Number names
Encyclopedia
In linguistics
, number names (or numerals) are specific words in a natural language
that represent
number
s.
In writing
, numerals are symbols also representing numbers. In mathematics (including computing) there are other meanings and definitions of numbers, over the different stages of the history of science.
, the terms representing numbers can be classified according to their use:
Terms such as most, least, some, and others like them are not technically numerals, but quantifiers. Quantifiers do not enumerate, or designate a specific number, but give another, often less specific, indication of amount.
and Pilagá, Culina
and pre-contact Jarawara
, Jabutí, Canela-Krahô
, Botocudo (Krenák)
, Chiquitano, the Campa languages
, Arabela
, and Achuar
. Some languages of Australia, such as Warlpiri
, do not have words for quantities above two, as did many Khoisan languages
at the time of European contact. Such languages do not have a word class of 'numeral'.
Most languages with both numerals and counting use base 8, 10, 12, or 20. Base 10 appears to come from counting one's fingers, base 20 from the fingers and toes, base 8 from counting the spaces between the fingers (attested in California), and base 12 from counting the knuckles (3 each for the four fingers).
For very large (and very small) numbers, traditional systems have been superseded by the use of scientific notation
and the system of SI prefix
es. Traditional systems continue to be used in everyday life.
have (or once had) counting systems based on parts of the body which do not have a numeric base; there are (or were) no numerical words, but rather words for relevant parts of the body—or simply pointing to the relevant spots—were used for quantities. For example, 1–4 may be the fingers, 5 'thumb', 6 'wrist', 7 'elbow', 8 'shoulder', etc., across the body and down the other arm, so that the opposite pinkie represents a number between 17 (Torres Islands) to 23 (Eleman). For numbers beyond this, the torso, legs and toes may be used, or one might count back up the other arm and back down the first, depending on the people.
and some Papua New Guinea
ns count with the base number four, using the term asu and aso (derived from Javanese
asu: dog
), as the ubiquitous village dog has four legs. This is argued by anthropologists to be also based on early humans noting the human and animal shared body feature of two arms and two legs as well as its ease in simple arithmetic and counting. As an example of the system's ease a realistic scenario could include a farmer returning from the market with fifty asu heads of pig (200), less 30 asu (120) of pig bartered for 10 asu (40) of goats noting his new pig count total as twenty asu: 80 pigs remaining. The system has a correlation to the dozen
counting system and is still in common use in these areas as a natural and easy method of simple arithmetic.
systems are based on the number 5. It is almost certain the quinary system developed from counting by fingers (five fingers per hand). An example is Api, a language of Vanuatu, where 5 is luna 'hand', 10 lua-luna 'two hand', 15 tolu-luna 'three hand', etc. 11 is then lua-luna tai 'two-hand one', and 17 tolu-luna lua 'three-hand two'.
5 is a common auxiliary base, or sub-base, where 6 is 'five and one', 7 'five and two', etc. Aztec was a vigesimal (base-20) system with sub-base 5.
is a rare example of a language with base 6. The Sko languages
, however, and base-24 with a subbase of 6.
is a counting system based on the number 8. It is used in the Yuki language
of California
and in the Pamean languages of Mexico
, because the Yuki
and Pamean keep count by using the four spaces between their fingers rather than the fingers themselves.
numeral system
. Anthropologists hypothesize this may be due to humans having five digits
per hand, ten in total. There are many regional variations including:
Historically, its use was first employed by the ancient Egyptians
, who invented a wholly decimal system, and later extended by the Babylonians, and also a system of pictorial representation, substituting letters and other reminders with symbols.
An English
farmer coined the term notch, defined as ten, from the tally sticks of the livestock
, a full deep score
for every twenty, a half score or notch for ten.
systems are based on 12.
These include:
Duodecimal numeric systems have some practical advantages over decimal. It is much easier to divide the base digit twelve
(which is a highly composite number
) by many important divisors in market
and trade settings, such as the numbers 2, 3, 4 and 6. It is still common usage and is found in idiom. For example, "A dime
a dozen" refers to something so common or numerous as to be of little worth or noteworthiness.
The system of basing counting on the number 12, is widespread, across many cultures.
Examples include:
Consequently, languages evolved or loaned terms such dozen
, gross
and great gross, which allow for rudimentary and arguably immediately comprehensible duodecimal nomenclature
(e.g., stating: "two gross and six dozen
" instead of "three hundred and sixty"). Ancient Romans
used decimal for integers, but switched to duodecimal
for fractions, and correspondingly Latin
developed a rich vocabulary for duodecimal-based fractions (see Roman numerals). A notable fictional duodecimal system was that of J. R. R. Tolkien
's Elvish languages
, which used duodecimal as well as decimal.
numbers use the number 20
as the base number for counting. Anthropologists are convinced the system originated from digit counting, as did bases five and ten, twenty being the number of human fingers and toes combined
The system is in widespread use across the world. Some include the classical Mesoamerica
n cultures, still in use today in the modern indigenous languages of their descendants, namely the Nahuatl
and Mayan languages
(see Maya numerals
). A modern national language which uses a full vigesimal system is Dzongkha
in Bhutan.
