Das Paradox

[artanis_neravar]

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?

Yes but in your favor

 

[deathandtaxes]

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

While this may seem like a paradox in a conversational sense in an numerical sense it is actually not a paradox as to cover half the remaining distance you would have to also half your velocity and stride length with every half of the distance so you will never actually reach your destination. Assuming it was physically possible you could go on halving your velocity, stride and distance to your goal to infinity.

 

[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.

While this may seem like a paradox in a conversational sense in an numerical sense it is actually not a paradox as to cover half the remaining distance you would have to also half your velocity and stride length with every half of the distance so you will never actually reach your destination. Assuming it was physically possible you could go on halving your velocity, stride and distance to your goal to infinity.

That's the paradox, that you will never get to your destination

 

[marc951]

dude, u get 27 dolars if u KEEP the 2 dolars
or am i missing anything

 

[artanis_neravar]

If a crocodile steals a child and promises its return if the father can correctly guess what the crocodile will do, how should the crocodile respond in the case that the father guesses that the child will not be returned?

 

[BGH122]

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?

That's not a paradox! It's a trick question you wily minx!

Play by play:

Start: Guests have $30, Manager has $0
End: Guests have $3, Manager has $27

The trick here is in the addition of $2 to the $27 because the $2 is already included in the sum and doesn't need to be added at all. The guests really paid $30-3 and the manager really received $25+2.

OP: My favourite paradox (on the Portal theme) is Russell's:

Let us call a set "abnormal" if it is a member of itself, and "normal" otherwise. For example, take the set of all squares. That set is not itself a square, and therefore is not a member of the set of all squares. So it is "normal". On the other hand, if we take the complementary set that contains all non-squares, that set is itself not a square and so should be one of its own members. It is "abnormal".

Now we consider the set of all normal sets, R. Attempting to determine whether R is normal or abnormal is impossible: If R were a normal set, it would be contained in the set of normal sets (itself), and therefore be abnormal; and if it were abnormal, it would not be contained in the set of normal sets (itself), and therefore be normal. This leads to the conclusion that R is neither normal nor abnormal: Russell's paradox.

Since this is a bit long to find scrawled on a wall, Portal 2 made do with "Does a set of all sets contain itself?"

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

While this may seem like a paradox in a conversational sense in an numerical sense it is actually not a paradox as to cover half the remaining distance you would have to also half your velocity and stride length with every half of the distance so you will never actually reach your destination. Assuming it was physically possible you could go on halving your velocity, stride and distance to your goal to infinity.

The point of Zeno's Paradox is to prove that movement is mathematically impossible. To reach x I must reach half x ad infinitum. The paradox isn't that velocity etc can't be halved, it's that the necessity to cross half of a distance no matter how small makes reaching any distance mathematically impossible.

 

[EllEzDee]

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

 

[Grospoliner]

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.

That's wonderfully wrong. In physics objects are only at rest when an object is stationary to a relative frame of reference. In this case the arrow is moving in reference to the bow, the shooter, and all other observers, thus, the arrow is not at rest. The arrow, from a frame of reference to itself, is at rest while the world moves about it. In reality though the arrow possesses acceleration and velocity to some other reference frame and as such can never actually be at rest, even when it embeds itself into another object as that object itself has acceleration and velocity (imparted to it by the movement of the planet, impact of the arrow, etc). Everything is moving constantly and as such nothing can actually be truly at rest. I suppose from a technical standpoint the only time the universe could be at rest (or any closed adiabatic system) would be when entropy has reached maximum for that system.

 

[artanis_neravar]

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?

That's not a paradox! It's a trick question you wily minx!

Play by play:

Start: Guests have $30, Manager has $0
End: Guests have $3, Manager has $27

The trick here is in the addition of $2 to the $27 because the $2 is already included in the sum and doesn't need to be added at all. The guests really paid $30-3 and the manager really received $25+2.

