471 research outputs found

    What if Achilles and the tortoise were to bargain? An argument against interim agreements

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    Zeno's paradoxes of motion, which claim that moving from one point to another cannot be accomplished in finite time, seem to be of serious concern when moving towards an agreement is concerned. Parkinson's Law of Triviality implies that such an agreement cannot be reached in finite time. By explicitly modeling dynamic processes of reaching interim agreements and using arguments similar to Zeno's, we show that if utilities are von Neumann-Morgenstern, then no such process can bring about an agreement in finite time in linear bargaining problems. To extend this result for all bargaining problems, we characterize a particular path illustrated by \cite{ra}, and show that no agreement is reached along this path in finite time.Zeno's paradox, bargaining problems, interim agreements, vNM utility

    Engaging the Paradoxical: Zeno\u27s Paradoxes in Three Works of Interactive Fiction

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    For over two millennia thinkers have wrestled with Zeno\u27s paradoxes on space, time, motion, and the nature of infinity. In this article we compare and contrast representations of Zeno\u27s paradoxes in three works of interactive fiction, Beyond Zork, The Chinese Room, and A Beauty Cold and Austere. Each of these works incorporates one of Zeno\u27s paradoxes as part of a puzzle that the player must solve in order to advance and ultimately complete the story. As such, the reader must engage more deeply with the paradoxes than he or she would in a static work of fiction. In addition, each of the three works presents a different perspective on the intellectual challenges associated with the paradoxes

    Zeno meets modern science

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    ``No one has ever touched Zeno without refuting him''. We will not refute Zeno in this paper. Instead we review some unexpected encounters of Zeno with modern science. The paper begins with a brief biography of Zeno of Elea followed by his famous paradoxes of motion. Reflections on continuity of space and time lead us to Banach and Tarski and to their celebrated paradox, which is in fact not a paradox at all but a strict mathematical theorem, although very counterintuitive. Quantum mechanics brings another flavour in Zeno paradoxes. Quantum Zeno and anti-Zeno effects are really paradoxical but now experimental facts. Then we discuss supertasks and bifurcated supertasks. The concept of localization leads us to Newton and Wigner and to interesting phenomenon of quantum revivals. At last we note that the paradoxical idea of timeless universe, defended by Zeno and Parmenides at ancient times, is still alive in quantum gravity. The list of references that follows is necessarily incomplete but we hope it will assist interested reader to fill in details.Comment: 40 pages, LaTeX, 10 figure

    The Fallacy in the Paradox of Achilles and the Tortoise

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    Zeno's ancient paradox depicts a race between swift Achilles and a slow tortoise with a head start. Zeno argued that Achilles could never overtake the tortoise, as at each step Achilles arrived at the tortoise's former position, the tortoise had already moved ahead. Though Zeno's premise is valid, his conclusion that Achilles can "never" pass the tortoise relies on equating infinite steps with an infinite amount of time. By modeling the sequence of events in terms of a converging geometric series, this paper shows that such an infinite number of events sum up to a finite distance traversed in finite time. The paradox stems from confusion between an infinite number of events, which can happen in a finite time interval, and an infinite amount of time. The fallacy is clarified by recognizing that the infinite number of events can be crammed into a finite time interval. At a given speed difference after a finite amount of time, Achilles will have completed the infinite series of gaps at the "catch-up time" and passed the tortoise. Hence this paradox of Achilles and the tortoise can be resolved by simply adding "before the catch-up time" to the concluding statement of "Achilles would never overtake the tortoise".Comment: 4 page

    Zeno's Achilles\Tortoise Race and Reconsiderations of Some Mathematical Paradigms

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    An original observation of Zeno's Achilles\Tortoise Race Paradox is introduced. It leads to novel understanding of the foundations of mathematical science, especially by observing Nonlocality and Locality as its fundamental building-blocks. Locality is precisely its own formula, thus this formula cannot be used as a solution for anything else but its own unique case. Nonlocality is a formula that can be used as a solution for more than one case. Locality on its own is total isolation. Non-locality on its own is total connectivity. No total realm is researchable. A researchable realm only exists if Non-locality and Locality are not total. Under Nonlocality\ Locality Linkage we get a universe where Non-locality is its common law; this is expressed by many Localities that are gathered by the common law, but can never be Nonlocal,as is the common law. Non-locality\Locality Linkage can be perceived as "The Tree of Knowledge", which is the one organic and ever complex (and therefore non-entropic) realm that enables one, and only one simple law (Non-locality), to be the common knowledge of many Local expressions of it (we show that Leibniz Chaitin Complexity [11] Challenge is the organic incompleteness of Non-locality\Locality Linkage)
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