I've been getting into paradoxes lately, to be honest they're pretty awesome.
If anyone is confused, a paradox is "
a statement or group of statements that leads to a contradiction or a situation which (if true) defies logic or reason, similar to circular reasoning.
" (wiki)
A paradox I heard awhile ago is one about a man and a turtle racing, AKA Achilles and the tortoise.
"
In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.
" (wiki)
Another one that has been grabbing for my attention as of recently is Newcomb's Paradox.
"
A person is playing a game operated by the Predictor, an entity somehow presented as being exceptionally skilled at predicting people's actions. The exact nature of the Predictor varies between retellings of the paradox. Some assume that the character always has a reputation for being completely infallible and incapable of error; others assume that the predictor has a very low error rate. The Predictor can be presented as a psychic, as a superintelligent alien, as a deity, as a brain-scanning computer, etc. However, the original discussion by Nozick says only that the Predictor's predictions are "almost certainly" correct, and also specifies that "what you actually decide to do is not part of the explanation of why he made the prediction he made". With this original version of the problem, some of the discussion below is inapplicable. The player of the game is presented with two boxes, one transparent (labeled A) and the other opaque (labeled B). The player is permitted to take the contents of both boxes, or just the opaque box B. Box A contains a visible $1,000. The contents of box B, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box B, or both boxes. If the Predictor predicts that both boxes will be taken, then box B will contain nothing. If the Predictor predicts that only box B will be taken, then box B will contain $1,000,000. By the time the game begins, and the player is called upon to choose which boxes to take, the prediction has already been made, and the contents of box B have already been determined. That is, box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Before the game begins, the player is aware of all the rules of the game, including the two possible contents of box B, the fact that its contents are based on the Predictor's prediction, and knowledge of the Predictor's infallibility. The only information withheld from the player is what prediction the Predictor made, and thus what the contents of box B are.
" (wiki)
At first when I saw this I thought that for sure the best way to go was to take both boxes. The Predictor, or "Supreme Being" is how I knew it, already made his choice! He can't go back now! Certainly if he predicted you to take box B and you took both you would have $1,001,000! If you took just box B you would have only $1,000,000! Same for if he thought you would take both. You still would have $1000 instead of zero!
Later my mind went into some conflicting arguments, which I tell you was not helped by advice from outside sources. Pretty soon my view changed and I thought taking only B was the way to go. Why waste a whole million dollars on just a thousand! It wouldn't be worth the risk taking both. If the Supreme Being is infallible then I'd better get the million I deserve.
My stance is basically indifferent for both sides now, but it still shifts to one direction every now and then.
The wiki article in which I got the paradox from actually is really enthralling as well. This stuff is deep, man.
Ah I could go on and on...
Anyhoo, I guess in this thread discuss paradoxes, share your own and also your views on such paradoxes.
Because if you take the square root of false and then add that to a handgun and you multiply by depression you get sucide. But if you take the square root of truth which is false and then do the problem you get crazed white supremist with a gun. Now if you completely throw out logic you will find the truth somewhere between a rock and a hard place. So when i got there there was a gold aying on the ground and his name was steve. He told told me the key to life is YOLO. When he said i snapped his neck because that saying old but i reliezed he didnt have a neck. So the next thing i know i ceated a whole big war between Fish and fluffy bunnie of DOOM. The weird part is the war came down to one bunny and he went cammando killing all the fish except 1. The bunny had to cross a major highway to kill the elder fish. he throws a grenade arcoss the highway and kills the fish. He reliezes that the fish has they key to solving paradox and as the bunny cross the street he gets hit by a bycicle. So the guy on the bike grabs the solving thingy and rides home. Well he came up with a problem to solve it
The statement is false so is it true= life + hair tearing out / forrest gump - upside down face + the sqaure of 69 + the meaning of life - dumb logic
1. Barbershop Paradox - Briefly, the story runs as follows: Uncle Joe and Uncle Jim are walking to the barber shop. There are three barbers who live and work in the shopâ"Allen, Brown, and Carrâ"but not all of them are always in the shop. Carr is a good barber, and Uncle Jim is keen to be shaved by him. He knows that the shop is open, so at least one of them must be in. He also knows that Allen is a very nervous man, so that he never leaves the shop without Brown going with him.
