wandelaar

Are Zeno's paradoxes solved by modern science?

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9 hours ago, Taoist Texts said:

Zeno's paradoxes, when rephrased, are very simple and very irrefutable:

Splitting a unit of space or a unit of matter  into progressively smaller bits will eventually end in bits that are ungraspable to our senses or to our measuring tools, i.e this process will end in nothingness

Which in turn means that the spacematter consists of nothingness.

Also, it means that the spacematter is fundamentally unknowable. 

 

This is an excellent observation, but was it Zeno's intent to convey this or has this been attributed to him by those that followed?

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@ OldDog

 

We had a topic about this some time ago. There is a form of logic promoted by Graham Priest that claims that true contradictions (or paradoxes) exist, and that investigates how to logically reason with them.

 

A good candidate is this one:

 

This sentence is not true.

 

Is the above sentence true?

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22 minutes ago, Lost in Translation said:

This is an excellent observation, but was it Zeno's intent to convey this or has this been attributed to him by those that followed?

 

That was probably not the intent of Zeno, because the option that the constituents are nothing is considered as absurd.

 

See:  https://www.iep.utm.edu/zeno-par/#SSH3biv

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23 minutes ago, Lost in Translation said:

 

This is an excellent observation, but was it Zeno's intent to convey this or has this been attributed to him by those that followed?

It was his intent, albeit misunderstood by all except myself. It is a complicated matter due to Parmenides himself  being misunderstood according to  

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Kingsley’s work argues that the writings of the presocratic philosophers Parmenides and Empedocles, usually seen as rational or scientific enterprises, were in fact expressions of a wider Greek mystical tradition that helped give rise to western philosophy and civilisation. This tradition, according to Kingsley, was a way of life leading to the direct experience of reality and the recognition of one's divinity. 

Parmenides, most famous as the “father of western logic” and traditionally viewed as a rationalist, was a priest of Apollo and iatromantis(lit. healer-prophet).[4] Empedocles, who outlined an elaborate cosmology that introduced the enormously influential idea of the four elements into western philosophy and science, was a mystic and a magician.[5][6] 

 

 

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10 hours ago, Taoist Texts said:

... this process will end in nothingness.

 

Not sure it is fair to say "nothingness". Isn't that jumping to a conclusion? Is nothingness the same as ungraspable ... inconclusive?

 

1 hour ago, wandelaar said:

... the option that the constituents are nothing is considered as absurd.

 

Likewise, "absurd" is jumping to a conclusion by labeling it derisively as a triviality not worth furth consideration. 

 

The most that can be said is that one has exhausted all attempt to resolve. Thus it must be an issue that is parked until alternative methods or insight is found.

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On 1/2/2019 at 10:22 AM, Jeff said:

 

Faulty logic is faulty logic...  

 

But if you are going to assume the logic stream, and want to break it, simply have Achilles run farther than the 100 meters before checking. Have him run 200 meters and then check where the tortoise is relative to him.  If he goes 2x the distance, he will pass. Or, since it is a relative time based logic trap, simply have Achilles constantly watching the tortoise, so that you get infinite looks at the infinite 1/2, which then also breaks the paradox and he passes the Tortoise, as Infinity * 1/2 is still = Infinity.

 

The math here is calculus. Newton and Leibniz solved it in the 1700s, bypassing the old greek method of exhaustion that your paradox states. Can read about the death of Zeno paradox here...

 

https://en.wikipedia.org/wiki/History_of_calculus

 

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simply have Achilles constantly watching the tortoise, so that you get infinite looks at the infinite 1/2,

Never heard of the Quantum Zeno Paradox? It was discovered by Yakir Aharonov.

 

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I realize the OP is self-censoring since I am supposedly "hiding" behind science.

But math professor Joe Mazur is to have his book published this year:

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. His ..... was a postdoctoral fellow at Stanford and Yale Universities. .... Zeno's Quiver: The Story of Time and Its Effects on Our Lives ... Acclaimed mathematician Joseph Mazur has mused on this conundrum for ... of time perception in digital culture.

Math professor Joe Mazur said my music math research was important and he asked me to submit it for publication to a math journal. That was about 15 years ago. Then he asked me to review his book on Zeno's Paradox.  It's on Amazon.

