Quote:
Originally Posted by romansh  Hi Shadee
Sorry I misread your post.... This is not how I understand Zenon's paradox .... it's actually where you get close to the turtle but never reach. It's the sum of half of the differences. The reply below answers my understanding of Zenon's paradox Quote:
Do this seven times and sum the distances.... Achilles has overtaken the turtle..... Now Zenon chose 11 m for his calculation then the calculation does not "allow" Achilles to reach the turtle.
But in reality of the problem, the time associated with Achilles reaching the turtle is also halving. It's like Zenon telling us, you can only take one step towards the turtle and I don't care how you divide up that step!
It goes back to the series of numbers 1/1, 1/2, 1/4, 1/8, 1/16 .....the sum of which approach the value of two but never quite gets there. We are adding an infinite number of numbers, but they are are getting infinitely smaller.
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I guess we both just have a different way of looking at the paradox.
Since he's put it in so many different scenarios I just look past the puzzles themselves and am just intrigued at finding out that there are endless halfway points to any destination and if you think of it that way then in math you can really never get to any destination because you'd have to cross an infinite number of halfway points. And that's what I believe he meant to achieve. The way I look at it is, the puzzles are pillows, and the fact that numbers are endless in math but that that doesn't seem to be the way things work in real life is a box with an engagement ring which he's put under one of the pillows. He basically asks people which pillow is fluffier. A lot of people get so preoccupied with figuring out which pillow is fluffier that they don't realize that he doesn't care, he just wanted you to find the engagement ring and be amazed
