Topic: one thing i do not understand about the Achilles and the tortoise paradox?
Anonymous A started this discussion 13 years ago #31,809
Okay as i understand it, the paradox makes the mistake of thinking that because you can divide a distance forever itmeans that the distance is infinite when its not because there are only a certain amounts of points between point A and B. What i don't understand is, what exactly are those points between A and B? at what point do you go decide that you can't divide the distance anymore because you are making up nonexistent points?
squeegee joined in and replied with this 13 years ago, 3 minutes later[^] [v] #447,295
What about the tortoise? How does that come into play?
(Edited 22 seconds later.)
Anonymous A (OP) replied with this 13 years ago, 8 minutes later, 12 minutes after the original post[^] [v] #447,296
@previous (squeegee)what are you talking about man i don't even see how this has really anything to do with the tortoise
squeegee replied with this 13 years ago, 16 minutes later, 29 minutes after the original post[^] [v] #447,298
Anonymous A (OP) replied with this 13 years ago, 6 minutes later, 36 minutes after the original post[^] [v] #447,300
Syntax joined in and replied with this 13 years ago, 12 minutes later, 49 minutes after the original post[^] [v] #447,301
!KThEOwLwbU joined in and replied with this 13 years ago, 25 minutes later, 1 hour after the original post[^] [v] #447,302
> Before an object can travel a given distance d, it must travel a distance d/2. In order to travel d/2, it must travel d/4, etc. Since this sequence goes on forever, it therefore appears that the distance d cannot be traveled. The resolution of the paradox awaited calculus and the proof that infinite geometric series such as sum_(i=1)^(infty)(1/2)^i=1 can converge, so that the infinite number of "half-steps" needed is balanced by the increasingly short amount of time needed to traverse the distances.
Syntax replied with this 13 years ago, 18 minutes later, 1 hour after the original post[^] [v] #447,305
That solution is really a single order solution.
It does not take in2 account the real world. Wind - Plate Tectonics. Aliens beaming up the tortoise for anal probes and returning tortoise in2 Achilles palms.
It does not take in2 account the real world. Wind - Plate Tectonics. Aliens beaming up the tortoise for anal probes and returning tortoise in2 Achilles palms.
Anonymous E joined in and replied with this 13 years ago, 1 hour later, 2 hours after the original post[^] [v] #447,310
Anonymous F joined in and replied with this 13 years ago, 17 minutes later, 3 hours after the original post[^] [v] #447,312
The mistake is in thinking that physical space is continuous.
Xeno's paradox proves that it is, in fact discrete.
Xeno's paradox proves that it is, in fact discrete.
(Edited 22 seconds later.)
!KThEOwLwbU replied with this 13 years ago, 3 minutes later, 3 hours after the original post[^] [v] #447,313
Anonymous F replied with this 13 years ago, 6 minutes later, 3 hours after the original post[^] [v] #447,314
squeegee replied with this 13 years ago, 1 hour later, 4 hours after the original post[^] [v] #447,320
@447,300 (A)
Sorry. I'm not talking to you until you explain the tortoise.
Actually I'm not sorry, that was a dick move.
Sorry. I'm not talking to you until you explain the tortoise.
Actually I'm not sorry, that was a dick move.
Anonymous G joined in and replied with this 13 years ago, 3 hours later, 8 hours after the original post[^] [v] #447,416
@447,312 (F)
> Xeno's paradox proves that it is, in fact discrete.
eh? What exactly are these discrete units?
> Xeno's paradox proves that it is, in fact discrete.
eh? What exactly are these discrete units?
Anonymous H joined in and replied with this 13 years ago, 2 hours later, 10 hours after the original post[^] [v] #447,419
The discrete units of matter are the vibrating strings of String Theory. Thanks.
Anonymous G replied with this 13 years ago, 4 minutes later, 10 hours after the original post[^] [v] #447,420
@previous (H)
You are describing discrete particles there, not the spacetime they are moving through, bub.
You are describing discrete particles there, not the spacetime they are moving through, bub.
