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=                            Tally marks                             =
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                            Introduction
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Tally marks, also called hash marks, are a unary numeral system. They
are a form of numeral used for counting. 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
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Counting aids other than body parts appear in the Upper Paleolithic.
The oldest tally sticks date to between 35,000 and 25,000 years ago,
in the form of notched bones found in the context of the European
Aurignacian to Gravettian and in Africa's Late Stone Age.

The so-called 'Wolf bone' is a prehistoric artifact discovered in 1937
in Czechoslovakia during excavations at Vestonice, 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.

The Ishango bone, found in the Ishango region of the present-day
Democratic Republic of Congo, is dated to over 20,000 years old. Upon
discovery, it was thought to portray a series of prime numbers. 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 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.


                             Clustering
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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, Zimbabwe,
Australia, New Zealand and North America. 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 tally by
forming the character �, which consists of five strokes.
File:Tally marks 2.png|Tally marks used in France, Spain, their former
colonies and Brazil. 1 to 5 and so on. These are most commonly used
for registering scores in card games, like Truco
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 and related
fields.
File:Indian numerals 100AD.svg|Brahmi numerals (lower row) in India in
the 1st century CE


                          Writing systems
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Roman numerals, the Chinese numerals for one through three (� � �),
and rod numerals were derived from tally marks, as possibly was the
ogham script.

Base 1 arithmetic notation system is an unary positional system
similar to tally marks. It is rarely used as a practical base for
counting due to its difficult readability. It is made by the
concatenation of zero.

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
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In 2015, Ken Lunde and Daisuke Miura submitted a proposal to encode
various systems of tally marks in the Unicode Standard. However, the
box tally and dot-and-dash tally characters were not accepted for
encoding, and only the five ideographic tally marks (� 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.


License
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All content on Gopherpedia comes from Wikipedia, and is licensed under CC-BY-SA
License URL: http://creativecommons.org/licenses/by-sa/3.0/
Original Article: http://en.wikipedia.org/wiki/Tally_marks