please help me on paradox's

[Tom]

Please could you brainy people out there give me your best examples of paradox's. I'm really stuffed otherwise

the one's I know are...

The statement on the other side is....

Chicken and the egg

Kill you father in the past

(not sure if this one's a paradox)if a tree falls, does it make a sound.

Anything please....


Thank you

 

[atomka]

paradoxs

I believe you are confusin paradox's with parables. A parable is something like if a tree falls in the woods......... A parable is something that is used to clear your own mind for meditation, or to explain ones own philosophy. A paradox is something that cannot be answered. Like is the glass half full or half empty. Something that is almost under ones opinion. An example of one in math is Zeno's Paradox. He states that to get to one place to another you have to travel half that distance, so you will eventually never get there. Why? Because there is an infinite number of halves. You can go half that distance and then half that and then half that into infinity. Get it?

 

[James R]

3 paradoxes

<b>Who shaves the barber?</b>

A barber in a small town shaves every man who does not shave himself. Who shaves the barber?

<b>Execution</b>

The same town has a law. When a traveller approaches the town they are asked their business. If they lie about what they will do in the town, they are executed on the gallows. If they tell the truth, they are not executed.

A man approaches the town and is asked his business. He says "I will be executed on the gallows here."

<b>The unexpected egg</b>

I have here 10 boxes in a row. One of them contains an unexpected egg. You are allowed to open the boxes, but only in numerical order (i.e. box 1 first, then box 2, then 3 etc.). Can the egg truly be unexpected?

Think about this: It can't be unexpected if it is in box 10, since after opening boxes 1 to 9 and finding them empty you will expect it to be in box 10. So, it can't be in box 10. But then, by the same reasoning, it can't be in box 9, because box 10 is impossible and box 9 would not be unexpected after finding boxes 1 to 8 empty. By this reasoning process the unexpected egg cannot be in any of the boxes.

So, you start opening the boxes one by one and look! In box 6 there's a totally unexpected egg! What went wrong?

 

[Twilight]

what is a paradox - opinion

A paradox is usually a misunderstanding of a given item. If we want to give only an yes-or-no answer to some questions, we discover that none of our answers is true. So (I think) paradoxes are only in our mind. Why should it be the egg OR the chicken? Isn't the egg a very-young chicken? Think at the evolution of species... you will find the question to be unfounded.
Another way to explain this is the following: if paradoxes do REALLY exist, then the world couldn't be continuous nor inteligible. But it is, wich means there are no real paradoxes, but only the ones we imagined ourselves.
Of course, this is only my point of view. If someone does not agree with this, he's free to explain why and where I'm I wrong. Thanx.

 

[Benji]

I think Tom was referring to paradox's in time travel, for example if I build a time machine and go back into time and kill my great grandfather then how could I do this as once he is dead I cease to exist.
I think if you did this history would find a way to cover it up, time would in essence cover any tracks you can make as anything you did in the past has already happened, what im saying is changing history is not possible as anything you go back and do has already happened so you might change something but history would never record that you did you would not change history as it is recorded.
Almost a self defeating purpose, for example if you went back and killed Hitler, history recorded you didn't so it would never appear as you did, even if you did that point becomes irrelevant because this is a paradox.

 

[rde]

Re: 3 paradoxes

Originally posted by James R
These aren't paradoxes...
<b>Who shaves the barber?</b>
She doesn't shave.

<b>Execution</b>
They move the gallows.

<b>The unexpected egg</b>
What went wrong? Nothing. If it's logical that there's no egg in 6, then it's unexpected if you find one. Of course, this is predicated on the possiblity of there being an 'unexpected egg'.

 

[Stryder]

How about this for a paradoxical statement.

"I'll pay you tomorrow"

Of course tomorrow never actually comes, because when that day arrives it becomes today, it would have a new tomorrow and today would be called yesterday.

Or how about a script paradox for HTML/Javascript fanatics everywhere!

<HTML><HEAD>
<TITLE>Annoying terminal loop</TITLE>
<SCRIPT LANGUAGE="Javascript">

function Again(){
TerminalLoop();
}

function TerminalLoop(){
alert('Terminal loops step into infinity.');
Again();
}
</SCRIPT></HEAD>
<BODY ONLOAD="Javascript:TerminalLoop()"></BODY></HTML>

Don't of course attempt that unless your going to Alt+F4 your way out of it.

How about:
[/B]Heads I win, Tails you Lose[/B]

 

[James R]

Re: Re: 3 paradoxes

<b>Who shaves the barber?</b>
<i>She doesn't shave.</i>

Nice. I hadn't heard that one. Now what if we add that the barber is male?

