Das Paradox

[MysteriousStranger]

Paradox. par·a·dox/ˈparəˌdäks/: "A statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory."

I have to thank the brilliant Portal 2 for this. Having completed the game i really wanted to take a closer look at these so called Paradoxes. Never have i found a subject so facinating. I love the complexity and thought, and have started trying to create my own. One that took me a while to figure out was a Paradox called 'Zeno's Paradox - The Arrow' which states:,

EDITED: I know this first one is strictly not a true paradox! However is a slightly different way to look at things beyond the facts.

"Suppose you shoot an arrow from a bow. The arrow in flight is really at rest. For at every point in its flight, the arrow must occupy a length of space exactly equal to its own length. After all, it cannot occupy a greater length, nor a lesser one. But the arrow cannot move within this length it occupies. It would need extra space in which to move, and it of course has none. So at every point in its flight, the arrow is at rest. And if it is at rest at every moment in its flight, then it follows that it is at rest during the entire flight. So, the arrow cannot move."

"Does a set of all sets contain itself?" Taken from Portal 2

So i ask you this! What is your favourite Paradox, also if you like you can also comment as to why and if you fully understand it.[/b]

 

[Trippy Turtle]

i like paradoxes that involve time.

 

[Dr Jones]

i like paradoxes that involve time.

WHAT HAVE YOU DONE SNAKE?! YOU'VE CAUSED A TIME PARADOX!

ps. i've got a time paradox. Say you travel back in time to before you were born and killed your grandfather. Logically he'd be dead and you would never have been born. But now, if you were never born, then how was the grandfather killed? He was killed by you, but since you were never born he should be perfectly fine...

TIME PARADOX

 

[Exterminas]

What you have there is not a paradox, because you used faulty logic steps to generate it:

1. You shoot an arrow.
(Implicit: Shoot arrow -> arrow moves)

2. The arrow is at rest.
Reason: The arrow occupies space.

3. So: The arrow is at rest.

Leaving aside the fact that you created a circular argument there, you also misused the definition of "rest" since being at rest is not defined as "something occupies space"

You also overstep certain basic discoveries of quantum mechanics. Things actually chance their lenght when moving. But that of course is entirely secundary here.

Regarding your questions:
There are very little true paradox. Most, if not all of them are the result of fallacious logic or the use of unclarified terms.

 

[Dango]

My favorite is not really a paradox, but statistics that blows your mind.

Imagine you are in a contest where you can win a car. All you need to do is to chose the right panel - you've got three panels to chose from. Once you point at one panel, someone (who knows behind which panel the car is) reveals one of the other two panels. Now you can either stick to the panel you've selected originaly, or select the remaining one. Which one will you chose?

I'll stick to the panel I chose. Why would I have chosen that panel in the first place if I didn't think it was the right one?

 

[razer17]

TIME PARADOX

Nooooooo! Fission Mailed!

Ahem. I like Schrödinger's cat, which is basically about whether an object can both exist and not exist at the same time.

 

[razer17]

I'll stick to the panel I chose. Otherwise why would I choose it in the first place?

I saw this once on some show, and strangely enough you should choose the other panel. I can't remember exactly why, but statistically your more likely to win if you change.

 

[Houi]

My favorite is not really a paradox, but statistics that blows your mind.

Imagine you are in a contest where you can win a car. All you need to do is to chose the right panel - you've got three panels to chose from. Once you point at one panel, someone (who knows behind which panel the car is) reveals one of the other two panels. Now you can either stick to the panel you've selected originaly, or select the remaining one. Which one will you chose?

This is one of those annoying questions that aren't as simple as they first appear due to probability being evil.

The answer is change panels.

The reasoning? Each panel has a 33% chance of being right, thus whatever you choose you have a 66% chance of being wrong. Removing one panel doesn't change this fact. Based on your original choice there is now a 66% chance for the other panel to be correct, thus you should always swap.

This differs from most peoples gut feeling that it should have become a 50/50 choice.

 

[Dango]

I'll stick to the panel I chose. Why would I have chosen that panel in the first place if I didn't think it was the right one?

Wrong. You have 66% percent probability to get the car, if you select the OTHER panel. Seriously.

Why?

Imagine you have not 3, but 10 panels. You select one. The other person reveals you 8 panels. Now, do you stick to the original one or switch to the one remaining? Of course you select the other one, because there's just 10% probability you chose the right one in the first place, but 90% that the car is behind the remaining one.

Same applies when there are just 3 panels.

So let me look this over. There are three panels. I choose one, then I have the chance to choose a different one instead of choosing the one of I have. Since I still only have one panel, why aren't my chances are still 33%?

 

[Kyle Roberts]

Scholongers cat.
I have no idea if i spelt that right but its amazing how the cat is DEAD and alive.

AT THE SAME TIME PARADOX!

see what i did there.

 

[artanis_neravar]

My favorite is not really a paradox, but statistics that blows your mind.

Imagine you are in a contest where you can win a car. All you need to do is to chose the right panel - you've got three panels to chose from. Once you point at one panel, someone (who knows behind which panel the car is) reveals one of the other two panels. Now you can either stick to the panel you've selected originaly, or select the remaining one. Which one will you chose?

I'll stick to the panel I chose. Why would I have chosen that panel in the first place if I didn't think it was the right one?

Its an old game show, statistically you have a better chance of winning if you switch doors

 

[Lizardon]

I'm not sure if this counts as a paradox or not, but it's an interesting thought

Lets say you have a boat. As parts of the boat wear out, you replace them with new parts. Eventually, you have replaced every part of the boat. Is it still the same boat?

