When speakers of a language coin words for one, two, three, four, etc., for the first time, where do they come up with the forms? Are there any common methods used across language families?

Pirahã has words for "few" and "many". Numerous other languages have only "one" and "many", possibly adding "two", especially among isolated hunter-gatherer tribes. If they do express numbers higher than that, it's by counting on their fingers in front of someone else. (See chapters 1 and 2 of The Number Concept, written by Levi Leonhard Conant in 1896.) But once people invent agriculture and trade, languages tend to come to have some system for counting and expressing, say, the number of animals in a flock or the number of days' travel to some other village.

If you can get past the use of "savage" and "rude" to refer to hunter-gatherers and "Aryan" for Indo-European, Conant continues to describe a common strategy for "five" through "ten". The word five is often some variant on "having finished one hand"; this is true of PIE as well where *pénkʷe (five) is related to "finger". Ten can be "having finished both hands" or (in the case of shod cultures) "one man", and six through nine "one more [than five]" through "four more"; nine is just as often "one less [than ten]". Barefoot cultures often adopt base 20 ("one man") with sub-base 5.

Some languages borrow numbers when their speakers borrow other cultural concepts. For example, most European languages borrowed "zero" from Arabic, and Swahili appears to have borrowed six through ten from the same language. Proponents of the Nostratic hypothesis will cite similarity between "six" and "seven" in IE and Semitic as evidence of common descent, if those words weren't also borrowed.

Conant lamented that the names of one through four appeared opaque in the vast majority of languages studied. Have the past 120 years produced any more clarity on trends in number word etymology among several language families? I tried Google basic numbers etymology but most results appeared irrelevant, most simply tracing English back to PIE or reiterating that zero was borrowed from Arabic.

  • Some progress must have been made since 1896. I just googled "language number system" and got 362 million hits. Here's an interesting looking article from SIL: www-01.sil.org/sil/news/2010/4000-number-systems.htm (SIL has sponsored a vast amount of work on the lesser known languages of the world). – Greg Lee Feb 8 '15 at 20:48
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    @GregLee The news article from SIL links to Eugene S. L. Chan's website which links to an article "Typology of Numeral Systems" by Bernard Comrie. Comrie's article largely agrees with Conant on strategies used for building names of larger numbers but doesn't touch on where languages get their words for, say, 1-4. Did I miss some related material on Chan's site? – Damian Yerrick Feb 9 '15 at 1:36
  • I haven't looked at Chan's website or Comrie's article. – Greg Lee Feb 9 '15 at 2:05
  • Are you interested only in number words in PIE? There has been a great amount of work on numbers, counting, and enumeration in the world's languages. Do you have a specific question? – Teusz Feb 9 '15 at 10:08
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    Is *pénkʷe in any way related to "pinky"? – Zgialor Feb 21 '15 at 21:08

Piotr Gąsiorowski has very recently put forth a hypothesis on the origin of Indo-European kwetwor "four."

'Four: A Map'

He argues that it comes from an archaic word for "pair" or "to pair." The semantic evidence is good; unfortunately, there are not many branches with a non-"four" reflex of kwet in them.

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    "there are not many branches with a non-"four" reflex of kwet in them" - hmm Russian чета "cheta" meaning a spouse pair is a clear reflex of PIE q̆eta̯ "pair". Russian has other reflexes as well: сочетание "composition", четный "even", счёт "count", читать "to read", число "number" (< PIE q̆et(s)tlom). Also evidently the Latin clitic -que is related – Anixx May 28 '15 at 22:55

This is a common cross-linguistic trend. I remember reading a section of a book about it - in fact, I was searching for that book when I found this thread - but alas, I can't seem to find it.

As a non-Indo-European example, Yu'pik does something similar, but a little more thorough. Very roughly:

  1. "that which is indivisible"
  2. "following unit"
  3. "addendum"
  4. "spread out"
  5. "arm"
  6. "one having crossed over"
  7. "one having two" (?)
  8. "one having three" (?)
  9. "not quite ten"
  10. "above"
  11. "it goes down"
  12. "ten two"
  13. "ten three"
  14. "not quite fifteen"
  15. "other side"
  16. "fifteen one"
  17. "fifteen two"
  18. "fifteen three"
  19. "not quite twenty"
  20. "whole person"

When a number is used in the gloss, obviously, it can be broken down to its own constituents, so 12 is "following unit above", etc. The only exception is that the "one" in 6-8 is a pronoun, similar to "something".

http://www.languagesandnumbers.com/how-to-count-in-yupik/en/ypk-esu/ (this source translates 7 and 8 as "two having crossed over" and "three having crossed over", but this appears to be in error) https://books.google.ca/books?isbn=311027857X (pp. 398-401)


I find it interesting that Indo-European numerals from 1 to 4 are declinable and have ablaut nature; meanwhile numerals 5 and higher are indeclinable "stumps". The only explanation is that numerals 5 and higher were used in simple sequantial counting: 5, 6, 7, 8, perhaps in trade with non-Indo-European tribes. *septm being an obvious borrowing suggests that all the numerals from 5 to 10 could be loanwords from some sort of ancient pidgin, and Indo-Europeans themselves casually counted only up to 4.

