Finger counting
Encyclopedia
Finger counting, or dactylonomy, is the art of counting
along one's finger
s. Though marginalized in modern societies by Arabic numerals
, formerly different systems flourished in many cultures, including educated methods far more sophisticated than the one-by-one finger count taught today in preschool education
.
Finger counting can also serve as a form of manual communication
, particularly in marketplace
trading – including hand signaling during open outcry
in floor trading
– and also in games such as morra.
Finger counting varies between cultures and over time, and is studied by ethnomathematics
. Cultural differences in counting are sometimes used as a shibboleth
, particularly to distinguish nationalities in war time. These form a plot point in the film Inglourious Basterds, by Quentin Tarantino
, and in the novel Pi in the Sky, by John D. Barrow
.
-speaking cultures, when another person's fingers are being counted (that is, when another person holds up their fingers to signal a number), the count starts at the index finger (1) and goes to the little finger (4), and then the thumb is raised last to signal five. In German
or French
-speaking cultures, the thumb in the same context is counted as one and the count then proceeds from the index to the little finger. Thus, an American ordering for three drinks would raise his index, middle, and ring fingers, while a German would raise his thumb, index, and middle fingers.
In various regions, different methods of finger counting are used. In Western and Central Europe fingers are extended, beginning with the thumb and finishing at the little finger. In Eastern Europe, fingers are folded towards the palm in reverse order. In the United States, counting usually starts on the pointer finger and ends on the thumb.
Chinese number gestures
count up to 10, and themselves exhibit some regional differences.
It is possible to count to 12 using a single hand, with your thumb acting as a pointer touching each finger bone in turn. A traditional finger counting system still in use in many regions of Asia works in this way, and could help to explain the prevalence of numeral systems based on 12 and 60 besides those based on 10, 20 and 5. In this system, the one (usually right) hand counts repeatedly to 12, displaying the number of iterations on the other (usually left), until five dozens, i. e. the 60, are full.
in the first chapter of his De temporum ratione, (725), entitled "De computa vel loquela digitorum", which allowed counting up to 9,999 on two hands, though it was apparently little-used for numbers of 100 or more. This system remained in use through the European middle ages, being presented in slightly modified form by Luca Pacioli
in his seminal Summa de Arithmetica (1494).
Counting
Counting is the action of finding the number of elements of a finite set of objects. The traditional way of counting consists of continually increasing a counter by a unit for every element of the set, in some order, while marking those elements to avoid visiting the same element more than once,...
along one's finger
Finger
A finger is a limb of the human body and a type of digit, an organ of manipulation and sensation found in the hands of humans and other primates....
s. Though marginalized in modern societies by Arabic numerals
Arabic numerals
Arabic numerals or Hindu numerals or Hindu-Arabic numerals or Indo-Arabic numerals are the ten digits . They are descended from the Hindu-Arabic numeral system developed by Indian mathematicians, in which a sequence of digits such as "975" is read as a numeral...
, formerly different systems flourished in many cultures, including educated methods far more sophisticated than the one-by-one finger count taught today in preschool education
Preschool education
Preschool education is the provision of learning to children before the commencement of statutory and obligatory education, usually between the ages of zero and three or five, depending on the jurisdiction....
.
Finger counting can also serve as a form of manual communication
Manual communication
Manual communication systems use articulation of the hands to mediate a message between persons. Being expressed manually, they are received visually, and sometimes tactually...
, particularly in marketplace
Marketplace
A marketplace is the space, actual, virtual or metaphorical, in which a market operates. The term is also used in a trademark law context to denote the actual consumer environment, ie. the 'real world' in which products and services are provided and consumed.-Marketplaces and street markets:A...
trading – including hand signaling during open outcry
Open outcry
Open outcry is the name of a method of communication between professionals on a stock exchange or futures exchange. It involves shouting and the use of hand signals to transfer information primarily about buy and sell orders...
in floor trading
Floor trading
Floor trading is where traders or stock brokers meet at a specific venue referred to as a trading floor or pit to buy and sell financial instruments using open outcry method to communicate which each other. These venues are typically stock exchanges or futures exchanges and transactions are...
– and also in games such as morra.
Finger counting varies between cultures and over time, and is studied by ethnomathematics
Ethnomathematics
In mathematics education, ethnomathematics is the study of the relationship between mathematics and culture . Often associated with "cultures without written expression" , it may also be defined as "'the mathematics which is practised among identifiable cultural groups'" In mathematics education,...
. Cultural differences in counting are sometimes used as a shibboleth
Shibboleth
A shibboleth is a custom, principle, or belief distinguishing a particular class or group of people, especially a long-standing one regarded as outmoded or no longer important...
