Das Paradox

[Fetzenfisch]

The plural still is paradoxa

 

[Hero in a half shell]

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

The point of the box is that it's impenetrable to ANY kind of observation from outside. No cameras, no sound from the box, no nothing. That's the point. As soon as inside and outside of the box collide (say, by observation), it's no longer the original 'paradox'.

Yes, but just because you do not know something, our physical universe will not warp around our knowledge. To the scientist, the cat could either be alive or dead, and in an abstract way can be said to be both alive or dead at the same time, that is a psychological observation, but in our physical universe the cat will be one state or the other inside the box, it cannot be both. There will be a definite outcome, even if we do not know what it is.

 

[artanis_neravar]

Oh yeah, paradoxes are fun, but cheap science jokes and statistics are even more fun.

I still love the old 2+2=5 for large quantities of 2.

No because 2=2

 

[2xDouble]

This statement is a lie.

 

[Celtic_Kerr]

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]

The thing with paradoxes are the wording of them. You manipulate the wording so that it suits you. Zeno's arrow takes the word "rest" and does this. Sure the arrow never takes up more space or less space than before, as Mass cannot be created or destroyed, and this would break the laws of physics.

Fire a bullet, then drown out the scenery and watch the bullet in slow mo. If you were "Walking" along the bullet at the same speed and looked over, the bullet would not appear to be moving, just rotating. However, once you add the scenery into the equation, you can see the bullet is clearly moving.

It's the same with the Arrow. In relation to itself, the arrow technically never moves. Human being's skin grows if we gro fat, it ripples, expands, contracts. Technically, throw a stone and it never moves, in relation to itself, as it doesn't swell. But it IS moving.

Zeno's Arrow was always, unfortunately, just cheap word play and an attempt to stump people.

Zeno was of the belief that all motion is illusion and nothing moves at all. He believed there was no such thing as change. His paradoxes are more philosophical furthering and support than actual paradox for the sake of paradox

 

[The SettingSun]

Can omni-potent god (an all powerful god) create a stone which he cannot lift.

If he can't create it then he isn't all powerful.

If he creates it but then is unable to lift it he still isn't all powerful.

 

[Custard_Angel]

"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."

An arrow doesn't move from point to point occupying space, but instead travels in one direction at a rate as determined by the sum of its supporting and opposing forces.

i.e. an arrow doesn't move from Point A to Point B over a distance of 10m in 1 second, it is fired from Point A in the direction of Point B at an average rate of 10m/s.

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

Yes. It is a set that repeats ad infinitum. This is exceptionally easy to achieve when dealing with non-tangible sets like electronic data. It can be achieved with a simple mathematical function.

 

[artanis_neravar]

Can omni-potent god (an all powerful god) create a stone which he cannot lift.

If he can't create it then he isn't all powerful.

If he creates it but then is unable to lift it he still isn't all powerful.

An all powerful god can will paradoxes out of existence and win that way

 

[ChocoFace]

snip

You have successfully driven me mad.
God damn it.

 

[loodmoney]

Any sorites paradox is pretty mad:

Say you have a grain of sand. It is not a heap of sand. Now, add another grain of sand, to make two grains. If one grain is not a heap, then two grains is not a heap. Add another... etc. Eventually, you have a billion grains of sand, but not a heap of sand. The same argument can be made the other way (30, 000 grains of sand is a heap, so 29, 999 grains is also a heap...).

Conclusion: there is no such thing that is a heap, as "heap" is a self-contradictory concept.

Scarier conclusion, if you change the argument a bit: there is no such thing as a person, as "person" is a self-contradictory concept. You do not exist.

 

[shadrath]

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

say all this happened and then another guest is brought in, they choose the one you picked. They would then have a 50% chance of having picked the right one> Would that panal has, at the same time, a 50% chance and a 33% chance of winning?

 

[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

say all this happened and then another guest is brought in, they choose the one you picked. They would then have a 50% chance of having picked the right one> Would that panal has, at the same time, a 50% chance and a 33% chance of winning?

Yes, 33% for you, and 50% for them (assuming they don't know what has happened up to this point and just believe that there are 2 doors with a car behind one of them)

 

[Hero in a half shell]

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

It's based off the idea that quantum 'stuff' doesn't have to have a position until we look for one. This has been experimentally proven.

