Confounded by someone who died before the invention of zero

[ashling]

http://www.slate.com/articles/health_and_science/science/2014/03/zeno_s_paradox_how_to_explain_the_solution_to_achilles_and_the_tortoise.html

What Is the Answer to Zeno’s Paradox?

The Greek philosopher Zeno wrote a book of paradoxes nearly 2,500 years ago. “Achilles and the Tortoise” is the easiest to understand, but it’s devilishly difficult to explain away. For those who haven’t already learned it, here are the basics of Zeno’s logic puzzle, as we understand it after generations of retelling:

Achilles, the fleet-footed hero of the Trojan War, is engaged in a race with a lowly tortoise, which has been granted a head start. Achilles’ task initially seems easy, but he has a problem. Before he can overtake the tortoise, he must first catch up with it. While Achilles is covering the gap between himself and the tortoise that existed at the start of the race, however, the tortoise creates a new gap. The new gap is smaller than the first, but it is still a finite distance that Achilles must cover to catch up with the animal. Achilles then races across the new gap. To Achilles’ frustration, while he was scampering across the second gap, the tortoise was establishing a third. The upshot is that Achilles can never overtake the tortoise. No matter how quickly Achilles closes each gap, the slow-but-steady tortoise will always open new, smaller ones and remain just ahead of the Greek hero.

It’s tempting to dismiss Zeno’s argument as sophistry, but that reaction is based on either laziness or fear. Laziness, because thinking about the paradox gives the feeling that you’re perpetually on the verge of solving it without ever doing so—the same feeling that Achilles would have about catching the tortoise. Fear, because being outwitted by a man who died before humans conceived of the number zero delivers a significant blow to one’s self-image. But what if your 11-year-old daughter asked you to explain why Zeno is wrong? Would you just tell her that Achilles is faster than a tortoise, and change the subject? That would be pretty weak. Zeno assumes that Achilles is running faster than the tortoise, which is why the gaps are forever getting smaller. But it doesn’t answer the question.

[OriginalGeek]

1. I never heard of Zeno

but if Achilles is always only going to where the tortoise was, he'll never get to where the tortoise is.

[ashling]

5. You obviously don't know what a badass Achilles is

[OriginalGeek]

8. meh

he was such a heel

[ashling]

12. He did have a tendoncy to act out

[Ron Obvious]

2. I've never really understood why this was considered a paradox

There must be a subtlety here that I'm missing, but if you slice the time interval ever smaller, naturally the distance covered in that time interval gets proportionally smaller, and therefore the actual moment of overtaking is approached closer and closer.

How to go from that premise to the moment of overtaking never taking place escapes me, but philosophy was never my strong suit.

[Xyzse]

3. Interesting.

Separate the two.

Discuss the distance between Achilles' to the finish line, and the Tortoise's to the finish line as well.
Ask who will get there first, given running speed to the distance.

The idea is who would get to the goal first.
Not the idea of Achilles getting to where the Tortoise is to occupy the same space.

Otherwise mention.

The guy is incapable of understanding negatives or units I guess.
The turtle creates smaller and smaller gaps as Achilles gets closer. However, that also does not mean that Achilles slows down either. So he moves in units greater than the gaps the tortoise creates. At some point or another, the unit of movement that Achilles makes is greater than the gap that the tortoise creates, which allows him to overtake the tortoise.

[ashling]

6. I had a box turtle once,

and that dude was FAST!!

[Xyzse]

7. I picked up a turtle near my drive-way once.

I had no idea how he got there since there is no body of water for at least 2 miles in my area.

I took care of it for a few weeks before going to the regional park with a lake.
As soon as I put the turtle to the water, it stopped a little bit while swimming, and then hauled ass afterwards.

It was FAST!

[rug]

4. It's the battle between the abstract and the real.

[hunter]

9. I always figure a few ancient peoples knew zero, algebra, and calculus...

... but only a odd mnemonics survived periods of bad politics and bad religion.

Look what happened when the Europeans took the Americas. Not only were they hell bent on destroying the indigenous people themselves, they were also hell bent on destroying any knowledge that conflicted with their own world view.

Certainly there is a lot of superstition and nonsense in any world view (and our modern society is NOT exempt) but it's very depressing to think about how much hard won human knowledge, experience, and art has been lost to the murderous book-burning, one-language, ignorant-holy-under-god mobs.

[Chan790]

10. I never liked that one as much as the bridge paradox.

Where a man crosses half a bridge, then half the remainder, then half the remainder...and never reaches the other side.

[jmowreader]

11. It doesn't work that way

You have Achilles, who can run 10 mph (880 fpm) and a turtle, who can walk 1 mph (88 fpm). The race course is one mile.

Achilles runs the race in 6 minutes, vs 1 hr for the turtle.

If we release the turtle 30 minutes prior to Achilles, it will take Achilles 3 min to cover 2640 ft. In that 3 min the turtle goes 264 more feet. We have already said Achilles is going 880fpm, so it should take less than 30 more seconds to pass the turtle.