Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

Achilles and the Tortoise

4 replies to this topic

#1 Haiming

Haiming

Newbie

• Members
• 12 posts
• Gender:Male
• Location:Colfax, NC

Posted 05 June 2012 - 01:54 AM

Zeno's second paradox of motion, of Achilles and the tortoise, is probably the best known of his four paradoxes of motion. In this problem, the fleet Greek warrior runs a race against a slow-moving tortoise. Assume Achilles runs at ten times the speed of the tortoise (1 meter per second to 0.1 meter per second). The tortoise is given a 100-meter handicap in a race that is 1,000 meters. By the time Achilles reaches the tortoise's starting point T0, the tortoise will have moved on to point T1. Soon, Achilles will reach point T1, but by then the tortoise would have moved on to T2, and so on, ad infinitum. Every time Achilles reaches a point where the tortoise has just been, the tortoise has moved on a bit. Although the distances between the two runners will diminish rapidly, Achilles can never catch up with the tortoise, or so it would seem.
• 0

#2 Ghostofblueflamefis

Ghostofblueflamefis

Newbie

• Members
• 4 posts

Posted 05 June 2012 - 07:45 AM

Weird...
• 0

#3 joshuagenes

joshuagenes

Junior Member

• Members
• 22 posts

Posted 22 December 2012 - 10:28 AM

Motion itself is a truthful resolution of an underlying paradox  to our perspective. Motion is made up of time and distance. Truth may be communicated instantly between objects but to a particular perspective it must communicate the order and structure of the objects it is communicating and this communication has a revealed order which we call time. Distance is simply the degree of truthful separation. Distance or space has a time element to it as further objects must be communicated after near objects but time is much more than distance or space because it involves "other" events where A has to happen before B which has to happen before C in a linear vector sort of manner. This being said truth itself is discrete and Achilles smallest halfway point will reach it and cross it in a flash.

• 0

#4 bonanova

bonanova

bonanova

• Moderator
• 6161 posts
• Gender:Male
• Location:New York

Posted 16 February 2013 - 03:16 AM

Zeno  simply describes Achilles' approach to the tortoise in vanishingly small increments of distance.

It does not describe what happens after that. In fact, the tortoise does not even have to be present.

We could examine his separation from a fixed wall at geometrically decreasing intervals of time.

The fact that an infinite number of snapshots can be taken before the time of intercept does not prove

the wall will not be reached or the tortoise overtaken.  It's a pseudo paradox.

Any supposed difficulty here belies lack of familiarity with the nature of real numbers.

• 0

Vidi vici veni.

#5 Kikacat123

Kikacat123

Senior Member

• Members
• 507 posts
• Gender:Female
• Location:In a chair, held captive by the cat on my lap

Posted 22 March 2013 - 02:27 AM

This paradox can obviously be proven false by Achilles actually racing the tortoise, but its explanation is quite complicated. A simplified version of the explanation is that while Achilles must reach the spot where the tortoise was, he will most likely be moving so swiftly as to pass that point and get ahead of the tortoise mid-stride. This paradox only works if both Achilles and the tortoise go a certain length, stop, and start again.
• 0
"Silflay hraka, u embleer Rah!" - Thlayli, Watership Down

0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users