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Alternative Number System

 Alternative Number System
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 Alternative Number System
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Alternative Number System
 Alternative Number System
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AlternativeNumberSystem
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The numeral system used by most of the modern world today is called the decimal system, involving ten digits ("Base 10"). Sometimes, if a writer wants to portray a society as being significantly alien to our own, they will include a mention of an alternative numeral system for this society, with the "base" being a number other than ten.
This may be used to indicate the collective intelligence of the society that produced it, if it is portrayed as more sophisticated or more primitive than our system. There may also be an inferred correlation between the ten digits in our numeral system and the ten digits on the average pair of human hands. Therefore, a race of aliens with Four-Fingered Hands may use a base eight numeral system. Finally, it is very common for robots or other computer-based intelligences to count in base two.
This sort of thing is generally used as an insignificant throwaway joke, with "ordinary" numbers applying before and after, as it may be a difficult concept for some viewers to grasp.
 Alternative Number System
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2024-02-21T07:16:11Z
 Alternative Number System
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2024-02-21T07:16:11Z
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Foundation
 Alternative Number System
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DBTropes
 Alternative Number System / int_10ec248
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Alternative Number System
 Alternative Number System / int_10ec248
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In The Elements of Friendship, the Equestrians use base 12, complete with neologisms for the new names for numbers of years. The author even wrote a blog post explaining the system.
Discord notably doesn't do this, and at one point offhandedly derides the ponies for not using the decimal system.
 Alternative Number System / int_10ec248
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Alternative Number System / int_10ec248
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Alternative Number System
 Alternative Number System / int_150c3efe
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Empire from the Ashes: During the scenes set on the Achuultani ships, The characters mention "Twelves, Higher Twelves and Greater Twelves".
 Alternative Number System / int_150c3efe
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1.0
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Alternative Number System / int_150c3efe
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Alternative Number System
 Alternative Number System / int_16d5ac2a
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In The Frantics' sketch "Roman Numerals" a Roman citizen is baffled by the new decimal system.
When Arabic positional decimal notation (i.e. today's numbers) were first introduced in Europe, some regions passed laws against the use of "deceptive ciphers" and mandated continuing the use of "real quantities" (i.e. Roman numerals).
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Alternative Number System / int_16d5ac2a
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Alternative Number System
 Alternative Number System / int_1a65dd0
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One puzzle in Star Trek: 25th Anniversary involves figuring out the alien code that is more difficult because the aliens in question used a base 3 system.
 Alternative Number System / int_1a65dd0
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Alternative Number System / int_1a65dd0
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Alternative Number System
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Contact: A message is encoded in base 11, by someone or something capable of messing with the values of mathematical constants.
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Alternative Number System
 Alternative Number System / int_1d4d5420
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Obduction, Myst's Creator-Driven Successor, features a base-four system associated with one of the setting's alien races. They also use a particular notation based on drawing lines among a diagonal grid of dots: lines attached to the central dot are ones; the dot above represents fours, the one on the right represents sixteens, and so on in an expanding spiral.
 Alternative Number System / int_1d4d5420
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Alternative Number System
 Alternative Number System / int_261c8d3f
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In The Simpsons Principal Skinner wishes he had enough funding for his school to buy, amongst other things, "math books that don't have that base 6 crap in them". This is almost certainly a reference to New Math, a way of teaching mathematics that was briefly popular in The '60s but very rapidly fell out of favour.
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 Alternative Number System / int_26ef42e7
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Alternative Number System
 Alternative Number System / int_26ef42e7
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In Kevin & Kell when Dorothy took over accounting for Aby's business she converted all the numbers to "rabbit numbers" to keep the mostly carnivorous employees from getting ideas. By which she meant base six, for their average litter size.
 Alternative Number System / int_26ef42e7
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 Alternative Number System / int_2a458d08
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Alternative Number System
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In the Zones of Thought novel A Fire Upon the Deep, the doglike Tines have two different numeral systems: one where they count "by legs" (in base 4) and one where they count "by fore-claws" (in base 10). Confusion between these two systems leads to the accidental meeting of two of the major characters. Amdiranifani is housed in room 33, Jefri is supposed to be imprisoned in room 15 (33 in base 4), and the guard who's taking him there uses the wrong numbering system.
 Alternative Number System / int_2a458d08
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Alternative Number System
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The iCarly episode "iTwins" features an In-Universe example: upon finally discovering that her trainee Chuck is mean, Carly gets Revenge by making up a number between five and six called "Derf", which Chuck uses on his math test and fails, thus ending the tutoring.
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 Alternative Number System / int_39209872
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Alternative Number System
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FE000000 lets the players choose from base 2 to base 36 for both the display and the exponent. For example, if the display base is set to 10 and the exponent base is set to 32, 1048576 would be written as 1e3, when it's normally 1.048e6.
