Finger-counting, also known as dactylonomy, is the act of
counting
Counting is the process of determining the number of elements of a finite set of objects, i.e., determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every ele ...
using one's fingers. There are multiple different systems used across time and between cultures, though many of these have seen a decline in use because of the spread of
Arabic numerals
Arabic numerals are the ten numerical digits: , , , , , , , , and . They are the most commonly used symbols to write Decimal, decimal numbers. They are also used for writing numbers in other systems such as octal, and for writing identifiers ...
.
Finger-counting can serve as a form of
manual communication
Manual communication systems use articulation of the hands (hand signs, gestures, etc.) to mediate a message between persons. Being expressed manually, they are received visually and sometimes tactually. When it is the primary form of communic ...
, particularly in
marketplace
A marketplace or market place is a location where people regularly gather for the purchase and sale of provisions, livestock, and other goods. In different parts of the world, a marketplace may be described as a '' souk'' (from the Arabic), ' ...
trading – including
hand signaling during
open outcry
Open outcry is a method of communication between professionals on a stock exchange or futures exchange, typically on a trading floor. It involves shouting and the use of hand signals to transfer information primarily about buy and sell order ...
in
floor trading
Open outcry is a method of communication between professionals on a stock exchange or futures exchange, typically on a trading floor. It involves shouting and the use of hand signals to transfer information primarily about buy and sell orde ...
– and also in games such as
morra.
Finger-counting is known to go back to
ancient Egypt at least, and probably even further back.
Georges Ifrah Georges Ifrah (1947 – 1 November 2019) was a teacher of mathematics, a French author and a self-taught historian of mathematics, especially numerals.
His work, ''From One to Zero: A Universal History of Numbers'' (1985, 1994) was translated into ...
notes that humans learned to count on their hands. Ifrah shows, for example, a picture of Boethius
Anicius Manlius Severinus Boethius, commonly known as Boethius (; Latin: ''Boetius''; 480 – 524 AD), was a Roman senator, consul, ''magister officiorum'', historian, and philosopher of the Early Middle Ages. He was a central figure in the tr ...
(who lived 480–524 or 525) reckoning on his fingers in .[ notes that as early as the 3rd millennium BCE, in Egypt's ]Old Kingdom
In ancient Egyptian history, the Old Kingdom is the period spanning c. 2700–2200 BC. It is also known as the "Age of the Pyramids" or the "Age of the Pyramid Builders", as it encompasses the reigns of the great pyramid-builders of the Fourth ...
, in the Pyramid texts
The Pyramid Texts are the oldest ancient Egyptian funerary texts, dating to the late Old Kingdom. They are the earliest known corpus of ancient Egyptian religious texts. Written in Old Egyptian, the pyramid texts were carved onto the subterranea ...
' "Spell for obtaining a ferry-boat", the ferryman might object "Did you bring me a man who cannot number his fingers?". This spell was needed to cross a canal of the nether-world, as detailed in the Book of the Dead
The ''Book of the Dead'' ( egy, 𓂋𓏤𓈒𓈒𓈒𓏌𓏤𓉐𓂋𓏏𓂻𓅓𓉔𓂋𓅱𓇳𓏤, ''rw n(y)w prt m hrw(w)'') is an ancient Egyptian funerary text generally written on papyrus and used from the beginning of the New Kingdom ...
.
Historical counting
Complex systems of dactylonomy were used in the ancient world.
The Greco-Roman author Plutarch, in his
Lives
Lives may refer to:
* The plural form of a ''life''
* Lives, Iran, a village in Khuzestan Province, Iran
* The number of lives in a video game
* '' Parallel Lives'', aka ''Lives of the Noble Greeks and Romans'', a series of biographies of famous m ...
