Zeno's Paradox - Achilles versus the Tortoise

[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.

[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

[CroissantOrange]

They didn't know about acceleration at the time or what?

[MachiavelliNZ]

@CroissantOrange Several of Zeno's paradoxes rely on the idea that spaces can be divided again and again. This idea of continually dividing a space means that there are conceptually infinite steps between one point and another: e.g. going from A to B involves A->1->2->3->...->N->B. As long as it is TRUE that space is infinitely divisible then any movement should be impossible in principle. Of course, velocity IS movement between points so I think that's the trick so the solution.

[CroissantOrange]

@MachiavelliNZ So is it like to say we can never draw a circle from a given diameter parameter since Pi is interminable therefore it is unidentifiable (or the circle is gonna infinity large)? The transition from human perception into mathematics abstraction is not always that smooth i can see...

[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 :)

[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?

[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 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 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]

@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.

[SodaTeaches]

I have a idea on how to solve this paradox but bear with me I`m 13.

Okay, so to move it takes `time``. for example, moving one step takes a few seconds. Achilles would have passed the tortoise if the time it takes to catch up to the tortoise is shorter then the time for which the tortoise takes to move.

[mijav2]

Awesome video!!!

[MathDoobler]

ARROW "PARADOX" SUKS ASS IT'S FAKE

[lecheparavaka]

finally undestand it! nice video!

[MachiavelliNZ]

@lecheparavaka Hooray, glad to see it made sense and was helpful :)

[GodmyX]

Oh .. but we have forgotten speed Zeno, haven't we ? xD... No point of Achilles slowing down when reaching the meeting point with tortoise.

[MachiavelliNZ]

@GodmyX Yeah, the greeks had unusual ideas about speeds and distances. Look up the arrow paradox by Zeno to see another proof that movement is impossible!

[symphodude]

Oh Zeno....you crazy ancient!

[albat23ross]

nice work.make some more paradoxes.

[smellincoffee]

Achilles has a colorful way of expressing himself.

[1985sanoj]

what is the song that playing?

[MachiavelliNZ]

If I recall correctly, it's "Chariots of Fire" by the Greek, electronica artist, Vangelis. That's why there is an advertisement for it that pops up!