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Alternative Number System / int_39209872
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Alternative Number System
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No Evil uses a variation of Mayan numerals, as seen in this video.
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Alternative Number System
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Currency in the Harry Potter universe is a mixture of base 17 (17 sickles to the galleon) and base 29 (29 knuts to the sickle). This is possibly a joke based on the currency units of RL Britain until the 70s (though at least they didn't use prime numbers).
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Alternative Number System
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There is a popular theory among Half-Life fans that the Combine use a base-17 system, based on how prominent 17 seems to be. If nothing, it reinforces the utterly alien nature of the Combine.
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Alternative Number System / int_3b7abee2
 Alternative Number System / int_426a7572
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Alternative Number System
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Done subtly in Animaniacs. Snow White imprisons Dot for being too cute, and Dot counts the time in hashmarks that only have four strokes each... presumably because she's a cartoon character.
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Alternative Number System
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SCP Foundation:
SCP-033 is a paranormal version of this. It's an equation which adds up to a "missing number", an integer which non-paranormal mathematics has somehow missed. If it's recorded in any sort of computing device or written on machine-made paper, whatever it's recorded on starts to physically degrade.
SCP-233 is a 23-sided (impossible) polyhedron that magically accelerates calculations done in base-23, but reacts extremely violently to the number [REDACTED] (nine) and causes rounding errors in every calculation not done in base-23.
 Alternative Number System / int_42ffb88e
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Alternative Number System
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In the Discworld books, trolls apparently have a "base Many" system (actually base four). As in, "one, two, three, many, many-one, many-two..." This is revealed in Men at Arms, when it turns out that Detritus is not incompetent with numbers, he is in fact very good at counting in powers of two.
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 Alternative Number System / int_4874d04a
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Alternative Number System
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Numberphile: Discussed in videos:
There's a video about base 12 (a.k.a. duodecimal, dozenal)
one about base 16 (a.k.a. hexadecimal)
one by Tom Scott that explores the surprisingly many different ways numbers are expressed in different cultures, including a group in Papua New Guinea that uses base-27. And naturally, any video relating to computer science will at least mention binary or hexadecimal.
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Alternative Number System
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In Incandescence, the insectoid aliens of the Splinter have six legs, and their number system is based on that. Their word for "very many" translates to "thirty-six times thirty-six."
 Alternative Number System / int_49c5717a
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Alternative Number System / int_49c5717a
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Alternative Number System
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Averted in the Triptych Continuum. Equestria uses base ten. Neither Celestia nor Luna have any idea why.
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Alternative Number System
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In Myst III: Exile, Saavedro's journal pages are numbered in a base 5 system similar to tallies, but with a leaf motif in keeping with the rest of his culture.
 Alternative Number System / int_4e936006
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Alternative Number System
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In Dolphin Island, the dolphins' number system is binary because they only have two flippers. When Professor Kazan and Dr. Keith are translating a recording of an old dolphin folk tale, they disagree on whether an object is said to be the length of 128 or 256 dolphins.
 Alternative Number System / int_585c28a6
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Alternative Number System
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Schlock Mercenary: Implied. An alien with an odd number of fingers (and an odd number of bodies) says a long, complicated number will be easy to remember since it's a round number. It's certainly not round in Base 10. Most of the galaxy uses Base 10, likely because of human cultural supremacy.
 Alternative Number System / int_5c897f4a
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Alternative Number System
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A subversion in The Restaurant at the End of the Universe: When Douglas Adams revealed that the question which produced the Ultimate Answer (42) was What do you get if you multiply six by nine?, somebody pointed out that the math actually did add up, using base 13. Adams responded, "I may be a sad individual, but I don't make jokes in base 13."
 Alternative Number System / int_5d84baa1
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Alternative Number System
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Stranger in a Strange Land: The Martians apparently have a numerical system based on three and powers of three. "Three fulfilled," they call it.
 Alternative Number System / int_5e42de8e
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Alternative Number System
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In Childhood's End by Arthur C. Clarke, the Overlords are mentioned to count in base 14 (their hands have five fingers and two thumbs).
 Alternative Number System / int_60249eb3
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Alternative Number System
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According to the Dragon article "The Ecology of the Spellweaver", these Dungeons & Dragons monsters count in base six, although they also have a decimal notation. The number six is really significant to spellweavers, who not only have six arms, but can regenerate on death six times, following which they produce six offspring.
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Alternative Number System
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Vogons in The Hitchhiker's Guide to the Galaxy (2005) have a unary system, meaning that writing the number 1,000 means writing 1 a thousand times.
 Alternative Number System / int_6bc0f10a
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Alternative Number System
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Stargate SG-1:
A throwaway comment in the episode "The Fifth Race" implies that the Ancients counted in base eight.