Partial vigesimal systems are found in some European languages: Basque
, Celtic languages
, French
(from Celtic), Danish
, and Georgian
. In these languages the systems are vigesimal up to 99, then decimal from 100 up. That is, 140 is 'one hundred two score', not *seven score, and there is no numeral for 400.
The term score
originates from tally
sticks, where taxmen and farmers would groove a notch for every ten, and a full score for every twenty.
The English term score, now rarely used, is a remnant of vigesimal numeration in the word score
. It was widely used to learn the pre-decimal British currency in this idiom: "a dozen pence and a score
of bob
" , referring to the 20 shillings in a pound. For Americans the term is most known from the opening of the Gettysburg Address
: "Four score and seven years ago, our forefathers...".
has a base-60 system. Sumer
ia had a base-60 system with a decimal subbase, perhaps a conflation of the decimal and a duodecimal systems of its constituent peoples, which was the origin of the numbering of modern degrees, minutes, and seconds
.
is said to have a base-80 system; it counts in twenties (with 5 and 10 as subbases) up to 80, then by eighties up to 400, and then by 400s (great scores).
799 [i.e. 400 + (4 x 80) + (3 x 20) + {10 + (5 + 4)}]’
10², thousand 10³, million
10⁶, and hiɡher powers of thousand (short scale) or of million (long scale). (See names of large numbers
.) In East Asia, the higher units are hundred, thousand, myriad
10⁴, and powers of myriad. In India, they are hundred, thousand, lakh
10⁵, crore
10⁷, and so on
. The Mesoamerican system, still used to some extent in Mayan languages
, was based on powers of 20: bak’ 400 (20²), pik 8000 (20³), kalab 160,000 (20⁴), etc.
Languages may also have numerals for numbers between the base and its powers. Balinese
, for example, currently has a decimal system, with numerals for 10, 100, and 1000, but has additional numerals for 25 (with a second word for 25 only found in a compound for 75), 35, 45, 50, 150, 175, 200 (with a second found in a compound for 1200), 400, 900, and 1600.
in Leipzig, Germany. The database currently contains data for about 4000 languages.
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
, number names (or numerals) are specific words in a natural language
Natural language
In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written...
that represent
Sign (linguistics)
There are many models of the linguistic sign . A classic model is the one by the Swiss linguist Ferdinand de Saussure. According to him, language is made up of signs and every sign has two sides : the signifier , the "shape" of a word, its phonic component, i.e...
number
Number
A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....
s.
In writing
History of writing
The history of writing records the development of expressing language by letters or other marks. In the history of how systems of representation of language through graphic means have evolved in different human civilizations, more complete writing systems were preceded by proto-writing, systems of...
, numerals are symbols also representing numbers. In mathematics (including computing) there are other meanings and definitions of numbers, over the different stages of the history of science.
Types of numerals
In linguisticsLinguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
, the terms representing numbers can be classified according to their use:
- CardinalNames of numbers in EnglishEnglish numerals are words for numbers used in English-speaking cultures.-Cardinal numbers: Cardinal numbers refer to the size of a group....
numerals: these describe quantity – one, two, three, etc. - OrdinalOrdinal number (linguistics)In linguistics, ordinal numbers are the words representing the rank of a number with respect to some order, in particular order or position . Its use may refer to size, importance, chronology, etc...
numerals: describe position in a sequential order – first, second, third, etc. (the terms next and last may also be considered a kind of ordinals) - Ranking numerals: describe order, based on relevance or importance – primary, secondary, tertiary, etc.
- Partitive numerals: describe division into fractions – whole, half, third, etc.
- Composite numerals: describe composition – unary, binary, ternary, etc.
- Multiplicative numerals: describe repetition - once, twice, and thrice
- Reproductive numerals: describe replication – single, double, triple, etc. (multiple serves as a generic plural)
- Collective numerals: describe sets – pair, triad, dozen, etc. (musical terms: solo, duo/duet, trio, etc. / kinship terms: twin, triplet, etc.) The term is also used for a specialized type of numeral in the Polish number system.
- Distributive numerals: describe an alternating pattern – each person (one), every other week (entailing two weeks), every third person, etc. Note that the English language does not have distinct distributive numerals (though it does have distributive adjectives/pronouns, such as each, either and every), but some other languages such as GeorgianGeorgian languageGeorgian is the native language of the Georgians and the official language of Georgia, a country in the Caucasus.Georgian is the primary language of about 4 million people in Georgia itself, and of another 500,000 abroad...
and Latin do have them, e.g. Latin singuli ("one by one"), bini ("in pairs", "by twos"), terni ("three each"), etc. - Morphological numerals: are mainly used only metalinguistically to describe grammatical numberGrammatical numberIn linguistics, grammatical number is a grammatical category of nouns, pronouns, and adjective and verb agreement that expresses count distinctions ....
in language – singular, dual, trial, and quadral (to include plural)
Terms such as most, least, some, and others like them are not technically numerals, but quantifiers. Quantifiers do not enumerate, or designate a specific number, but give another, often less specific, indication of amount.
