Supertasks | Paradoxes of infinity | Mathematical paradoxes
Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490–430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. It is usually assumed, based on Plato's Parmenides (128a–d), that Zeno took on the project of creating these paradoxes because other philosophers had created paradoxes against Parmenides' view. Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one." Plato has Socrates claim that Zeno and Parmenides were essentially arguing exactly the same point. Some of Zeno's nine surviving paradoxes (preserved in Aristotle's Physicsand Simplicius's commentary thereon) are essentially equivalent to one another. Aristotle offered a refutation of some of them. Three of the strongest and most famous—that of Achilles and the tortoise, the Dichotomy argument, and that of an arrow in flight—are presented in detail below. Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum, also known as proof by contradiction. They are also credited as a source of the dialectic method used by Socrates. Some mathematicians and historians, such as Carl Boyer, hold that Zeno's paradoxes are simply mathematical problems, for which modern calculus provides a mathematical solution. Some philosophers, however, say that Zeno's paradoxes and their variations (see Thomson's lamp) remain relevant metaphysical problems. The origins of the paradoxes are somewhat unclear. Diogenes Laërtius, a fourth source for information about Zeno and his teachings, citing Favorinus, says that Zeno's teacher Parmenides was the first to introduce the paradox of Achilles and the tortoise. But in a later passage, Laërtius attributes the origin of the paradox to Zeno, explaining that Favorinus disagrees. (Wikipedia).
Parmenides, Nothingness, & Zeno's Paradoxes
An introductory discussion of the Eleatic school, including Parmenides on the ultimate unchanging oneness of reality and some of the issues that arise regarding multiplicity and change (basically because such phenomena involve non-being, which is something that cannot itself be thought and
From playlist Aristotle
What is Zeno's Dichotomy Paradox? - Colm Kelleher
View full lesson: http://ed.ted.com/lessons/what-is-zeno-s-dichotomy-paradox-colm-kelleher Can you ever travel from one place to another? Ancient Greek philosopher Zeno of Elea gave a convincing argument that all motion is impossible - but where's the flaw in his logic? Colm Kelleher illu
From playlist Math of the impossible
The Paradox of Achilles and the Tortoise
SUPPORT CR on PATREON: http://bit.ly/2qBHcvf The Greek philosopher Zeno famously wrote a book of paradoxes 2,500 years ago that still continues to baffle scientists and philosophers today. One of his paradoxes, titled Achilles and the Tortoise, examines the idea of infinity in great philo
From playlist Concerning Everything
Zeno, Infinite Divisibility, & Indivisibility
This is a clip of Richard Sorabji discussing whether space is infinitely divisible or instead is made up of indivisible units. He considers some of the problems with each view, including one of the famous paradoxes from Zeno of Elea. This comes from a talk which Richard Sorabji gave back i
From playlist Logic & Philosophy of Mathematics
This Paradox Proves Motion is a Lie (Achilles and the Tortoise)
The Greek philosopher Zeno famously wrote a book of paradoxes 2,500 years ago that still continues to baffle scientists and philosophers today. One of his paradoxes, titled Achilles and the Tortoise, examines the idea of infinity in great philosophical complexity. Figuring out the answer t
From playlist Concerning Education
Relativity: how people get time dilation wrong
Einstein’s special theory of relativity is notorious for being easy to misuse, with the result that sometimes result in claims of paradoxes. When one digs more carefully into the theory, you find that no such paradoxes actually exist. In this video, Fermilab’s Dr. Don Lincoln describes a
From playlist Relativity
The continuum, Zeno's paradox and the price we pay for coordinates 117 | Math Foundations
In this video we venture into a range of topics, from the nature of the continuum, to the paradoxes of Zeno, to an understanding of some of the consequences for mathematics in the shift from geometry to arithmetic that flowed from the Cartesian revolution. As we let go of the real number
From playlist Math Foundations
Four Fascinating Paradoxes | Wondrium Perspectives
Paradoxes can be mind-bending, frustrating, or enjoyable puzzles to solve. Whether they come from the realm of time travel or everyday life, paradoxes can spur some of our deepest thinking and most perplexing views of the world around us. In this episode of Perspectives, several experts c
From playlist Wondrium Perspectives
Easter Special - Zeno's Paradox
In this holiday special, Tori explains the math behind the first two of Zeno's paradoxes, themed for Easter. John can indeed catch up to the Easter Bunny on his bike!
From playlist Center of Math BLOG: Holiday Mathematics
Zeno and Anti-Zeno effects in Quantum Mechanics by Nalini Dattatreya Gurav
21 November 2016 to 10 December 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Quantum Theory has passed all experimental tests, with impressive accuracy. It applies to light and matter from the smallest scales so far explored, up to the mesoscopic scale. It is also a necessary ingredie
From playlist Fundamental Problems of Quantum Physics
3 Paradoxes That Gave Us Calculus
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From playlist Math
Intro to Infinite Series | Real Analysis
We introduce the definition of infinite series, the definition of a convergent series and the limit of a series, as well as divergent series. We'll discuss partial sums, terms of an infinite series, and look at various examples including geometric series, the harmonic series, and p-series.
From playlist Real Analysis
Twins Paradox: The Complete Explanation
The twins paradox is easily the most famous paradoxes of all time. Using spacetime diagrams and the rules of relativity, we can show the paradox only happens because people are being lazy with special relativity. http://brilliant.org/ScienceAsylum ________________________________ VIDEO ANN
From playlist Einstein's Relativity
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From playlist Knowledge
Detecting a quantum particle by Abhishek Dhar
ICTS IN-HOUSE 2020 Organizers: Amit Kumar Chatterjee, Divya Jaganathan, Junaid Majeed, Pritha Dolai Date:: 17-18th February 2020 Venue: Ramanujan Lecture Hall, ICTS Bangalore inhouse@icts.res.in An exclusive two-day event to exchange ideas and discuss research amongst member
From playlist ICTS In-house 2020
Paradoxes and Supertasks: Zeno, Littlewood-Ross and Thomson's Lamp
Tom Rocks Maths intern Kira Miller discusses the philosophy of 'supertasks' and how they are related to Zeno's Paradox, Thomson's Lamp and the Littlewood-Ross Paradox. Zeno's Paradox looks at convergent infinite sequences in the context of Achilles racing against a tortoise which is given
From playlist Mathstars