trajectory, the correct view is to see a wave of energy following the arrows trajectory with much greater mass/energy presence at certain instances of space time.
That understanding is radically different from the ancients such as Zeno. For the ancients just as geometric points had no dimension just location so also material loci were either void (kenon) or contained atoms. It is fair to say that geometric points and atoms corresponded to each other in the ancient conception of physics. For some, probably most, ancients matter and energy were not transmutable: rather the indestructible nature of atoms was a presumption of at least some ancients.

47. PhilSci Archive - Zeno's Paradox: A Response To Mr. Lynds
Zeno s paradox A response to Mr. Lynds. Engle, Eric Allen (2003) Zeno s paradoxA response to Mr. Lynds. Zeno s paradox A response to Mr. Lynds.
http://philsci-archive.pitt.edu/archive/00001333/
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Zeno's Paradox: A response to Mr. Lynds
Engle, Eric Allen (2003) Zeno's Paradox: A response to Mr. Lynds. Full text available as: HTML
Abstract
A brief explanation of the heuristic value of paradoxes as well as a critique of Mr. Lynds's argument by reductio ad absurdam. Commentary on: Lynds, Peter (2003) Zeno's Paradoxes: A Timely Solution. EPrint Type: Preprint Keywords: Zeno's Paradox, Lynds, Physics, Paradox, Reductio, Time Subjects: Specific Sciences Physics ID Code: Deposited By: Engle, Eric Deposited On: 15 August 2003 Additional Information: A brief critique of Mr. Lynds theory Alternative Locations: http://www.lexnet.bravepages.com/ZENO.html
Commentary/Response Threads

48. Phorum - Humor - Zeno's Paradox
Zeno s paradox. Author Glyn (10.33.40.) Date 02-01-01 1657 A mathematicianand a physicist agree to a psychological experiment.
http://www.hiw.kuleuven.ac.be/phorum/read.php?f=5&i=3&t=3

49. Zeno's Paradox And Quantum Physics
Zeno s paradox and quantum physics By totse Mar 12, 2004, 1157. Title Can tget there from here; quantum physics puts a new twist on Zeno s paradox.
http://www.unexplainable.net/artman/publish/article_617.shtml
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Zeno's paradox and quantum physics
By totse
Mar 12, 2004, 11:57
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

50. American-Scientist-Open-Access-Forum: Zeno's Paradox And The Road To The Optimal
Zeno s paradox and the Road to the Optimal/Inevitable. From Stevan ZENO Sparadox AND THE ROAD TO THE OPTIMAL/INEVITABLE. Zeno s paradox
http://www.ecs.soton.ac.uk/~harnad/Hypermail/Amsci/0819.html
Zeno's Paradox and the Road to the Optimal/Inevitable
From: Stevan Harnad ( harnad@COGPRINTS.SOTON.AC.UK
Date: Sat Sep 02 2000 - 22:40:56 BST ZENO'S PARADOX AND THE ROAD TO THE OPTIMAL/INEVITABLE
Zeno's Paradox was the one about the philosopher who thought: "How can
I possibly get across this room? For before I can do that, I have to

51. American-Scientist-Open-Access-Forum: Re: Zeno's Paradox And The Road To The Opt
Re Zeno s paradox and the Road to the Optimal/Inevitable. Maybe in reply toStevan Harnad Zeno s paradox and the Road to the Optimal/Inevitable ;
http://www.ecs.soton.ac.uk/~harnad/Hypermail/Amsci/0823.html
Re: Zeno's Paradox and the Road to the Optimal/Inevitable
From: Stevan Harnad ( harnad@COGPRINTS.SOTON.AC.UK
Date: Sun Sep 03 2000 - 12:08:40 BST I leave it to others to reply further to Joseph Ransdell if they wish;
to me it seems he is debating irrelevant points of ideology and
interpretation, rather than points of susbtance and practice. He thinks
self-archiving papers in the Ginsparg Archives is primary publication.
Fine, let him call it what he wishes, as long as authrs actually go
ahead and do it, rather than taking such interpretations as a further
basis for Zeno's Paralysis. But his misinterpretation of the CALL to
self-archive-so-as-to-free-the-literature rather than the
self-archiving itself as the actual freeing of the literature [1]
seems so off-the-mark that one can only think it willful.

52. Another Point Of View On Zeno S Paradox - Technology Services
paradox. View Thread Another point of view on Zeno s paradox. ClickHere Another point of view on Zeno s paradox. Doron
http://www.physicsforums.com/archive/t-4470
Physics Help and Math Help - Physics Forums Physics General Physics Theory Development View Thread : Another point of view on Zeno's paradox
Another point of view on Zeno's paradox
Doron Shadmi If we use the idea of sets and look at their contents from
a structural point of view, we can find this:
Let power be the simplest level of existence of some set's content.
So, from a structural point of view, we have a quantum-like leap.
Now, let us explore the two basic structural types that exist.
0^0 = [oo]^0 = 1 and we can see that we can't distinguish between
Continuum and Discreteness by their Quantity property.
In the Common Math the Continuum is a container of infinitely many points with no gaps between them, but if you think about the meaning of "points with no gaps..." you find a simple contradiction when you connect the word "points" to "no gaps".
Through this approach you don't have any contradiction between the Discreteness and the Continuum concepts, because any point is not in the Continuum, but an event that breaks the Continuum.
The Continuum does not exist in this event, but any two events can be connected by a Continuum, for example the end of a line is an event that breaks the line and it turns to a nothingness, so from one side we have the Continuum, from the other side we have the nothingness, and between them we have a break point, that can be connected to another break point that may exist on the other side of the continuous line.