, mentions finger counting as being used in Persia in the first centuries CE, so the practice may have originated in Iran. It was later used widely in medieval Islamic lands. The earliest reference to this method of using the hands to refer to the natural numbers may have been in some Prophetic traditions going back to the
early days of Islam during the early 600s. In one tradition as reported by Yusayra,
Muhammad
Muhammad ( ar, مُحَمَّد; 570 – 8 June 632 Common Era, CE) was an Arab religious, social, and political leader and the founder of Islam. According to Muhammad in Islam, Islamic doctrine, he was a prophet Divine inspiration, di ...
enjoined upon his female companions to express praise to God and to count using their fingers (=واعقدن بالأنامل )( سنن الترمذي).
In Arabic, dactylonomy is known as "Number reckoning by finger folding" (=حساب العقود ). The practice was well known in the
Arabic-speaking world
The Arab world ( ar, اَلْعَالَمُ الْعَرَبِيُّ '), formally the Arab homeland ( '), also known as the Arab nation ( '), the Arabsphere, or the Arab states, refers to a vast group of countries, mainly located in Western As ...
and was quite commonly used as evidenced by the numerous references to it in Classical Arabic literature. Poets could allude to a miser by saying that his hand made "ninety-three", i.e. a closed fist, the sign of avarice. When an old man was asked how old he was he could answer by showing a closed fist, meaning 93. The gesture for 50 was used by some poets (for example Ibn Al-Moutaz) to describe the beak of the goshawk.
Some of the gestures used to refer to numbers were even known in Arabic by special technical terms such as Kas' (=القصع ) for the gesture signifying 29, Dabth (=الـضَـبْـث ) for 63 and Daff (= الـضَـفّ) for 99 (فقه اللغة).
The polymath Al-Jahiz advised schoolmasters in his book Al-Bayan (البيان والتبيين) to teach finger counting which he placed among the five methods of human expression. Similarly, Al-Suli, in his Handbook for Secretaries, wrote that scribes preferred dactylonomy to any other system because it required neither materials nor an instrument, apart from a limb. Furthermore, it ensured secrecy and was thus in keeping with the dignity of the scribe's profession.
Books dealing with dactylonomy, such as a treatise by the mathematician Abu'l-Wafa al-Buzajani, gave rules for performing complex operations, including the approximate determination of square roots. Several pedagogical poems dealt exclusively with finger counting, some of which were translated into European languages, including a short poem by Shamsuddeen Al-Mawsili (translated into French by
Aristide Marre
Eugène Aristide Marre (7 March 1823, Mamers (Sarthe) – 18 February 1918, aged 95, Vaucresson) was a French linguist.
Works
*1846"Trouver la somme de toutes les permutations d'un nombre donné"in ''Nouvelles annales de mathématiques''
*1846 ...
) and one by Abul-Hasan Al-Maghribi (translated into German by Julius Ruska).
A very similar form is presented by the English monk and historian
Bede
Bede ( ; ang, Bǣda , ; 672/326 May 735), also known as Saint Bede, The Venerable Bede, and Bede the Venerable ( la, Beda Venerabilis), was an English monk at the monastery of St Peter and its companion monastery of St Paul in the Kingdom o ...
in the first chapter of his ''De temporum ratione,'' (725), entitled "Tractatus de computo, vel loquela per gestum 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
Fra Luca Bartolomeo de Pacioli (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting ...
in his seminal ''
Summa de arithmetica
' (''Summary of arithmetic, geometry, proportions and proportionality'') is a book on mathematics written by Luca Pacioli and first published in 1494. It contains a comprehensive summary of Renaissance mathematics, including practical arithmeti ...
'' (1494).
By country or region
Finger-counting varies between cultures and over time, and is studied by
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 identifiabl ...
. Cultural differences in counting are sometimes used as a
shibboleth
A shibboleth (; hbo, , šībbōleṯ) is any custom or tradition, usually a choice of phrasing or even a single word, that distinguishes one group of people from another. Shibboleths have been used throughout history in many societies as passwor ...