Also invoked when they nearly set off a Tobin mine by entering in the wrong code due to Daniel failing to factor in a zero into his translation. He argues the Phoenicians they were descended from never used a number zero, but Carter points out in order to program something as complex as a mine, the Tobin's would have had to have added a zero component.
There's a fan theory that the constellations on the gate actually correspond to digits in a base-38 numeral system. Which means that a gate address is not six arbitrary points in space with the destination at the intersection,note which contradicts the in-series assertion that all addresses are unique but three two-digit base-38 coordinates.
 Alternative Number System / int_70814599
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Alternative Number System
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Halo fans speculate that the Forerunners might have counted using a Base-7 counting system.
 Alternative Number System / int_755b343f
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Alternative Number System
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Mass Effect mentions math systems not based on ten, such as a superweapon that relies on specialized base-12 mathematics and a krogan NPC muttering about the stupidity of base-10 math and the consequences of having extra fingers.
 Alternative Number System / int_7988cb68
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Footfall: The Fithp use base 8, as expected for a species whose finger-equivalents number 8.
 Alternative Number System / int_7d1f75f6
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In Traveller, the various alien species use different base mathematics. The Aslan use Base 8, the Hivers use Base 16, and the Droyne use Base 6. Most of the various Human Aliens, as well as the Vargr, use Base 10.
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Alternative Number System
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In The Lord of the Rings:
According to the appendices, elves habitually count in base 12. This is not because they have a different number of fingers. Most likely though, it's because patterns based on 3, 6 and 12 are very common in nature: particularly plants, constellations and crystals. Though Tolkien never completely committed to this: in other instances he seems to imply a base ten system. He waffled back and forth about this for his entire life.
The Wild Men seem to use a base-20 system. When Ghan-buri-Ghan counts the number of soldiers in the Rohan army, he expresses it as "A score of scores counted ten times and five" (6,000).
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Star Trek:
According to The Klingon Dictionary, the Klingons used to count in a ternary (base-three) system, but have since switched over to decimal.
The Megarites use base 8, according to Star Trek: Ex Machina.
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Alternative Number System
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In Girl Genius' world of mad science there's bound to be examples showing up: "Tell the landlord that he is to stop trying to make change in base eight, or he'll pay his taxes in base twelve."
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The characters in Albedo: Erma Felna EDF use base 8, albeit by Translation Convention all the numbers are translated to base-10 for the readers' sake. This later becomes a plot point when the characters find an human ship who uses base-10 for obvious reasons.
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Rendezvous with Rama: The aliens appear to use base 3.
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At one point in The Fangs of K'aath, the Funny Animal civilization's use of base 8 is explained (due, again, to their fingers) by one character to another; they write 8 as "10". They are apparently fond of mathematics, too, which is fitting, as this particular Fantasy Counterpart Culture is based on the medieval Islamic lands.
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Known Space: The Kzinti count in base eight due to having four-fingered hands.
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Aeon Natum Engel: The narration from the Migou POV and their dialogue goes to great lengths to convey their alien thought processes, including a base-36 numbering system.
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Even Discworld's trolls are better with numbers than the tree frogs of the Nomes Trilogy, who can only grasp "one" as a number. Faced with the quandary of two different bromeliads, a frog genius makes a breakthrough when it comprehends them as "one, and one more one".
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The rabbits of Watership Down can count up to four, presumably because that's how many paws they have. The number "hrair" in their language of Lapine means "any quantity greater than four" and/or "too many to count"; depending on context, it may also be translated into English as "five" or "a thousand".
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Little Fuzzy, a series begun by H. Beam Piper, uses a modified form of base 5. 1, 2, 3, 4, one hand. At 125, they've reached a hand of hands. It then goes to many, and many many. The fuzzies soon adopt the humans' base 10 system.
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In Futurama, robots sometimes use base 2.
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In a throwaway joke in Agatha H. and the Clockwork Princess, Prince Aaronev Sturmvoraus sends a message to one of his subjects stating that if he's caught making change in base 8 one more time, he'll be paying his taxes in base 12.
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The aliens in Iji use a ternary numeral system.
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The Themis Files: The ancient inscriptions, for reasons which remain unexplained, use base-7 numerals.
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The Kilrathi from Wing Commander use Base 8 for their numbering system, given that they have a total of eight fingers. For the most part this isn't really mentioned much, but it's prominent in the dates for history of the Kilrathi war from their viewpoint as done in the manual for Armada, "Voices of War".
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Out of the Dark gives us the Shongairi, who count in base-twelve. Possibly.
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In Hoofstuck, Twilight Sparkle mentions that Equestria uses base eight rather than ten, since there's nothing on a pony you can use to count to ten (whereas four hooves times two make more sense). They used to run with base four originally, symbolising the four races (earth ponies, pegasi, unicorns, alicorns) but the earth ponies took offense at being considered the "zeroes".