Basis of counting system
Not all languages have numeral systems. Specifically, there is not much need for numeral systems among hunter-gatherers who do not engage in commerce. Many languages around the world have no numerals above two to four—or at least did not before contact with the colonial societies—and speakers of these languages may have no tradition of using the numerals they did have for counting. Indeed, several languages from the Amazon have been independently reported to have no numerals other than 'one'. These include Nadëb, pre-contact MocovíMocovi language
The Mocoví language is a Guaicuruan language of Argentina spoken by about 4,500 people mostly in Santa Fé province.- External links :**http://www.mpi.nl/DOBES/INFOpages/Posters/Argentina/Argentina.pdf*http://www.newadvent.org/cathen/10412b.htm...
and Pilagá, Culina
Culina language
Kulina is an Arawan language of Brazil and Peru spoken by about 4,000 people.- Grammar :...
and pre-contact Jarawara
Jarawara language
Jarawara is a dialect of Madi, an Arauan language spoken in Amazonas, Brazil. Jarawara is spoken by approximately 155 people.-Vowels:-Consonants:The glottal stop has a limited distribution....
, Jabutí, Canela-Krahô
Canela language
-External links:**...
, Botocudo (Krenák)
Botocudo
Botocudo , is the foreign name for a tribe of South American Indians of eastern Brazil, also known as the Aimorés, Aimborés, or Krenak people...
, Chiquitano, the Campa languages
Campa languages
The Campa languages, Pre-Andine Maipurean / Arawakan, are Arawakan languages of the Peruvian Amazon. The best known is Ashéninka.-Languages:Kaufman gives the following breakdown:...
, Arabela
Arabela language
Arabela is an indigenous American language of the Zaparoan family spoken in two Peruvian villages in tropical forest along the Napo tributary of the Arabela river....
, and Achuar
Jivaroan languages
Jivaroan is a small language family, or perhaps a language isolate, of northern Peru and eastern Ecuador.-Family division:Jivaroan consists of 4 languages:-Genetic relations:...
. Some languages of Australia, such as Warlpiri
Warlpiri language
The Warlpiri language is spoken by about 3000 of the Warlpiri people in Australia's Northern Territory. It is one of the Ngarrkic languages of the large Southwest branch of the Pama–Nyungan family, and is one of the largest aboriginal languages in Australia in terms of number of speakers.-...
, do not have words for quantities above two, as did many Khoisan languages
Khoisan languages
The Khoisan languages are the click languages of Africa which do not belong to other language families. They include languages indigenous to southern and eastern Africa, though some, such as the Khoi languages, appear to have moved to their current locations not long before the Bantu expansion...
at the time of European contact. Such languages do not have a word class of 'numeral'.
Most languages with both numerals and counting use base 8, 10, 12, or 20. Base 10 appears to come from counting one's fingers, base 20 from the fingers and toes, base 8 from counting the spaces between the fingers (attested in California), and base 12 from counting the knuckles (3 each for the four fingers).
For very large (and very small) numbers, traditional systems have been superseded by the use of scientific notation
Scientific notation
Scientific notation is a way of writing numbers that are too large or too small to be conveniently written in standard decimal notation. Scientific notation has a number of useful properties and is commonly used in calculators and by scientists, mathematicians, doctors, and engineers.In scientific...
and the system of SI prefix
SI prefix
The International System of Units specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decadic multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol...
es. Traditional systems continue to be used in everyday life.
No base
Many languages of MelanesiaMelanesia
Melanesia is a subregion of Oceania extending from the western end of the Pacific Ocean to the Arafura Sea, and eastward to Fiji. The region comprises most of the islands immediately north and northeast of Australia...
have (or once had) counting systems based on parts of the body which do not have a numeric base; there are (or were) no numerical words, but rather words for relevant parts of the body—or simply pointing to the relevant spots—were used for quantities. For example, 1–4 may be the fingers, 5 'thumb', 6 'wrist', 7 'elbow', 8 'shoulder', etc., across the body and down the other arm, so that the opposite pinkie represents a number between 17 (Torres Islands) to 23 (Eleman). For numbers beyond this, the torso, legs and toes may be used, or one might count back up the other arm and back down the first, depending on the people.
