Zeno's Paradox(es)

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Zeno's Paradox(es)

Postby James S Saint » Sat Jul 12, 2014 9:25 pm

Zeno of Elia proposed a well known set of paradoxes wherein his reasoning would indicate that no one could ever move from wherever they are. Although worded differently, the basic idea is as the following;

    If you look at the distance between yourself and the doorway and realize that you would have to get half way to the door before you could get to 3/4 distance before you got to 5/8th before you got to 11/16th before ... ..., you could never get to the doorway.

I recently did a web search for solutions to this paradox and found something that bothers me still. All of the proposed solutions are only "pseudo-solutions" it seems. Maybe there is one out there that reveals the simple truth of it, but I can only find the solutions from Bertrand Russel and other famous and professional people who more often than not are simply dismissing the paradox, not resolving it. Some come up with "solutions" that aren't really applicable, but they don't seem to realize it. And I am again temped to proclaim, "What ... is ... wrong ... with you people??", not that I don't already know, I just have a hard time fully accepting it.

So okay, maybe if I think that I know the solution and so very many others don't seem to know it, maybe "my solution" has something wrong with it (many would love to think so). So gauge for yourself and argue as you will;

The JSS solution to Zeno Paradoxes
It is true that if one takes half of the distance between where ever one is and where ever he is going, there will be an infinite number of such steps. And if each step took the same amount of time, he could never get anywhere at all. Fortunately, each step doesn't take the same amount of time.

For each division of distance traveled, there is an equal division of time it takes to traverse that distance. If we say that half way to the door is 1 meter (thus the door is 2 meters away) and this takes 1 second, then the next step, only half of that half, is 1/2 meter and only requiring 1/2 second, and so on. So the problem concerning the time it takes to get to the door is a simple infinite series;

    1 + .5 + .25 + .125 + ....
    Or
    1 + Σ (1/2)^n for n = 1 to infinity

    And the solution to that series is simply 2.

    And what is 2 times half of the distance to the door? The whole distance to the door.
    And that is how people get to where they are going as well as how Achilles overtakes the tortoise.

Now what am I missing such that famous philosophers and mathematicians throughout history haven't been able to just say that instead of the complex, excuse making explanations they gave?


And then another more philosophically clever solution is simply that all things are actually always in motion, thus "the doorway" wasn't the real destination, but rather past the doorway. And one can get to part way to one's destination without Zeno's infinite number of steps concern. 8-[
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
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Re: Zeno's Paradox(es)

Postby James S Saint » Sat Jul 12, 2014 11:06 pm

And perhaps I should mention that this exact same concern resolves the common mistake that concludes with the notion that the universe itself had to begin at some point long ago, the "Big Bang Theory".

A common reply to the mention of the universe having always existed is that "it couldn't have existed for an infinite amount of time, else it couldn't ever get to where it is now". That is the same concern as Zeno's paradox.

The simple truth of the matter is that if you start at any moment in history, it takes exactly that long to get back up to the present. And if the universe "started" an infinite amount of time in the past, it would have taken an infinite amount of time to get to the present. And so it has. The universe really has taken an infinite amount of time to get to the present and still has an infinite amount of time to get to its destination. The time-line is infinite in both directions. It has no beginning and no end. Why is that such a hard thing to accept?
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
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Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

Re: Zeno's Paradox(es)

Postby iambiguous » Sun Jul 13, 2014 12:22 am

Nowadays though we have the technology to set up a live feed from the room where someone [a celebrity say] simply walks from where they are straight through the doorway. Millions could tune in to watch it.
He was like a man who wanted to change all; and could not; so burned with his impotence; and had only me, an infinitely small microcosm to convert or detest. John Fowles

Start here: viewtopic.php?f=1&t=176529
Then here: viewtopic.php?f=15&t=185296
And here: viewtopic.php?f=1&t=194382
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Re: Zeno's Paradox(es)

Postby Amorphos » Sun Jul 13, 2014 1:19 am

The proposed distance is metaphoric, an imagined point one has to reach, and then inevitably one may only make it in stages. However a real step towards said goal is a whole step ~ and that is a real 'amount', ergo there are real distances/amounts, and projected/metaphoric or otherwise unreal amounts/distances.
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Re: Zeno's Paradox(es)

Postby Only_Humean » Mon Jul 14, 2014 12:16 pm

James S Saint wrote:Now what am I missing such that famous philosophers and mathematicians throughout history haven't been able to just say that instead of the complex, excuse making explanations they gave?


Nothing, I don't think. I'm not aware of many famous people being genuinely stumped by it... It puzzled his contemporaries because they weren't familiar with infinitesimals, but your explanation is a formal mathematical version of Aristotle's :)
http://en.wikipedia.org/wiki/Zeno's_par ... _solutions
I've not seen most of the later solutions, but yours/Aristotle's seems quite good enough to me. The others seem to be more creative approaches.
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Re: Zeno's Paradox(es)

Postby James S Saint » Mon Jul 14, 2014 12:27 pm

Only_Humean wrote:
James S Saint wrote:Now what am I missing such that famous philosophers and mathematicians throughout history haven't been able to just say that instead of the complex, excuse making explanations they gave?


Nothing, I don't think. I'm not aware of many famous people being genuinely stumped by it... It puzzled his contemporaries because they weren't familiar with infinitesimals, but your explanation is a formal mathematical version of Aristotle's :)
http://en.wikipedia.org/wiki/Zeno's_par ... _solutions
I've not seen most of the later solutions, but yours/Aristotle's seems quite good enough to me. The others seem to be more creative approaches.

I knew I liked Aristotle for a reason. 8)

But honestly, that was 2300 years ago. So why is there so much nonsense being spread concerning the issue (do a Google search on it) and why are they still promoting the Big Bogus Bang theory, which is actually the same issue?
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
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Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm

Re: Zeno's Paradox(es)

Postby Arminius » Tue Aug 05, 2014 3:49 am

James S Saint wrote:So why is there so much nonsense being spread concerning the issue (do a Google search on it) and why are they still promoting the Big Bogus Bang theory, which is actually the same issue?

Because the powerful people get more power, when they are spreading more nonsense than sense.
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Re: Zeno's Paradox(es)

Postby James S Saint » Tue Aug 05, 2014 6:53 am

Arminius wrote:
James S Saint wrote:So why is there so much nonsense being spread concerning the issue (do a Google search on it) and why are they still promoting the Big Bogus Bang theory, which is actually the same issue?

Because the powerful people get more power, when they are spreading more nonsense than sense.

Yep, control strategy 101: "Make everything else weaker than yourself" (a part of the Relativity paradigm). But as they say, "What goes around, comes around" ... through time.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
James S Saint
ILP Legend
 
Posts: 25976
Joined: Sun Apr 18, 2010 8:05 pm


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