Finger counting

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Finger counting, or dactylonomy, is the art 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 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.[1][2]

Cultural differences

English-speaking countries

For English speakers, primarily in North America and the United Kingdom, and occasionally in Australia, the count to 5 starts with the extension of the index finger (number 1) and continues to the little finger (number 4). The extension of the thumb indicates five. The process is repeated on the other hand for numbers up to 10. For example, the number 7 is indicated by an open palm with all five digits extended on one hand, the extension of the index and middle finger on the other.

A person indicating a numeral to another will hold up their fingers to signal the specific number. For example, an English speaker will raise their index, middle, and ring fingers vertically to signal the number 3.[3]

Europe

For Western Europeans, such as Germans, Italians, Belgians, Austrians, the Swiss, the Dutch, the Spanish, the Portuguese, or the French, the thumb represents the first digit to be counted (number 1). 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, Western Europeans would use their thumb, and index, middle and ring fingers to express the number 4.[3]

Eastern Europeans generally use the same system as Western Europeans. However, for Russians and citizens of former USSR countries, counting begins with all digits extended. Numbers are expressed by folding fingers and the thumb inwards.

Asia

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.[4][Note 3][5]

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 Eastern Europe, 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 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.[6] Number 10 is displayed by presenting both hands open with outward palms.

Sports

In some sports, like in individual time-trials in the Tour de France, an official gives a countdown on the fingers of his hand to a starting cyclist. At the start, there is a countdown from 5 to 1. The numbers in this system are given with the following system:

  • 5: All fingers including the thumb
  • 4: All fingers excluding the thumb
  • 3: Thumb, index and middle finger
  • 2: Index and middle finger
  • 1: Thumb, but sometimes also the index finger
  • "Top": All fingers are extended again, but the hand is held horizontal and moved away from the rider. This signals the rider can start.

Piano

In the piano pedagogy, fingers are numbered from the thumbs (numbered 1), counting outward to the little finger (numbered 5).


Historical counting

Complex systems of dactylonomy were used in the ancient world.[7] This counting was in use in Persia in the + first century, and thus may have originated there; it continued in the Islamic world through the Middle Ages, and is mentioned in poetry and the Quran.[7] 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",[2][7] 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).

See also

Wikimedia Commons has media related to Counting gestures.

Notes

  1. ↑ 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.
  2. ↑ 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.
  3. ↑ 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.

References

  1. ↑ Barrow, John D. (1993). Pi in the Sky. Penguin. p. 26. ISBN 978-0140231090. 
  2. ↑ 2.0 2.1 "Dactylonomy". Laputan Logic. 16 November 2006. Retrieved May 12, 2012. 
  3. ↑ 3.0 3.1 Pika,Simone; Nicoladis, Elena; and 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. 
  4. ↑ 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 
  5. ↑ 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. 
  6. ↑ Namiko Abe. "Counting on one's fingers" (in Japanese url=http://japanese.about.com/library/weekly/aa112198.htm). About.com. 
  7. ↑ 7.0 7.1 7.2 Bloom, Jonathan M. (2001). "Hand sums: The ancient art of counting with your fingers". Yale University Press. Retrieved May 12, 2012. 
  • 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. 

Further reading

External links

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