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Warhammer 40,000:
The Tau use base 8 owing to their Four-Fingered Hands, leading to a delicious little Stealth Pun: their battlesuits' designations are based on their size, such as XV25 for the smaller Stealth suits, XV8 for the main Crisis suit, or XV88 for the heavy Broadside variant. Which means that the new XV9 Hazard Close Support Armour units are taking things even further.
The Orks only use the numbers one through five. Anything higher than that is referred to as "lotz."
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It's never mentioned in the books themselves, or the series, but the "Gallifreyan numerals" used on the spines and chapter headings of the Doctor Who New Series Adventures (9th and 10th Doctors) are in base 7.
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Centaurians in The Pentagon War have 4 tentacle-fingers on each of 4 hands. When a Centaurian named Torra Zorra reads that a cable's diameter is 3 x 10-5 meters, we get this parenthetical aside:
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In some of the Chakona Space stories, Caitians are mentioned to be using base 8 math and the less mathematically minded ones struggle with everyone else's usage of base 10 math.
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During Portal's boss fight, after GLaDOS takes a missile hit she'll announce "Two plus two equals... ten! In base four I'm fine!"
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In the Myst games:
The D'ni have a base 25 system, in keeping with the games' general tendency to use powers of five as Arc Numbers. It has a base 5 subsystem: the symbol for 5 is a 1 rotated, 10 is a rotated 2, and so on, up to a unique figure for 25.
In Myst III: Exile, Saavedro's journal pages are numbered in a base 5 system similar to tallies, but with a leaf motif in keeping with the rest of his culture.
Obduction, Myst's Creator-Driven Successor, features a base-four system associated with one of the setting's alien races. They also use a particular notation based on drawing lines among a diagonal grid of dots: lines attached to the central dot are ones; the dot above represents fours, the one on the right represents sixteens, and so on in an expanding spiral.
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A significant portion of the game Rama, based on Arthur C. Clarke's novel series of the same name, involves solving mathematical puzzles based on the native numeral systems of the Avians (base 16) and Octospiders (base 8). (Which is at odds with the Ramans, who use base 3. Neither the Avians nor the Octospiders are Ramans. They're just samples of other space-faring species that the Ramans had gathered.)
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In Star Wars Legends, the Hutts use a base 8 system due to only having four fingers on each hand. Being Hutts, they don't always tell this to their business partners, most of whom use base 10.
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In the Eldraeverse, the Eldrae use base 12, and had a brief flirtation with base 16. Not because of their number of digits (baseline Eldrae have as many as humans), but because their language was standardized by mathematical philosophers.
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Getting the Shinigami Eyes in Death Note gives you the ability to see a person's name and remaining lifespan when you look at their face. Sadly the lifespan only appears in a number system recognisable to Shinigami that just looks like random numbers to a human.
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The Schoolhouse Rock! music video for "Little Twelvetoes" briefly touches on the idea of what counting with a base-twelve system would be like, and demonstrates with the titular twelve-fingered alien character.
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The Megarites use base 8, according to Star Trek: Ex Machina.
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The Culture: The Culture uses a nonary (base nine, that is) system for their writing, by means of writing binary in a 3x3 square. Binary is mentioned as being used by some civilisations, and powers of two are the closest thing to a universally-regarded "round number".
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On Gor, the alien species the Kurii use base-12, presumably because they have 12 digits on their "hands."
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In ElfQuest, the elves likewise use base 8 because of their Four-Fingered Hands — that page has more details.
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In the opening of The Lord of the Rings, the elves can be seen marching in formations of 144 troops each. This is a shout out to the books where it is mentioned that elves use a dozenal counting system. Naturally then, they would divide their armies into units in multiples of 12 rather than 10.
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Gully dwarves from Dragonlance, being astonishingly stupid, can only count up to two. Any higher quantity is described as "One and one and no more than two."
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Nine Hours, Nine Persons, Nine Doors:
One of the puzzles in the Kitchen requires you to use base 16 in order to figure out the code to open a locked safe.
The Nonary Game itself, per its name, indirectly involves base 9 via digital roots. The last door, represented by the letter q, is locked behind at least base 27.
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Babylon 5:
The Minbari use base eleven (a byproduct of using fingers, toes, and the head as "digits" for counting).
According to tie-in RPG materials, the Dilgar used base 25.
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In the Fighting Fantasy book Rebel Planet, the two-fingered Arcadians count in binary. Converting binary to decimal is necessary to solve a couple of puzzles, though the reader is fortunately provided with a handy grid.
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In Star Trek: The Next Generation, the Bynars use base 2 (i.e. binary).
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The following is a list of statements referring to the current page from other pages.

 Alternative Number System
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Alien Tropes
 Alternative Number System
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Math Tropes
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processingCategory2
Number Tropes
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Speculative Fiction Tropes
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