 

[artanis_neravar]

Paradox. par·a·dox/ˈparəˌdäks/: "A statement or proposition that, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory."

I have to thank the brilliant Portal 2 for this. Having completed the game i really wanted to take a closer look at these so called Paradoxes. Never have i found a subject so facinating. I love the complexity and thought, and have started trying to create my own. One that took me a while to figure out was a Paradox called 'Zeno's Paradox - The Arrow' which states:,

"Suppose you shoot an arrow from a bow. The arrow in flight is really at rest. For at every point in its flight, the arrow must occupy a length of space exactly equal to its own length. After all, it cannot occupy a greater length, nor a lesser one. But the arrow cannot move within this length it occupies. It would need extra space in which to move, and it of course has none. So at every point in its flight, the arrow is at rest. And if it is at rest at every moment in its flight, then it follows that it is at rest during the entire flight. So, the arrow cannot move."

It makes sense, in which case nothing moves. We as humans are just occupying the space around us and nothing more. We are just seamlessly going from empty space to empty space, or thats just how i perceive it, i could be completly wrong.



So i ask you this! What is your favourite Paradox, also if you like you can also comment as to why and if you fully understand it.

If at any point in time the arrow has velocity it is not at rest

 

[artanis_neravar]

As for a paradox, you are standing ten feet away from your goal, with every step you take you cover half the remaining distance.

 

[deathandtaxes]

I like the paradox of separation.

one way of describing it goes something like this. Draw two dots on a new piece of paper, having done so you can see that the dots are separate. However the dots are only separated by the space on the paper and they are on the same piece of paper, therefore they are still connected by that which separates them.

In sociology we talk about this as a reason as to why all notions of binary opposition in humans (black vs white thinking) are wrong. As difference can only be talked about in relation to similarity as you can only say something is different if you have something to compare it to, a similar context thus in truth all things in the realm of the social are similar but only by degree's.

 

[Anjel]

My brain. You broked it.

 

[Hero in a half shell]

Scholongers cat.
I have no idea if i spelt that right but its amazing how the cat is DEAD and alive.

AT THE SAME TIME PARADOX!

see what i did there.

Hahahaha, It's Schrodingers, but I actually prefer your spelling, it sounds kind of naughty. I take up issue with Schrodinger and his cat, the cat is either dead or alive, it can't be neither, because if it were dead or alive that would imply that you could perform another action that would change the result either way, but you cannot make the cat alive again if it was killed in the box. The world does not revolve around us.

I'll put it another way. A cat is put into a box, wth a camera, linked to a seperate room. Now the cat either lives or dies, and the scientists in the room with the box have no way of knowing which, but the cat isn't both alive and dead at the same time, as the scientists in the other room will be able to testify, as they can see it, even though the scientists in the room at the time do not know, basically physical reality does not warp around our limited knowledge

You've got a sword that can penetrate any shield and a shield invincible to any sword or sharp object. What happens when your special sword hits your special shield?

A wild Chuck Norris springs fully formed from the impact.

 

[Dango]

So let me look this over. There are three panels. I choose one, then I have the chance to choose a different one instead of choosing the one of I have. Since I still only have one panel, why aren't my chances are still 33%?

Because one of the panel is turned and you have two remaining. One would guess there's 50:50 chance now, but it's actually 33:66. It took me a while to understand, check Wikipedia - Monty Hall problem [http://en.wikipedia.org/wiki/Monty_Hall_problem].

But once you pick another panel, isn't it still a 33:66 chance?

Edit: Here's my problem with it. Say you're looking at the three panels and you think "I want to pick number three, but there's a better chance to get it right if I switch." So instead of picking three and sticking with it, you pick panel one and then switch to three. That doesn't make it so the prize is more likely to be behind the third panel... or does it... is that a paradox within itself?

 

[artanis_neravar]

I'll stick to the panel I chose. Why would I have chosen that panel in the first place if I didn't think it was the right one?

Wrong. You have 66% percent probability to get the car, if you select the OTHER panel. Seriously.

Why?

Imagine you have not 3, but 10 panels. You select one. The other person reveals you 8 panels. Now, do you stick to the original one or switch to the one remaining? Of course you select the other one, because there's just 10% probability you chose the right one in the first place, but 90% that the car is behind the remaining one.

Same applies when there are just 3 panels.

So let me look this over. There are three panels. I choose one, then I have the chance to choose a different one instead of choosing the one of I have. Since I still only have one panel, why aren't my chances are still 33%?

I can explain this, you have three doors right? and behind one is your winning whatever. so you pick one and you have a 33% chance that you are right and a 66% chance that you are wrong. now the host reveals one of the losing doors, however your chances do not change there is still a 33% chance that you have picked right and a 66% chance that you picked wrong (because the statistics do not change when a door is opened). Therefore switching is the right thing to do

 

[MysteriousStranger]

What you have there is not a paradox, because you used faulty logic steps to generate it:

1. You shoot an arrow.
(Implicit: Shoot arrow -> arrow moves)

2. The arrow is at rest.
Reason: The arrow occupies space.

3. So: The arrow is at rest.

Leaving aside the fact that you created a circular argument there, you also misused the definition of "rest" since being at rest is not defined as "something occupies space"

You also overstep certain basic discoveries of quantum mechanics. Things actually chance their lenght when moving. But that of course is entirely secundary here.

Regarding your questions:
There are very little true paradox. Most, if not all of them are the result of fallacious logic or the use of unclarified terms.

Fair point! I know strictly it is not a paradox however, i wanted to stray as far away as possible from the genric "This statement is false" and the like. Plus it made me doubt what i original though, which was the point you made.