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Since mankind began to count, they've wanted to assign importance to numbers. This might be due to the desire to assign significance to everything. This might be to make it easier to have common threads in stories. Maybe it's just to look cool.
Regardless of reason, numbers are often given significance in stories, and mention of a number in a story can indicate a meaning beyond just counting out items. Equally often, people will interpret these numbers to see significance where none exists. Here are some of the more common motifs.
See also Arc Number
Zero - This number represents The Void, the complete absence of being. It's usually something menacing, and it's always a bad moment when there's nothing left. Characters named after the number Zero form the trope My Hero Zero -- though they're as likely to be villainous.
One - This is the number for The Hero, and it represents his standing alone as the best. One also represents the beginning, and the primal source of power. This is why a hero will succeed if there's only One Bullet Left or a Million-to-One Chance - One is just that powerful. The Ace, representing the number One, is also typically the strongest card in standard poker.
Two - Two represents duality - and thus, it stands in for The Villain. Sometimes, it's rather blatant (such as Two-Face in Batman), but other times it's more subtle. Two is the prime source of moments where the villain says that he and the hero are Not So Different. Also, because two identical people represent the loss of individuality, Two also pops up as Creepy Twins. Internally, a hero divided in two may have any number of varieties of an Enemy Within.
Conversely, two represents the number of parties in any basic Conflict, be it with The Villain, parallel protagonists, former friends, Destiny, Star-Crossed Lovers, what-have you. Placing two images or characters side-by-side puts them in implied opposition.
Of course, it is possible to feature two in a positive light: this generally shows up represented in a pair of characters who are very close, such as Bash Brothers or a Hero and Lancer duo. Two can also represent a cosmic force of balance: think yin and yang, and the Balance Between Good and Evil.
Three - Three is the most basic way to represent a structure, in a triangle, so it has representations of power. This is the origin of tropes such as the Rule of Three, the Power Trio, The Hecate Sisters and The Three Faces of Eve. Christianity believes that God originated this, having always been Father, Son, and Holy Spirit.
A basic theme in Blue Man Group is that three is the fewest number of people needed to have an alienation or unpopularity. In most voting political systems, getting this also comes into play (majority is 2 out of every 3 votes). Otherwise known as two is company, three is a crowd.
Four - Four actually has different meanings in different parts of the world. In European traditions, four represented the physical world, and the four elements that made up everything (fire, water, earth, and air). They also corresponded with the four cardinal directions (north, south, east, and west), and thus represent a grounding in reality and are generally positive. In Christian traditions, the number four symbolises the Horsemen of the Apocalypse, and is negative. Classically-based Elemental Powers use this pattern. See also Four-Temperament Ensemble.
However, in Asian traditions, the number sounds almost like the word for "death" in all languages that borrow from Chinese, which arises in the trope Four Is Death. Curiously, the one aversion are The Four Gods, although they frequently are depicted as rather dangerous (and at least one is frequently depicted as explicitly evil, like Seiryu in Fushigi Yuugi).
Five - Also distinct in both Eastern and Western traditions, although not as radically different as they are with four. In the Asian tradition, the physical world was tied with five, and they classically had a five-pronged elemental system (adding wood and metal to the four Europeans used while removing air). The relationship between them was much more complex, as was the Elemental Rock-Paper-Scissors associated with them. This balance directly led to the formation of Five Man Bands.
In Europe, five also represented a fifth element, but there it represented Ether, or Quintessence, the mystical substance which made up spirits and the like. It thus represented the esoteric and the spiritual plane, and was considered completely detached from the physical realm. This is most obvious in pentagrams. Some people holding to the idea of four distinct personality types also hold the idea of a fifth type, balanced between the extremes of the four. It either has all their strengths (superior, above), none of their strengths or weaknesses (equal, between), or none of their strengths (inferior, empty). In some Japanese systems including that of Musashi's Book of Five Rings, the fifth element is void, with associations similar to Western quintessence but a strong Zen flavor.
"Five" in Japanese is said as "go", which can lead to a pun. See One, Two, Three, Four, Go.
