Talk:Zeno's paradoxes

Bibliography

This list is intended to collect references thought to be relevant for the article. Delete entries only when they are blatantly and obviously inappropriate. In general, we want not only to collect useful references, but also be able to check new additions against previous discussions that lead to exclusion. Provide diffs, and update section links when they get archived.

The 2001 edition of Salmon's anthology lists at least 218 sources, so it is safe to say that this bibliography cannot be considered anywhere near comprehensive before we have passed the 200 mark.

• Grünbaum, Adolf (1967). Modern science and Zeno's paradoxes. Wesleyan University Press. Retrieved 13 February 2010.

• Grünbaum, Adolf (1968). Modern science and Zeno's paradox. Retrieved 13 February 2010.

• Salmon, Wesley C. (March 2001). Zeno's paradoxes. Hackett Publishing. ISBN 9780872205604. Retrieved 13 February 2010.

Salmon's book is one of the best on the subject. Huggett, in his article "Zeno's Paradoxes" in the Stanford Encyclopedia of Philosophy [1] writes: After the relevant entries in this encyclopedia, the place to begin any further investigation is Salmon (2001), which contains some of the most important articles on Zeno up to 1970, and an impressively comprehensive bibliography of works in English in the Twentieth Century . Paul August ☎ 14:22, 13 February 2010 (UTC)

The bibliography of my 1970 hardcover edition has 143 entries, the 2001 edition cited above has at least 218 (preview limit, sorry). Paradoctor (talk) 08:32, 25 February 2010 (UTC)

• Alper, Joseph S.; Bridger, Mark (1997). "Mathematics, Models and Zeno's Paradoxes". Synthese. 110 (1): 143–166. doi:10.1023/A:1004967023017. ISSN 0039-7857.

Abstract from the official page at Springer: "A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in discussing motion, only intervals, rather than instants, of time are meaningful. The approach presented here reconciles resolutions of the paradoxes based on considering a finite number of acts with those based on analysis of the full infinite set Zeno seems to require. The paper concludes with a brief discussion of the classical and quantum mechanics of performing an infinite number of acts in a finite time."

• Sewell, Kip K. (1 October 1999). The Cosmic Sphere. Nova Publishers. ISBN 9781560726616. Retrieved 1 March 2010.

Pages 14-15 (section 3 "Infinite Time" of chapter 1 "the Container of All Things") discuss the arrow paradox.

Footnote 10 on page 410 (for page 15 in section 3 "Infinite Time" of chapter 1 "the Container of All Things") discusses "proposals at the ability to cross an infinite provided infinite acceleration is assumed".

From Amazon's author page (WebCite): 'Kip Sewell holds an MLIS from the University of South Carolina and currently works as an information professional. He has also received BA and MA degrees in Philosophy and has been a college lecturer. "The Cosmic Sphere" (1999) is Sewell's first work on the subject of cosmology. He is currently revising the book and continues to explore issues in science, philosophy, and theology as an independent researcher.'

Apart from this book, Scirus, Google Scholar and WorldCat turned up nothing by Sewell.

IMO, a minor primary source, apparently not peer-reviewed, by a philosopher very early in his career. Paradoctor (talk) 01:17, 2 March 2010 (UTC)

• Paul A. Fishwick, ed. (1 June 2007). "15.6 "Pathological Behavior Classes" in chapter 15 "Hybrid Dynamic Systems: Modeling and Execution" by Pieter J. Mosterman, The Mathworks, Inc.". Handbook of dynamic system modeling. Chapman & Hall/CRC Computer and Information Science (hardcover ed.). Boca Raton, Florida, USA: CRC Press. pp. 15–22 to 15–23. ISBN 9781584885658. Retrieved 5 March 2010.

Defines "Zeno behavior", a concept from the field of verification and design of timed event and hybrid systems.

• Verelst, Karin. "Zeno's Paradoxes. A Cardinal Problem - I. On Zenonian Plurality" (PDF). PhilPapers. Retrieved 5 March 2010. arXiv:math/0604639

Criticizes the "Received View" on Zeno as untenable. Maintains that a "generally overlooked" key to Zeno arguments is that "they do not presuppose space, neither time". Paradoctor (talk) 17:33, 5 March 2010 (UTC)

Her official homepage (5 March 2010) Paradoctor (talk) 19:52, 5 March 2010 (UTC)

to do

• Paul Hornschemeier's most recent graphic novel, The Three Paradoxes, contains a comic version of Zeno presenting his three paradoxes to his fellow philosophers.
• Zadie Smith references Zeno's arrow paradox, and, more briefly, Zeno's Achilles and tortoise paradox, at the end of Chapter 17 in her novel White Teeth.
• Brian Massumi shoots Zeno's "philosophical arrow" in the opening chapter of Parables for the Virtual: Movement, Affect, Sensation.
• Philip K. Dick's short science-fiction story "The Indefatigable Frog" concerns an experiment to determine whether a frog which continually leaps half the distance to the top of a well will ever be able to get out of the well.
• Allama Iqbal's book The Reconstruction of Religious Thought in Islam discusses the paradox in Lecture II The Philosophical Test of the Revelations of Religious Experience, and suggests that motion is not continuous but discrete.
• Ursula K. Le Guin's character of Shevek in The Dispossessed discusses the arrow paradox in great amusement with his un-understanding classmates as a child.
• add missing refs from Rucker section below
• add refs deleted with this edit

Non-paradox

Zeno's paradox is not actually a paradox at all. Infinity cannot be done or completed.

