Das Paradox

[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.

 

[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?