Six - Most of six's meanings have been swallowed by the fact that the number six-hundred sixty-six is supposed to be the Number of the Beast.
From a mathematical standpoint, six is an important number, since it is the first number that is divisible by two other numbers, and thus may be used to represent stability and order (see twelve, below). This is related to the fact that carbon-based life exists, due to the flexibility of evenly-spaced covalent bonds. Still, the imagery at this point invariably depicts six as a negative number, and only evil characters attach themselves to it. Six is considered evil in the Bible because it falls short of seven, the perfect number.
This is taken even further in German, where it is pronounced very similar to sex (as in intercourse), also adding a dirty connotation (and source for double entendres). In Swedish the two words are pronounced and indeed spelled the same, leading to many a juvenile joke.
Interestingly enough, 666 is considered a good number in Chinese culture. For example, on June 6th 2006, there were many Chinese marriages, whereas most Westerners would try to avoid this.
Seven - Seven is the most popular lucky number, and was originally the number of the holy virtues man was said to have. Of course, their opposites are much more memorable, but seven is still overall a positive force, to the point that days of the week are still numbered in seven. Dante's Paradiso exemplified this best, with seven layers of heaven. Of course, biblically, seven can also be the number of finality: the seven hills of Rome, the seven angels and the seven seals, etc. There are Seven Heavenly Virtues that oppose Seven Deadly Sins. In Japanese culture this manifests in The Seven Mysteries. Also, in the Japanese language, Seven Is Nana. See also The Magnificent Seven Samurai, the Ensemble that falls under this number.
In Christianity (and in Judaism before it), seven is the number of perfection, and thus the number of God.
For songwriters, "seven" is a convenient rhyme for "heaven", and is also useful because it scans as two syllables.
Seven also comes up as a limit on human minds - people are said to be able to remember only seven different numbers in a single trial. Similarly, the Incident Command System for dealing with emergencies forbids each person from giving direct orders to more than seven people.
Seven also comes up in gambling, specifically the roll of two dice, in which the most common resultant sum is seven. This helped cement its place as a "lucky" number.
Eight - Eight typically has notions of the hidden and esoteric, in part because it looks like an infinity symbol on its side (which was Lampshaded on The Tick). It doesn't come up much, but expect plenty of mysteries when it does.
Eight is also the luckiest of lucky numbers if you are Chinese, so an office on the eighth floor at number 88 8th Avenue, for instance, would be considered to have excellent Feng Shui no matter how the furniture was arranged.
Some Neo-Nazis use the number 88 as a code for the phrase "Heil Hitler," H being the eighth letter of the alphabet. A further group used to call themselves Combat 18, 18 here standing for AH, Adolf Hitler.
Eight is also an important number atomically, as any given valence shell can only contain 8 electrons. Positively and negatively charged ions bond to other ions to reach 8 electrons between them. Until you get past the first three rows of the periodic table. Something similar holds in nuclear physics, which is why oxygen (with eight protons and eight neutrons) is one of the most stable and therefore common elements.
Eight also has both 2 and 4 as factors, so it's convenient for combining pairs of things with quadruplets of things--such as between the parts of Golden Sun, where the two halves together have two characters representing each of four elements.
Eight is also an important number in the Shinto religion of Japan. It is said in the creation myth that Izanagi-no-Mikoto and Izanami-no-Mikoto had a group of eight perfect children who became the islands of Japan. Another instance is in the belief that the kami (deities) represent all things, and are "countless", which in Japanese can be read as "eight million".
Nine - Nine is the apex of the single digits, and thus the apex of worldly power. Appearances of this are usually sources of great power, since it's essentially a trio of Power Trios. Very big in Norse Mythology, which may be why Tolkien, fan of the Vikings that he was, made nine Ringwraiths (and nine Walkers). Also, there are nine orders of angels in Judaeo-Christian theology.
Another facet of Nine is gestation , as in nine months, and thus it is closely associated with childbirth and fruition.