We can cover the distance from 0 to 1 in innumerably many ways:

1/2 + 1/2 = 1 8/10+2/10 = 1 1/4 + 1/2 + 1/2 = 1 --> Your linear combination here

Now, if we were to cover the distance in the way Zeno described (*), it is TRUE that we will NEVER cover the distance from 0 to 1. There is NO paradox whatsoever!

(*) 1/2 + 1/4 + 1/8 + ... means we NEVER get to 1.

People are misunderstanding and reading the nonsense on Wikipedia isn't helping. The non-paradox emphasizes that if motion is done in a certain way, then it can be impossible to complete a given distance.

"...in order for an object to get to a position a distance away (let's call 1) it must first get halfway there."

It must also get 3/4 of the way there or 7/8 of the way there. So what?! That is a non-statement. It must pass a lot of places, but NONE of them are passed "FIRST". Be careful of how mainstream math cranks word their drivel - it is meant to throw you off. No distance is passed "first" - that's just hand waving or smoke and mirrors.

You need to be alert to the misguided and misleading way that this non-paradox is stated.

herman weyl

"According to this, the length of the hypotenuse of a right angled triangle in discretized space is always equal to the length of one of the two sides, in contradiction to geometry." -this sentence seems problematic, because it relates space with a distinstive attribute (discretized) to geometry without an an attribute. i cannot propose a solution since the meaning of "discretized" is unbeknowst to me, but i can propose an initial direction of reseach that is try replacing "geometry" with " euclidian geometry" as a formal (linguistical) corrction and check the meaning and reltiobn between "discretionalized" and "euclidian".

also im missing from the article a simple worded paragraph that would tell that the zeno paradoxes result in an so to say impossibility of the event observed in reality because the question is framed to look at a time frame that by its definition excludes the event of achilles reaching the turtle or the arrow reaching its target.

also theres this italian guy, carlo rovelli who deserves mention as the author of some books proposing that the infinite division used in the zeno paradoxes actually is in contradiction with the physical nature of the world. its not that he talks about zeno, its that when his quantum physics theory becomes proven enough to be accepted as not just a theory but rather the actual dscription of reality (if and when that happens) it will remind us that zeno was wrong in his assumption about infinite divisibility and that can be taken as a simple cause of his paradoxes. (if i take correctly a paradox takes a seemingly correct line of arguments and points to a result with it that is obviously contradicting reality, saying either the line of thought is not as correct as we think and then lets find the mistake in it, or reality is not what it is belived and then lets find the mistake in the belief about it.)89.134.199.32 (talk) 15:04, 2 February 2020 (UTC).

Remove the distance vs. time graph in § Achilles and the Tortoise?

The image supposes that a tortoise can run 5 m/s. No source supports this speed, and neither Zeno nor Aristotle supposes this to be possible. The world record for tortoises is 0.28 m/s and the accompanying text, unlike the image caption, implies a speed of 0.2 m/s.

Is the image worth preserving? I propose to delete it. It adds nothing to the text. It merely illustrates what is obvious anyhow, that Achilles, running at 10 m/s, will overtake anything running more slowly including, for example, a squirrel running at 5 m/s. (Squirrels can go that fast, though they're not noted for sustained effort.)

In the French Wikipedia, the graph is associated with a section on the resolution of the paradox . This makes more sense, as the figure illustrates how each of the successive stages in the race takes less time and brings Achilles closer to the tortoise until the tortoise is overtaken. The exposition is immediately followed by a discussion of the associated convergent infinite series. In the English Wikipedia, the infinite-series discussion is in a different article, Infinity § Zeno: Achilles and the tortoise. The figure should be here, if anywhere, though the argument in this section supposes the tortoise's speed to be 0.1 m/s. Modifying the graph to suppose that the tortoise is going 0.1 or 0.2 m/s is impractical, since the line for the tortoise would be nearly horizontal.

Peter Brown (talk) 22:52, 25 August 2020 (UTC)

If Zeno can get you asking the wrong questions...

The resolution of the paradoxes comes from understanding that if someone can direct your attention to an irrelevant part of a system, while you think you are looking at the whole system, they can convince you of foolish things about the whole system. So if you look at shorter and shorter segments of time (of a runner's or a Hare's motion), because a questioner like Zeno led you down that path, you discover the "paradox" that your inquiry doesn't tell you anything accurate about the characteristics of the overall motion. Or as Thomas Pynchon wrote in Gravity's Rainbow, "If they can get you asking the wrong questions, they don't have to worry about the answers."

So this "paradox" has nothing to do with infinities or calculus, and everything to do with attention, focus, and distraction.

I have not found a Runcible Source that has noticed this, so it is not suitable for the article yet. Gnuish (talk) 04:40, 11 October 2022 (UTC)

One risk of being a debunker or skeptic is that you might not be skeptical about your own skepticism. Your explanation is great until you unequivocally declare "nothing to do with infinities". I think the history of math will bear out that the notion of limits is a very old problem (not initially solved by Newton and Leibnitz when they formulated calculus) and Zeno was a key motivator by framing it as a paradox. But what do I know? I'm not a historian of science. Martindo (talk) 05:11, 11 October 2022 (UTC)