4: quaternary
Some Austronesian and Melanesian ethnic groups, including the Māori, some SulawesiSulawesi
Sulawesi is one of the four larger Sunda Islands of Indonesia and is situated between Borneo and the Maluku Islands. In Indonesia, only Sumatra, Borneo, and Papua are larger in territory, and only Java and Sumatra have larger Indonesian populations.- Etymology :The Portuguese were the first to...
and some Papua New Guinea
Papua New Guinea
Papua New Guinea , officially the Independent State of Papua New Guinea, is a country in Oceania, occupying the eastern half of the island of New Guinea and numerous offshore islands...
ns count with the base number four, using the term asu and aso (derived from Javanese
Javanese language
Javanese language is the language of the Javanese people from the central and eastern parts of the island of Java, in Indonesia. In addition, there are also some pockets of Javanese speakers in the northern coast of western Java...
asu: dog
Dog
The domestic dog is a domesticated form of the gray wolf, a member of the Canidae family of the order Carnivora. The term is used for both feral and pet varieties. The dog may have been the first animal to be domesticated, and has been the most widely kept working, hunting, and companion animal in...
), as the ubiquitous village dog has four legs. This is argued by anthropologists to be also based on early humans noting the human and animal shared body feature of two arms and two legs as well as its ease in simple arithmetic and counting. As an example of the system's ease a realistic scenario could include a farmer returning from the market with fifty asu heads of pig (200), less 30 asu (120) of pig bartered for 10 asu (40) of goats noting his new pig count total as twenty asu: 80 pigs remaining. The system has a correlation to the dozen
Dozen
A dozen is a grouping of approximately twelve. The dozen may be one of the earliest primitive groupings, perhaps because there are approximately a dozen cycles of the moon or months in a cycle of the sun or year...
counting system and is still in common use in these areas as a natural and easy method of simple arithmetic.
5: quinary
QuinaryQuinary
Quinary is a numeral system with five as the base. A possible origination of a quinary system is that there are five fingers on either hand. The base five is stated from 0-4...
systems are based on the number 5. It is almost certain the quinary system developed from counting by fingers (five fingers per hand). An example is Api, a language of Vanuatu, where 5 is luna 'hand', 10 lua-luna 'two hand', 15 tolu-luna 'three hand', etc. 11 is then lua-luna tai 'two-hand one', and 17 tolu-luna lua 'three-hand two'.
5 is a common auxiliary base, or sub-base, where 6 is 'five and one', 7 'five and two', etc. Aztec was a vigesimal (base-20) system with sub-base 5.
6: sexal
KanumKanum language
Kanum is a series of languages, with difficult mutual intelligibility, spoken by the Kanum people.Kanum has a base-6 numeral system. For example, the numeral 200 is:...
is a rare example of a language with base 6. The Sko languages
Sko languages
The Sko or Skou languages are a small language family spoken by about 7000 people, mainly along the coast of Sandaun Province in Papua New Guinea, with a few being inland from this area and at least one just across the border in the Indonesian province of Papua . Skou languages are unusual in New...
, however, and base-24 with a subbase of 6.
8: octal
OctalOctal
The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three...
is a counting system based on the number 8. It is used in the Yuki language
Yuki language
The Yuki language, also known as Yukian, Ukiah, Ukomno'm, was a language of California, spoken by the indigenous American Yuki people, formerly in the Eel River area, the Round Valley Reservation, northern California. It became extinct some time in the 20th century...
of California
California
California is a state located on the West Coast of the United States. It is by far the most populous U.S. state, and the third-largest by land area...
and in the Pamean languages of Mexico
Mexico
The United Mexican States , commonly known as Mexico , is a federal constitutional republic in North America. It is bordered on the north by the United States; on the south and west by the Pacific Ocean; on the southeast by Guatemala, Belize, and the Caribbean Sea; and on the east by the Gulf of...
, because the Yuki
Yuki tribe
The Yuki are a Native American people from the zone of Round Valley, in what today is part of the territory of Mendocino County, Northern California. Yuki tribes are thought to have settled as far south as Hood Mountain in present-day Sonoma County...
and Pamean keep count by using the four spaces between their fingers rather than the fingers themselves.
10: decimal
A majority of traditional number systems are based on the decimalDecimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....
numeral system
Numeral system
A numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
. Anthropologists hypothesize this may be due to humans having five digits
Digit (anatomy)
A digit is one of several most distal parts of a limb, such as fingers or toes, present in many vertebrates.- Names:Some languages have different names for hand and foot digits ....
per hand, ten in total. There are many regional variations including:
- Western system: based on thousands, with variants (see English-language numerals)
- Indian system: croreCroreA crore is a unit in the Indian number system equal to ten million , or 100 lakhs. It is widely used in India, Bangladesh, Nepal, and Pakistan....
, lakhLakhA lakh is a unit in the Indian numbering system equal to one hundred thousand . It is widely used both in official and other contexts in Pakistan, Bangladesh, India, Maldives, Nepal, Sri Lanka, Myanmar and is often used in Indian English.-Usage:...
(see Indian numbering systemIndian numbering systemThe South Asian numbering system, used today in the Indian subcontinent , is based on grouping by two decimal places, rather than the three decimal places commonplace in most parts of the world. This system of measurement introduces separators into numbers in places appropriate to the two-digit...
. Indian numeralsIndian numeralsMost of the positional base 10 numeral systems in the world have originated from India, where the concept of positional numeration was first developed...
