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Finger-counting

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Finger-counting or dactylonomy is counting using the fingers. Various systems have existed over time and across cultures, although many have declined in use because of the spread of Arabic numerals.

Woman counts to ten in English, using her fingers.

Finger-counting can serve as a form of manual communication, particularly in marketplace trading – including hand signaling during open outcry in floor trading – and also in hand games, such as morra.

Finger-counting goes back to ancient Egypt at least.[Note 1]

Historical counting

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Round tessera showing left hand with middle two fingers folded towards palm
Roman tessera with finger gesture
Round tessera with Roman numeral IIII
Reverse of tessera, showing number 4

Dactylonomy was used in the ancient world, probably originating in Egypt as early as the Old Kingdom (3rd millennium BCE).[1]

The same system was used in the Roman Empire and in the Islamic world for centuries. Algorithms for arithmetic using this system are also documented.[1]

In the Roman Empire, this system is mentioned starting in the 3rd century BCE, but not described in detail.[2] However, it appears in various media, such as tesserae and sculptural reliefs.[3][4] Bede described the system in 725 CE in his "Tractatus de computo, vel loquela per gestum digitorum";[5][6] it 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 Summa de arithmetica (1494).

Finger positions used for counting up to 9999 from Luca Pacioli's 1494 Summa de arithmetica, based on the earlier Roman system.

Plutarch's Lives says that finger counting was used in Persia in the first centuries CE.[citation needed]

The same system (using the opposite hand) was also used in the Islamic world.[1] The earliest reference to it may go back to the early days of Islam during the early 600s.[6] In one hadith, Muhammad enjoined his female companions to count using their fingers واعقدن بالأنامل.[7] In Arabic, dactylonomy is called حساب العقود 'number reckoning by finger folding'. It was well known in the Arabic-speaking world and was often mentioned in Classical Arabic literature. For examples, 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 had special technical terms such as Kas' (القصع) '29', Dabth (الـضَـبْـث) '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.[citation needed]

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 and one by Abul-Hasan Al-Maghribi.[8]

By country or region

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Finger-counting is studied by ethnomathematics. Cultural differences 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 book Pi in the Sky, by John D. Barrow.[9][5]

Asia

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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. 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.[10][11]

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.[12] A closed palm indicates number 5. By reversing the action, number 6 is indicated by extending the little finger.[13] 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.[14] Number 10 is displayed by presenting both hands open with outward palms.

In Korea, Chisanbop allows for signing any number between 0 and 99.

Western world

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In the Western world 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.[15]

In the system used for example in Germany and France, the thumb represents 1, the thumb plus the index finger represents 2, and so on, until the thumb plus the index, middle, ring, and little fingers 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 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.

In the United Kingdom, counting starting with the thumb and counting starting with the index finger are both equally acceptable.

Non-decimal finger counting

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In finger binary (base 2), each finger represents a different bit, for example thumb for 1, index for 2, middle for 4, ring for 8, and pinky for 16. This allows counting from zero to 31 using the fingers of one hand, or 1023 using both.

In senary finger counting (base 6), one hand represents the units (0 to 5) and the other hand represents multiples of 6. It counts up to 55senary (35decimal). 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

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Undoubtedly the decimal (base-10) counting system came to prominence due to the widespread use of finger counting[citation needed], but many other counting systems have been used throughout the world. Likewise, base-20 counting systems, such as used by the Pre-Columbian Mayan, 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".[18] 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".[19]

Even the French language today shows remnants of a Gaulish base-20 system in the names of the numbers from 60 through 99. For example, sixty-five is soixante-cinq (literally, "sixty [and] five"), while seventy-five is soixante-quinze (literally, "sixty [and] fifteen"). Eighty is quatre-vingt (literally "four (times) twenty") bug not in France, not in Switzerland or Belgium for European French speaking countries. Ninety is quatre-vingt-dix (literally "four (times) twenty (and) ten"), only in France too for Europe.

The Yuki language in California and the Pamean languages[20] in Mexico have octal (base-8) systems because the speakers count using the spaces between their fingers rather than the fingers themselves.[21] More specifically, the Yuki were described as counting using sticks placed between the fingers.[22]

Counting to 27 with the body-part tally used by the Sibil Valley people of Western New Guinea[23]

In languages of New Guinea and Australia, such as the Telefol language of Papua New Guinea, 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.[24]

See also

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Notes

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  1. ↑ 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.

