Why did people start counting (on development of numerals)?

[The Hanged Man]

Recently, I've been reading some articles on origin of indo-european and uralic numerals, and also about numerals in other languages of the world. I won't wonder here how numerals in different languages evolve - from what I've read, they develop from body-part nouns and simple aritmethic operations, and that kind of origin of numerals is more or less visible in reconstructions of some proto-languages, and in present state of some other tongues. What I'm wondering is rather when and why they evolve. Here I'm discussing internal motivations for development of numerals (thus excluding borrowing of numeral systems from neighbours), that I think were important, depending on economical practices:

- in societies practicing trade, there is need for numerals for obvious reasons (counting money and/or traded items)

- in case of early farmers (I may be wrong, but I think that trade was developed after agriculture, or at least it became more widespread due to overproduction of food and proffesional specialisation, possible in agricultural societies), I think numerals were used, too. For example, for counting fields, surface areas of fields, and herd animals (after some of them were domesticated). Another, perhaps even more important use for numerals in such cultures, was using a calendar: people sure had to be able to count to use it, and they had to use it to at least sew and plant in proper time of a year.

- in case of hunters-gatherers, the things become less obvious. We still have some societies of this kind, and apparently they may, or may not have functional numerals and/or counting systems.

My first conclusion: From these points, I conclude, that counting developed in hunter-gatherer societies (without consideration of cases when it developed due to language contact). And why did it developed? I think two factors may have played role in it:

- necessity of food storage. This depended on climate, because biodiversity in some climates wouldn't be sufficient for production of enough food, at least seasonally. And when you store something, you need to remember places where you stored it, and in case of food, you should be able to divide and count rations, which implies counting

- necessity of food division when resources are scarce. This would be important even if food couldn't be stored, or there was no need for stroing it (although, I think that conditions that cause food shortage also force people to store it). And of course it would depend on biodiversity, and thus on climate, too.

- possibility of food storage - again, depending on climate. In colder climates, there is a possiblity to store food for long, at least during winter. if there is frost. On the other hand, in warm areas it wasn't possible, especially in places with a lot of rainfall: decomposition would spoil stored food.

And here is my second conclusion: if numerals develop in hunter gatherer societies as a mean to keep track on stored food, or as a mean to save scarce food resources, then obviously they can develop when climate is cold - because cold climate implies physical possiblity to store food, and a necessity to do it. What can we see from data on WALS?

http://tinyurl.com/cvcmu9l

We can see that from languages included here, most with restricted numeral systems are used by people who live in areas where hunting and gathering is still a base of local economy, or where it is at least expected to be so. Another common characteristics of these places are: long-term food storage is impossible or highly limited due to climatic conditions (hot or warm climate), or biodiversity can provide enough food all year long, or both.

As far as I'm concerned, my ideas about cause of development of numeral systems seem plausible. However, I know there could be an additional situation, when hunters could develop counting: they probably needed to express numbers of animals they can see or track during hunt, at least from time to time, although I don't know if it would be enough to develop lexicalized numerals. Perhaps counting only in that situations was not very often, and could give rise only to some non-lexicalized body-part expressions? What do you think about it?

What do you think about my conclusions, or about particular parts of my reasoning?

[zompist]

As you may know, I did a good deal of research on numbers, though I won't say I'm an expert.

To my knowledge, only two languages are reported to have no numbers: Yumbri (SE Asia) and Piraha (Amazon), and the latter has been disputed.

You can't always trust reports of "restricted" numeral systems. Many languages are poorly documented, and the original contact was by people who expected an IE-style set of fixed roots. If "three" was expressed as "two-one" or "one one one", they often didn't bother to record this. Too often I've found conflicting records of a language, one with a 'restricted' set of numbers, one with a full set.

Also, don't assume that because numerals didn't exist, people couldn't count. People have fingers.

I don't buy your "cold" theory, for several reasons. One is that the map you're looking at isn't a good guide to the hunter-gatherer societies of 15,000 years ago. Another is that I don't see any particular reason why storing things in ice, as I guess you're referring to, would encourage numeration any more than (say) Kalahari Bushmen remembering where they saw immature melons so they can go get them later.

[Seamus]

The BBC documentary "The Story of 1" explains the history and evolutions of counting and numbers. You can watch the whole thing on Youtube at http://www.youtube.com/watch?v=6A5h3ZK1mMA. It is an hour long but it's pretty interesting and I think it answers your question avout how counting came to be. I remembered watching it in math class last year in school during the day before a holiday break (when all the classes do absolutely nothing). Anyway, I ended up liking it due to my love for linguistics and bought the DVD myself.

The documentary also touches on some groups of people such as some Australian Aboriginies have no numbers whatsoever just as Mark mentioned in the previous post. If you don't want to watch the entire documentary (I don't blame you, it's an hour) I suggest you just watch the parts from 7:25 to 9:27. This is when the host Terry Jones interviews some of the aborigines that have no numbers and shows what they would use in place of them.