) - East Asian system: based on ten-thousands10000 (number)10000 is the natural number following 9999 and preceding 10001.-Name:Many languages have a specific word for this number: In English it is myriad, in Ancient Greek , in Aramaic , in Hebrew רבבה , in Chinese , in Japanese [man], in Korean [man], and in Thai หมื่น [meun]...
(see below)
Historically, its use was first employed by the ancient Egyptians
Egyptians
Egyptians are nation an ethnic group made up of Mediterranean North Africans, the indigenous people of Egypt.Egyptian identity is closely tied to geography. The population of Egypt is concentrated in the lower Nile Valley, the small strip of cultivable land stretching from the First Cataract to...
, who invented a wholly decimal system, and later extended by the Babylonians, and also a system of pictorial representation, substituting letters and other reminders with symbols.
An English
English people
The English are a nation and ethnic group native to England, who speak English. The English identity is of early mediaeval origin, when they were known in Old English as the Anglecynn. England is now a country of the United Kingdom, and the majority of English people in England are British Citizens...
farmer coined the term notch, defined as ten, from the tally sticks of the livestock
Livestock
Livestock refers to one or more domesticated animals raised in an agricultural setting to produce commodities such as food, fiber and labor. The term "livestock" as used in this article does not include poultry or farmed fish; however the inclusion of these, especially poultry, within the meaning...
, a full deep score
Score
Score may refer to:*Score , a 2006 album by Dream Theater*Score , a number of points achieved in a sporting event or game*Score , a 1972 sexplotaition film*Score , a pornographic magazine...
for every twenty, a half score or notch for ten.
12: duodecimal
DuodecimalDuodecimal
The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'...
systems are based on 12.
These include:
- Chepang languageChepangChepang is the commonly used name given to an indigenous ethnic group living in central and southern Nepal.The language is also known as Chepang but is called Chyo-bang by the people themselves. Some Bahun Chettri castes call these people the "Praja" meaning "political subjects"...
of NepalNepalNepal , officially the Federal Democratic Republic of Nepal, is a landlocked sovereign state located in South Asia. It is located in the Himalayas and bordered to the north by the People's Republic of China, and to the south, east, and west by the Republic of India...
, - Mahl language of Minicoy Island in IndiaIndiaIndia , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
- Nigerian Middle BeltMiddle BeltThe Middle Belt is a human geographical term designating the region of central Nigeria populated largely by minority ethnic groups and stretching across the country longitudinally. The Middle Belt is indeterminate in that it lacks designated "borders" and is charactized by a heterogeneity and...
areas such as Janji, Kahugu and the Nimbia dialect of GwandaraGwandara languageGwandara is a West Chadic language, and the closest relative of Hausa. Its several dialects are spoken in northern Nigeria by about 30,000 people....
. - MelanesiaMelanesiaMelanesia is a subregion of Oceania extending from the western end of the Pacific Ocean to the Arafura Sea, and eastward to Fiji. The region comprises most of the islands immediately north and northeast of Australia...
- PolynesiaPolynesiaPolynesia is a subregion of Oceania, made up of over 1,000 islands scattered over the central and southern Pacific Ocean. The indigenous people who inhabit the islands of Polynesia are termed Polynesians and they share many similar traits including language, culture and beliefs...
- reconstructed proto-Benue–Congo
Duodecimal numeric systems have some practical advantages over decimal. It is much easier to divide the base digit twelve
12 (number)
12 is the natural number following 11 and preceding 13.The word "twelve" is the largest number with a single-morpheme name in English. Etymology suggests that "twelve" arises from the Germanic compound twalif "two-leftover", so a literal translation would yield "two remaining [after having ten...
(which is a highly composite number
Highly composite number
A highly composite number is a positive integer with more divisors than any positive integer smaller than itself.The initial or smallest twenty-one highly composite numbers are listed in the table at right....
) by many important divisors in market
Market
A market is one of many varieties of systems, institutions, procedures, social relations and infrastructures whereby parties engage in exchange. While parties may exchange goods and services by barter, most markets rely on sellers offering their goods or services in exchange for money from buyers...
and trade settings, such as the numbers 2, 3, 4 and 6. It is still common usage and is found in idiom. For example, "A dime
Dime
Dime may refer to:Currency* Dime * Dime Media and entertainment* Dime , by Guardian* "Dime" , by Beth* The Dimes, a musical group* Dime novel, a type of popular fictionSports* Dime...
a dozen" refers to something so common or numerous as to be of little worth or noteworthiness.
The system of basing counting on the number 12, is widespread, across many cultures.
Examples include:
- time divisions (twelve months in a year, the twelve-hour clock)
- measurement imperial system of units (twelve inches to the foot, twelve troy ounces to the troy pound)
- traditional British monetary system (twelve pence to the shillingShillingThe shilling is a unit of currency used in some current and former British Commonwealth countries. The word shilling comes from scilling, an accounting term that dates back to Anglo-Saxon times where it was deemed to be the value of a cow in Kent or a sheep elsewhere. The word is thought to derive...