, particularly to distinguish nationalities in war time. These form a plot point in the film ''
Inglourious Basterds
''Inglourious Basterds'' is a 2009 war film written and directed by Quentin Tarantino, starring Brad Pitt, Christoph Waltz, Michael Fassbender, Eli Roth, Diane Kruger, Daniel Brühl, Til Schweiger and Mélanie Laurent. The film tells an alter ...
,'' by
Quentin Tarantino
Quentin Jerome Tarantino (; born March 27, 1963) is an American film director, writer, producer, and actor. His films are characterized by stylized violence, extended dialogue, profanity, Black comedy, dark humor, Nonlinear narrative, non-lin ...
, and in the book ''Pi in the Sky,'' by
John D. Barrow
John David Barrow (29 November 1952 – 26 September 2020) was an English cosmologist, theoretical physicist, and mathematician. He served as Gresham Professor of Geometry at Gresham College from 2008 to 2011. Barrow was also a writer of pop ...
.
Asia
Finger-counting systems in use in many regions of Asia allow for counting to 12 by using a single hand. The thumb acts as a pointer touching the three
finger bones of each finger in turn, starting with the outermost bone of the
little finger
The little finger, or pinkie, also known as the baby finger, fifth digit, or pinky finger, is the most ulnar and smallest digit of the human hand, and next to the ring finger.
Etymology
The word "pinkie" is derived from the Dutch word ''pink ...
. One hand is used to count numbers up to 12. The other hand is used to display the number of completed base-12s. This continues until twelve dozen is reached, therefore 144 is counted.
[Translated from the French by David Bellos, E.F. Harding, Sophie Wood and Ian Monk. Ifrah supports his thesis by quoting idiomatic phrases from languages across the entire world.][It is actually possible to count to 156, as one hand will represent 144, with the other having 12]
Chinese number gestures
Chinese number gestures are a method to signify the natural numbers one through ten using one hand. This method may have been developed to bridge the many varieties of Chinese—for example, the numbers 4 () and 10 () are hard to distinguish ...
count up to 10 but can exhibit some regional differences.
In Japan, counting for oneself begins with the palm of one hand open. Like in East Slavic countries, the thumb represents number 1; the little finger is number 5. Digits are folded inwards while counting, starting with the thumb. A closed palm indicates number 5. By reversing the action, number 6 is indicated by extending the little finger. A return to an open palm signals the number 10. However to indicate numerals to others, the hand is used in the same manner as an English speaker. The index finger becomes number 1; the thumb now represents number 5. For numbers above five, the appropriate number of fingers from the other hand are placed against the palm. For example, number 7 is represented by the index and middle finger pressed against the palm of the open hand. Number 10 is displayed by presenting both hands open with outward palms.
In Korea,
Chisanbop
Chisanbop or chisenbop (from Korean ''chi (ji)'' finger + ''sanpŏp (sanbeop)'' calculation 지산법/指算法), sometimes called Fingermath, is an abacus-like finger counting method used to perform basic mathematical operations. According to ' ...
allows for signing any number between 0 and 99.
Western world
In the
Western world
The Western world, also known as the West, primarily refers to the various nations and state (polity), states in the regions of Europe, North America, and Oceania. a finger is raised for each unit. While there are extensive differences between and even within countries, there are, generally speaking, two systems. The main difference between the two systems is that the "German" or "French" system starts counting with the thumb, while the "American" system starts counting with the index finger.
In the system used for example in Germany and France, the
thumb
The thumb is the first digit of the hand, next to the index finger. When a person is standing in the medical anatomical position (where the palm is facing to the front), the thumb is the outermost digit. The Medical Latin English noun for thumb ...
represents 1, the thumb plus the
index finger
The index finger (also referred to as forefinger, first finger, second finger, pointer finger, trigger finger, digitus secundus, digitus II, and many other terms) is the second digit of a human hand. It is located between the thumb and the mid ...
represents 2, and so on, until the thumb plus the index,
middle,
ring
Ring may refer to:
* Ring (jewellery), a round band, usually made of metal, worn as ornamental jewelry
* To make a sound with a bell, and the sound made by a bell
:(hence) to initiate a telephone connection
Arts, entertainment and media Film and ...
