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Tally marks, also called hash marks, are a
unary numeral system
The unary numeral system is the simplest numeral system to represent natural numbers: to represent a number ''N'', a symbol representing 1 is repeated ''N'' times.
In the unary system, the number 0 (zero) is represented by the empty string, that ...
(
arguably).
They are a form of
numeral used for
counting. They are most useful in
counting or tallying ongoing results, such as the
score
Score or scorer may refer to:
*Test score, the result of an exam or test
Business
* Score Digital, now part of Bauer Radio
* Score Entertainment, a former American trading card design and manufacturing company
* Score Media, a former Canadian ...
in a game or sport, as no intermediate results need to be erased or discarded.
However, because of the length of large numbers, tallies are not commonly used for static text. Notched sticks, known as
tally stick
A tally stick (or simply tally) was an ancient memory aid device used to record and document numbers, quantities and messages. Tally sticks first appear as animal bones carved with notches during the Upper Palaeolithic; a notable example is the ...
s, were also historically used for this purpose.
Early history
Counting aids other than body parts appear in the
Upper Paleolithic
The Upper Paleolithic (or Upper Palaeolithic) is the third and last subdivision of the Paleolithic or Old Stone Age. Very broadly, it dates to between 50,000 and 12,000 years ago (the beginning of the Holocene), according to some theories coin ...
. The oldest
tally stick
A tally stick (or simply tally) was an ancient memory aid device used to record and document numbers, quantities and messages. Tally sticks first appear as animal bones carved with notches during the Upper Palaeolithic; a notable example is the ...
s date to between 35,000 and 25,000 years ago, in the form of notched bones found in the context of the
European Aurignacian
The Aurignacian () is an archaeological industry of the Upper Paleolithic
associated with European early modern humans (EEMH) lasting from 43,000 to 26,000 years ago. The Upper Paleolithic developed in Europe some time after the Levant, where ...
to
Gravettian
The Gravettian was an archaeological industry of the European Upper Paleolithic that succeeded the Aurignacian circa 33,000 years BP. It is archaeologically the last European culture many consider unified, and had mostly disappeared by 2 ...
and in Africa's
Late Stone Age
The Later Stone Age (LSA) is a period in African prehistory that follows the Middle Stone Age.
The Later Stone Age is associated with the advent of modern human behavior in Africa, although definitions of this concept and means of studying it a ...
.
The so-called ''
Wolf bone
A tally stick (or simply tally) was an ancient memory aid device used to record and document numbers, quantities and messages. Tally sticks first appear as animal bones carved with notches during the Upper Palaeolithic; a notable example is the ...
'' is a prehistoric artifact discovered in 1937 in
Czechoslovakia
, rue, Чеськословеньско, , yi, טשעכאסלאוואקיי,
, common_name = Czechoslovakia
, life_span = 1918–19391945–1992
, p1 = Austria-Hungary
, image_p1 ...
during excavations at
Vestonice,
Moravia
Moravia ( , also , ; cs, Morava ; german: link=yes, Mähren ; pl, Morawy ; szl, Morawa; la, Moravia) is a historical region in the east of the Czech Republic and one of three historical Czech lands, with Bohemia and Czech Silesia.
The ...
, led by
Karl Absolon. Dated to the
Aurignacian
The Aurignacian () is an archaeological industry of the Upper Paleolithic
associated with European early modern humans (EEMH) lasting from 43,000 to 26,000 years ago. The Upper Paleolithic developed in Europe some time after the Levant, where ...
, approximately 30,000 years ago, the bone is marked with 55 marks which may be
tally marks. The head of an ivory
Venus figurine
A Venus figurine is any Upper Palaeolithic statuette portraying a woman, usually carved in the round.Fagan, Brian M., Beck, Charlotte, "Venus Figurines", ''The Oxford Companion to Archaeology'', 1996, Oxford University Press, pp. 740–741 Most ...
was excavated close to the bone.
The
Ishango bone, found in the
Ishango region of the present-day
Democratic Republic of Congo
The Democratic Republic of the Congo (french: République démocratique du Congo (RDC), colloquially "La RDC" ), informally Congo-Kinshasa, DR Congo, the DRC, the DROC, or the Congo, and formerly and also colloquially Zaire, is a country in ...
, is dated to over 20,000 years old. Upon discovery, it was thought to portray a series of
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
s. In the book ''How Mathematics Happened: The First 50,000 Years'', Peter Rudman argues that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after
10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes that "no attempt has been made to explain why a tally of something should exhibit multiples of two,
prime numbers
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
between 10 and 20, and some numbers that are almost multiples of 10."
Alexander Marshack examined the Ishango bone microscopically, and concluded that it may represent a six-month
lunar calendar
A lunar calendar is a calendar based on the monthly cycles of the Moon's phases ( synodic months, lunations), in contrast to solar calendars, whose annual cycles are based only directly on the solar year. The most commonly used calendar, t ...
.
[Marshack, Alexander (1991): ''The Roots of Civilization'', Colonial Hill, Mount Kisco, NY.]
Clustering
![Unary8](https://upload.wikimedia.org/wikipedia/commons/8/8d/Unary8.svg)
Tally marks are typically clustered in groups of five for legibility. The cluster size 5 has the advantages of (a) easy conversion into decimal for higher arithmetic operations and (b) avoiding error, as humans can far more easily
correctly identify a cluster of 5 than one of 10.
File:Tally marks.svg, Tally marks used in most of Europe
Europe is a large peninsula conventionally considered a continent in its own right because of its great physical size and the weight of its history and traditions. Europe is also considered a Continent#Subcontinents, subcontinent of Eurasia ...