, particularly to distinguish nationalities in war time. These form a plot point in the film Inglourious Basterds, by Quentin Tarantino
Quentin Tarantino
Quentin Jerome Tarantino is an American film director, screenwriter, producer, cinematographer and actor. In the early 1990s, he began his career as an independent filmmaker with films employing nonlinear storylines and the aestheticization of violence...
, and in the novel Pi in the Sky, by John D. Barrow
John D. Barrow
-External links:****** The Forum-Publications available on the Internet:************...
.
Cultural differences
In EnglishEnglish language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...
-speaking cultures, when another person's fingers are being counted (that is, when another person holds up their fingers to signal a number), the count starts at the index finger (1) and goes to the little finger (4), and then the thumb is raised last to signal five. In German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
or 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...
-speaking cultures, the thumb in the same context is counted as one and the count then proceeds from the index to the little finger. Thus, an American ordering for three drinks would raise his index, middle, and ring fingers, while a German would raise his thumb, index, and middle fingers.
In various regions, different methods of finger counting are used. In Western and Central Europe fingers are extended, beginning with the thumb and finishing at the little finger. In Eastern Europe, fingers are folded towards the palm in reverse order. In the United States, counting usually starts on the pointer finger and ends on the thumb.
Chinese number gestures
Chinese number gestures
Chinese number gestures are a method of using one hand to signify the natural numbers one through ten. This method may have been developed to bridge the many varieties of Chinese—for example, the numbers 4 and 10 are hard to distinguish in some dialects...
count up to 10, and themselves exhibit some regional differences.
It is possible to count to 12 using a single hand, with your thumb acting as a pointer touching each finger bone in turn. A traditional finger counting system still in use in many regions of Asia works in this way, and could help to explain the prevalence of numeral systems based on 12 and 60 besides those based on 10, 20 and 5. In this system, the one (usually right) hand counts repeatedly to 12, displaying the number of iterations on the other (usually left), until five dozens, i. e. the 60, are full.
Japan
Japanese uses separate systems for counting for oneself and for displaying numbers to others, which both proceed up to ten. For counting, one begins with the palm open, then counts up to five by curling up (folding down) the fingers, starting from the thumb – thus one has just the thumb down (and others extended), while four has only the little finger extended, and five has a fist. One then counts up to ten by proceeding in the reverse order, extending the fingers, starting at the little finger – thus six is the same as four, seven the same as three, and so forth, with ten ending with the palm open. While this introduces ambiguity, it is not used to present to others, so this is generally not a problem. When displaying for others, one starts with the hand closed, and extends fingers, starting with the index, going to the little finger, then ending with the thumb, as in English. For numbers above five, one uses an open hand (indicating five) and places the appropriate number of fingers from the other hand against the palm (palms facing each other) – so six has the index finger against the palm, and so forth. To display ten, one presents both hands open and palm outwards.Historical counting
Complex systems of dactylonomy were used in the ancient world. This counting was in use in Persia in the first century CE, and thus may have originated there; it continued in the Islamic world through the middle ages, and is mentioned in poetry and the Quran. A very similar form is presented by the English monk and historian BedeBede
Bede , also referred to as Saint Bede or the Venerable Bede , was a monk at the Northumbrian monastery of Saint Peter at Monkwearmouth, today part of Sunderland, England, and of its companion monastery, Saint Paul's, in modern Jarrow , both in the Kingdom of Northumbria...
in the first chapter of his De temporum ratione, (725), entitled "De computa vel loquela digitorum", which allowed counting up to 9,999 on two hands, though it was apparently little-used for numbers of 100 or more. This system remained in use through the European middle ages, being presented in slightly modified form by Luca Pacioli
Luca Pacioli
Fra Luca Bartolomeo de Pacioli was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and seminal contributor to the field now known as accounting...
in his seminal Summa de Arithmetica (1494).
See also
- Finger binaryFinger binaryFinger binary is a system for counting and displaying binary numbers on the fingers and thumbs of one or more hands. It is possible to count from 0 to 31 using the fingers of a single hand, or from 0 through 1023 if both hands are used.- Mechanics :In the binary number system, each numerical...
- Chisanbop
- Tally marksTally marksTally marks, or hash marks, are a unary numeral system. They are a form of numeral used for counting. They allow updating written intermediate results without erasing or discarding anything written down...
- Prehistoric numerals
- Colombian numerals
- Chinese number gesturesChinese number gesturesChinese number gestures are a method of using one hand to signify the natural numbers one through ten. This method may have been developed to bridge the many varieties of Chinese—for example, the numbers 4 and 10 are hard to distinguish in some dialects...
External links
- http://www.lifeprint.com/asl101/pages-layout/numbersdiscussion.htmcounting in American Sign LanguageAmerican Sign LanguageAmerican Sign Language, or ASL, for a time also called Ameslan, is the dominant sign language of Deaf Americans, including deaf communities in the United States, in the English-speaking parts of Canada, and in some regions of Mexico...
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