"Nazi theory indeed specifically denies that such a thing as "the truth" exists... The implied objective of this line of thought is a nightmare world in which the Leader, or some ruling clique, controls not only the future but the past. If the Leader says of such and such an event, 'It never happened' — well, it never happened. If he says that two and two are five — well, two and two are five."
Lampshaded/spoofed in The Invisibles when Sir Miles is using the drug Key 17 to mess with King Mob's mind. He causes King Mob to see, among other things, five fingers where there are four. The illustration is subtly creepy.
At the end, when King Mob escapes, he returns the favor: "How many fingers am I holding up, Sir Miles? Just two."
The Attorney General wanted to find which was his best law enforcement agency, so he held a contest. The FBI, the CIA, and the NYPD all took part, meeting the AG at the edge of a large forest. The AG said, "There is a rabbit out in the woods. Each agency will take turns, and whoever finds it in the least amount of time is the best. The FBI went first. They returned two hours later without a rabbit and made a report: "We surveilled the rabbit, bugged his house, and built an airtight case against him." The AG said, "Bull. You guys never found the rabbit". The CIA went into the woods. An hour later, they came out without the rabbit and made a report: "We kidnapped the rabbit, turned him by offering him money and female rabbits, and now he works for us, spying on other rabbits." The AG said, "Bull, you guys never found the rabbit." The NYPD detectives went into the woods. Fifteen minutes later a bear walked out, bruised, black eyed, and swollen holding his hands in the air and yelled, "Alright, I'm a rabbit, I'm a rabbit".
In Russia, this joke was formerly told with the KGB as the butt of the joke.
George Orwell used this for 1984. Winston Smith writes that freedom is the ability to say "two plus two is four," then later tries to make himself believe in Doublethink by changing it to five. During his torture, the torturer forces him to see five fingers when there are only four. After Winston is released, he at one point subconsciously writes "2 + 2 = 5" on a coffee table's dust layer. Interestingly, several editions of the book list "2 + 2 = " instead, giving the impression of a Hope Spot. Alas, it's actually a typo: Winston really did write "2 + 2 = 5"
Dostoevsky offers us this joyful piece of wisdom:
"Once it's proved to you that, essentially speaking, one little drop of your own fat should be dearer to you than a hundred thousand of your fellow men, and that in this result all so-called virtues and obligations and other ravings and prejudices will finally be resolved, go ahead and accept it, there's nothing to be done, because two times two is-mathematics. Try objecting to that."
Dostoevsky is actually inverting this trope: the torture comes from the reality that 2*2 = 4 and that there is no realistic hope to escape from it. Only when you can say 2*2 = something other than 4, can there be hope and freedom.
In one of The Stainless Steel Rat books, "the grey men" mess with Jim's mind using hypnosis to make him think they've chopped off his hands and reattached them.
In the children's book Jim Button and Luke the Engine Driver (Jim Knopf und Lukas der Lokomotivführer) by Michael Ende, the dragon Mrs. Grindtooth (Frau Mahlzahn) tries to use this technique on her pupil/slave Li Si. Li Si, being both very intelligent and very brave, refuses to fold.
Part of what happened to Tycho Celchu between the comics and the books of the X-Wing Series. He was bent pretty terribly by Isard but didn't actually break. When she overlaid Rebel and Imperial insignia and tried to transfer his loyalty to one over to the other, the contradiction sent him into a catatonic state. She later tried it on Corran Horn with even less success.
A Song of Ice and Fire: In the fifth book, Ramsay Bolton tortures Theon Greyjoy and conditions him to accept a completely different identity.
Alias: Some of the bad guys attempt this with Sydney but as she can't be brainwashed she merely pretends to be broken.
The image source comes from the Star Trek: The Next Generation episode "The Chain of Command, Part II." Picard is captured during a black op and taken to Gul Madred (masterfully played by David Warner), who thinks that Picard knows Federation defense plans. Madred tries to force Picard to tell him that there are five lights on the wall when there are really only four. Every time Picard insists that there are four, Madred zaps him with an Agony Beam. When Picard is finally released, he proclaims "THERE! ARE! FOUR! LIGHTS!" but it's not as triumphant as it seems—later, Picard admits to Troi that not only would he have said there were five lights if he hadn't been released at that exact moment, but he could actually see five lights.
In the Babylon 5 episode "Intersections in Real Time," John Sheridan's torture and interrogation of is based around manipulating perspective and convincing Sheridan to accept the fact that the truth is fluid, and therefore he's a mutineer, a conspirator, a terrorist, and a victim of alien influence. They needed him to sincerely believe his confession in order to fool telepathic scans. However, he manages to rather effectively turn the logic around against his interrogator by saying that, essentially, just as their truth is valid to them, so is his to himself.
John Sheridan: You know, it's funny, I was thinking about what you said, that the preeminent truth of our age is that you cannot fight the system. But if, as you say, the truth is fluid, that the truth is subjective, then maybe you can fight the system. As long as just one person refuses to be broken, refuses to bow down.
Interrogator: But can you win?
John Sheridan: Every time I say "no."
In the first episode of The Thick of It, Malcolm tries to "persuade" journalists that minister Hugh Abbott did make an important announcement at an earlier press conference (though he did no such thing) - it's just that journalists missed it.
Parodied in a TV show by Swedish comedian Hans Alfredsson, in which he plays the leader of a small semi-Nazi organization, whose main targets are "svartskallar" — literally "blackheads", a common ethnic slur in Sweden. The Movement is supposed to be vegetarian and celibate, but when a rich and influential member tells the Leader that he owns a sausage factory and is not about to give up his wife, the Leader tells everyone that from now on, sausages and women are vegetables. At the end of the story, the Leader meets his mother for the first time... and she turns out to be black. When someone asks what this means for party policy the Leader declares that from now on, red is black and black is red... and the members turn on the single red-headed member with evil glee.