  • In Sanskrit all the numbers are declinable. – fdb Sep 5 '16 at 19:03
  • There's a peculiar book claiming a fourth, ephemeral section in the partition, otherwise held to be tripartite, of the Proto-Indo-European society. At least it was god enough for the university library book shelfs. I don't remember the name though. – vectory May 9 at 20:49

If one puts oneself into the situation of an early age where the invention of words for numbers begins there is only one way to do it, by paraphrasing. You can express five by saying as many as fingers on your hand. Two: the number of your arms or feet, etc. Four: the legs of a cow or a dog One: the head of a man or head/tail of an animal

If signs and geometrical signs have been developed it is possible to say: Three: the corners of a triangle Four: the corners of a rectangle or square. Latin quattuor (four) is very similar to quadratum (rectangle) or quadrus/a/um (rectangular).

If words for one, two, three have been developed it is easy to express more numbers: Ten: two hands - Behind Latin decem (ten) might be two hands. Seven: a hand + two. Nine: two hands minus one. Eight: two fours.

The further development of paraphrases will be shortening and contraction till a word form that is short and easy to speak comes into being.

Probably the first stage was by means of gestures, such as showing the hand, pointing to the nose or to the legs. Maybe conventions developed for addition and subtraction of two simple numbers.

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    "Latin quattuor (four) is very similar to quadratum (rectangle) or quadrus/a/um (rectangular)." Rectangle is called so because it has 4 sides, not other way around! – Anixx Feb 10 '15 at 15:05
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    This answer appears to be pure speculation. -1 – Colin Fine Mar 24 '15 at 11:40

However, I think it's rather interesting to take a graphic approach over the alphabet.

  1. seed kernel (cp. Arab safran to sifr "zero"), nothing but a kernel of truth, a blank slate, fresh soil under which the seed isn't seen.

  2. a shoot, stalk; a seed, egg -- through confusion because of the eternally pertinant question whether zero is a natural number or not (it depends: ordinal or cardinal?).

  3. a branch, cp. twig.

  4. a tree

  5. ... ? wildcard.

This kind of enumeration works with different sets of items: man (alif), mother (beta), wife, children (giml, stick, staff); house, firewood; eenie meenie mini moe. You get the idea. These can then be mixed, picking one from each set, like Alpha Bravo Charlie Dallas to meet several constraints of clearness, rhyme and you haven't seen it, perhaps not as much on purpose as the American call signs, but rather naturally through evolution of unfit forms. Some of those enumerations are idiomatic with little variation in the sequence: "Auge, Nase, Mund" (eye, nose, mouth), or "Mutter, Vater, Kind". Thus I'd compare eye and egg as is usually done by hobbyists and add one and legume. This won't lead anywhere because:

It's reasonable to assume that number words dissimilate, because they form a special category; Speakers wonder nevertheless and may lexicalize similar looking looking or sounding words together--that's called folk etymology.

Oh, the question was for references. Few people are crazy enough, and if they are, they become drowned in mystic numerology to pack books full of it, that are interesting to skim but remain inconclusive. Refer to the previous paragraph on why nothing good on the matter can exist.

And then there's Nostratic. No number words are listed there. I faintly remember *diK "digit" proposed as an ultra-conserved word, though, that I chalked up as "two". Now I see */kiwæ/ ~ /kiwe/ ~ /kiwi/ 'stone' listed, which looks plausible and could as well relate to *kwetwores, if that in turn means square, cp. Ger. "Vierkant" (beam, bar), and Faust-Keil. I'd be keen to see a cluster of roots glossed to cut that contain *k (and I'm repeating that too often) and then there's */ʔekh₁-/ 'to move quickly, to rage; to be furious, raging, violent, spirited, fiery, wild (of a horse)', PIE */h₁ek-u-/ "to move quick. Naively thinking, German quetschen "to squish, mash*, Dutch kwetsen "to hurt" come to mind. Perhaps from Latin quatare "to shake". If the basic sense was grinding [under a stone] and thus mixing, than a sense to pair could develop from that. Cp. Ger. verquicken "to pair, mix, join". Also note that PIE *-wr is otherwise handled as a suffix, but seemingly not in *kwtur~kwetwor-. If it relates to fire, ... and Beekes considers Greek suffix -ro, -ros a sign of a pre-greek substrate.

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    "You get the idea" -- on the contrary, I for one haven't the faintest idea what this answer is trying to say. – TKR May 9 at 22:10
  • @TKR I am saying that threefold associations in a fixed expression, like "game, set, match" do have an inner coherencr relating to order sorted by size, importance or whatever, and thus lend well to an analogy for enumeration and the best one I could find symbolizes numericity with the first three items. You get the idea? Further than that, I am just trying to shoe horn it into a relevant andwer to the question. Once I had a halway coherent text, I tried to see how far I could drag it down into the mud. But then I got tired. – vectory May 9 at 22:36
  • "giml, stick staff" symbolizing children is an allusion to another thread from this weak. – vectory May 9 at 22:38

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