Tally marks

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Tally marks on a chalkboard
Counting using tally marks at Hanakapiai Beach. The number shown is 82.

Tally marks, also called hash marks, are a form of numeral used for counting. They can be thought of as a unary numeral system.

They are most useful in counting or tallying ongoing results, such as the score 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 sticks, were also historically used for this purpose.

Early history

Main article:
Prehistoric numerals

Counting aids other than body parts appear in the

European Aurignacian to Gravettian and in Africa's Late Stone Age
.

The so-called

Dolní Věstonice, Moravia, led by Karl Absolon. Dated to the Aurignacian, approximately 30,000 years ago, the bone is marked with 55 marks which may be tally marks. The head of an ivory Venus figurine was excavated close to the bone.[1]

The

prime numbers between 10 and 20, and some numbers that are almost multiples of 10."[2] Alexander Marshack examined the Ishango bone microscopically, and concluded that it may represent a six-month lunar calendar.[3]

Clustering

Various ways to cluster the number 8. The first or fifth mark in each group may be written at an angle to the others for easier distinction. In the fourth example, the fifth stroke "closes out" a group of five, forming a "herringbone". In the fifth row the fifth mark crosses diagonally, forming a "five-bar gate".

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.[citation needed]

  • Tally marks representing (from left to right) the numbers 1, 2, 3, 4 and 5 that was used in most of Europe, the Anglosphere, and Southern Africa.[citation needed] In some variants, the diagonal/horizontal slash is used on its own when five or more units are added at once.
    Tally marks representing (from left to right) the numbers 1, 2, 3, 4 and 5 that was used in most of Europe, the Anglosphere, and Southern Africa.[citation needed] In some variants, the diagonal/horizontal slash is used on its own when five or more units are added at once.
  • Cultures using Chinese characters tally by forming the character 正,[a] which consists of five strokes.[4][5]
    Cultures using
    strokes.[4][5]
  • Tally marks used in France, Portugal, Spain, and their former colonies, including Latin America. 1 to 5 and so on. These are most commonly used for registering scores in card games, like Truco.
    Tally marks used in France, Portugal, Spain, and their former colonies, including Latin America. 1 to 5 and so on. These are most commonly used for registering scores in card games, like Truco.
  • 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 and related fields.[6]
    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 and related fields.[6]

Writing systems

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Roman numerals, the Brahmi and Chinese numerals for one through three (一 二 三), and rod numerals were derived from tally marks, as possibly was the ogham script.[7]

positional system 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[8]

1, 11, 111, 1111, 11111, 111111 ...

Base 1 notation is widely used in type numbers of flour; the higher number represents a higher grind.

Unicode

In 2015,

Unicode Standard.[9] However, the box tally and dot-and-dash tally characters were not accepted for encoding, and only the five ideographic tally marks (正 scheme) and two Western tally digits were added to the Unicode Standard in the Counting Rod Numerals
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.

Counting Rod Numerals[1][2]
Official Unicode Consortium code chart (PDF)
  0 1 2 3 4 5 6 7 8 9 A B C D E F
U+1D36x
𝍠
𝍡
𝍢
𝍣
𝍤
𝍥
𝍦
𝍧
𝍨
𝍩
𝍪
𝍫
𝍬
𝍭
𝍮
𝍯
U+1D37x
𝍰
𝍱
𝍲
𝍳
𝍴
𝍵
𝍶
𝍷
𝍸
Notes
1.^ As of Unicode version 15.1
2.^ Grey areas indicate non-assigned code points

See also

Wikimedia Commons has media related to Tally marks.

Notes

  1. ^ This character was apparently chosen purely due to appropriateness of the physical process of writing it using the conventional stroke-order system—i.e., the physical movements of the strokes have a distinct alternation right-down-right-down-right working down the character, but the semantics of the character have no particular relation to the concept of "5" (neither in the character etymology nor the word etymology, which in languages using Chinese characters are two originally-separate-but-historically-complexly-interacting things). By contrast, the character for "five", 五, which looks like it also has 5 distinct lines, has only 4 strokes when written using conventional stroke-order.)

References

  1. ISBN 978-0-486-42165-0
    , pp. 41-42.
  2. ISBN 978-1-59102-477-4
    .
  3. ^ Marshack, Alexander (1991): The Roots of Civilization, Colonial Hill, Mount Kisco, NY.
  4. doi:10.2307/2683999
  5. ^ Ken Lunde, Daisuke Miura, L2/16-046: Proposal to encode five ideographic tally marks, 2016
  6. ^ Schenck, Carl A. (1898) Forest mensuration. The University Press. (Note: The linked reference appears to actually be "Bulletin of the Ohio Agricultural Experiment Station", Number 302, August 1916)
  7. ^ Macalister, R. A. S., Corpus Inscriptionum Insularum Celticarum Vol. I and II, Dublin: Stationery Office (1945).
  8. ISBN 9780724809400
    .
  9. ^ Lunde, Ken; Miura, Daisuke (30 November 2015). "Proposal to encode tally marks" (PDF). Unicode Consortium.
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