(Edited 1 minute later.)
Anonymous H replied with this 13 years ago, 1 minute later, 10 hours after the original post[^] [v] #447,421
@previous (G)
Discrete unit exist in three-dimensional space, thus creating length. This paradox in question discusses length and infinity. As long as length is composed of discrete units, then it is, by definition, finite.
Discrete unit exist in three-dimensional space, thus creating length. This paradox in question discusses length and infinity. As long as length is composed of discrete units, then it is, by definition, finite.
Anonymous G replied with this 13 years ago, 7 minutes later, 10 hours after the original post[^] [v] #447,422
Anonymous H replied with this 13 years ago, 45 seconds later, 10 hours after the original post[^] [v] #447,423
Anonymous G replied with this 13 years ago, 6 minutes later, 10 hours after the original post[^] [v] #447,424
@previous (H)
Let me spell it out: Length is not composed of discrete units. The matter moving through it is. If you want to talk about quantized spacetime or assert that a Planck length is, in fact, a fundamental unit of length, then that might make sense. But you are then talking about something more akin to loop quantum gravity.
Let me spell it out: Length is not composed of discrete units. The matter moving through it is. If you want to talk about quantized spacetime or assert that a Planck length is, in fact, a fundamental unit of length, then that might make sense. But you are then talking about something more akin to loop quantum gravity.
Anonymous H replied with this 13 years ago, 3 minutes later, 10 hours after the original post[^] [v] #447,425
@previous (G)
You are sophistically splitting hair. The matter moving through length is, in fact, composed of discrete units, is it not?
You are sophistically splitting hair. The matter moving through length is, in fact, composed of discrete units, is it not?
Anonymous G replied with this 13 years ago, 3 minutes later, 10 hours after the original post[^] [v] #447,428
@previous (H)
You are not measuring the space by the object moving through it. That's like saying tortoises are discrete units, so therefore length is composed of discrete units. We're not talking about particles or tortoises. We are talking about the space they are moving through.
You are not measuring the space by the object moving through it. That's like saying tortoises are discrete units, so therefore length is composed of discrete units. We're not talking about particles or tortoises. We are talking about the space they are moving through.
Anonymous H replied with this 13 years ago, 2 minutes later, 10 hours after the original post[^] [v] #447,429
@previous (G)
But what is length, without anything to occupy it? Can length exist devoid of all matter? Likewise, can time exist, devoid of all motion?
But what is length, without anything to occupy it? Can length exist devoid of all matter? Likewise, can time exist, devoid of all motion?
Anonymous G replied with this 13 years ago, 5 minutes later, 10 hours after the original post[^] [v] #447,433
@previous (H)
Well, there's a lot of pretty empty space in the observable universe. I'm glad you bring up time though, because Achilles and the tortoise have to move through both space and time. They have the same problem spatially and temporally. This is one reason the "string theory says particles can only be so big" answer is unsatisfactory.
Well, there's a lot of pretty empty space in the observable universe. I'm glad you bring up time though, because Achilles and the tortoise have to move through both space and time. They have the same problem spatially and temporally. This is one reason the "string theory says particles can only be so big" answer is unsatisfactory.
Anonymous H replied with this 13 years ago, 5 minutes later, 10 hours after the original post[^] [v] #447,436
Anonymous G replied with this 13 years ago, 3 minutes later, 11 hours after the original post[^] [v] #447,437
Anonymous H replied with this 13 years ago, 4 minutes later, 11 hours after the original post[^] [v] #447,439
Anonymous G replied with this 13 years ago, 8 minutes later, 11 hours after the original post[^] [v] #447,441
@previous (H)
> Space is defined by the matter in it.
Most of the universe is space with no matter in it. An atom is mostly empty space.
That matter (and energy) move through space (and time) seems to be pretty evident to most observers.
> Space is defined by the matter in it.
Most of the universe is space with no matter in it. An atom is mostly empty space.
That matter (and energy) move through space (and time) seems to be pretty evident to most observers.