Is Motion Continuous According to Xeno's Paradoxes?

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Discussion Overview

The discussion revolves around the nature of motion in the context of Zeno's paradoxes, exploring whether motion is continuous or discontinuous. Participants engage with philosophical implications, mathematical interpretations, and historical perspectives, touching on concepts from calculus, quantum mechanics, and ontology.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation
  • Historical

Main Points Raised

  • Some participants suggest that the density of real numbers may refute Zeno's paradoxes, while others express uncertainty about the implications of this idea.
  • One participant argues that the resolution to the paradox lies in the finiteness of time intervals, noting that the sum of an infinite series can be finite.
  • Another participant critiques Zeno's paradoxes as mere wordplay, asserting that motion is impossible if one considers moments as isolated instants where the arrow is always at rest.
  • Some participants discuss the historical context of Zeno's paradoxes, mentioning interpretations by Aristotle and the complexities involved in understanding Zeno's original arguments.
  • A later reply introduces the idea that Zeno's paradoxes may question the continuity of motion rather than deny it outright, suggesting that the paradoxes lead to deeper philosophical inquiries about the nature of reality.
  • One participant raises the question of whether infinite divisibility is physically meaningful, referencing quantum mechanics and the Heisenberg uncertainty principle.
  • There is a discussion about the interpretations of Zeno's paradoxes, with some arguing that there is no consensus on what Zeno intended, leading to various interpretations of his arguments.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the implications of Zeno's paradoxes, with no clear consensus on whether motion is continuous or discontinuous, or how to interpret Zeno's original arguments.

Contextual Notes

Participants note the lack of precise texts from Zeno, leading to various interpretations and assumptions about his arguments. The discussion highlights the complexity of reconciling mathematical concepts with philosophical implications regarding motion.

  • #31
heusdens said:
In the classical sense, Zeno's paradox is resolved by infinitesimal calculations.
This however is no longer a resolution in respect with quantum physics.
Although I don't have reference here, QM resolves the Zeno (pseudo) paradoxes also, but in a different way.

Why would one use QM when dealing with quarks that move at Zeno speed?
 
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  • #32
sd01g said:
Why would one use QM when dealing with quarks that move at Zeno speed?

Because Achille's position cannot be measured infinitely sharply.
 
  • #33
D H said:
That philosophers are still struggling Zeno's paradox illustrates, to me, the utter arrogance and utter uselessness of philosophy. If a physicist, after scribbling on a white board for the better part of a day, finally arrived at the conclusion v_{\text{light}}=0, said physicist would say "#@$&! Where did I make my stupid mistake?" If a mathematician, after building a new callus by fiddling with math on paper all day long, finally arrived at the conclusion 0=1, said mathematician would utter a similar four-word remark and begin a hunt for the stupid mistake. Fast vehicles overtake slow ones, arrows fly through the air. Why don't philosophers similarly say, "where is my stupid mistake?"
If philosophers were programmers, their programming language would include new control structure, "what if".
 
  • #34
xantox said:
Because Achille's position cannot be measured infinitely sharply.

More specifically, because of Heizenberg uncertainty relationship.
 

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