53. Zeno's Paradox Of The Arrow
Zeno’s paradox of the Arrow. A reconstruction of the argument. Go toprevious lecture on the Zeno s paradox of the Race Course, part 2.
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. (

54. Forays Into Mathematics
Zeno s paradox The Race Between Achilles and the Tortoise. Achilles wasa mythological Greek warrior who was also famous as a very fast runner.
http://www.psyber.com/~jacob/math/math.html

55. Election Snared In Zeno's Paradox: Absurdity Knows No Bounds
Zeno s paradox and the 2000 Election The Limits of Absurdity. As the marginnarrows we are trapped in ever finer distinctions Zeno s paradox.
http://www.nexial.org/ION/zeno.htm
Institute of Nexialism Zeno's Paradox and the 2000 Election: The Limits of Absurdity John J. Kineman
Nexial Institute
Boulder, Colorado
November 13, 2000 Xenophanes was a Greek philosopher who lived in the 6 th Century BC. He is famous for "Zeno's Paradoxes," which were logical, or mathematical puzzlers. One of them is told as a race between a tortoise and a hare (or Achilles, in the original version). The Hare, wanting very badly to race, agrees to give the tortoise a half-way head start. The tortoise agrees, but on the condition that this is done repeatedly for each segment. It then follows that dividing the distance in half indefinitely this way will never end, and thus the hare cannot win. Zeno's paradox is a logical trap that appears in certain problems; and, as it turns out, in popular elections. Take another example: the distance from Los Angeles to San Francisco. What paradox can exist in that, you ask? We can certainly calculate the flying distance. We all know that the road distance will be longer because of all the curves. What about the distance along the coastline? Well, if you follow all the coves and inlets, it is quite long. And if you follow smaller features the variations within the coves, the individual rocks, the sand grains, and so on then how long is it? If the wiggliness of the water's edge (the "fractal dimension" of the coastline) remains about the same at any scale, then the distance is infinite Zeno's Paradox! There is a practical solution, of course. The paradox is a matter of

56. Zeno's Paradox. The New Dictionary Of Cultural Literacy, Third Edition. 2002
2002. Zeno’s paradox. (ZEEnohz) A paradox is an apparent falsehoodthat is true, or an apparent truth that is false. Zeno, an
http://www.bartleby.com/59/5/zenosparadox.html
Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia Cultural Literacy World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations Respectfully Quoted English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference The New Dictionary of Cultural Literacy World Literature, Philosophy, and Religion PREVIOUS ... BIBLIOGRAPHIC RECORD The New Dictionary of Cultural Literacy, Third Edition. ZEE -nohz) A paradox is an apparent falsehood that is true, or an apparent truth that is false. Zeno, an ancient Greek, argued that a number of apparent truths such as motion and plurality are really false. A well-known, simplified version of one of his paradoxes is that an arrow can never reach its target, because the distance it must travel can be divided into an infinite number of subdistances, and therefore the arrow must take an infinite amount of time to arrive at its destination.

57. Metamanda's Weblog: Zeno's Paradox
August 04, 2003. Zeno s paradox.
http://www.metamanda.com/blog/oldstuff/000117.html
Main
August 04, 2003
Zeno's Paradox
Ground-breaking work in understanding of time , via slashdot While I couldn't find the paper in question, "Time and Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity" by Peter Lynds, I did find this other paper he wrote, which is pretty cool: Zeno's Paradoxes: A Timely Solution (pdf). It cites his quantum mechanics paper, and I'm guessing actually reuses a lot of the content. NB: this paper does exhibit some signs that the author is a crackpot. But it's kind of fun to read anyway. Reviewers of the paper seem to think it's either Einsteinianly brilliant, or "based on profound ignorance or misunderstanding of basic analysis and calculus". Found the paper I was originally talking about , but haven't read it yet. I'm a sucker for paradoxes by old greek guys. The only thing more delicious than Zeno is Epimenides . "Preceded by its own quotation yields falsehood" preceded by its own quotation yields falsehood. Their are three erors in this sentence. Ah.... it sends shivers up my spine. TrackBack
Comments Signs of a not so good writer maybe, but signs of a crack pot? Geez.

58. Metamanda S Weblog Comment On Zeno S Paradox
Metamanda s Weblog. Comments Zeno s paradox. Signs of a not so good writermaybe, but signs of a crack pot? Geez. I m glad you enjoyed the paper.
http://www.metamanda.com/cgi-bin/mt-comments.cgi?entry_id=117

59. Minding The Planet: Zeno's Paradox, Finally Solved?
August 06, 2003. Zeno s paradox, Finally Solved? Listed below are linksto weblogs that reference Zeno s paradox, Finally Solved? Comments.
http://novaspivack.typepad.com/nova_spivacks_weblog/2003/08/zenos_paradox_f.html
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    Debra is a good friend; she's a really talented fashion designer. She started the yoga fashion craze. Check out her site.

60. Totse.com | A New Quantum- Physics Twist On Zeno's Paradox Of M
www.totse.com A new quantum- physics twist on Zeno s paradox ofm - A new quantum-physics twist on Zeno s paradox of motion.
http://www.totse.com/en/fringe/fringe_science/zeno.html
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. They called this surprising phenomenon the quantum Zeno effect. Now

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