The Dichotomy Paradox

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WanderingGaze22
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The Dichotomy Paradox

Post by WanderingGaze22 »

Imagine that you’re about to set off walking down a street. To reach the other end, you’d first have to walk half way there. And to walk half way there, you’d first have to walk a quarter of the way there. And to walk a quarter of the way there, you’d first have to walk an eighth of the way there. And before that a sixteenth of the way there, before that, a thirty-second of the way and so on.

Ultimately, in order to perform even the simplest of tasks like walking down a street, you’d have to endure an infinite number of smaller tasks—something that, by definition, is utterly impossible. Not only that, but no matter how small the first part of the journey is said to be, it can always be halved to create another task; the only way in which it cannot be halved would be to consider the first part of the journey to be of absolutely no distance whatsoever, and in order to complete the task of moving no distance whatsoever, you can’t even start your journey in the first place. Do you agree with this?
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Pattern-chaser
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Re: The Dichotomy Paradox

Post by Pattern-chaser »

This is Zeno's Paradox, which isn't a paradox at all, it's just a tricky story. Think of it as variable 'slo-mo'; that your journey is being filmed with a very capable variable-slow-motion camera. As your journey progresses, you increase the slowness of the motion, so that you cannot reach your destination until the slo-mo-zoom reaches its limits. And, if there are no such limits, it will appear that you never reach your goal. This is because you are continually slowing down your apparent progress to ensure this happens, or seems to happen.
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LuckyR
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Re: The Dichotomy Paradox

Post by LuckyR »

This is an excellent example of the reality that "logical" analysis is an extremely poor substitute for experience. Mosquitos notwithstanding.
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WanderingGaze22
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Re: The Dichotomy Paradox

Post by WanderingGaze22 »

Pattern-chaser wrote: January 14th, 2022, 9:18 am This is Zeno's Paradox, which isn't a paradox at all, it's just a tricky story. Think of it as variable 'slo-mo'; that your journey is being filmed with a very capable variable-slow-motion camera. As your journey progresses, you increase the slowness of the motion, so that you cannot reach your destination until the slo-mo-zoom reaches its limits. And, if there are no such limits, it will appear that you never reach your goal. This is because you are continually slowing down your apparent progress to ensure this happens, or seems to happen.
Almost like how time moves slower when you focus on the clock and the watched pot never boils anecdote: it's all relative.
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Pattern-chaser
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Re: The Dichotomy Paradox

Post by Pattern-chaser »

Pattern-chaser wrote: January 14th, 2022, 9:18 am This is Zeno's Paradox, which isn't a paradox at all, it's just a tricky story. Think of it as variable 'slo-mo'; that your journey is being filmed with a very capable variable-slow-motion camera. As your journey progresses, you increase the slowness of the motion, so that you cannot reach your destination until the slo-mo-zoom reaches its limits. And, if there are no such limits, it will appear that you never reach your goal. This is because you are continually slowing down your apparent progress to ensure this happens, or seems to happen.
WanderingGaze22 wrote: January 15th, 2022, 3:18 am Almost like how time moves slower when you focus on the clock and the watched pot never boils anecdote: it's all relative.
No, no it's not. The trick of Zeno's Paradox is that time is actively manipulated to produce the supposed paradox. It's not "relative", it just trickery.
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EricPH
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Re: The Dichotomy Paradox

Post by EricPH »

WanderingGaze22 wrote: January 14th, 2022, 4:52 am
Ultimately, in order to perform even the simplest of tasks like walking down a street, you’d have to endure an infinite number of smaller tasks—something that, by definition, is utterly impossible.
My name is Buzz Lightyear; I can go to infinity and beyond our street, but only in the dark and when no one is looking!
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Sculptor1
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Re: The Dichotomy Paradox

Post by Sculptor1 »

WanderingGaze22 wrote: January 14th, 2022, 4:52 am Imagine that you’re about to set off walking down a street. To reach the other end, you’d first have to walk half way there. And to walk half way there, you’d first have to walk a quarter of the way there. And to walk a quarter of the way there, you’d first have to walk an eighth of the way there. And before that a sixteenth of the way there, before that, a thirty-second of the way and so on.

Ultimately, in order to perform even the simplest of tasks like walking down a street, you’d have to endure an infinite number of smaller tasks—something that, by definition, is utterly impossible. Not only that, but no matter how small the first part of the journey is said to be, it can always be halved to create another task; the only way in which it cannot be halved would be to consider the first part of the journey to be of absolutely no distance whatsoever, and in order to complete the task of moving no distance whatsoever, you can’t even start your journey in the first place. Do you agree with this?
Your problem is wrong. We all know that we can and do complete journeys all the time. So there must be something wrong with your description and conception of the journey.
Motion is continuous and the limits you have set are arbitary.
I simply walk all the way and stop.
Xeno's paradox is an artifact of units of measurement which are no more than a human conceit. The universe is analogue but we try to understand it atomistically.
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