In Japanese culture, however, nine is often considered a cursed numeral because the word for it, "ku", is pronounced the same as the Japanese word for pain and suffering. Despite this, it does have connotations of power as well. Kitsune (fox spirits), for instance, wield magical powers whose strength and power are indicated by how many tails they have, and the maximum number of tails a Kitsune can have are nine tails (kyubi).
Ten - Since most people are born with ten fingers (which are the basis for beginning to count), ten is a comfortable number to express, either via powers of it or the number itself. It's extraordinarily popular for grouping, to the point that people will try to make things fit into a group of ten whether or not they'll fit. The entire Persian/Arabic numeral system (the one most Westerners use, because it's better than the Roman system) is based entirely on the number ten, as is the metric system. Tropes spawned of this shoehorning include Exty Years From Now. In certain numerologies, ten is also used as shorthand for 'lots'.
Eleven - With ten as a maximum, eleven means going one step past the limit and breaking the rules. Conversely, thinking about it as the time on a clock has more or less the opposite meaning- "the eleventh hour" is the last hour before midnight and typically involves getting things done just on time. Being a symmetrical number can also bear some sinister connotations (see two, above).
Twelve - 1, 2, 3, 4, and 6 are all factors of this number, making it an early highly composite number. It symbolizes completeness as a result, and is easy to divide into smaller groups. It also has heavy mystic implications--for example, the twelve signs of the zodiac (Western and Eastern alike). It can be used for time symbology as well, as 12 o'clock is midnight and noon; the end and beginning of a day, or the apex of a day. It is also often the largest number for which a stand-alone word or symbol exist, and being so heavily associated with harmony and completeness, it's surprising no major culture has a base-12 counting system.
Being "a dozen", it signifies the largest easily comprehensible small number; anything over "a dozen" can be rounded down in common parlance. Most non-decimal measurement systems are divisible by twelve (pieces of eight being an exception).
Big in The Bible. Twelve tribes of Israel, twelve apostles, twelve days of Christmas (close enough), etc. This may have something to do with three (the Trinity) being multiplied by four (the four corners of creation). See Thirteen for further examples.
Also notable in Greek Mythology; the Olympian gods form a set of twelve called the Dodekatheon (later imported to Rome as the Dii Consentes). The exact roster varies depending on which source you check, but twelve is a recurring theme for the principal gods.
Thirteen - The number of full moons in a year, the number of people seated at the Last Supper, the traditional number of witches or Satanists in a coven, the age at which someone officially becomes a teenager etc. Bad medicine. Often not assigned to a house (it will be numbered 11A or 12A depending on the numbering system) or to a floor in a tower. The Eighties' Eagle comic strip The Thirteenth Floor featured a Holodeck run by the building's A.I. occupying the unlucky floor, seeing as how nobody wanted to live there. Also used to suggest certain words beginning with the letter M (the 13th letter of the alphabet).
Thirteen has a long history of being unlucky; the Greek pantheon kicked out Hestia, goddess of the hearth, to make room for Dionysus, god of wine, in their circle of twelve; it was believed back then that having a thirteenth deity in the highest echelons of the pantheon would lead to ruin, and that alcohol was much more important on the sacred scale than the home. Judas Iscariot, the thirteenth attendee at the Last Supper, was the one who betrayed Jesus, and it was believed that Jesus's crucifixion happened on Friday the 13th -- or if The Da Vinci Code is accurate, The Purge of the original Knight Templar occurred on that date. There is evidence of other cultures developing forms of triskaidekaphobia before even that. Conversely, many Wiccans and witches consider thirteen a lucky, most likely due to its historical associations with witchcraft.