References

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  1. 1 2 3 Ifrah, Georges; Ifrah, Georges (2000). The universal history of numbers: from prehistory to the invention of the computer. New York: Wiley. pp. 52–61. ISBN 978-0-471-37568-5.
  2. ↑ Minaud, Gérard (2006). "Des doigts pour le dire: Le comput digital et ses symboles dans l'iconographie romaine". Histoire & mesure. XXI (1): 3–34. doi:10.4000/histoiremesure.1534. ISSN 0982-1783.
  3. ↑ AlföLdi-Rosenbaum, Elisabeth (1971-12-31). "The Finger Calculus in Antiquity and in the Middle Ages Studies on Roman Game Counters I". Frühmittelalterliche Studien. 5 (1): 1–9. doi:10.1515/9783110242058.1. ISSN 1613-0812.
  4. ↑ Bowes, Kimberly Diane (2025). Surviving Rome: the economic lives of the ninety percent. Princeton: Princeton University Press. pp. 33–36. ISBN 978-0-691-27335-8.
  5. 1 2 "Dactylonomy". Laputan Logic. 16 November 2006. Archived from the original on 2004-10-17. Retrieved May 12, 2012.
  6. 1 2 Bloom, Jonathan M. (2001). "Hand sums: The ancient art of counting with your fingers". Yale University Press. Archived from the original on September 29, 2011. Retrieved May 12, 2012.
  7. ↑ Abū ʿĪsā al-Tirmidhī, سنن الترمذي al-Kutub al-Sittah
  8. ↑ Julius Ruska, Arabische Texte über das Fingerrechnen, available at Digilibrary.de.
  9. ↑ Barrow, John D. (1993). Pi in the Sky. Penguin. p. 26. ISBN 978-0140231090.
  10. ↑ Ifrah, Georges (2000). The Universal History of Numbers: From prehistory to the invention of the computer. Translated by Bellos, David; Harding, E.F.; Wood, Sophie; Monk, Ian. John Wiley and Sons. p. 48. ISBN 0-471-39340-1.
  11. ↑ 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.
  12. ↑ Jagatia, Anand (2 September 2021). "How the way you count reveals more than you think". BBC Future.
  13. ↑ Borgers, Marie (September 13, 2021). "How to Count in Japanese Numbers". VOYAPON.
  14. ↑ Namiko Abe. "Counting on one's fingers" (in Japanese). About.com. Archived from the original on January 20, 2013. Retrieved May 12, 2012.
  15. ↑ 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. S2CID 11209951.
  16. ↑ "What's A-O.K. in the U.S.A. Is Lewd and Worthless Beyond". The New York Times. 18 August 1996. Retrieved 15 November 2018.
  17. ↑ Merritt, Anne (22 September 2010). "10 common gestures easily misunderstood abroad". Matador Network. Retrieved 17 September 2018.
  18. ↑ Flegg, Graham (1989). Numbers Through the Ages. Macmillan International Higher Education. p. 34. ISBN 9781349201778.
  19. ↑ Menninger, Karl (1992). Number Words and Number Symbols. Dover Publications. p. 35. ISBN 9780486319773.
  20. ↑ Avelino, Heriberto (2006). "The typology of Pame number systems and the limits of Mesoamerica as a linguistic area" (PDF). Linguistic Typology. 10 (1): 41–60. doi:10.1515/LINGTY.2006.002. S2CID 20412558.
  21. ↑ Marcia Ascher. "Ethnomathematics: A Multicultural View of Mathematical Ideas". The College Mathematics Journal. JSTOR 2686959.
  22. ↑ Overmann, Karenleigh A. (2025). Cultural Number Systems: A Sourcebook. Springer. ISBN 978-3-031-83382-3.
  23. ↑ Barry Craig (June 2010). "Tally Systems of the Upper Sepick and Central New Guinea" (PDF). Macmillan International Higher Education. p. 3.
  24. ↑ Flegg, Graham (1989). Numbers Through the Ages. Macmillan International Higher Education. p. 36. ISBN 9781349201778.
  • Neugebauer, Otto E. (1952). The Exact Sciences in Antiquity. Acta Historica Scientiarum Naturalium et Medicinalium. Vol. 9. Princeton University Press. pp. 1–191. ISBN 1-56619-269-2. PMID 14884919. {{cite book}}: ISBN / Date incompatibility (help); 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.
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