Uncle Joe insists that Carr is certain to be in, and then claims that he can prove it logically. Uncle Jim demands the proof. Uncle Joe reasons as follows.
Suppose that Carr is out. If Carr is out, then if Allen is also out Brown would have to be inâ"since someone must be in the shop for it to be open. However, we know that whenever Allen goes out he takes Brown with him, and thus we know as a general rule that if Allen is out, Brown is out. So if Carr is out then the statements "if Allen is out then Brown is in" and "if Allen is out then Brown is out" would both be true at the same time.
Uncle Joe notes that this seems paradoxical; the hypotheticals seem "incompatible" with each other. So, by contradiction, Carr must logically be in.
2.interesting number paradox - Claim: There is no such thing as an uninteresting natural number.
Proof by Contradiction: Assume that there is a non-empty set of natural numbers that are not interesting. Due to the well-ordered property of the natural numbers, there must be some smallest number in the set of uninteresting numbers. Being the smallest number of a set one might consider not interesting makes that number interesting after all: a contradiction.
3. Berry paradox - Consider the expression:
"The smallest positive integer not definable in under eleven words." Since there are finitely many words, there are finitely many phrases of under eleven words, and hence finitely many positive integers that are defined by phrases of under eleven words. Since there are infinitely many positive integers, this means that there are positive integers that cannot be defined by phrases of under eleven words. By the well ordering principle, if there are positive integers that satisfy a given property, then there is a smallest positive integer that satisfies that property; therefore, there is a smallest positive integer satisfying the property "not definable in under eleven words". This is the integer to which the above expression refers. The above expression is only ten words long, so this integer is defined by an expression that is under eleven words long; it is definable in under eleven words, and is not the smallest positive integer not definable in under eleven words, and is not defined by this expression. This is a paradox: there must be an integer defined by this expression, but since the expression is self-contradictory (any integer it defines is definable in under eleven words), there cannot be any integer defined by it.
One of those paradoxes is one of the more famous Zeno's paradoxes. I believe, however, that they've been solved through rigorous mathematical methods. I think I saw a proof using only basic calculus.
I enjoy Cantor's paradox, which is basically a paradox about infinity and implies that there is an infinite number of infinities.
One of those paradoxes is one of the more famous Zeno's paradoxes. I believe, however, that they've been solved through rigorous mathematical methods. I think I saw a proof using only basic calculus.
Yeah, it's easy enough for me to just imagine the lines of both beings on a graph and when one passes the other.
I guess it also ties in with the idea of actual infinity too, that all things in an infinite set can exist as a finite total.
The paradox of Achilles and the tortoise is a bit flawed. It considers that Achilles is trying to get to the point where the tortoise currently is, which leads in the described distance converging to zero. But the current point of the tortoise is not Achilles' goal; it is the end of the race. Imagine you build two towers with two different types of blocks. One tower uses smaller blocks, the other larger ones. If you repeatedly simultaneously put a block on each tower, the one with the larger blocks will grow faster and eventually surpass the other one. Same as with a race with a faster and a slower runner.
I really love time paradoxes Especially the ones created by the Rule of First
By that rule, something that by trying to change the future, and by that, you go to the past, but in a result, everything repeats for eternity, is possible only if it has a beginning point.
Like in the last episode of Doctor Who.
They read the book, that tells them where Rory is. But for that to happen, the book first have to be written. The book is written by Amy.
This proves that if Rory lives with Amy, the book will be written, But because of the book, they find him, and that is impossible, because when Rory is taken for first time, they don't have the book.
Also at the end Rory reads its tombstone, and he is take. This is the unchanged future, the one with Amy with him, but the problem is that only Rory is taken, and on the tombstone it says only Rory. Amy is taken next, but only then her name appears on the tombstone.
