Das Paradox

[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)

 

[Ldude893]

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?

Ah now I like this one, and I can disprove it. Say you have a red ball, the words 'red' and 'ball' describe that object and only that object. Now a sword that can penetrate any shield no wonly describes that sword, but also describes every single shield in the universe. Likewise a shield that can be penetrated by no sword does not only describe the shield, but says that no sword in existance is strong enough to penetrate it. Therefor, the two objects cannot possibly exist in the same universe, so they can never meet!

The marvels of simple logic, eh?

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.

Ah, if he can't do both things then God isn't powerful either way, and thus he is not omni-potent.

 

[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.

 

[artanis_neravar]

There is no life in the universe (operating under the assumption that there are an infinite number of planets) There are an infinite number of planets in the universe, however we know that no all planet have life, therefore only a finite number of planets in the universe have life. to figure out the percentage of planets with life you need to divide a finite number by infinity. For simplicity sake I'm going to use 1 for the finite number and % to represent infinity. in order to solve 1/% you must take the limit of 1/x as x approaches infinity, as x gets large 1/x gets smaller (1/4 is smaller then 1/2). The limit of 1/x as x approaches infinity is 0 therefore there is no life in the universe and everyone you meet is just a figment of your imagination.
(From the Hitchhikers Guide to Galaxy I just used calculus to prove it)

 

[theultimateend]

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.

The unfortunate thing about most paradoxes is that they are written out of ignorance.

Because as it turns out ignorance is good at creating paradoxes.

 

[ipop@you]

Well I like the old going back in time with a purpose thing. If you go back in time to let's say kill Hitler then you go back and shoot him but then in your time he is already dead so there is no reason to come back and kill him so you don't go, but if you don't go then he is still alive so you have a reason to go and kill him and the cycle starts again. Another one I like is not much of a paradox but just an interesting thing: what happens if an unstoppable force hits an immoveable (immoveable also means you can't go through it) object? Finally I love Schroedinger's cat, the cat is both alive and dead as well as neither alive and dead.

 

[deathandtaxes]

There is no life in the universe (operating under the assumption that there are an infinite number of planets) There are an infinite number of planets in the universe, however we know that no all planet have life, therefore only a finite number of planets in the universe have life. to figure out the percentage of planets with life you need to divide a finite number by infinity. For simplicity sake I'm going to use 1 for the finite number and % to represent infinity. in order to solve 1/% you must take the limit of 1/x as x approaches infinity, as x gets large 1/x gets smaller (1/4 is smaller then 1/2). The limit of 1/x as x approaches infinity is 0 therefore there is no life in the universe and everyone you meet is just a figment of your imagination.
(From the Hitchhikers Guide to Galaxy I just used calculus to prove it)

Fortunately the universe is finite.

 

[slacker09]

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!

Wouldn't that be $25(Paid)+3(returned)+2(kept). There is no extra 2.

 

[artanis_neravar]

There is no life in the universe (operating under the assumption that there are an infinite number of planets) There are an infinite number of planets in the universe, however we know that no all planet have life, therefore only a finite number of planets in the universe have life. to figure out the percentage of planets with life you need to divide a finite number by infinity. For simplicity sake I'm going to use 1 for the finite number and % to represent infinity. in order to solve 1/% you must take the limit of 1/x as x approaches infinity, as x gets large 1/x gets smaller (1/4 is smaller then 1/2). The limit of 1/x as x approaches infinity is 0 therefore there is no life in the universe and everyone you meet is just a figment of your imagination.
(From the Hitchhikers Guide to Galaxy I just used calculus to prove it)

Fortunately the universe is finite.

Prove it

 

[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?

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.

Let's make the assumption that all people with the rock are the same. No you's from an alternative universe or anything. Just this universe. Just you. And your rock buddy "Boon". Having fun adventures trough time. By the means of TARDIS or something.

 

[Celtic_Kerr]

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.

The cat is not alive alive and dead at the same time. That's mis-interpretation. When writing the possibilities down mathematically, you must do the math taking into consideration the possibility of the cat being alive, and the possibility of it being dead. So on paper, mathematically, the cat is both alive and dead at the same time, but only because we need to take both points of view into consideration in the same equation.

Off the page, we know that there is a box, in the box is a cat. The cat can be dead OR alive, we have no idea which though. Therefore there is exists the possibility of the cat being alive and dead at the same time, the probability of which one is true is influenced by certain factors (leaving the cat in the box for a longer period of time with no food increases probability of death).

Since the possibility of the cat being alive or dead exists within our mind, the cat is thought to be both alive alive an dead by our brains in order to take both outcomes into consideration and to be prepared for the sight you see when it comes out.

 

[Redingold]

There is no life in the universe (operating under the assumption that there are an infinite number of planets) There are an infinite number of planets in the universe, however we know that no all planet have life, therefore only a finite number of planets in the universe have life. to figure out the percentage of planets with life you need to divide a finite number by infinity. For simplicity sake I'm going to use 1 for the finite number and % to represent infinity. in order to solve 1/% you must take the limit of 1/x as x approaches infinity, as x gets large 1/x gets smaller (1/4 is smaller then 1/2). The limit of 1/x as x approaches infinity is 0 therefore there is no life in the universe and everyone you meet is just a figment of your imagination.
(From the Hitchhikers Guide to Galaxy I just used calculus to prove it)

Fortunately the universe is finite.

Prove it

It started out as a point, and has expanded at a finite rate for 13.7 billion years. It cannot have grown to infinity in this time. Besides, even if it was infinite, you'd still be wrong, because infinity (the number of planets) minus any finite number (the number of known uninhabited planets) is still infinity (the number of potentially inhabited planets left).