, the Anglosphere
The Anglosphere is a group of English-speaking nations that share historical and cultural ties with England, and which today maintain close political, diplomatic and military co-operation. While the nations included in different sources vary, t ...
, and Southern Africa
Southern Africa is the southernmost subregion of the African continent, south of the Congo and Tanzania. The physical location is the large part of Africa to the south of the extensive Congo River basin. Southern Africa is home to a number o ...
. In some variants, the diagonal/horizontal slash is used on its own when five or more units are added at once.
File:Tally marks 3.svg, Cultures using Chinese characters
Chinese characters () are logograms developed for the writing of Chinese. In addition, they have been adapted to write other East Asian languages, and remain a key component of the Japanese writing system where they are known as ''kanji ...
tally by forming the character 正, which consists of five stroke
A stroke is a medical condition in which poor blood flow to the brain causes cell death. There are two main types of stroke: ischemic, due to lack of blood flow, and hemorrhagic, due to bleeding. Both cause parts of the brain to stop functionin ...
s.[Ken Lunde, Daisuke Miura]
''L2/16-046: Proposal to encode five ideographic tally marks''
2016
File:Tally marks 2.svg, Tally marks used in France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...
, Portugal
Portugal, officially the Portuguese Republic ( pt, República Portuguesa, links=yes ), is a country whose mainland is located on the Iberian Peninsula of Southwestern Europe, and whose territory also includes the Atlantic archipelagos of ...
, Spain
, image_flag = Bandera de España.svg
, image_coat = Escudo de España (mazonado).svg
, national_motto = ''Plus ultra'' (Latin)(English: "Further Beyond")
, national_anthem = (English: "Royal March")
, i ...
, and their former colonies, including Latin America
Latin America or
* french: Amérique Latine, link=no
* ht, Amerik Latin, link=no
* pt, América Latina, link=no, name=a, sometimes referred to as LatAm is a large cultural region in the Americas where Romance languages — languages derived f ...
. 1 to 5 and so on. These are most commonly used for registering scores in card game
A card game is any game using playing cards as the primary device with which the game is played, be they traditional or game-specific.
Countless card games exist, including families of related games (such as poker). A small number of card ...
s, like Truco
Truco, a variant of Truc, is a trick-taking card game originally from Valencia and the Balearic Islands, popular in South America and Italy. It is usually played using a Spanish deck. Two people may play, or two teams of two or three players ...
File:Dot and line tally marks.jpg, In the dot and line (or dot-dash) tally, dots represent counts from 1 to 4, lines 5 to 8, and diagonal lines 9 and 10. This method is commonly used in forestry
Forestry is the science and craft of creating, managing, planting, using, conserving and repairing forests, woodlands, and associated resources for human and environmental benefits. Forestry is practiced in plantations and natural stands. Th ...
and related fields.
Writing systems
Roman numerals
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...
, the
Brahmi
Brahmi (; ; ISO 15919, ISO: ''Brāhmī'') is a writing system of ancient South Asia. "Until the late nineteenth century, the script of the Aśokan (non-Kharosthi) inscriptions and its immediate derivatives was referred to by various names such ...
and
Chinese numerals
Chinese numerals are words and characters used to denote numbers in Chinese.
Today, speakers of Chinese use three written numeral systems: the system of Arabic numerals used worldwide, and two indigenous systems. The more familiar indigenous sy ...
for one through three (一 二 三), and
rod numerals
Counting rods () are small bars, typically 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any integer or rational number.
The written fo ...
were derived from tally marks, as possibly was the
ogham
Ogham (Modern Irish: ; mga, ogum, ogom, later mga, ogam, label=none ) is an Early Medieval alphabet used primarily to write the early Irish language (in the "orthodox" inscriptions, 4th to 6th centuries AD), and later the Old Irish langua ...
script.
Base 1 arithmetic
notation system is a
unary positional system
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which th ...
similar to tally marks. It is rarely used as a practical base for
counting due to its difficult readability.
The numbers 1, 2, 3, 4, 5, 6 ... would be represented in this system as
[.]
:0, 00, 000, 0000, 00000, 000000 ...
Base 1 notation is widely used in
type numbers of flour; the higher number represents a higher grind.
Unicode
In 2015,
Ken Lunde
Ken Roger Lunde (, born 12 August 1965 in Madison, Wisconsin)Lunde, 2008. is an American specialist in information processing for East Asian languages.
Academic Background
Ken majored in linguistics at University of Wisconsin–Madison in 1985, w ...
and Daisuke Miura submitted a proposal to encode various systems of tally marks in the
Unicode Standard
Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, whic ...
.
However, the box tally and dot-and-dash tally characters were not accepted for encoding, and only the five
ideographic
An ideogram or ideograph (from Greek "idea" and "to write") is a graphic symbol that represents an idea or concept, independent of any particular language, and specific words or phrases. Some ideograms are comprehensible only by familiarit ...
tally marks (正 scheme) and two Western tally digits were added to the Unicode Standard in the
Counting Rod Numerals
Counting Rod Numerals is a Unicode block containing traditional Chinese counting rod symbols, which mathematicians used for calculation in ancient China, Japan, Korea, and Vietnam. The orientation of the Unicode characters follows Song dynasty co ...
block in Unicode version 11.0 (June 2018). Only the tally marks for the numbers 1 and 5 are encoded, and tally marks for the numbers 2, 3 and 4 are intended to be composed from sequences of tally mark 1 at the font level.
See also
Notes
References
{{Reflist, 30em
Elementary mathematics
Mathematical notation
Numeral systems
Numerals
Korean language