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Invisibleraytrace
Stranger

Registered: 01/15/02
Posts: 720
Achilles & the tortoise
    #622924 - 04/30/02 07:33 AM (14 years, 7 months ago)

the very fast runner Achilles took the challenge to race with the turtle. the turtle was given a head start in a desperate act to add some suspense, since Achilles was 10 times faster.

so, the turtle is X meters in front of Achilles and the race begins?

Achilles starts running fast, but by the time he reached point X, the turtle has, of course, proceeded to the point X + 1/10*X

so, Achilles runs some more?

by the time Achilles reached X + 1/10*X, the turtle moved to X + 1/10*X + 1/10*1/10*X

poor Achilles, chased the turtle further to this point, but to his surprise (yet not so surprisingly) the turtle has moved even further?. (X + 1/10*X + 1/100*X + 1/1000*X)

as you can clearly see, no matter what your personal experience says, Achilles will never reach the turtle?.

so, as the Greek philosopher Zenon would have warned you some 2,5 millennia back, avoid racing with turtles? (or maybe you?re faster than Achilles? heh heh?)



dedicated to Swami?.


Edited by raytrace (04/30/02 07:48 AM)


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InvisibleSwami
Eggshell Walker

Registered: 01/19/00
Posts: 15,413
Loc: In the hen house
Re: Achilles & the tortoise [Re: raytrace]
    #622935 - 04/30/02 08:38 AM (14 years, 7 months ago)

dedicated to Swami?.
Very cool, my first dedication! Thanks, bro :smile:

As the The_Lord said in another post, "This was way too easy, give me a harder one." I will let someone else point out the flaw in your logic here. I think that you probably already know what it is.

You seem to forget that I have been around the block. This one reminds me of when I was playing with some  kids at the pool this weekend (ages 4 to 8) and they did the "Hey, watch me pull my thumb off trick." Some tricks only work on people much younger or less experienced.

Good try though! 


--------------------



The proof is in the pudding.


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InvisibleSclorch
Clyster

Folding@home Statistics
Registered: 07/13/99
Posts: 4,805
Loc: On the Brink of Madness
Re: Achilles & the tortoise [Re: raytrace]
    #623136 - 04/30/02 01:15 PM (14 years, 7 months ago)

Yeah yeah we've all read Godel, Escher, Bach...


--------------------
Note: In desperate need of a cure...


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OfflineNomad
Mad Robot

Registered: 04/30/02
Posts: 422
Last seen: 8 years, 11 months
Re: Achilles & the tortoise [Re: Swami]
    #623343 - 04/30/02 05:08 PM (14 years, 7 months ago)

I will let someone else point out the flaw in your logic here.

Thanks.

It's the same on every trip: the most interesting thing to do is watch time. Let's assume that the race starts at time t = 0. When Achilles reaches the point x, the time is t = x/s (s being the speed of Achilles). At time t = x/s, the turtle has proceeded to the point x + 1/10 * x. When Achilles reaches the point x + 1/10 * x, the time is t = x/s + x/(10*s), which is, for example, earlier than time t = 2 * x/s. Meanwhile, the turtle has reached point X + 1/10*X + 1/10*1/10*X. When Achilles reaches this point, the time is t = x/s + x/(10*s) + x/(100*s), which is STILL earlier than time t = 2 * x/s. No matter how long you play the game, the time in your logical framework will NEVER reach t = 2 * x/s.

Thus, you have only proved that for certain instants of time, Achilles doesn't reach the turtle. You did not, however, prove anything about what happens at time t = 2 * x/s. (Note that I don't claim that Achilles reaches the turtle at this point in time, I'm merely pointing out a flaw in your logic.)

as you can clearly see, no matter what your personal experience says, Achilles will never reach the turtle?.

Since "never" includes the point of time t = 2 * x/s, about which you did not state anything, your implication is false. QED.


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Invisibleraytrace
Stranger

Registered: 01/15/02
Posts: 720
Re: Achilles & the tortoise [Re: Swami]
    #623431 - 04/30/02 07:18 PM (14 years, 7 months ago)

Very cool, my first dedication! Thanks, bro
you're welcome :smile:

As the The_Lord said in another post, "This was way too easy, give me a harder one."
it is just for warming up...   


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Invisibleraytrace
Stranger

Registered: 01/15/02
Posts: 720
Re: Achilles & the tortoise [Re: Sclorch]
    #623437 - 04/30/02 07:23 PM (14 years, 7 months ago)

Yeah yeah we've all read Godel, Escher, Bach...
please, refrain from generalizations. i haven't read them.

i only know this as one of Zenon's paradoxes


Edited by raytrace (04/30/02 07:33 PM)


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Invisibleraytrace
Stranger

Registered: 01/15/02
Posts: 720
Re: Achilles & the tortoise [Re: Nomad]
    #623443 - 04/30/02 07:28 PM (14 years, 7 months ago)

hey, take it easy man... it's your first post... you should be saying something like "Hi, everybody! I am Nomad"...


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InvisibleSwami
Eggshell Walker

Registered: 01/19/00
Posts: 15,413
Loc: In the hen house
Re: Achilles & the tortoise [Re: raytrace]
    #623458 - 04/30/02 07:47 PM (14 years, 7 months ago)

Yeah yeah we've all read Godel, Escher, Bach...
please, refrain from generalizations. i haven't read them.


He meant that all of the cool people have read them.


--------------------



The proof is in the pudding.


Edited by Swami (04/30/02 07:49 PM)


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Invisibleraytrace
Stranger

Registered: 01/15/02
Posts: 720
Re: Achilles & the tortoise [Re: Swami]
    #623478 - 04/30/02 08:24 PM (14 years, 7 months ago)

He meant that all of the cool people have read them.
yep? that?s what I thought he meant?

so, also you should refrain from making useless indications...


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Anonymous

Re: Achilles & the tortoise [Re: Swami]
    #623480 - 04/30/02 08:27 PM (14 years, 7 months ago)

I haven't read Godel, Escher, Bach, but I knew the logic of this 'paradox' was flawed when my oldest brother came home during his first year in college and told it to me. I said to him, 'Philosophy sounds like bullshit to me.' Then my dad took me to the restroom and put a bar of Zest in my mouth (filthy language and all that).


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OfflineNomad
Mad Robot

Registered: 04/30/02
Posts: 422
Last seen: 8 years, 11 months
Re: Achilles & the tortoise [Re: raytrace]
    #623816 - 05/01/02 07:52 AM (14 years, 7 months ago)

Yeah, but let's kill the dead before we introduce the living. I really hate this paradox stuff.

And the sound of one hand clapping is, obviously, half the sound of two hands clapping.


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Invisibleraytrace
Stranger

Registered: 01/15/02
Posts: 720
Re: Achilles & the tortoise [Re: ]
    #624039 - 05/01/02 02:23 PM (14 years, 7 months ago)

'Philosophy sounds like bullshit to me.'
does it still sound like that?


Edited by raytrace (05/01/02 02:25 PM)


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Anonymous

Re: Achilles & the tortoise [Re: raytrace]
    #624466 - 05/02/02 12:45 AM (14 years, 7 months ago)

Much of it.


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