) - the ancient Babylonian concept of 360 days in the year (12 months x 30 days) from which we get 360 degrees to a circle
Consequently, languages evolved or loaned terms such dozen
Dozen
A dozen is a grouping of approximately twelve. The dozen may be one of the earliest primitive groupings, perhaps because there are approximately a dozen cycles of the moon or months in a cycle of the sun or year...
, gross
Gross (unit)
A gross is equal to a dozen dozen, i.e. 12 × 12 = 144.It can be used in duodecimal counting. The use of gross likely originated from the fact that 144 can be counted on the fingers using the fingertips and first two joints of each finger when marked by the thumb of one hand. The other hand...
and great gross, which allow for rudimentary and arguably immediately comprehensible duodecimal nomenclature
Nomenclature
Nomenclature is a term that applies to either a list of names or terms, or to the system of principles, procedures and terms related to naming - which is the assigning of a word or phrase to a particular object or property...
(e.g., stating: "two gross and six dozen
Dozen
A dozen is a grouping of approximately twelve. The dozen may be one of the earliest primitive groupings, perhaps because there are approximately a dozen cycles of the moon or months in a cycle of the sun or year...
" instead of "three hundred and sixty"). Ancient Romans
Ancient Rome
Ancient Rome was a thriving civilization that grew on the Italian Peninsula as early as the 8th century BC. Located along the Mediterranean Sea and centered on the city of Rome, it expanded to one of the largest empires in the ancient world....
used decimal for integers, but switched to duodecimal
Duodecimal
The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'...
for fractions, and correspondingly Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...
developed a rich vocabulary for duodecimal-based fractions (see Roman numerals). A notable fictional duodecimal system was that of J. R. R. Tolkien
J. R. R. Tolkien
John Ronald Reuel Tolkien, CBE was an English writer, poet, philologist, and university professor, best known as the author of the classic high fantasy works The Hobbit, The Lord of the Rings, and The Silmarillion.Tolkien was Rawlinson and Bosworth Professor of Anglo-Saxon at Pembroke College,...
's Elvish languages
Elvish languages
J. R. R. Tolkien constructed many Elvish languages. These were the languages spoken by the tribes of his Elves. Tolkien was a philologist by profession, and spent much time on his constructed languages. The Elvish languages were the first thing he imagined for his secondary world. Tolkien said that...
, which used duodecimal as well as decimal.
20: vigesimal
VigesimalVigesimal
The vigesimal or base 20 numeral system is based on twenty .- Places :...
numbers use the number 20
20
Year 20 was a leap year starting on Monday of the Julian calendar. At the time, it was known as the Year of the Consulship of Messala and Cotta...
as the base number for counting. Anthropologists are convinced the system originated from digit counting, as did bases five and ten, twenty being the number of human fingers and toes combined
The system is in widespread use across the world. Some include the classical Mesoamerica
Mesoamerica
Mesoamerica is a region and culture area in the Americas, extending approximately from central Mexico to Belize, Guatemala, El Salvador, Honduras, Nicaragua, and Costa Rica, within which a number of pre-Columbian societies flourished before the Spanish colonization of the Americas in the 15th and...
n cultures, still in use today in the modern indigenous languages of their descendants, namely the Nahuatl
Nahuatl
Nahuatl is thought to mean "a good, clear sound" This language name has several spellings, among them náhuatl , Naoatl, Nauatl, Nahuatl, Nawatl. In a back formation from the name of the language, the ethnic group of Nahuatl speakers are called Nahua...
and Mayan languages
Mayan languages
The Mayan languages form a language family spoken in Mesoamerica and northern Central America. Mayan languages are spoken by at least 6 million indigenous Maya, primarily in Guatemala, Mexico, Belize and Honduras...
(see Maya numerals
Maya numerals
Maya Numerals were a vigesimal numeral system used by the Pre-Columbian Maya civilization.The numerals are made up of three symbols; zero , one and five...
). A modern national language which uses a full vigesimal system is Dzongkha
Dzongkha language
Dzongkha , occasionally Ngalopkha, is the national language of Bhutan. The word "dzongkha" means the language spoken in the dzong, – dzong being the fortress-like monasteries established throughout Bhutan by Shabdrung Ngawang Namgyal in the 17th century."Bhutani" is not another name for...
in Bhutan.
Partial vigesimal systems are found in some European languages: Basque
Basque language
Basque is the ancestral language of the Basque people, who inhabit the Basque Country, a region spanning an area in northeastern Spain and southwestern France. It is spoken by 25.7% of Basques in all territories...
, Celtic languages
Celtic languages
The Celtic languages are descended from Proto-Celtic, or "Common Celtic"; a branch of the greater Indo-European language family...
, French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
(from Celtic), Danish
Danish language
Danish is a North Germanic language spoken by around six million people, principally in the country of Denmark. It is also spoken by 50,000 Germans of Danish ethnicity in the northern parts of Schleswig-Holstein, Germany, where it holds the status of minority language...