, and
little finger
The little finger, or pinkie, also known as the baby finger, fifth digit, or pinky finger, is the most ulnar and smallest digit of the human hand, and next to the ring finger.
Etymology
The word "pinkie" is derived from the Dutch word ''pink ...
s represents 5. This continues on to the other hand, where the entire one hand plus the thumb of the other hand means 6, and so on.
In the system used in
the Americas
The Americas, which are sometimes collectively called America, are a landmass comprising the totality of North America, North and South America. The Americas make up most of the land in Earth's Western Hemisphere and comprise the New World. ...
, the index finger represents 1; the index and middle fingers represents 2; the index, middle and ring fingers represents 3; the index, middle, ring, and little fingers represents 4; and the four fingers plus the thumb represents 5. This continues on to the other hand, where the entire one hand plus the index finger of the other hand means 6, and so on.
File:Thumb up.JPG, European starting point: one thumb up
File:Index finger = to attention.JPG, American starting point: index finger up
File:Little finger 3.JPG, Middle East starting point: one pinky up
By base
Binary
''See also :
Finger binary
Finger binary is a system for counting and displaying binary numbers on the fingers of either or both hands. Each finger represents one binary digit or bit. This allows counting from zero to 31 using the fingers of one hand, or 1023 using both: ...
''
Senary
''See also :
Senary#Finger counting''
In senary finger counting, one hand represents ones' place and the other hand represents
six
6 is a number, numeral, and glyph.
6 or six may also refer to:
* AD 6, the sixth year of the AD era
* 6 BC, the sixth year before the AD era
* The month of June
Science
* Carbon, the element with atomic number 6
* 6 Hebe, an asteroid
People ...
's place; it counts up to 55
senary (35
decimal). Two related representations can be expressed: wholes and sixths (counts up to 5.5 by sixths), sixths and
thirty-sixths (counts up to 0.55 by thirty-sixths).
For example, "12" (left 1 right 2) can represent eight (12 senary), four-thirds (1.2 senary) or two-ninths (0.12 senary).
Other body-based counting systems
Undoubtedly the
decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...
(base-10) counting system came to prominence due to the widespread use of finger counting, but many other counting systems have been used throughout the world. Likewise,
base-20
vigesimal () or base-20 (base-score) numeral system is based on twenty (in the same way in which the decimal numeral system is based on ten). '' Vigesimal'' is derived from the Latin adjective '' vicesimus'', meaning 'twentieth'.
Places
In ...
counting systems, such as used by the
Pre-Columbian
In the history of the Americas, the pre-Columbian era spans from the original settlement of North and South America in the Upper Paleolithic period through European colonization, which began with Christopher Columbus's voyage of 1492. Usually, th ...
Mayan
Mayan most commonly refers to:
* Maya peoples, various indigenous peoples of Mesoamerica and northern Central America
* Maya civilization, pre-Columbian culture of Mesoamerica and northern Central America
* Mayan languages, language family spoken ...
, are likely due to counting on fingers and toes. This is suggested in the languages of Central Brazilian tribes, where the word for twenty often incorporates the word for "feet". Other languages using a base-20 system often refer to twenty in terms of "men", that is, 1 "man" = 20 "fingers and toes". For instance, the Dene-Dinje tribe of North America refer to 5 as "my hand dies", 10 as "my hands have died", 15 as "my hands are dead and one foot is dead", and 20 as "a man dies".
Even the French language today shows remnants of a
Gaulish
Gaulish was an ancient Celtic languages, Celtic language spoken in parts of Continental Europe before and during the period of the Roman Empire. In the narrow sense, Gaulish was the language of the Celts of Gaul (now France, Luxembourg, Belgium ...
base-20 system in the names of the numbers from 60 through 99. For example, sixty-five is (literally, "sixty
ndfive"), while seventy-five is (literally, "sixty
ndfifteen").
