History Main / AlternativeNumberSystem

29th Apr '18 8:29:26 AM MarqFJA
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The number 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 number 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 number system and the ten digits on the average pair of human hands. Therefore, a race of aliens with FourFingeredHands may use a base eight number system. Finally, it is very common for robots or other computer-based intelligences to count in base two.

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The number 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 number 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 number numeral system and the ten digits on the average pair of human hands. Therefore, a race of aliens with FourFingeredHands may use a base eight number numeral system. Finally, it is very common for robots or other computer-based intelligences to count in base two.



* In ''Literature/AFireUponTheDeep'' by Creator/VernorVinge, the doglike Tines have two different number 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.

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* In ''Literature/AFireUponTheDeep'' by Creator/VernorVinge, the doglike Tines have two different number 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.



* Creator/GregEgan's ''Literature/{{Orthogonal}}'' trilogy is presumably fed to the reader through a ''thick'' soup of TranslationConvention, and thus all numbers are in decimal. Despite this, it's easy to infer that the alien race uses a duodecimal (base-12) number system. For one thing, ''all'' of their units (length, mass, etc.) increment in powers of 12.

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* Creator/GregEgan's ''Literature/{{Orthogonal}}'' trilogy is presumably fed to the reader through a ''thick'' soup of TranslationConvention, and thus all numbers are in decimal. Despite this, it's easy to infer that the alien race uses a duodecimal (base-12) number numeral system. For one thing, ''all'' of their units (length, mass, etc.) increment in powers of 12.



** There's a fan theory that the constellations on the gate actually correspond to digits in a base-38 number 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[[/note]] but three two-digit base-38 coordinates.

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** There's a fan theory that the constellations on the gate actually correspond to digits in a base-38 number 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[[/note]] but three two-digit base-38 coordinates.



* The aliens in ''VideoGame/{{Iji}}'' use a ternary number system.

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* The aliens in ''VideoGame/{{Iji}}'' use a ternary number numeral system.



* A significant portion of the game ''{{VideoGame/Rama}}'', based on Arthur C. Clarke's novel series of the [[TheGameOfTheBook same name]], involves solving mathematical puzzles based on the native number 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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* A significant portion of the game ''{{VideoGame/Rama}}'', based on Arthur C. Clarke's novel series of the [[TheGameOfTheBook same name]], involves solving mathematical puzzles based on the native number 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.)
14th Apr '18 2:07:27 PM Racoon7
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** Due to the influence of German, both "thirty-six" and "six and thirty" are gramatically correct in Czech, although the big-endian version is more common.
12th Mar '18 10:00:13 PM TomWalpertac2
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* ''Literature/EmpireFromTheAshes'': During the scenes set on the Achuultani ships, The characters "twelves, Higher Twelves and Greater Twelves".

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* ''Literature/EmpireFromTheAshes'': During the scenes set on the Achuultani ships, The characters "twelves, mention "Twelves, Higher Twelves and Greater Twelves".
12th Mar '18 9:59:32 PM TomWalpertac2
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* ''Literature/EmpireFromTheAshes'': During the scenes set on the Achuultani ships, The characters "twelves, Higher Twelves and Greater Twelves".
12th Mar '18 3:08:07 PM Bosco13
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* Vogons in ''Film/TheHitchhikersGuideToTheGalaxy'' have a unary system, meaning that writing the number ''1,000'' means writing ''1'' a thousand times.
15th Jan '18 11:15:24 AM Rytex
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** Spanish is another language that zig-zags. Your little endians go all the way to fifteen, switch to big-endian to twenty (''veinte''), switch ''again'' to little-endian, and then end again at thirty (''treinta''), so you have your singulars (''uno, seis'' 1, 6) your teens (''doce, catorce'', 12, 14), your big-endian teens (''diecisiete'', "ten and seven"), and then your twenties (''veintiuno, veintiocho'', 21, 28) before it goes entirely to big endian from there (''treinta y nueve'', "thirty-and-nine"). The cycle repeats once you make it to triple-digits, as they are referred to a lot closer to English but with the aforementioned endian cycle (''dos cientos cuarenta y tres'', "Two hundred forty-and-three").
17th Sep '17 8:23:03 PM PaulA
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-->-- Music/TomLehrer, ''New Math''.

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-->-- Music/TomLehrer, ''New Math''.
'''Music/TomLehrer''', "New Math", ''Music/ThatWasTheYearThatWas''
27th Aug '17 7:47:02 PM FordPrefect
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* Roman numerals could be considered a combination of base 5 and base 10. With unique symbols for 1 (I), 5 (V), 10 (X), 50 (L), 100 (C), 500 (D), and 1,000 (M). All other numbers being an additive or subtractive combination of the unique signs.

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* Roman numerals could be considered a combination of base 5 and base 10. With 10, with unique symbols for 1 (I), 5 (V), 10 (X), 50 (L), 100 (C), 500 (D), and 1,000 (M). All (M), all other numbers being an additive or subtractive combination of the unique signs.



** Some languages are weirder: Arabic stays little-endian until ''100''. So "16" is ''sitta-`ashar'' (six-ten) and "36" is ''sitta-wa-thalaathuun'' (six-and-thirty), but "136" is ''mi'ah wa sitta wa thalaathuun'' (a-hundred-and-six-and-thirty). This, however, is a relatively modern construction. Like the language itself, the numbers were read from right to left; "sitta wa thalaathuun wa mi'ah" (six-and-thirty-and-hundred)

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** Some languages are weirder: Arabic stays little-endian until ''100''. So "16" is ''sitta-`ashar'' (six-ten) and "36" is ''sitta-wa-thalaathuun'' (six-and-thirty), but "136" is ''mi'ah wa sitta wa thalaathuun'' (a-hundred-and-six-and-thirty). This, however, is a relatively modern construction. Like the language itself, the numbers were read from right to left; left, e.g. "sitta wa thalaathuun wa mi'ah" (six-and-thirty-and-hundred)(six-and-thirty-and-hundred).



* Up until the 1970s, British currency was a mix of base 12 (12 pence to the shilling), and base 20 (20 shillings to the pound). They were the last first world nation to switch to a decimal based currency.

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* Up until the 1970s, British currency was a mix of base 12 (12 pence to the shilling), shilling) and base 20 (20 shillings to the pound). They were the last first world First World nation to switch to a decimal based currency.
8th Jul '17 9:30:01 PM FredTheFourth
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** 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).
25th May '17 3:56:25 PM ScorpiusOB1
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* The origin of base 10 is, of course, that we (usually) have a total of 10 fingers in our hands, like other terrestrial vertebrates in their forward claws or whatever[[note]]Those that have less have lost them during their evolution[[/note]], as a legacy of the ancestor of all vertebrates. Had that creature had [[https://en.wikipedia.org/wiki/Polydactyly_in_early_tetrapods a different number of them]], it's very likely we'd be counting in base (# of fingers in our two hands).

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* The origin of base 10 is, of course, is very likely just that we (usually) have a total of 10 fingers in our hands, like other terrestrial vertebrates in their forward claws or whatever[[note]]Those that have less have lost them during their evolution[[/note]], as a legacy of the ancestor of all vertebrates.them. Had that creature had [[https://en.wikipedia.org/wiki/Polydactyly_in_early_tetrapods a different number of them]], it's very likely we'd be counting in base (# of fingers in our two hands).hands) and base 10 would be something reserved for mathematicians.
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