Marvin Parke from Jamaica on January 03, 2013: What if Zeno is right if he examined the paradox from a quantum physics point of view. Dan Harmon (author) from Boise, Idaho on August 02, 2013: Perhaps I wasn't entirely clear - Zeno was interested in disproving the new mathematics, not in applying his work to reality. Perhaps we need a new sub-field in Math. Zeno’s Paradox of the Tortoise and Achilles Zeno of Elea (c. 450 BCE) is credited with creating several famous paradoxes, and perhaps the best known is the paradox of the Tortoise and Achilles. The first "Proof of the Impossibility of Physical Movement" uses science's own reliance on strict determinism (namely: identifiable, verifiable physical causes for each and every physical effect) to demonstrate the utter impossibility of physical movement. Thank you. For objects that move in this Universe, physics solves Zeno's paradox. Zeno's paradoxes rely on an intuitive conviction that. This agrees with practical experience; for a constant velocity of 64 meters per second a ball will take exactly 2 seconds to travel 128 meters. The physics of space did not enter his mind. It is amazing that we can use Pi to make circles. Calculus (infinite series) does not resolve the Zeno's Paradoxes. At every moment of its flight, the arrow is in a place just its own size. © 2021 Maven Media Brands, LLC and respective content providers on this website. same solution to Zeno’s paradox should apply. More explained at http://beliefinstitute.com/blog/steaphen-pirie/pro... Dan Harmon (author) from Boise, Idaho on November 03, 2011: Glad that you enjoyed it - there is a lot hidden in mathematics that can be fascinating to try to understand. Moreover, some of the proposed solutions gave rise to a new collection of problems so exciting as Zeno's paradoxes [18, 1,19,20,12,21]. The fault of most, if not all, the proposed solutions to Zeno's paradox is the assumption that Zeno's proposed procedure was correct. In effect, for the ball to traverse the endless (infinite) micro-increments in travel (which according to standard infinite-series solutions, it MUST do so), then the ball is "superpositioned" well "outside" of where it precisely and exactly HAS to be (according to the algebra of infinite-series solutions) at EVERY point in time, while ever it is traveling from point A to B. Moreover, some of the proposed solutions gave rise to a new collection of problems so exciting as Zeno's paradoxes [18, 1,19,20,12,21]. Dan Harmon (author) from Boise, Idaho on November 01, 2011: Thanks, Dzy. With the understanding of Planck space our universe is known to be digital and not continuous. A great addition here - thanks! By my understanding, the more the distance between the two objects approaches zero, the number of half-way points crossed approaches infinity. ", Do something today that your future-you will thank you for. Basically the ball will have stopped moving, for all practical purposes. As can be seen, the time to each successive halfway point is decreasing while the distance to the light beam is also decreasing. Or some other time; it probably won't be 2 seconds. The charts below show the distance to the light beam and the velocity at various times. Now joining these two premises: a) the solution of Zeno' s paradox of motion has to do with the kind of topological connectivityof the underlyingspace, and b) a structureapt to bear the solution of Zeno' s paradox has to be discon- tinuous, the details of the intended solution slowly mightbecome evident. Carrie Smith from Dallas, Texas on October 30, 2011: Congratulations on being the hub of the day! 3. To top it all off, even if you do try an infinite number of times (infinity isn’t a number, but for the sake of argument), you still wouldn’t be able to reach the door. This paradox has flaws. All other solutions that rely on infinite-series (typical of the vast majority of solutions offered in textbooks, universities and the Internet) require the assumption of 'perfect continuity' of space-time and physical motion, an assumption that is not supported by the evidence of quantum mechanics. MonetteforJack from Tuckerton, NJ on October 25, 2011: HubPages is truly interesting with such hubs like yours and hubbers like you, I am learning. Thumbs up. Thank you! This is a very interesting topic and very easy to understand it the way you broke it down. Dan Harmon (author) from Boise, Idaho on October 17, 2015: I'll try to explain the reasoning. Nevertheless, calculus does indeed solve Zeno's paradoxes; those studies are based on infinitesimals whether they can occur in nature or not. Thanks. To say or believe otherwise requires a small-ego (selfish) persona that seeks to remain disconnected in order to avoid responsibility for the resultant reality. At the 10 second mark the ball is only 1/8 of a meter from the light beam, but is also only traveling at 1/8 meter per second. Solution to Zeno's Paradox *Zeno's Paradox (actually the first of four) purports to show that motion is impossible. Again, if you have physical evidence to the contrary, the Nobel is all yours. Londontours from London on October 30, 2011: Dan Harmon (author) from Boise, Idaho on October 30, 2011: Yes, acceleration will make a huge difference, and I would think that the acceleration of a dragster would diminish as speed builds. In its simplest form, Zeno's Paradox says that two objects can never touch. His entire thrust was to "prove" that the new math field was wrong by using that assumption of movement. Tim Mitchell from Escondido, CA on October 30, 2011: Awesome wilderness. Zeno questioned how physical things moved. You're headed in the right direction -- an invisible NONLOCAL "meta-space" supports the physical visible space many incorrectly assume to be perfectly continuous. If you have evidence to the contrary, I suggest you submit your work to the various physics organisations and await your Nobel Prize. Yet, as the value of both assets classes is correlated with the state of the economy, I guess I know now! *Scratches head*. But at the quantum level, an entirely new paradox emerges, known as the quantum Zeno … Zeno is a Greek philosopher who lived around the time of 490 to 430 BC. Nevertheless, Pi is an important number in the universe that we can access and works every time right to the limits of our ability to measure. zeno's paradox, as it is presented, ignores the passage of time. It is kinda' like two balls if I understand correctly. 35 Now joining these two premises: a) the solution of Zeno' s paradox of motion has to do with the kind of topological connectivityof the underlyingspace, and b) a structureapt to bear the solution of Zeno' s paradox has to be discon- tinuous, the details of the intended solution slowly mightbecome evident. A length that is physically impossible to attain. loufabbiano@yahoo.com on August 13, 2018: Is there a another single word which can describe the 1/2 way point of a 1/2 point progression other than a Zeno's Paradox? Sometimes, some people spell Zeno with an X as in Xeno. Penelope Hart from Rome, Italy on January 03, 2013: Followed every word and yes, I almost got it - so many thanks. @ Wesman: Thank you. That is, they are at least not contrary to experimental or physical evidence. In illistrating your point one thought occurred to me... You should be a politician! @ lord de cross: Although I had heard of Zeno's paradox prior to writing this hub, I had no idea that he devised it to disprove the precursor of modern Calculus. We see in this example that Zeno's Paradox can be applied to actual, real events we see every day, but that it takes mathematics not available to him to solve the problem. You can say that, in the last second, or in the entire trip, the ball actually *does* cross an infinite amount of half-way points. MATHEMATICAL SOLUTIONS OF ZENO’S PARADOXES 303 Now, 0/0 is not a well defined expression and is what is known as an indeterminate form. I'm not sure what would happen to the T (time) if a constant negative acceleration was used. Exactly (given that our measurements must be rounded off because they are always imperfect to some degree). Am adding Zeno 's paradoxes '' various 'thought-experiments ' easily and inexorably undermine the standard 'perfect-continuity assumptions! 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