The
Yuki language in
California
California is a U.S. state, state in the Western United States, located along the West Coast of the United States, Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the List of states and territori ...
and the Pamean languages in
Mexico
Mexico (Spanish: México), officially the United Mexican States, is a country in the southern portion of North America. It is bordered to the north by the United States; to the south and west by the Pacific Ocean; to the southeast by Guatema ...
have
octal (base-8) systems because the speakers count using the spaces between their fingers rather than the fingers themselves.
In languages of New Guinea and Australia, such as the
Telefol language
Telefol is a language spoken by the Telefol people in Papua New Guinea, notable for possessing a base-27 numeral system.
History
The Iligimin people also spoke Telefol, but they were defeated by the Telefol proper.
Orthography
Single and r ...
of
Papua New Guinea
Papua New Guinea (abbreviated PNG; , ; tpi, Papua Niugini; ho, Papua Niu Gini), officially the Independent State of Papua New Guinea ( tpi, Independen Stet bilong Papua Niugini; ho, Independen Stet bilong Papua Niu Gini), is a country i ...
, body counting is used, to give higher base counting systems, up to base-27. In Muralug Island, the counting system works as follows: Starting with the little finger of the left hand, count each finger, then for six through ten, successively touch and name the left wrist, left elbow, left shoulder, left breast and sternum. Then for eleven through to nineteen count the body parts in reverse order on the right side of the body (with the right little finger signifying nineteen). A variant among the Papuans of New Guinea uses on the left, the fingers, then the wrist, elbow, shoulder, left ear and left eye. Then on the right, the eye, nose, mouth, right ear, shoulder, wrist and finally, the fingers of the right hand, adding up to 22 ''anusi'' which means little finger.
See also
*
Finger binary
Finger binary is a system for counting and displaying binary numbers on the fingers of either or both hands. Each finger represents one binary digit or bit. This allows counting from zero to 31 using the fingers of one hand, or 1023 using both: ...
*
Chisanbop
Chisanbop or chisenbop (from Korean ''chi (ji)'' finger + ''sanpŏp (sanbeop)'' calculation 지산법/指算法), sometimes called Fingermath, is an abacus-like finger counting method used to perform basic mathematical operations. According to ' ...
*
Tally marks
Tally marks, also called hash marks, are a unary numeral system ( arguably).
They are a form of numeral used for counting. They are most useful in counting or tallying ongoing results, such as the score in a game or sport, as no intermediate ...
*
Prehistoric numerals
Counting in prehistory was first assisted by using body parts, primarily the fingers. This is reflected in the etymology of certain number names, such as in the names of ''ten'' and ''hundred'' in the Proto-Indo-European numerals, both contain ...
*
Chinese number gestures
Chinese number gestures are a method to signify the natural numbers one through ten using one hand. This method may have been developed to bridge the many varieties of Chinese—for example, the numbers 4 () and 10 () are hard to distinguish ...
Notes
References
* ; 2nd edition, Brown University Press, 1957; reprint, New York: Dover publications, 1969; reprint, New York: Barnes and Noble Books, 1993.
*{{cite book, last=Wedell, first=Moritz, title=Was zählt, year=2012, publisher=Böhlau, location=Köln, Weimar, Wien, isbn=978-3-412-20789-2, pages=15–63, author-link=Actio - loquela digitorum - computatio
External links
Counting in American Sign LanguageCounting with your fingers in FranceFinger Counting Questionnaire*
Yutaka Nishiyama
is a Japanese mathematician and professor at the Osaka University of Economics, where he teaches mathematics and information. He is known as the "boomerang professor". He has written nine books about the mathematics in daily life. The most recen ...
Counting With The Fingers.
Articles containing video clips