Zeno's Paradox - Achilles versus the Tortoise

A film made for my Philosophy of Logic class presentation at Canterbury University.

Zeno has several paradoxes. In this one, Achilles and the Tortoise have a race. The Tortoise has a head start. When Achilles runs to where the Tortoise USED to be, the Tortoise has already moved to the next point (half the distance away). However, by the time Achilles reaches where the Tortoise is, the Tortoise has moved on again by a tiny amount. In this way the Tortoise stays ahead by increasingly smaller amounts and Achilles never catches the Tortoise.

Category:

Education

Tags:

• zeno
• paradox
• university
• christchurch
• new zealand
• philosophy

[1000000ed]

Nifty touches well done! i like it so much better than the little cartoon where the turtle keeps shooting out little puffs of red gas!! thanks.

[MachiavelliNZ]

@zasabiibasaz Precisely. That's the correct answer to the arrow paradox. Zeno has the same error with the race problem. He doesn't consider distance/time for each runner.

[zasabiibasaz]

@MachiavelliNZ I didn't say a you can measure something smaller than a planck length so no I'm not incorrect. The arrow paradox isn't a misrepresentation of velocity, its a misrepresentation of movement itself. Velocity is just a rate of movement, the arrow paradox doesn't account for the necessity of time to occur for movement to be documented.

[MachiavelliNZ]

@zasabiibasaz Incorrect. A Planck length is the shortest measurable length. However, the assumptions that are also wrong in Zeno's paradoxes involve an incorrect understanding of velocity.

e.g. Imagine firing an arrow. At any given "snapshot" of time the arrow is fixed at a point. Like an arrow in a photo, the arrow at one point in time is "unmoving" with zero speed. How, when you examine the entire series of points that make up an arrow's motion, can a collection of unmoving arrows "move"?

[zasabiibasaz]

@MachiavelliNZ A given line can in fact be bisected infinitely, there is no limit. For example imagine I have an object 1 planck length long, then I can bisect it into two equal pieces 0.5 planck lengths long. I can do this for eternity. What assumptions are you referring to that is wrong in this paradox?

[zasabiibasaz]

@CroissantOrange Since Pi is interminable it is incommensurable meaning it cannot be accurately measured in the physical world. Like if you make a circle out of a 1 inch piece of string then its diameter would be incommensurable, in fact the diameter of a circle with circumference 1 would be 1/Pi which is a length that cannot be accurately measured since it is interminable. The only reason mathematics isn't perfectly characterized into the real world is because of imperfections in the universe.

[qazplm9548]

I don't get it? All races has a finish line right? in this race, where is it? pls explain.

[examinfo]

It took almost 2000 years (until Calculus: Liebniz & Newton) to deal with these paradoxes . The big assumption is that spaces can be divided; and moments can be divided. I think this is where it gets hairy.

[mquiroz90]

i say the motions are possible and supertask

[MachiavelliNZ]

@CroissantOrange I'm not sure about the Pi example but you hit it perfectly with your comment about mathematical abstraction. We know about things like planck length, that a given line cannot be bisected infinitely. There is a limit. But obviously people in Zeno's day had other theories. The ancient greeks came up with some amazing stuff but they weren't perfect. If you pick the wrong assumptions you get silly answers e.g. Zeno's paradoxes. But its all about science and learning, we improve :)