In the Mini SeriesRoots, Kunta Kinte is whipped until he says that his name is Toby, the slave name given to him by his master.
Though it involves no torture, in the Red Dwarf episode "Camille", Lister tries to break Kryten's Cannot Tell a Lie programming by showing him an apple and getting him to say it's an orange. He doesn't want to make him believe it — just to get him to say something he knows to be untrue.
On The X-Files, this is pretty much the objective of the military guards torturing Mulder in "The Truth." After breaking into a government facility and finding "the truth", as well as several other things the government was hiding, Mulder is captured and denied food, water, clothes and sleep. Whenever the guards come in, they ask him what he's thinking, and beat him for answering truthfully. What is the correct answer? They want Mulder to admit that he illegally entered the facility to obtain non-existant information and killed a man, even though none of those things are true. Why? They're holding a Kangaroo Court and are hoping to get rid of him once and for all. It appears to work, as Mulder repeats the words back. Turns out he's just saying it to get them to leave him alone.
They did this to Baltar in the reimagined Battlestar Galactica to the point that his mind was so mixed up and he was talking so much gibberish that when he confessed to having done some terrible crimes, no one believed him.
Radiohead has a song titled "2 + 2 = 5" that was inspired by 1984.
Living Colour's "Cult of Personality" also refers to the concept with the lyrics, "I'll tell you one and one makes three".
Private Plato in Beetle Bailey creates an instant demonstration by giving Lt. Sonny Fuzz a black piece of paper and expressing confusion over the alleged fact that the general said it was white.
This is part of the treatment Petruchio gives Katharine in order to "tame" her in The Taming of the Shrew, when he insists that the food is bad and the clothes are ugly and refuses to allow her to eat or keep them. He also obstinately claims that it is 7 o'clock, when it is only 2. "...it shall be what o'clock I say it is." She later gives in to his game, agreeing with Petruchio that, in spite of it being broad daylight, that the moon is shining, and shortly after agrees with him that it is not the moon after all, but in fact the sun. This is potentially Shakespeare's ode to Gaslighting.
According to some interpretations, though, this is a subversion; Katharine takes Petruchio's lies and stretches them even further, coming up with speeches so patently ridiculous it's hard to think she's not making fun of him. And this may be where they reach an understanding with each other - from this point forward, they start teaming up to terrorize other people instead of each other.
In Equivocation, Shag protests that a Gunpowder Plot conspirator's confession obtained by torture isn't the best evidence by pointing out the misspelling of his own name (Winter where it should be Wintour). Cecil threatens he can have similar done to Shag, giving justification to playwright Bill Cain's use of William Shagspeare in place of the well-known William Shakespeare.
In an episode of ChalkZone a horrible counselor sets out to make sure that Rudy understands what is "real" and what isn't. She straps him to a chair that shows him two pictures (generally a photo and a cartoon image) and asks him which is better. Every time he gets it wrong, it honks loudly at him. Later in the episode, we see him feebly trying to answer and getting honk after honk after honk until he says "whatever you say", which is the answer she was looking for.
Possibly a reference to the Red Dwarf example above, in the American Dad! episode where Deputy Director Bullock (Patrick Stewart, partial Trope Namerand big Red Dwarf fan) is sleeping with Hayley, Stan tries to make her ex-boyfriend Jeff more assertive by beating him up and getting him to say various fruit are something else.
Though in this case Jeff will just agree that the orange is a banana because he's such a wimp. Stan was trying to get him to stand up and disagree with him.
One reason for the Blatant Lies in the pronouncements of repressive regimes (like North Korea's statement that their country is one of the happiest places on Earth) is that citizens wind up repeating them (to avoid being accused of disloyalty) even though they know the statements are untrue. This makes the citizens psychologically complicit in the regime's lies, and less likely to resist. That's the theory, anyway.
And judging by the (seemingly legitimate) outpouring of grief after Kim Jong-Il's death, the new theory is that, like Winston, the populace also convinces itself of this reality.
Joseph Goebbels: "The principle and which is quite true in itself and that in the big lie there is always a certain force of credibility; because the broad masses of a nation are always more easily corrupted in the deeper strata of their emotional nature than consciously or voluntarily." In short: "The bigger the lie, the more it will be believed."
And this is where the infamous phrase "A lie repeated a thousand times becomes the truth" comes from.
In Germany's case the torture was economic collapse and Hitler was the one to say 2+2=5.
Hitler had this trope backfire against him in the later stages of WW2 when his subordinates started forging military reports and making false claims about e.g. troop strengths to avoid punishment from their delusional Führer. This is where the saying "Never trust any statistics that you didn't forge yourself" originated, which was then (possibly as a by-product of Nazi propaganda) falsely attributed to Winston Churchill.
Consistent with the Dostoevsky's version: the torture is 2+2 = 4 that you can't escape from and the escape is fantastical and "unscientific."
Not torture, but a similar concept: a common trick in hypnosis shows is to convince the person under hypnosis that a number (say, 8) doesn't exist, leading to confusion when the person is then asked to count his or her fingers and invariably winds up at eleven, despite knowing that there should only be ten fingers.
This is one of the arguments against "enhanced interrogation techniques": are they really giving up what they know, or are you just making them say what you think they know so you'll stop? Actual stats on the reliability of information gained from torture suggests that Real Life is not an episode of 24.