It's to do with waves, the weirdness of electro magnetic radiation, uncertainty principle etc etc
http://en.wikipedia.org/wiki/Quantum_decoherence

*Sigh* I know, I just don't like quantum mechanics, and all it's crazy theorys and impossible rule bending and breaking, Einstein didn't like it either, but he couldn't disprove it no matter how hard he tried.

That actually gives me the idea to write a surreal 'Twilight' style novel, where the protagonist, who is a metaphor for the universe, must choose to romance between Eistein and Schrodinger, Einstein is stable, kind but a bit predictible, whereas Schrodinger is wild, exciting, but kind of insane. Also is Einstein is dead, and Schrodinger periodically turns into a cat, and sometimes dissappears altogether.

 

[Flatfrog]

Related to the Monty Hall problem is my favourite paradox, which I have never got my head round.

I give you two envelopes, and I tell you that each one has some money in it, with one having twice as much money as the other. You pick an envelope and open it, then you have the option to keep the money or take the money in the other envelope.

Say you open envelope A and find $10 in it. You now know that the other envelope has either $5 or $20. Either option is equally probable, so your expected winnings by switching envelopes is $12.50. This is greater than $10, so your best option is to switch envelopes.

But the same argument would work however much money was in the envelope you opened. So how can it *always* be better to switch?!

Spoiler

I've argued more about this than any other puzzle and I still don't know the answer. The only explanation I've seen that makes any sense is this one: there is no way to pick a random amount of money with equal probability (there is no uniform probability distribution over an infinite set). Any method has to be skewed in some way, which means that the two envelopes actually *don't* have the same probability of being double or half.

 

[deathandtaxes]

\

It's paradoxes that literally prove time travel is completely impossible. And it'll never change...

I wasn't aware the Chicargo school of Economics had a theoretical physics department.

But snide comments aside time travel is extremely possible as we all do it every day and travelling forward in time faster than most people do requires simply travelling closer to the speed of light or being near a large enough gravity field neither of which are terribly complicated. Travel to times which have to our perception passed is also possible although somewhat more difficult and possibly problematic in the case of paradoxes however this in no way means that it is impossible.

 

[TheEvilCheese]

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.

See 'http://en.wikipedia.org/wiki/Monty_Hall_problem' to explain that one, I love asking people that myself.

Paradox? I can't think of a good one right now, but the whole concept of 'Simultaneously decayed and not decayed' Messed with my head a hell of a lot when I first came across it. Also, quantum entanglement, seriously that's not even funny.

I now take Physics.

 

[amppi1236]

Say you go back in time to give yourself a rock. You tell your past self to later go back in time to give your past self the same rock and tell him to do the same, and he does it. Here's the question: Where did the rock come from?

 

[2xDouble]

OK some other not-realy-a-paradox, but a mathematical weirdness:

Three people enter a motel and request a room. The room costs 30 dollars, so every guest pays 10 dollars.

In the morning, the hotel manager realizes the room actually costs only 25 dollars. Being unable to split 5 dollars evenly, he decided to give back 3 dollars to the guest (1 to each guest) and he kept the other 2.

So, each guest basically paid 9 dollars.

That's 3 x 9 = 27 dollars paid by guests.

The manager kept 2 dollars. 27 + 2 = 29 dollars.

Where is the missing dollar?

there isnt a missing dollar if the room only costs $25 and he gives them $3 back out of that $5 it would work out (if they added their $1 each to the $25) to $28 leaving the $2 that the manager kept

Actually it's just bad math. The guests paid $27, it's true. The manager kept $2, so $27-$2=$25, the cost of the room. The $2 tip is included in the $27 paid by the guests, so there is no need to add it in.

The real question isn't "where did the dollar go?", but "where did the extra $2 come from?". $27(paid) + $2("kept") + $3(returned) = $32.

Yay math!

 

[Moriarty70]

I have to say, my prefered paradox is the following:


Then again, I'm weird that way.

 

[deathandtaxes]

Say you go back in time to give yourself a rock. You tell your past self to later go back in time to give your past self the same rock and tell him to do the same, and he does it. Here's the question: Where did the rock come from?

Your making the assumption that the first you is indeed the one who gave the second you the rock. This feeds into the question about whether there is only one universe or multiple universes.