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Finger-counting, or dactylonomy, is the act of counting along one's fingers. Though marginalized in modern societies by Arabic numerals, formerly different systems flourished in many cultures,[Note 1][Note 2] including educated methods far more sophisticated than the one-by-one finger count taught today in preschool education.
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.
A person indicating a numeral to another will hold up their fingers to signal the specific number. For example, people from North America and the United Kingdom will raise their index, middle, and ring fingers vertically to signal the number 3.
For Continental Europeans, the thumb represents the first digit to be counted (number 1), as opposed to the index finger in North America and the UK. The index finger is number 2 through to the little finger as number 5. Fingers are generally extended while counting, beginning at the thumb and finishing at the little finger. For example, Europeans would use their thumb, and index, middle and ring fingers to express the number 4, whereas in North America and the UK they would use their index, middle, ring, and little finger.
Finger-counting systems in use in many regions of Asia allow the 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. 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.[Note 3]
Chinese number gestures 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 an extended thumb. 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.
Complex systems of dactylonomy were used in the ancient world. The Greco-Roman author Plutarch, in his Lives, mentions finger counting as being used in Persia in the first centuries AD, so the source of the system may lie in Iran. The practice 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, more than fourteen centuries ago. In one tradition as reported by Yusayra the Prophet Muhammad 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 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) 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 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 in his seminal Summa de arithmetica (1494).
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- Georges Ifrah notes that humans learned to count on their hands. Ifrah shows, for example, a picture of Boethius (who lived 480–524 or 525) reckoning on his fingers in Ifrah 2000, p. 48.
- Neugebauer 1952, p. 9 notes that as early as the 3rd millennium BCE, in Egypt's Old Kingdom, in the Pyramid texts' "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.
- 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.
- Barrow, John D. (1993). Pi in the Sky. Penguin. p. 26. ISBN 978-0140231090.
- "Dactylonomy". Laputan Logic. 16 November 2006. Retrieved May 12, 2012.
- Pika,Simone; Nicoladis, Elena; Marentette, Paula (January 2009). "How to Order a Beer: Cultural Differences in the Use of Conventional Gestures for Numbers". Journal of Cross-Cultural Psychology 40 (1): 70–80. doi:10.1177/0022022108326197.
- Ifrah, Georges (2000), The Universal History of Numbers: From prehistory to the invention of the computer., John Wiley and Sons, p. 48, ISBN 0-471-39340-1
- Macey, Samuel L. (1989). The Dynamics of Progress: Time, Method, and Measure. Atlanta, Georgia: University of Georgia Press. p. 92. ISBN 978-0-8203-3796-8.
- This is actual count numbers to 156 - first hand is used for 144 + 12 with second hand
- Namiko Abe. "Counting on one's fingers" (in Japanese). About.com. Retrieved May 12, 2012.
- Bloom, Jonathan M. (2001). "Hand sums: The ancient art of counting with your fingers". Yale University Press. Retrieved May 12, 2012.
- Julius Ruska, Arabische Texte über das Fingerrechnen, available at Digilibrary.de.
- Neugebauer, Otto E. (1952), The Exact Sciences in Antiquity, Princeton University Press, ISBN 1-56619-269-2; 2nd edition, Brown University Press, 1957; reprint, New York: Dover publications, 1969; reprint, New York: Barnes and Noble Books, 1993.
- Wedell, Moritz (2012). Was zählt. Köln, Weimar, Wien: Böhlau. pp. 15–63. ISBN 978-3-412-20789-2.