Languages and Numbers and Ways of Counting to 8 !

This article is about how small numbers are represented in various languages.

Acknowledgement: much of this article is taken from the Wikipedia page about positional notation.

Bases

The base is the mathematical term for the number of digits you would use to count in a language.

For example, if you used the fingers of both hands to count, you would be using a base of 10.

If you used the fingers of one hand to count, you would be using a base of 5.

If you used the fingers of both hands and the toes of both feet, you would be using a base of 20.

Base-20

Some languages have names for numbers that lead you to suspect that their users might have thought in terms of groups of 20.

French has an interesting way of describing numbers above 60.  In French, the word for 60 is “soixante”, the word for 75 is “soixante quinze” (sixty and fifteen) while 80 is “quatre-vingt” (four-twenties) and 95 is “quatre-vingt quinze” (four-twenties and fifteen).

And it is not just French.  English uses the word ‘score’ to describe a group of 20 things.  So, when we talk of “two score” we mean forty, and when we say “four score and seven” we mean 87.

The article also talks about Welsh and Irish and Maori:

The Irish language also used base-20 in the past, twenty being fichid, forty dhá fhichid, sixty trí fhichid and eighty ceithre fhichid. A remnant of this system may be seen in the modern word for 40, daoichead.

The Welsh language continues to use a base-20 counting system, particularly for the age of people, dates and in common phrases. 15 is also important, with 16–19 being “one on 15”, “two on 15” etc. 18 is normally “two nines”. A decimal system is commonly used.

Danish numerals display a similar base-20 structure.

The Maori language of New Zealand also has evidence of an underlying base-20 system as seen in the terms Te Hokowhitu a Tu referring to a war party (literally “the seven 20s of Tu”) and Tama-hokotahi, referring to a great warrior (“the one man equal to 20”).

Base-12

Another interesting system is the base-12 system.

The Wikipedia article says:

Twelve is a useful base because it has many factors. It is the smallest common multiple of one, two, three, four and six. There is still a special word for “dozen” in English, and by analogy with the word for 10², hundred, commerce developed a word for 12², gross. The standard 12-hour clock and common use of 12 in English units emphasize the utility of the base. In addition, prior to its conversion to decimal, the old British currency Pound Sterling (GBP) partially used base-12; there were 12 pence (d) in a shilling (s), 20 shillings in a pound (£), and therefore 240 pence in a pound. Hence the term LSD or, more properly, £sd.

Base-2

There was even a language that made use of a base-2 (binary) system for counting.  Base-2 (binary) is mainly used in computers today (because switches can represent binary numbers – a switch that is off represents the 0 digit and a switch that is on represents the 1 digit).  But apparently, native Australian languages use binary too.

A number of Australian Aboriginal languages employ binary or binary-like counting systems. For example, in Kala Lagaw Ya, the numbers one through six are urapon,ukasar, ukasar-urapon, ukasar-ukasar, ukasar-ukasar-urapon, ukasar-ukasar-ukasar.

Base-8

The article also says that there is some evidence of the use of base-8 in language:

A base-8 system (octal) was devised by the Yuki tribe of Northern California, who used the spaces between the fingers to count, corresponding to the digits one through eight.^[6] There is also linguistic evidence which suggests that the Bronze Age Proto-Indo Europeans (from whom most European and Indic languages descend) might have replaced a base-8 system (or a system which could only count up to 8) with a base-10 system. The evidence is that the word for 9, newm, is suggested by some to derive from the word for “new”, newo-, suggesting that the number 9 had been recently invented and called the “new number”.^[7]

So much for bases.

Some languages have two sets of names for numerals!

Two Sets of Names for Numbers in Japanese and Korean

Japanese and Korean use two sets of names for numbers while counting.

In Japanese, there is a set of names that are typically used when small quantities are involved:

“hitotsu”, “futatsu”, “mittsu”, “yottsu”, “itsutsu“, “muttsu”, “nanatsu“, “yattsu“, “kokonotsu“, “to” (1 to 10).

But for larger numbers and for zero, the names used are ones derived from Chinese.

“ichi”, “ni”, “san”, “shi”, “go”, “roku”, “shichi”, “hachi”, “kyu”, “ju”.

These numbers correspond to the Chinese digits:

“yī”, “èr”, “sān”, “sì”, “wǔ”, “liù”, “qī”, “bā”, “jiǔ”, “shí”.