Note that Thirteen is one more than a dozen, and thus comprises "A Baker's Dozen", i.e. a little something extra. Whether this is an aversion or an invocation of thirteen's unluckiness (on the principle that someone will order no more than a dozen hot cross buns, Elite Mooks, what have you) is hard to say. (The most widely held belief behind the reason for 13 being a baker's dozen is that the 13th roll, loaf, what-have-you, is intended as a redundancy in case one of the other twelve were somehow defective)
There were also thirteen states at the time of the US Declaration of Independence, as commemorated by the thirteen stripes on the flag. The $1 bill has several references to the number thirteen: thirteen stripes on a shield, thirteen stars, a branch with thirteen leaves and thirteen berries, a sheaf of thirteen arrows, and the phrase "E Pluribus Unum" which contains thirteen letters. (The fact that 13 constantly crops up in American symbolism has led numerous conspiracy loons to theories of ever-increasing inanity. They always over look the simple explanation of thirteen states.)
Thirteen may also indicate a change in circumstances. The thirteenth member of a group of people may change them or bring them closer to some goal. (e.g. Roxas in the Kingdom Hearts series.) This is likely due to the meaning of the Death card in the Tarot, which is card number thirteen. Note: Misinterpretation of this meaning may also lead to thirteen bringing about death. (e.g. in Doctor Who, The Doctor only has thirteen regenerations.)
- Scott Lynch's novel The Lies of Locke Lamora plays with this trope. The city of Camorr has twelve official gods, and a nameless thirteenth god worshiped in secret by thieves and swindlers.
- The Old World of Darkness loved the number thirteen (as do a number of Tabletop RPGs with a defined setting.)
- Don DeLillo's Underworld features characters consciously noticing the number 13 turning up in their lives, demonstrating the paranoid and self-defeating collective mind of the Cold War generation.
Fifteen - Little can be said about this number, although in Japan it is often associated with strawberries. This is because the Japanese word for strawberry, Ichigo, sounds like the way the number is written in arabic numerals (15 = One Five = Ichi Go). Ichigo is also a fairly common name (the most notable Ichigo probably being the main character of Bleach). Expect characters with this name to have associations with the number, the fruit or both. Since it is a multiple of both three & five, it may carry connotations of both those numbers. Also, fifteen represents the King in standard poker decks.
Fifteen is an important number in Hispanic culture: A girl's 15th birthday signifies her transition into adulthood. This is usually celebrated in an extravagant manner, somewhat like a mini-wedding.
Sixteen - In many cultures, sixteen is the age when someone is considered an adult, or at least bestowed some adult privileges. In many countries and states it's the age of consent or the age when one can start learning to drive. The passage into adulthood usually means the Call to Adventure will arrive, or some other event--see Dangerous Sixteenth Birthday.
Seventeen - In Italy, the number seventeen is considered to be at least as unlucky as thirteen because in Roman numerals, it's an anagram of the Latin word vixi which means "I have lived" which is the equivalent in Latin of meaning "I am dead" (the past tense of the word "live" meaning that one is no longer alive) making this superstition similar to the Asian cultural aversion to the number four.
Eighteen - The number of adulthood in the United States, when one can vote and go off to war. Other than that, it usually has connotations for being unlucky, which is why fictional teens who die in auto accidents tend to do so two days before their eighteenth birthday.
Twenty One - Being seven times three, 21 is almost always considered an auspicious number. It is also a number of full adulthood in some cultures where children stay at home longer (such as the U.S.) It is very popular in fiction for marking out random figures, as a longer number that has positive connotations and is easy to remember, e.g. 221b Baker Street, 1.21 Gigawatts, 21 Jump Street.
One of the number's more poignant connotations, however is a twenty-one gun salute. While it is a gesture of very deep respect, it is almost exclusively used as a salute in the context of a funeral or burial, and thus is often associated with mourning and bereavement.
Forty - In ancient literature, synonymous with "lots". Big in The Bible: "Forty days and forty nights", etc.
One Hundred And One, One Thousand And One etc. - Synonymous with "lots" for a modern audience.
One Hundred and One Dalmatians, A Thousand And One Nights, Million-to-One Chance, etc. A Year and a Day has the same role.
108 - see the entry.
Prime numbers in general are popular for the number of Plot Coupons, especially three and seven.
Any work that references numerology in general (or gematria, the Kabbalic study) will heavily reference this trope.
See also Arc Number.
More examples can be found at the 1kbwc Wiki
Here are some numbered tropes by number and type.