, and Georgian
Georgian language
Georgian is the native language of the Georgians and the official language of Georgia, a country in the Caucasus.Georgian is the primary language of about 4 million people in Georgia itself, and of another 500,000 abroad...
. In these languages the systems are vigesimal up to 99, then decimal from 100 up. That is, 140 is 'one hundred two score', not *seven score, and there is no numeral for 400.
The term score
20 (number)
20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.-In mathematics:*20 is the basis for vigesimal number systems....
originates from tally
Tally
-Last name:* Lura S. Tally; a retired legislator from North Carolina* Thomas Lincoln Tally; operated the Electric Theater in Los Angeles* William Tally; an American engineer and former CTO of Saleen, Inc...
sticks, where taxmen and farmers would groove a notch for every ten, and a full score for every twenty.
The English term score, now rarely used, is a remnant of vigesimal numeration in the word score
20 (number)
20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.-In mathematics:*20 is the basis for vigesimal number systems....
. It was widely used to learn the pre-decimal British currency in this idiom: "a dozen pence and a score
20 (number)
20 is the natural number following 19 and preceding 21. A group of twenty units may also be referred to as a score.-In mathematics:*20 is the basis for vigesimal number systems....
of bob
Shilling
The shilling is a unit of currency used in some current and former British Commonwealth countries. The word shilling comes from scilling, an accounting term that dates back to Anglo-Saxon times where it was deemed to be the value of a cow in Kent or a sheep elsewhere. The word is thought to derive...
" , referring to the 20 shillings in a pound. For Americans the term is most known from the opening of the Gettysburg Address
Gettysburg Address
The Gettysburg Address is a speech by U.S. President Abraham Lincoln and is one of the most well-known speeches in United States history. It was delivered by Lincoln during the American Civil War, on the afternoon of Thursday, November 19, 1863, at the dedication of the Soldiers' National Cemetery...
: "Four score and seven years ago, our forefathers...".
60: sexagesimal
EkariEkari language
Ekari is a Trans–New Guinea language spoken by about 100,000 people in the Paniai lakes region of the Indonesian province of Papua, including the villages of Mapia and Moanamani. This makes it the second-most populous Papuan language in Indonesian New Guinea after Western Dani. Language use is...
has a base-60 system. Sumer
Sumer
Sumer was a civilization and historical region in southern Mesopotamia, modern Iraq during the Chalcolithic and Early Bronze Age....
ia had a base-60 system with a decimal subbase, perhaps a conflation of the decimal and a duodecimal systems of its constituent peoples, which was the origin of the numbering of modern degrees, minutes, and seconds
Degree (angle)
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...
.
80: octogesimal
SupyireSupyire language
Supyire, or Suppire, is the name of a language centralized in the Sikasso Region region of southeastern Mali, in western Africa. Supyire is spoken by an estimated 364,000 Supyire people, according to Ethnologue. The language belongs to the larger language group of Senufo, a member of the Gur...
is said to have a base-80 system; it counts in twenties (with 5 and 10 as subbases) up to 80, then by eighties up to 400, and then by 400s (great scores).
| kàmpwóò | ŋ̀kwuu | sicyɛɛré | ná | béé-tàànre | ná | kɛ́ | ná | báár-ìcyɛ̀ɛ̀rè |
| fourhundred | eighty | four | and | twenty-three | and | ten | and | five-four |
799 [i.e. 400 + (4 x 80) + (3 x 20) + {10 + (5 + 4)}]’
Larger numerals
In many languages, numerals up to the base are a distinct part of speech, while the words used to form higher numbers belong to one of the other classes, such as nouns or adjectives. In English, these higher words are hundredHundred
Hundred usually refers to the number 100It may also refer to:* Hundred , historically a number not necessarily 100* Hundred , a mostly obsolete geographic term...
10², thousand 10³, million
Million
One million or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione , from mille, "thousand", plus the augmentative suffix -one.In scientific notation, it is written as or just 106...
10⁶, and hiɡher powers of thousand (short scale) or of million (long scale). (See names of large numbers
Names of large numbers
This article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions.The following table lists those names of large numbers which are found in many English dictionaries and thus have a special claim to being "real words"...
.) In East Asia, the higher units are hundred, thousand, myriad
Myriad
Myriad , "numberlesscountless, infinite", is a classical Greek word for the number 10,000. In modern English, the word refers to an unspecified large quantity.-History and usage:...
10⁴, and powers of myriad. In India, they are hundred, thousand, lakh
Lakh
A lakh is a unit in the Indian numbering system equal to one hundred thousand . It is widely used both in official and other contexts in Pakistan, Bangladesh, India, Maldives, Nepal, Sri Lanka, Myanmar and is often used in Indian English.-Usage:...
10⁵, crore
Crore
A crore is a unit in the Indian number system equal to ten million , or 100 lakhs. It is widely used in India, Bangladesh, Nepal, and Pakistan....
