This expression is famously used in George Orwell's Nineteen Eighty-four. In Nineteen Eighty-four, a good citizen is capable of practising doublethink, (holding two mutually exclusive ideas and knowing both to be true). An example of this kind of 'reality control' given to the key protagonist, Winston, is that 2+2=5.

Toward the end of the book, Winston writes

2 + 2 =
in the dust of a table, in the cafe in which he is drinking. The scene is sorry and he is a crushed man. BUT, despite everything, the incomplete equation leaves us with a little hope that he has not been entirely won over by Big Brother.

Little known but interesting fact:
In the original text, George Orwell actually wrote 2+2=5. From that, we would know that Winston loves Big Brother, and has lost all rebelliousness. Apparently, the (incredibly significant) numeral 5 fell out of the press, leaving the equation unfinished. This version has stuck.

It is too late now, because YOU HAVE NOT BEEN PAYING ATTENTION

2 + 2 = 5 (The Lukewarm.)

Artist: Radiohead
Album: Hail To The Thief
Length: 3 minutes 19 seconds
Release date: November 17, 2003

Lyric removed for copyright reasons

Lyrical interpretation

The album Hail To The Thief is mostly politically motivated, and this track is an example of this. It's about America. It's about apathetic voters ("I'll stay home forever"), about lies told by political leaders ("'All hail to the thief' But I'm not!"), about the wrong guy leading the country ("It's the Devil's way now"), global warming and the Kyoto treaty ("January has April's showers" - thanks JoeBaldwin), about the Orwellian brainwashing referred to above ("two and two always makes up five"). This, at least, is my hazy interpretation. If you have a better one, by all means /msg me. The meaning behind the song, however, is obviously secondary to

What the song sounds like

(7/4 time, according to Valrus.) "2 + 2 = 5" (subtitle: "The Lukewarm.") starts off sounding like amplifiers being plugged in and turned on - think the first scene in Back To The Future; appropriate for the start of the album. Soft guitar playing, Thom Yorke's vocals coming in quickly with his trademark acquired-taste high-pitched style. It's a good melody, with a little bit of a sting behind it. At the "Devil" line the song changes mood slightly and begins to build to something. At "BECAUSE" the song kicks off. Loud, hard and fast. YOU HAVE NOT BEEN PAYING ATTENTION. Repeat. Rock on. The tempo and volume are maintained while Yorke returns and rattles off the last forty or fifty seconds of lyric. Sudden end.

"2 + 2 = 5" sets a good tone for the rest of the album. Overall, it's an energetic number, comparable with the band's seminal "Paranoid Android" from OK Computer, with which it shares a few features, but "2 + 2 = 5" does not really exceed "Paranoid Android" in terms of style, variation, or, indeed length. Another minute or so would not have hurt it. Perfectly palatable Radiohead, however, and certainly worth a listen.

The video

AFAIK there is no video yet, but if this track were to be released separately, doubtless one would appear. I think of this as one of the album's better tracks and would love to see it released as a single, so if the band has the same idea as me, watch this space. 2+2=5 was released as a single on November 17, 2003. There was no accompanying video, according to quoi?, but some stations used footage of live shows instead. Seems a shame, given the awesome Radiohead videos we've grown used to.

This was track 1 from Hail To The Thief.
Next: Sit Down. Stand Up.

don't node lyrics, node the song

One of the more interesting properties of the real numbers is their notation: when we write "2.3543", we actually mean a number that is closer to 2.3543 than it is to 2.3542 or 2.3544 . Similarly, when we write "2", it actually means any real number closer to 2 than it is to 1 or 3 ("2.0" would represent a number closer to 2 than it is to 2.1 or 1.9) .

This property means that it is possible that the numeral 2 can refer to a real number close to 2.4 , and so ~2.4 + ~2.4 = ~4.8 . ~4.8 is closer to 5 than it is to 4 or 6, and therefore 2 + 2 = 5, for high values of 2, and 2 + 2 = 3 for low values of 2.