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Professor Mazur does an expert job of giving the behind-the-scenes wrangling of conceptual philosophy which gave rise to applied science. What is the difference between time and motion exactly? If that question seems too abstract, this book proves the opposite.

Most college graduates assume that Zeno's paradoxes of motion were solved by calculus with its continuous functions. Mazur puts the calculus at the heart of the book, from Descartes and Cavalieri to Galileo, Newton and last but not least Mazur's favorite: Gabrielle-Emilie de Breteuil.

In fact, upon investigation, one finds many top scientists still studying and learning from the anomalies in infinite measurement. Regarding relativity Mazur states the wonder of absolute motion is that it "conspires with our measuring instruments to prevent any possibility of detection."

As Mazur points out "we don't measure with infinitesmial instruments" and so the perceptual illusion of time continuity remains despite the reliance of science on discrete symbols. With attempts at a unification of quantum mechanics and relativity Zeno's paradoxes reemerge with full-force in the "Calabi-Yau manifold." Mazur writes that the original concept of dimension still holds but now means measuring more by abstract reason than by sight.

Although each scientist featured by Mazur appears to have increasingly solved the paradox of motion in the end I think Zeno will be avenged and science will return to right back where it started. There seems to be a deadlocked struggle between discreteness (particle) and continuity (wave) in science and Mazur argues that indeed Nature "makes jumps" despite seeming continuous. But Mazur admits we are left with "splitting operations that can take place only in the mind."

then I posted an update to a comment.

https://www.amazon.com/Motion-Paradox-500-Year-Puzzle-Mysteries/product-reviews/0525949925

The March 2015 experiment of splitting a single photon finally disproven Einstein's claim that spooky action at a distance was not possible. So indeed reality is based on a continuous information wave that is instantaneous, faster than the speed of light.

hey drew, nice to see you doing your things again

just googling your name along with this month dates but can't find you pissing off people in any forum

regards

p3l
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3 minutes ago, OldDog said:

Likewise, "absurd" is jumping to a conclusion by labeling it derisively as a triviality not worth furth consideration. 

 

This is not my opinion but how the paradox is constructed. Zeno reasoned that what doesn't increase something when added and does not diminish something when subtracted cannot be something. Now a point does not add to the length of an interval when added,  and does not subtract from the length of an interval when subtracted, so he (falsely) concluded that a point has to be nothing or non-existent. 

 

3 minutes ago, OldDog said:

The most that can be said is that one has exhausted all attempt to resolve. Thus it must be an issue that is parked until alternative methods or insight is found.

 

It took some time before a rigorous theory of the continuum was invented. But the problem can and has been solved. See for a book-size treatment of Zeno's paradoxes from the viewpoint of modern science:

 

https://books.google.nl/books/about/Modern_Science_and_Zeno_s_Paradoxes.html?id=eSpDAAAAIAAJ&redir_esc=y

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Posted (edited)
35 minutes ago, OldDog said:

 

Not sure it is fair to say "nothingness". Isn't that jumping to a conclusion? Is nothingness the same as ungraspable ... inconclusive?

It is the same. I used nothingness to keep with the current terminology of the current academia. The alternative term is 'the void'

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Likewise, "absurd" is jumping to a conclusion by labeling it derisively as a triviality not worth furth consideration. 

this modern scholarly nonsense made me laugh

https://www.iep.utm.edu/zeno-par/#SSH3biv

the author, some nobody prof of philosophy used the word 'mistake' 22 and 'absurd' 10 times in regard to the great Zeno.

 

Here is what a real philosopher thinks of Zeno

 

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Russell (1996 [1903]), p. 347: "In this capricious world nothing is more capricious than posthumous fame. One of the most notable victims of posterity's lack of judgement is the Eleatic Zeno. Having invented four arguments all immeasurably subtle and profound, the grossness of subsequent philosophers pronounced him to be a mere ingenious juggler, and his arguments to be one and all sophisms. After two thousand years of continual refutation, these sophisms were reinstated, and made the foundation of a mathematical renaissance..."

 

Edited by Taoist Texts
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11 hours ago, Taoist Texts said:

 

Here is what a real philosopher thinks of Zeno

 

 

yes Russell stated "the real numbers are a convenient fiction."

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