<b>Execution</b>
<i>They move the gallows.</i>

Remove "here" from the puzzle. What then?

<b>The unexpected egg</b>
<i>What went wrong? Nothing. If it's logical that there's no egg in 6, then it's unexpected if you find one. Of course, this is predicated on the possiblity of there being an 'unexpected egg'.</i>

But what went wrong with the logic?

 

[rde]

Re: Re: Re: 3 paradoxes

Originally posted by James R



But what went wrong with the logic?

It's not the logic that's at fault, it's the language. "This statement is false" is the shortest example, but there are an infinite number of others. Call them paradoxes if you like, but I prefer not to; the grandfather paradox is a paradox, at least until such time as someone invents time travel and proves that it's a load of bollocks.





Language has its limitations, but those limitations are also its strengths; you can do anything with it. Fiction, for example. For some reason people spend millennia pondering statements like yours above, and none at all over the equally implausible "He leaped over the tall building in a single bound".

 

[Riomacleod]

Think about this: It can't be unexpected if it is in box 10, since after opening boxes 1 to 9 and finding them empty you will expect it to be in box 10. So, it can't be in box 10. But then, by the same reasoning, it can't be in box 9, because box 10 is impossible and box 9 would not be unexpected after finding boxes 1 to 8 empty. By this reasoning process the unexpected egg cannot be in any of the boxes

The flaw in the logic is that you cant use the same reasoning for box 9 as you do for box 10, for this reason: In box 10 there could be an expected egg.
In the case of box 10, there is no box further down the line, therefore the egg would have to be there. And in all honesty, if you're told there's an egg in one of the boxes, none are really "unexpected".

 

[my_notebook]

unexpected egg

If the egg is to be unexpected, then you cannot be looking for the egg. Otherwise you will be expecting it.

If you open nine empty boxes with no idea you are looking for an egg, and then open #10 and find one, then that egg is still unexpected.

I agree that most "paradoxes" are just tricks of language.

Xeno's paradox is, in my mind, a real paradox. The grandfather one is, but it depends upon the assumption of time travel. Xeno's could actually be put into practice.

 

[rde]

Re: unexpected egg

Originally posted by my_notebook

Zeno's paradox is, in my mind, a real paradox. The grandfather one is, but it depends upon the assumption of time travel. Zeno's could actually be put into practice.

A little physics will see you through Xeno's paradoxes. One of them states that in order to travel from A to B, you must first travel half that distance. To travel that far, you'll have to travel half that distance, and so on. You can never reach your destination because you'll always have half the distance to travel before you can get to any point.

However, physics gives us Planck length. This indordately small measurement (about 10^-35m) can be considered the quanum of length, and therefore there's no such distance in the macro world as half a planck length.

Other paradoxes (such as the arrow) can be explained by calculus. Of course, you could argue that calculus is itself a fiction, but that's a debate for another day.

 

[my_notebook]

This indordately small measurement (about 10^-35m) can be considered the quanum of length, and therefore there's no such distance in the macro world as half a planck length.

(quantum?).

Does that mean that Planck's length is the smallest unit of length there is? How do they know? It is absolutely fascinating, and I have never heard of it before. It does indeed solve Xeno's paradox.

So if the smallest length is Planck's Length, then theoretically could a photograph be represented digitally with absolutely no loss in resolution, given that the pixel width was equal to Planck's Length?

 

[rde]

Originally posted by my_notebook




So if the smallest length is Planck's Length, then theoretically could a photograph be represented digitally with absolutely no loss in resolution, given that the pixel width was equal to Planck's Length?

Not sure that I understand it sufficiently to explain it, but I'll give it a go:

After Einstein published General Relativity, Planck realised that any measurement of time, length or gravity could be explained solely in terms of c, G and hbar. These are all absolutes, and any length they give is a multiple of (1.6x10^-35). Similarly, we've got Planck time (which isn't very long) and, presumably, Planck gravity.

Because any length measurable from first principles (so to speak) is a positive multiple of Planck length, it's reasonable to conclude that it's the quantum of length. I don't have the maths to explain it more completely, sorry.



Hope that goes some way to explaining it. And that it isn't completely wrong.

 

[FlowerPower]

Xeno's nose knows...

I think that the answer to Xeno’s paradox lies in the actual speed of the person (or thing) traveling to the end point.

Let me set up the situation where a marble rolls one meter at a constant velocity (1 meter/second) through an end point. We usually think of speed as having a length unit over time, such as meters per second or kilometers per hour. This is a rate, which can be explained by differential calculus as dy/dx, or the change in y over some x.

