Consider Zeno's paradox of Achilles and the tortoise
(go on, consider it).
Major Works: No extant works, but the following famous paradoxes are attributed to Zeno: Paradox of Achilles and the Tortoise, Paradox of the Arrow, Paradox of the Race Course, Paradox of the Stadium, Paradox of Plurality
The Paradox of Achilles and the Tortoise concludes that a swifter runner cannot overtake a slower.
The second of the arguments is the famous paradox known as The Paradox of Achilles and the Tortoise (as translated from Aristotle's Physics, book 6, chapter 9, by Philip H.
Imagine the race between Achilles and the tortoise as follows: The tortoise has taken the lead.
In Chapter 4, McGreal analyzes Zeno's Paradox of Achilles and the Tortoise.
But on the way she starts thinking about ``Zeno's famous paradox of Achilles and the tortoise
,'' and how if it were literally true, she would never have to face her husband, even if he were to rise and stroll to meet her.
In Section 5 we show that there exists a correspondence between the Littlewood-Ross super-task and Zeno's Achilles and the Tortoise.
While this reduction of a super-task to tasks was necessary to define the outcome of a super-task, the opposite, transforming a task into a super-task, is the core of one of the most famous paradoxes of all: Zeno's Achilles and the Tortoise, where a simple continuous movement for a finite period of time is split in an infinite number of steps.
This striking correspondence prompted us to create a mapping between a formulation of Zeno's Achilles and the Tortoise and the Littlewood-Ross super-task:
Let us assume that two runners, Achilles and the Tortoise, hold a race on a path of length 2.
As soon as one realizes that Achilles and the Tortoise do not consciously pass the infinitely many points that separate them from the finish in our mathematical model of the situation, the paradox disappears.