Correct

 

[Melon Hunter]

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?

The missing dollar is hidden in terrible arithmetic =P. The cost of the room is $25. The refund to the customers is $3. The amount kept by the manager is $2. 25+3+2=30. The reason why it comes out at $29 in the problem is the way it's worded; yes the guests technically paid $9 each for the room, but the extra $2 kept by the manager is what messes this up; the wording of the problem assumes that the customers paid $9 each to start with, but because they're still 2 dollars down at the end of this scenario, they really paid (28/3) dollars each for the room. The remainder $2 is why the original arithmetic is wrong.

Captcha: Roques, ofernate. Does that not sound like a command to the sidekick of the most British superhero ever?

 

[artanis_neravar]

That's wonderfully wrong. In physics objects are only at rest when an object is stationary to a relative frame of reference. In this case the arrow is moving in reference to the bow, the shooter, and all other observers, thus, the arrow is not at rest. The arrow, from a frame of reference to itself, is at rest while the world moves about it. In reality though the arrow possesses acceleration and velocity to some other reference frame and as such can never actually be at rest, even when it embeds itself into another object as that object itself has acceleration and velocity (imparted to it by the movement of the planet, impact of the arrow, etc). Everything is moving constantly and as such nothing can actually be truly at rest. I suppose from a technical standpoint the only time the universe could be at rest (or any closed adiabatic system) would be when entropy has reached maximum for that system.

This all depends on your reference point all engineering operates using the planet Earth as a stationary reference (as in anything sitting on the planets surface without a velocity of it's own is stationary, or at rest)

 

[Hosker]

I think this is called Curry's paradox:

If this statement is true, then Santa Claus exists.

It can be used to prove anything.

 

[HerbertTheHamster]

A set of all sets does contain itself.

As for the arrow; it is guaranteed to move through the dimension above.

 

[Halceon]

Zenos paradox works only with a timeless interpretation of movement, which doesn't work, since movement is a change of states over an interval of time.

"The ship wherein Theseus and the youth of Athens returned [from Crete] had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same."
?Plutarch, Theseus

Well, it's not as much a paradox as it is a contentious issue, but it's pretty close and mostly breeds some interesting debate.

 

[thethingthatlurks]

"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]

There is no set of sets
Although strictly speaking a set does contain itself as a subset, although that is one of the two trivial subsets (the other one is the empty subset).

Sooo...paradoxes, but not really. 1+1=0, 1+3=0, 2+5=0, etc. Yep, those are true statements, and those are indeed integers. If you can, prove why.

 

[Grospoliner]

[/quote]
This all depends on your reference point all engineering operates using the planet Earth as a stationary reference (as in anything sitting on the planets surface without a velocity of it's own is stationary, or at rest)[/quote]

I stated this in what I said. Nothing is ever actually at rest. It can only be at rest in reference to.

 

[SwiftBlade18]

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

 

[HerbertTheHamster]

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.

 

[artanis_neravar]

"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]

There is no set of sets
Although strictly speaking a set does contain itself as a subset, although that is one of the two trivial subsets (the other one is the empty subset).

Sooo...paradoxes, but not really. 1+1=0, 1+3=0, 2+5=0, etc. Yep, those are true statements, and those are indeed integers. If you can, prove why.

I would like to see you proof

 

[Scabadus]

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!

(Fun Fact: I almost typed 'meat' there.)

Now for my own paradox... or at least close enough. Similar to the arrow thing I think, didn't quite get that one. Imagine a world class sprinter racing a tortoise; the tortoise gets a ten meter head start then the sprinter starts running. In an amount of time the sprinter halves the distance between them, in another amount of time the sprinter halves the distance again, and so on, and so on for eternity. The amount of time get very, very small but they're always there. So logically... the sprinter never overtakes the tortoise. Fun, eh? This paradox can actually be very easily disproved using some aspects of probability-based quantum mechanics, but it's still a good one to think about.