Xeno has changed this definition of speed with the paradox. In Xeno’s rate of travel, the unit of ”length” keeps getting smaller by one half for every gain of one half. Xeno says that the marble must pass through a point half the distance to the end point, and after that point it must do it again infinitely many times. The important thing is that the rate of “one-half distance milestones” increases exponentially as Xeno’s unit of “length” gets exponentially smaller. These two things diverge such that a constant velocity is maintained through the end point. I would say that at the instance where the marble passes through the end-point, the rate of these milestones is infinity, and the unit of length in the rate is one-over-infinity (infinitesimally small).

But fuck it dude, let’s go bowling…

 

[my_notebook]

xeno evil, hear no evil

Flowerpower -

Putting it that way does explain it. But the paradox still stands in my mind, b/c the person/thing manages to maintain forward motion for "ever" without reaching the endpoint.

If you take a step forward and travel one yard, and you take that yard as a line in space, you can plot an infinite number of points on that line. But you have not travelled an infinite distance because those points have no length themselves. Likewise Xeno's "last milestone" has no length, b/c it's infinitely small.

I think that Xeno's paradox is really just the mystery of the existence of infinity in mathematics.

Maybe the real paradox is science; that we can actually take measurements in an infinite universe.

But I am still curious about Planck's length, which as explained by rde seems to quantify the universe. Anyone else wanna drop some knowledge on the Planck tip?

 

[tony1]

Re: 3 paradoxes

*Originally posted by James R
A barber in a small town shaves every man who does not shave himself. Who shaves the barber?*

Not a paradox.
Merely an example of fallacious reasoning based on a faulty premise.

*If they lie about what they will do in the town, they are executed on the gallows. If they tell the truth, they are not executed.

A man approaches the town and is asked his business. He says "I will be executed on the gallows here."*

Another faulty premise.

*I have here 10 boxes in a row. One of them contains an unexpected egg....

So, you start opening the boxes one by one and look! In box 6 there's a totally unexpected egg! What went wrong? *

Another faulty premise.
What is an unexpected egg?

If you expected to see an egg, then it is an expected egg.
If you didn't expect to see an egg, then it is unexpected and you wouldn't go thru the mental contortions you described.

*Originally posted by Twilight
there are no real paradoxes, but only the ones we imagined ourselves.*

Exactly.

*Originally posted by Benji
for example if I build a time machine and go back into time and kill my great grandfather then how could I do this as once he is dead I cease to exist. *

Another faulty premise.
What is a time machine?
Don't say it is a machine which allows you to travel backward in time, since there is no such thing.

*Originally posted by my_notebook
Xeno's paradox is, in my mind, a real paradox.*

It isn't a paradox at all.
It is a fallacy based on the false premise that time is of no consequence when comparing speeds.

*Does that mean that Planck's length is the smallest unit of length there is?*

Yes.
Set p = Planck's length.

Planck's length is twice the length of p/2, thus proving that Plancks' length is the smallest unit of length there is.
Of course, there is an infinity of proofs like that.
Such as "Planck's length is four times the length of p/4, thus proving that Plancks' length is the smallest unit of length there is."
*tongue-in-cheek*

Only theoretical physicists could come up with the concepts like the smallest unit of length.
Their next project will be the definitive establishment of the stupidest possible theoretical physicist.

Actually, Planck's length is the distance old-time pirates made people walk when they made them "walk the Planck."
Perhaps you've heard of that.

 

[James R]

In defence of theoretical physicists

tony1:

<i>Only theoretical physicists could come up with the concepts like the smallest unit of length. Their next project will be the definitive establishment of the stupidest possible theoretical physicist.</i>

Actually, the concept of the Planck length is more complicated than you make out. No theoretical physicist would ever call it "the smallest unit of length".

The Planck length is thought to be the length at which spacetime is likely to be quantised. If this is true, any object moving through spacetime would do so in a series of "steps" of minimum size equal to the Planck length.

We can easily imagine lengths smaller than the Planck length, but such lengths may well have no physical manifestation in our universe.

 

[Riomacleod]

James, seriously? That's kinda cool!


Tony, alot of research and work has gone into the theory of time travel. A significant sector of the physics community thinks that the concept is possible. Simply saying that the premise of the grandfather paradox is faulty because there are no time machines is pathologically absurd. Maybe you could go into deeper detail on why the gallows paradox's premise is faulty? Rather than just give blanket unbacked statements?

 

[my_notebook]

Set p = Planck's length.

Planck's length is twice the length of p/2, thus proving that Plancks' length is the smallest unit of length there is.
Of course, there is an infinity of proofs like that.

Ah, so p=2(p/2)

Yeah that "proof" really explains Plack's length. Thanks for clearing that up dude.

Their next project will be the definitive establishment of the stupidest possible theoretical physicist.

Nope... that has already been established.