And similarly in Korean, you would use one set of names for small quantities (for example, hours in the day):

“hana”, “dul”, “seth”, “neth”, “thasoth”, “yosoth”, “ilgop”, “yodolp”, “ahop”, “yol”.

But to describe larger quantities, like minutes or the days in a month, you’d go with names based on Chinese:

“il”, “i”, “sam”, “sa”, “o”, “yug”, “chhil”, “phal”, “ku”, “ship”.

Finally, we come to some interesting irregularities in south Indian languages.

Irregular Numbering

In Tamil (a language spoken in south India), the word for 90 is “pre-hundred”.

The first ten numbers in Tamil go:

“ondru”, “irendu”, “muundru”, “naangu”, “aindhu”, “aaru”, “eelu”, “ettu”, “ombadhu”, “patthu”

But the word “ombadhu” which means 9 is not used in 90.

Tamil

In Tamil, the name for 80 is derived from the name for 8 by adding a suffix like in English.  Just as “eight” becomes “eight-y”, in Tamil, “ettu” becomes “embathu”.

But the name for 90 is not derived from the number for 9.  Instead,it is “pre-hundred”.  (In Tamil, 90 is “thonnuuru” – hundred being “nuuru”).  So, when counting from 90 to 99, you use the suffix one would normally associate with the hundred’s position.

So 91 is “pre-hundred and one”.  It is pronounced “thonnuutri-ondru” in Tamil.  92 is “pre-hundred and two”.  It is pronounced “thonnuutri-rendu” in Tamil.

I’ve not come across many languages in which 90 is described as pre-hundred.  But Hindi (a language from the north of India) has a similar feature.

Hindi

In many Indian languages spoken in the north of India, the names of the first ten numbers are similar to their names in Latin.  For example, Hindi has:

“ek”, “dho”, “thiin”, “chaar”, “paanch”, “che”, “saath”, “aaT”, “nov”, “dhas”

The Hindi names for various numbers are similar to the Sanskrit names of those numbers:

“ekam”, “dve”, “thriini”, “chathvaari”, “pancha”, “shath”, “saptha”, “ashta”, “nava”, “dhasha”

But when you get to 29 in Hindi, you say “pre-30”.  The word in Hindi is “unthees” (“thees” means 30 in Hindi).

Similarly, 39 is “pre-40” (“unchaaliis” where “chaaliis” means 40).

This is different from how you count in Sanskrit.

Sanskrit

In Sanskrit, 39 is “navatrimshat” (nine and thirty) and 29 is “navavimshatihi” (nine and twenty).

Now the absence of a regular name for numbers with 9 in them supports a theory that Indic languages might once have used base-8 for counting.

I quote from the Wikipedia article again:

There is also linguistic evidence which suggests that the Bronze Age Proto-Indo Europeans (from whom most European and Indic languages descend) might have replaced a base-8 system (or a system which could only count up to 8) with a base-10 system. The evidence is that the word for 9, newm, is suggested by some to derive from the word for “new”, newo-, suggesting that the number 9 had been recently invented and called the “new number”.[7]

The assertion seems to have been made in an article titled ‘The Indo-European system of numerals from ‘1’ to ‘10’’ by Eugenio Ramón Luján Martínez.

Eugenio argues that each of the numerals in Indo-European languages gradually came into use when required by necessity, starting with the numbers 2 and 3 (which started as deictics – like in the words ‘duo’ and ‘trio’).

There’s an overview of his arguments in this article: http://smallislandnotesan.blogspot.in/2008/01/indo-european-numbers-1-10.html

Counting on the Fingers

To a twenty-first century human, a base-10 system of counting seems like the natural way to count.

But a base-8 system could have felt more natural than a base-10 system to early humans to count with.

This is because it is only possible to count to ten on the fingers of one’s hands if one has developed the technique of bending them to mark the number up to which one has counted.

If a person uses the technique of touching the thumb to a finger to mark a count, then one can only count up to 4 on each hand (and therefore only up to 8 on both hands).

Indian musicians still keep count of the rythmic patterns in music (the thaalas) by touching the tips of their fingers with the thumb (counting in multiples of 3 or 4).

So it is indeed possible that at some point in the distant past, speakers of Indo-European languages did indeed count in groups of 8.

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