[Vuvuzela]

As you may know, I did a good deal of research on numbers, though I won't say I'm an expert.

To my knowledge, only two languages are reported to have no numbers: Yumbri (SE Asia) and Piraha (Amazon), and the latter has been disputed.

Well, according to the Wikipedia article, the former isn't entirely numeral-less either, since Wikipedia claims that

Although it is possible to count up to ten in Mlabri, only the numerals one and two may be used to modify a noun, and the word for 'two' has uses closer to 'pair' or 'couple' in English than a numeral.

And according to this thing:

The first five Mlabri numerals are...

Unless the Yumbri variety specifically includes no numerals, while the other two have them but just don't use them. I can't find any information specific to Yumbri on the 'net. In which case, disregard what I just wrote.

[zompist]

FWIW Ruhlen distinguishes Yumbri and Mrabri. The Voegelins list Yumbri with half a dozen dialects and no Mrabri at all. So we're probably talking about different peoples. (This sort of naming confusion is all too common.)

[The Hanged Man]

As you may know, I did a good deal of research on numbers, though I won't say I'm an expert.

To my knowledge, only two languages are reported to have no numbers: Yumbri (SE Asia) and Piraha (Amazon), and the latter has been disputed.

You can't always trust reports of "restricted" numeral systems. Many languages are poorly documented, and the original contact was by people who expected an IE-style set of fixed roots. If "three" was expressed as "two-one" or "one one one", they often didn't bother to record this. Too often I've found conflicting records of a language, one with a 'restricted' set of numbers, one with a full set.

Also, don't assume that because numerals didn't exist, people couldn't count. People have fingers.

Well, perhaps I gave not the best title to my topic... it was meant to be more about causes of lexicalization of numerals (which of course is result of counting), than about actual counting. Although, I've read that many australian tribes do not traditionally count, so perhaps that made me to do so.

I don't buy your "cold" theory, for several reasons. One is that the map you're looking at isn't a good guide to the hunter-gatherer societies of 15,000 years ago.

I think it supports my theory just because of that. After all that time, all restricted numeral systems are used in warm climate areas (if the WALS map is accurate). You could of course say that in other areas numeral systems didn't necessarily develop internally, but could be borrowed... but why the scale of that development was much higher in cold areas, that in warm ones?

Another is that I don't see any particular reason why storing things in ice, as I guess you're referring to, would encourage numeration any more than (say) Kalahari Bushmen remembering where they saw immature melons so they can go get them later.

Well, that is a good point.

@Seamus: I've watched the documentary, to which you gave link here, and the parts about oldest evidence for counting and lack of numerals in Walpiri language were quite interesting . The rest was much less interesting for me, because it dealt more with development of ways of writing numbers and counting, than actuallinguistic development of numerals and numeral bases, in which I'm more interested (yes, the title of my topic is a bit misleading.. I'm going to improve that). Anyway, thanks

[Torco]

Counting to keep track of things as an explanation for the appearance of numerals is a bit problematic for the simple reason that there's a simpler way to keep track of quantitative data: matching. You don't need to count to check if, say, none of your sheep died since last year: you just take a stick and make a dent for each of your sheep, and then, after the year, you re-mark one dent for every sheep you have then: if the numbers add up, then you have the same amount of sheep, and that's good. Counting can be done without having names for the numbers, even if its especially useful to have them anyhow.

[Seamus]

@Seamus: I've watched the documentary, to which you gave link here, and the parts about oldest evidence for counting and lack of numerals in Walpiri language were quite interesting . The rest was much less interesting for me, because it dealt more with development of ways of writing numbers and counting, than actuallinguistic development of numerals and numeral bases, in which I'm more interested (yes, the title of my topic is a bit misleading.. I'm going to improve that). Anyway, thanks

I'm glad you liked it. It's one of my favorite documentaries. If you found the Walpiri people intresting, I suggest you think about making a culture in your conworld like them; one with a language with no words for numbers. I based my Pahahu culture off of the Walpiri. Like the Walpiri, the Pahahu people in my conworld Semea have no numbers except for pon (one), mon (a few, usually meaning 2-5) and mohel (many, usually meaning six and more). Again, this is only a suggestion. I just thought that this might be an interesting idea for
you considering you like me express an interest in the evolution of counting and numerals.

Earlier on the thread, it has been mentioned that the Piraha people of South America also lack numbers. I researched this on wikipedia (I attached the link so you can look too) [url]http://en.wikipedia.org/wiki/Pirah%C3%A ... cal_number[/
url] and discovered that they have two words for numbers, both containing the same sound only different in tone. The Wikipedia article also explains that some Piraha people were given a test where certain numbers of batteries were placed on a table and they had to identify how many batteries there were. Based on how they responded, the people who administered the test concluded that the two numbers the Piraha people used did not mean 'one' and 'many' but instead relative terms such as 'greater' and 'fewer.' How do you think this strange method of numbers came to be?