*THE CASE FOR ‘DUO-DECIMALISM’*
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*HIGH NOON*
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*AKA* –>
‘dozenalism’
(formerly billed as ‘duo-decimalism’)
(after overcoming our ‘base-10′ biases’)
(so that the system is not etymologically linked to the ‘base-10’ reference ‘decimal’)
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(the duodecimal system is a ‘positional notation numeral system’ using ’12’ as its ‘base’)
(in this ‘system’, the ‘number ten’ may be written by a rotated “2” (2) and the number ‘eleven’ by a rotated “3” (3))
(this ‘notation’ was introduced by “sir isaac pitman”…)
‘sir isaac pitman’
(1813 – 1897)
(just your average ‘english teacher’)
(/ or to be ‘clearer’, an ‘englishman’ who worked as a ‘teacher’)
(an advocate for ‘spelling reform’)
(based on ‘phonetic shorthand’)
(take that, you dumb ‘quora’ smug ‘first-responders’)
(much like the cranky ‘computer tekey types giving out ‘free advice’)
(like some sorta proto-‘open source’ crusader)
(good for him!)
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(these ‘digit forms’ are available as ‘unicode characters’ on ‘computerized systems’ since ‘june 2015’)
(british forms were accepted for ‘encoding’ as ‘characters’ at ‘code points’ (U+218A ↊ TURNED DIGIT TWO) and (U+218B ↋ TURNED DIGIT THREE))
(other notations use “A”, “T”, or “X” for ten and “B” or “E” for eleven)
(the number ‘twelve’ (that is, the number written as “12” in the ‘base-10 numerical system’) is instead written as “10” in duodecimal (meaning “1 dozen and 0 units”, instead of “1 ten and 0 units”), whereas the digit string “12” means “1 dozen and 2 units” (i.e. the same number that in decimal is written as “14”))
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(similarly, in ‘duodecimal system’) –>
“100” means “1 gross”
“1000” means “1 great gross”
“0.1” means “1 twelfth”
(instead of their decimal meanings “1 hundred”, “1 thousand”, and “1 tenth”))
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(the number ‘twelve’ (a ‘superior highly composite number’) is the smallest number with 4 ‘non-trivial factors’ (2, 3, 4, 6), + the smallest to include as factors all 4 numbers (1 to 4) within the ‘subitizing range’)
(‘increased factorability’ of the ‘radix’)
(‘increased divisibility’ by a wide range of the most ‘elemental numbers’)
(whereas ‘ten’ has only 2 ‘non-trivial factors’: 2 and 5 (and not 3, 4, or 6), ‘duodecimal representations’ fit more easily than ‘decimal ones’ into many ‘common patterns’, as evidenced by the higher ‘regularity’ observable in the ‘duodecimal multiplication table’)
(as a result, “duodecimal” has been described as the ‘optimal number system’)
(of its ‘factors’, ‘2’ and ‘3’ are ‘prime’, which means the ‘reciprocals’ of all ‘3-smooth’ numbers (such as 2, 3, 4, 6, 8, 9…) have a ‘terminating representation’ in ‘duodecimal’)
(in particular, the 5 most elementary fractions ( 1⁄2, 1⁄3, 2⁄3, 1⁄4 and 3⁄4) all have a short ‘terminating representation’ in ‘duodecimal’ (0.6, 0.4, 0.8, 0.3 and 0.9, respectively), and ‘twelve’ is the smallest ‘radix’ with this feature (because it is the ‘least common multiple’ of ‘3’ and ‘4’))
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(this all makes it a more convenient ‘number system’ for computing ‘fractions’ than most other ‘number systems’ in ‘common use’, such as…)
“decimal”
(base-10)
“vigesimal”
(base-20)
“binary”
(base-2)
“octal”
(base-8)
“hexadecimal”
(base-16)
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(although the ‘trigesimal’ (base-30) and ‘sexagesimal’ (base-60) systems (where the ‘reciprocals’ of all ‘5-smooth’ numbers terminate) do even better in this respect, this is at the cost of ‘unwieldy multiplication tables’ and a much larger number of ‘symbols’ to ‘memorize’)
(‘languages’ using ‘duodecimal number systems’ are uncommon)
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(examples of languages with ‘duodecimal numerals’…)
*languages’ in the ‘nigerian middle belt’*
(such as ‘janji’, ‘gbiri-niragu’ (aka ‘gure-kahugu’), ‘piti’,
(the ‘nimbia dialect’ of ‘gwandara’)
(the ‘chepang language’ of ‘nepal’)
(the ‘maldivian language’ (‘dhivehi’) of the people of ‘the maldives’ and ‘minicoy island’ in ‘india’)
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(‘germanic languages’ have special words for ’11’ and ’12’, such as eleven and twelve in ‘english’)
(however, they are considered to come from ‘proto-germanic’ *ainlif and *twalif (respectively one left and two left), both of which were ‘decimal’)
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(historically, ‘units’ of ‘time’ in many ‘civilizations’ are ‘duodecimal’) –>
(’12 signs’ of the ‘zodiac’)
(’12 months’ in a ‘year’)
(the ‘babylonians’ had ’12 hours’ in a ‘day’)
(although at some point this was changed to ’24’)
(traditional chinese ‘calendars’, ‘clocks’, and ‘compasses’ are based on the ’12 earthly branches’)
(’12 inches’ in an ‘imperial foot’)
(’12 troy ounces’ in a ‘troy pound’)
(’12 old british pence’ in a ‘shilling’)
(’24’ (or ’12’ × ‘2’) ‘hours’ in a ‘day’)
‘dozen’ –> ’12’
‘gross’ –> (’12’ x ’12’) –> ‘144’
‘great gross’ –> (’12’ x ’12’ x ’12’) –> ‘1728’
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(the ‘romans’ used a ‘fraction system’ based on ’12’, including the ‘uncia’ which became both the english words ounce and inch)
(pre-‘decimalization, ‘ireland’ and the ‘united kingdom’ used a mixed ‘duodecimal’ (base-12) / ‘vigesimal’ (base-20) currency system) –>
(’12 pence’ = ‘1 shilling’)
(’20 shillings’ –> ‘240 pence’ –> ‘1 pound sterling’ (or ‘irish pound’))
(‘charlemagne’ established a ‘monetary system’ that also had a ‘mixed base’ of ‘twelve’ and ‘twenty’, the remnants of which persist in many places)
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💕💝💖💓🖤💙🖤💙🖤💙🖤❤️💚💛🧡❣️💞💔💘❣️🧡💛💚❤️🖤💜🖤💙🖤💙🖤💗💖💝💘
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*🌈✨ *TABLE OF CONTENTS* ✨🌷*
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🔥🔥🔥🔥🔥🔥*we won the war* 🔥🔥🔥🔥🔥🔥