The point is the entire episode is impossible!
There is one episode of My Little Pony Friendship Is Magic, where the future Twilight appears to warn the past Twilight about something, and thus leading the past Twilight into turning the Future Twilight.
By the Rule of First, this is Impossible. The first( Original) Twilight, will not go in the past, because the only reason she would have is the warning of the Future Twilight, and she does not exist... she cant exist. Its Paradox
A person is playing a game operated by the Predictor, an entity somehow presented as being exceptionally skilled at predicting people's actions. The exact nature of the Predictor varies between retellings of the paradox. Some assume that the character always has a reputation for being completely infallible and incapable of error; others assume that the predictor has a very low error rate. The Predictor can be presented as a psychic, as a superintelligent alien, as a deity, as a brain-scanning computer, etc. However, the original discussion by Nozick says only that the Predictor's predictions are "almost certainly" correct, and also specifies that "what you actually decide to do is not part of the explanation of why he made the prediction he made". With this original version of the problem, some of the discussion below is inapplicable. The player of the game is presented with two boxes, one transparent (labeled A) and the other opaque (labeled B). The player is permitted to take the contents of both boxes, or just the opaque box B. Box A contains a visible $1,000. The contents of box B, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box B, or both boxes. If the Predictor predicts that both boxes will be taken, then box B will contain nothing. If the Predictor predicts that only box B will be taken, then box B will contain $1,000,000. By the time the game begins, and the player is called upon to choose which boxes to take, the prediction has already been made, and the contents of box B have already been determined. That is, box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Before the game begins, the player is aware of all the rules of the game, including the two possible contents of box B, the fact that its contents are based on the Predictor's prediction, and knowledge of the Predictor's infallibility. The only information withheld from the player is what prediction the Predictor made, and thus what the contents of box B are.
I personally like the Monty Hall problem, but it's only a paradox in that the answer SEEMS impossible, but really isn't.
Anyways, have a textwall:
Suppose you're on a game show and you're given the choice of three doors [and will win what is behind the chosen door]. Behind one door is a car; behind the others, goats [unwanted booby prizes]. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one [uniformly] at random. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?
I'm not going to give the answer in this thread for those that want to try to figure it out themselves.
Actually it is. Mathematically speaking this is a matter of pure statistics. Before the door is opened you have a 33% chance of being correct, sticking with that decision doesn't change that percentage but switching brings you to a 50% probability of choosing the door with a car behind it. The Achilles "aradox" is also flawed. Basic algebra can easily plot the points of each runner at any given time and show how quickly Achilles will overtake and pass the tortoise.
Personally I hate time paradoxes in most media, they tend to ruin the plot for me. Take Donnie Darko for instance. Donnie survived because a rift in time allowed the dead man in the rabbit suit to warn Donnie about the plane engine that was sent back in time by that same rift to crash into Donnie's room. That rift in time however only exists because Donnie survived when he wasn't supposed to, had he died it shouldn't have existed and therefore the plane engine shouldn't have been sent back in time to kill him. Which means he would have survived which creates the rift that kills him which prevents the rift which means he survives etc etc etc. If you really want to anger Harry Potter fans though pointing out the temporal paradox of the third book/movie works great. The only time paradox I've found that doesn't particularly bother me is when Futurama went back to the Roswell crash of the 1940s. Fry's grandfather is an idiot therefore Fry is an idiot. Being an idiot Fry accidentally kills his grandfather and has to become his own grandfather. Result, Fry's grandfather is an idiot therefore Fry is an idiot who accidentally kills his grandfather in the past and has to become his own grandfather.
The Achilles "aradox" is also flawed. Basic algebra can easily plot the points of each runner at any given time and show how quickly Achilles will overtake and pass the tortoise.
This is obvious if you were to consider each runner separately. It is because of this that the paradox exists. How are you to refute the rationale of the claim even though it's very clear that the claim is wrong?
