Finger counting

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,^[1][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.^[3][4]

Cultural differences

In English-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.^[5]

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.^{[citation needed]}

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.^[6][7]

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.^[8] To display ten, one presents both hands open and palm outwards.

Historical counting

Complex systems of dactylonomy were used in the ancient world.^[9] 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.^[9] A very similar form is presented by the English monk and historian Bede in the first chapter of his De temporum ratione, (725), entitled "De computa vel loquela digitorum",^[9][4] 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

• Finger binary
• Chisanbop
• Tally marks
• Prehistoric numerals
• Colombian numerals
• Chinese number 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. ^ John D. Barrow, Pi in the Sky, Penguin 1993, p. 26
4. ^ ^{a b} Dactylonomy, Laputan Logic
5. ^ See Simone Pika, Elena Nicoladis, and Paula Marentette, "How to Order a Beer: Cultural Differences in the Use of Conventional Gestures for Numbers," Journal of Cross-Cultural Psychology, Vol. 40, No. 1, 70-80 (2009).
6. ^ Ifrah 2000
7. ^ Macey, Samuel L. (1989). The Dynamics of Progress: Time, Method, and Measure. Atlanta, Georgia: University of Georgia Press. pp. 92. ISBN 978-0-8203-3796-8. http://books.google.com/books?id=xlzCWmXguwsC&pg=PA92&lpg=PA92. 
8. ^ Counting on one's fingers, About.com, Japanese Language, Namiko Abe
9. ^ ^{a b c} "Hand sums: The ancient art of counting with your fingers", Jonathan M. Bloom, excerpt from Paper before Print: The History and Impact of Paper in the Islamic World, 2001, Yale University Press

References

• 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 . 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.

• 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.

External links

• counting in American Sign Language

Further reading

• The Universal History of Numbers, Georges Ifrah