This notation only applies to real numbers, not to integers, or rational numbers. This often causes confusion in high school maths classes, as the concept of inaccurate real numbers is often only briefly touched upon, and never seen again, and the distinction between the meaning of decimal fractions when dealing with inaccurate real numbers, and the meaning of decimal fractions in the rest of the syllabus is not made clear enough.

In The Real World, accuracy is hardly ever an issue unless you're doing engineering or physics, and even then, it is often ignored. If the accuracy of a number is not mentioned, the following rules usually apply:

  • If accuracy is not mentioned at all, it is usually ignored. All numbers are assumed to be completely accurate
  • Numbers which could represent integers do.
  • Numbers in which the majority of the figures are significant are assumed to represent completely accurate rational numbers.
  • Numbers in which few of the figures are significant are as accurate as the number of significant figures
For example, "2" represents the integer 2 (and is therefore completely accurate). "2.124" represents the rational number 2124/1000 (and is therefore also completely accurate). 3x108 has only one significant figure, and could represent any real number from 2.5x108 to 3.5x108.

In the real world, 2+2=4. In physics and engineering, (2±0.5) + (2±0.5) = (4±1)

2 + 2 = 5 in a reality in which the majority of those entities engaged in it have the idea that when two is added to two, another number is added to it, as this is just the nature of things in this reality. This is the opposite of the idea that 2 + 2 = 4, or that when 2 is added to 2, there is not an exception to the mathematical rules which state that a 1 should be added. It is also possible that there is a universe which is founded on the idea that 4 is a number of less significance than the number 5, with the number 5 being seen as a number which is so powerful that it "sucks" the result of a mathematical statement that results in an answer of "4" into "5". It could also be said that there could be a universe in which the ideas that form its mathematical structure are such that the "+" sign is seen as an operation in which the process of addition must be accounted for as a number, as the mere act of adding changes the nature of the numbers involved, and requires that a "1" be tacked on to the result, to account for the change caused by taking two numbers and subjecting them to an "adding" force. In addition, there could be a universe where whenever an entity which is capable of doing math observes an operation in which the number "4" could be a result, their minds automatically telekinetically modify the result to add a 1, as this is just the nature of things in this alternate universe.

It is possible that there is a universe which takes any quantifiable collection of objects, swallows them whole when sentient beings try to do a mathematical operation, and spits out a randomized amount of said objects. Perhaps this is a universe inside of a quantum computer which has been programmed by someone who flunked high school Algebra.

Everything I just said is both true and false, both and neither at the same time, and yet both within time and outside of time, time being both an illusion and not an illusion, the concept of things being illusory being both true and false, both and neither at the same time. As for working within the accepted realm of ideas known as "mathematics", I shall not. I shall spit scalding hot coffee in the face of mathematicians, steal your TI-89 calculator, and modify the BIOS to output a stream of random numbers as the answer to any given operation. After all, where I'm going, this calculator isn't going to be useful for much more than playing Tetris and looking at monochrome low-res pornography. Maybe to animists, two rocks sitting next to each other know that they're two rocks. But I say that this creates the illusion of separateness, as the two rocks are both part of the ground, and by thinking of them as separate, you create an idea which divides them from the earth which they became detached from, thus dooming them to an existence of solitude. If only the rocks knew what you had done to them, why they must live separate from the earth in a state of lonely petrification, I'm sure they'd conspire with their fellow rocks to create some kind of animated rock-monster who eats mathematicians and defecates calculators which only give the answer "WRONG" as the answer to a given mathematical operation.

And reality? I refuse to operate within that paradigm as well! The idea of a solid, stable reality is currently being forcibly sodomized by me worse than a dead mathematician thrown to a pack of necropheliac orangutans who haven't had fresh meat in years. No, 2 + 2 = 5, 6, 7, 8, Banana, Lubrication, 23, Fortitude, pile of dead gods, don't you "pretentious" or "insipid" call me, 69, 69, 69, 69, 69, 69...

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