10⁷, and so on
Indian numbering system
The South Asian numbering system, used today in the Indian subcontinent , is based on grouping by two decimal places, rather than the three decimal places commonplace in most parts of the world. This system of measurement introduces separators into numbers in places appropriate to the two-digit...
. The Mesoamerican system, still used to some extent in Mayan languages
Mayan languages
The Mayan languages form a language family spoken in Mesoamerica and northern Central America. Mayan languages are spoken by at least 6 million indigenous Maya, primarily in Guatemala, Mexico, Belize and Honduras...
, was based on powers of 20: bak’ 400 (20²), pik 8000 (20³), kalab 160,000 (20⁴), etc.
Languages may also have numerals for numbers between the base and its powers. Balinese
Balinese language
Balinese or simply Bali is a Malayo-Polynesian language spoken by 3.3 million people on the Indonesian island of Bali, as well as northern Nusa Penida, western Lombok and eastern Java...
, for example, currently has a decimal system, with numerals for 10, 100, and 1000, but has additional numerals for 25 (with a second word for 25 only found in a compound for 75), 35, 45, 50, 150, 175, 200 (with a second found in a compound for 1200), 400, 900, and 1600.
Numerals in various languages
A database Numeral Systems of the World's Languages compiled by Eugene S.L. Chan of Hong Kong is hosted by the Max Planck Institute for Evolutionary AnthropologyMax Planck Institute for Evolutionary Anthropology
The Max Planck Institute for Evolutionary Anthropology is a research institute based in Leipzig, Germany, founded in 1997. It is part of the Max Planck Society network....
in Leipzig, Germany. The database currently contains data for about 4000 languages.
- Proto-Indo-European numeralsProto-Indo-European numeralsThe numerals of the Proto-Indo-European language have been reconstructed by modern linguists based on similarities found across all Indo-European languages. The following article lists and discusses their hypothesized forms.-Cardinal numbers:...
- English-language numerals
- Indian numbering systemIndian numbering systemThe South Asian numbering system, used today in the Indian subcontinent , is based on grouping by two decimal places, rather than the three decimal places commonplace in most parts of the world. This system of measurement introduces separators into numbers in places appropriate to the two-digit...
- Hindustani numeralsHindustani numeralsAs with many Indic languages, Hindustani has a decimal numeral system that is contracted to the extent that nearly every number 1–99 is irregular, and needs to be memorized as a separate numeral.Numbers from 100 up are more regular...
- Hindustani numerals
- Proto-Semitic numerals
- Hebrew numeralsHebrew numeralsThe system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet.In this system, there is no notation for zero, and the numeric values for individual letters are added together...
- Hebrew numerals
- Japanese numeralsJapanese numeralsThe system of Japanese numerals is the system of number names used in the Japanese language. The Japanese numerals in writing are entirely based on the Chinese numerals and the grouping of large numbers follow the Chinese tradition of grouping by 10,000...
- Korean numeralsKorean numeralsThe Korean language has two regularly used sets of numerals, a native Korean system and Sino-Korean system.-Construction:For both native and Sino- Korean numerals, the teens are represented by a combination of tens and the ones places...
- Dzongkha numeralsDzongkha numeralsDzongkha, the national language of Bhutan, has two numeral systems, one vigesimal , and a modern decimal system. The vigesimal system remains in robust use. Ten is an auxiliary base: the teens are formed with ten and the numerals 1–9.-Vigesimal:...
- Javanese numeralsJavanese numeralsThe Javanese language has a decimal numeral system with distinct words for the 'tweens' from 21 to 29, called likuran.The basic numerals 1–10 have independent and combining forms, the latter derived via a suffix -ng. The combining forms are used to form the tens, hundreds, thousands, and millions...
- Balinese numeralsBalinese numerals-Basic numerals:The numerals 1–10 have basic, combining, and independent forms, many of which are formed through reduplication. The combining forms are used to form higher numbers...
- Finnish numerals
- Polish numerals
- Yoruba numeralsYoruba numeralsThe Yoruba language has a rather elaborate vigesimal numeral system that involves both addition and subtraction.The base of the counting system is 'twenty' . There are words for each of the decades; units in 1–4 are created by adding to these, while units in 5–9 are created by subtracting from...
- Australian Aboriginal enumerationAustralian Aboriginal enumerationA common misconception among non-Aboriginals is that Aboriginals did not have a way to count beyond two or three. However, Alfred Howitt, who studied the peoples of southeastern Australia, disproved this in the late nineteenth century, although the myth continues in circulation today.The...
Related topics
- Long and short scalesLong and short scalesThe long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries use the short scale...
- Names of large numbersNames of large numbersThis article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions.The following table lists those names of large numbers which are found in many English dictionaries and thus have a special claim to being "real words"...
- Numeral systemNumeral systemA numeral system is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using graphemes or symbols in a consistent manner....
- Names of small numbersNames of small numbersThis article lists and discusses the usage and derivation of names of small numbers.-Table of names:The following table lists English language names of small numbers used in the long and short scales, along with the power of ten, engineering notation, and International System of Units symbols and...