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Rationale: While writing a document about foundations of computer science and describing that a number is a sequence of digits, I was wondering about our relation to the decimal system.

In English counting goes like this: "one", "two" and "three". If we create a number with 2 digits, the number might be called "forty-two". "Forty" is an alias for 4‧101 and "two" adds 2‧100. So it refers explicitly to the decimal system, because neither "forty-two" nor "ten" exists in binary1. The language uses decimal-based aliases. "Dreizehn" (3+10 = 13) and "quatre-vingt trois" (4*20+3 = 83) are instances of the same concept in German and French.

Cerberus has pointed out that Aztecs and Babylonians have used different number systems from the very beginning which of course became part of the spoken language (radix 20 and 60). A nice hint, but I am interested in modern, spoken languages.

My question: Which modern, spoken languages do not imply the decimal system2? I would be happy to be able to find 2 to that kind.

A related question is How do you pronounce numbers written in different bases?

1: It might be a valid point that "ten" is an alias for 1‧101 + 0‧100 and therefore "ten" can also be applied to the binary system with 102 = 210, but that is pretty uncommon and I am not sure about it. Correct me if I am wrong. See related link.

2: With "language without the implication" I mean "the pronunciation of a number is only a concatenation of the pronunciation of the individual digits".

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Whether or not a language describes numbers in decimal terms depends on whether the culture that it belongs to uses decimal numbers. There have been many cultures that use or used other systems, like the Aztecs and the Babylonians, I think, and no doubt they did not describe their numbers in decimal terms. – Cerberus Oct 5 '12 at 13:52
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Languages in the Nigerian Middle Belt such as Janji, Gbiri-Niragu (Kahugu), the Nimbia dialect of Gwandara; the Chepang language of Nepal and the Mahl language of Minicoy Island in India are known to use duodecimal numerals. / The Yuki language in California and the Pamean languages in Mexico have octal systems because the speakers count using the spaces between their fingers rather than the fingers themselves. – Cerberus Oct 5 '12 at 15:19
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It is possible for people to count on their fingers to 12 using one hand only, with the thumb pointing to each finger bone on the four fingers in turn. A traditional counting system still in use in many regions of Asia works in this way, and could help to explain the occurrence of numeral systems based on 12 and 60 besides those based on 10, 20 and 5. Wiki on "Radix - In numeral systems" - Follow links from there. – Cerberus Oct 5 '12 at 15:20
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calling a number "a sequence of digits" is really giving higher status to a conventional algorithm used for representing quantities in writing than to the quantities themselves. – jlovegren Oct 5 '12 at 19:26
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Any language which uses second (e.g. of time or of arc) to mean a sixtieth of the previous unit (such as minute) which is a sixtieth of the unit above that (hour or degree) is implicitly working in a form of base 60. – Henry Oct 9 '12 at 6:47
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2 Answers

up vote 9 down vote accepted

Modern Englishes, and many other well-known languages, use base 10 (ie decimal) systems of numerals. But there are many languages in the world that currently use different systems.

Eugene Chan has been studying the numeral systems of the world's languages for many years and his website contains a vast amount of information on this topic. I think a quote from Eugene's introduction is useful:

The surviving thousands of the world's ethnic groups use a variety of different numeral systems: duodecimal systems, decimal systems, quinary systems, quaternary systems, ternary systems, binary systems, incomplete decimal systems, mixed systems, body-part tally systems and so on. Certain South American indigenous languages even only distinguish the numbers "one" and "many".

Some examples:

  • Orokaiva (Trans-New Guinea): digit-tally system
  • Fas (Kwomtari): binary system (base 2)
  • Pazeh (Austronesian): quinary (base 5)
  • Amis (Austronesian): decimal (base 10)
  • Ron (West Chadic): duodecimal (base 12)
  • Barapasi (East Geelvink Bay): vigesimal (base 20)
  • Meyah (East Bird Head-Sentani): mixed-quinary/vigesimal
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From that link, Fas isn't really binary; it seems to be a doubled unary (non-positional) system. Would have been cool. – Mechanical snail♦ Jan 22 at 0:15
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WALS has a chapter on numeral bases. It appears most languages use either a decimal or a vigesimal (base 20) system (or some mixture thereof, as in Basque), with other patterns being relatively rare. There are also some language that cannot actually express all possible numbers but only a limited set. Pirahã is even claimed not to have any numerals at all (but every claim about Pirahã should be taken cum grano salis).

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Thanks you very much for your post. The WALS article is very interesting :) – meisterluk Oct 7 '12 at 12:09

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