A Conversation for Zeno's Paradox

Assumptions: Junk in Junk out

Post 1

Researcher 174789

I spend quite a bit of time in college thinking about Zeno's paradox. One thing that I realized is that while the argument appears logically valid, it is useless beyond being fodder for philosophical discussions. An applicable use of this paradox would be if the goal of a race were to "reach" the finish line, or for the arrow to exactly travel the distance from the archer to the target. But in both cases the goal is to exceed the finishline and the surface boundary of the target. Since the hare's goal was to "cross" the finish line, he/she could have passed the tortoise by simply extending a target significantly beyond the finishline.

It reminds me of a saying about an American football team, the Green Bay Packers: "They never lost, they just ran out of time."

Thinking about paradoxes such as Zeno's makes me think that maybe the answer is 42.

e7


Assumptions: Junk in Junk out

Post 2

Brian

Re the title: "Junk in Junk out", it occured to me that this is one (admittedly very inefficient) way of discovering new ideas. Or have I just written a load of junk?
Brian


Assumptions: Junk in Junk out

Post 3

Simonus

the problem with this is that, although the hare will overtake the tortoise, it will never actually reach the finishing line, as it is aiming for it - like most people would, rather than just after it.

eg if it aimed to finish just after them it would eventually reach the finishing line and be declared winner, if not, then it wouldnt reach it...

therefore the only way to ever get anything done would be seemingly to reach for something slightly farther away untill you have reached the original thing.....

may need some further thinking this smiley - smiley


Assumptions: Junk in Junk out

Post 4

Simonus

the problem with this is that, although the hare will overtake the tortoise, it will never actually reach the finishing line, as it is aiming for it - like most people would, rather than just after it.

eg if it aimed to finish just after them it would eventually reach the finishing line and be declared winner, if not, then it wouldnt reach it...

therefore the only way to ever get anything done would be seemingly to reach for something slightly farther away untill you have reached the original thing.....

may need some further thinking this smiley - smiley


Assumptions: Junk in Junk out

Post 5

Argon0 (50 and feeling it - back for a bit)

According to Xeno's the Hare, although running 10 times as fast as the Tortoise, he will never be able to overtake him. If the Tortoise sets his goal at a couple of metres beyond the finish line he will, on the other hand, be able to finish and win.....

That assumes that the original target of the Hare was to pass the Tortoise...


Assumptions: Junk in Junk out

Post 6

Simonus

sincing they are in a race, i recon that the hare wants to win so he will aim for or past the finishing line, and not anywhere else - in order that he will win and not be made a fool of by the tortoise...

if he sets his goal to only beat the tortoise then he might have problems, as he might not reach the end... however i still recon that when running a race you look to reach the end, rather than tokeep track of how someone else is doing and try to keep ahead of them...


Assumptions: Junk in Junk out

Post 7

Argon0 (50 and feeling it - back for a bit)

Ah, but the Hare only wants to beat the Tortoise - that is uppermost in his mind - and to do that he has to pass the Tortoise - meaning his first goal is to catch up with the Tortoise.... Whereas the Tortoise only Goal is to reach the Finishing line (or to get *over* the finish line....).....

Hmmm....


Assumptions: Junk in Junk out

Post 8

Simonus

hum, right, seemingly here we must know whether the hare wants just to beat the tortoise, or to catch up to him.. only then can we 'realistically' know whether he will pass him or not...

in this case the winning of the race doesnt matter, but whether he wants to pass the tortoise or just catch up to him does...


Assumptions: Junk in Junk out

Post 9

Argon0 (50 and feeling it - back for a bit)

But the goal of passing the Tortoise breaks down into 2 goals (at least) one of catching up to the Tortoise, the other of going past.

If the Hare were to ignore the Tortoise and make his/hare (smiley - groan) goal to get past the finish line then they would undoubtably win....


Assumptions: Junk in Junk out

Post 10

Simonus

"But the goal of passing the Tortoise breaks down into 2 goals (at least) one of catching up to the Tortoise, the other of going past."

hum, i would have to dissagree with you on this point, in the same way as if you turn a page of a book, you must first go halfway, not untill you cannot see the words anymore (or similar points through). in the same way the hare trying to reach the end does not split it up into catching the tortoise and then going past him (or whatever), he goes halfway and then the other half... unless by sheer coincedence the tortoise is halfway between the start and 'end point' (whether this be the finishing line or not)


Assumptions: Junk in Junk out

Post 11

Argon0 (50 and feeling it - back for a bit)

AHA!!!! Oh...

Well it depends on the Hare's Mental accuity!!!


Assumptions: Junk in Junk out

Post 12

Simonus

it most certainly does... perhaps we should ask Zeno some time, anyone got a time travel divice handy?


Assumptions: Junk in Junk out

Post 13

Argon0 (50 and feeling it - back for a bit)

would this do?


Assumptions: Junk in Junk out

Post 14

Simonus

hum i dunno... does it have an infinite improbability drive?


Assumptions: Junk in Junk out

Post 15

Argon0 (50 and feeling it - back for a bit)

Not sure - it just popped into existence 'neath my Bum! (which was nice.....)


Assumptions: Junk in Junk out

Post 16

Simonus

well its gotta be good then!


Assumptions: Junk in Junk out

Post 17

Argon0 (50 and feeling it - back for a bit)

Yes!!!

Slumps and grabs for the Remote Control - wots on TV this Xmas?


Assumptions: Junk in Junk out

Post 18

Bubbles the Wandering Thingite Theoretical Mind (I am Heaven.)

Here's some more garbage:
Whatever the hare is "aiming" at, it has to reach the halfway point. Therefore, for that time the halfway point becomes the goal and the hare first has to travel a quarter of the original distance. This continues and eventually the motion becomes infinitesimal (or however that dang thing is spelled). The point of aim then becomes irrelevant, so all other factors do to. Now that we've got that out of the way, it's time for sleep.


Assumptions: Junk in Junk out

Post 19

Simonus

hum.... interesting....... true mind you!


Assumptions: Junk in Junk out

Post 20

Simonus

the only way i can think of doing it is not to aim at any point except knowing that you are running, in this way you are going to run an (at least theoretical)infinite distance, which cannot be halved in the normal use of the term. in this way you will cross the line to win the race, but you cannot be running to actually win it per se, it would just have to be a consequence of you running. pesonally id rather forget the race than spend an eternity running!!!


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