How to count to 1296 in Ngkolmpu

How to count to 1296 in Ngkolmpu

In order to feed his family for the year, and prove himself a worthy man, a man living in southern New Guinea is expected to grow 1296 yams (dioscorea sp.) each season. In Ngkolmpu, a language spoken by around 200 people who live in this region in a single village 15kms within the Indonesian side of the border between West Papua and Papua New Guinea, there is a single word for this number ntamnao.

To speakers of English, this seems like an arbitrarily specific number; yet to Ngkolmpu speakers it’s perfectly natural. Ngkolmpu, along with most of its related languages, has what is known as a senary numeral system also known as a base-six system. In English, we use a decimal system which is based on recursions of ten units while senary systems are based around recursions of six. In Ngkolmpu, the words for one to six are naempr, yempoka, yuow, eser, tampui and traowow. Seven is naempr traowo naempr or ‘one six and one;’ thirteen is yempoka traowo naempr or ‘two six and one.’ You should be starting to see the pattern now. But what happens when you get to six groups of six, i.e. 62 or 36? Well there is a specific word for that ptae.  In fact, in Ngkolmpu there are words for 62, 63, 64 and 65. That’s all the way up to 7776! Related language Komnzo even has a word wi which is used for 66 or 46,656! If you want to learn how to count to 7776 in Ngkolmpu the entire system is presented in Table 1.

1 naempr
2 yempoka
3 yuow
4 eser
5 tampui
6 61 traowo
7 naempr traowo naempr
8 naempr traowo yempoka
13 yempoka traowo naempr
36 62 ptae
216 63 tarumpao
1296 64 ntamnao
7776 65 ulamaeke

Table 1 – Senary numerals in Ngkolmpu

While we are used to decimal counting systems in English, lots of languages around the world use different systems. What is remarkable is that these senary systems are essentially unique to the southern New Guinea region. As far as we know, the only languages which use base-six are found in this region. In Ndom, a completely unrelated language to Ngkolmpu spoken on Yos Sudarso Island around 250kms away have a sort of light six-base system. Ndom displays unique words for the numbers one to six, but no words higher terms and no way to construct them from lower numerals; this is what is known as a ‘restricted numeral system.’ As far as we know, this complex base-six system as we see in Ngkolmpu and its relatives are an entirely unique development. This then raises a crucial question: How and why did such a system emerge?

Pic 1 – Yams and plantains for distribution after a feast

This is a hard question to answer. The leading theory on this is based on the primary use of the counting systems: yam tallying. In the communities of southern New Guinea, the various species of dioscorea aka yam are extremely important for every part of life. They are the primary food staple and, as we said before, the general consensus is that it takes a ntamnao of yams to feed a family for a year. Good yam gardeners count their yams to ensure they have enough food for the year but just as importantly for the bragging rights that accompany being a good gardener. Additionally, yams serve many ceremonial roles, for instance a wedding feast can’t be held without a ntamnao of yams which are meticulously counted, brought to the bride’s village and counted again with all parties present. Smaller feasts might require a tarumpao (216) which are counted and distributed to participants as in Picture 2. The significance of counting yams in these cultures has been hypothesised as the motivation for the development this counting system; something we don’t really see anywhere else in the world. The next question is why base six and not some other number? Well, the main yams consumed in this region are teardrop shaped with a round end and a narrow end. These when placed into small piles naturally fall into neat piles of 6 (Picture 3). This provides a motivation for a specifically 6 based system and supports the claim that numeral system emerged through the practice of tallying yams.

Pic 2 – 6 yams in a pile

The Ngkolmpu system only has numerals up to 7776 but hypothetically could be used to count to any number. Numeral systems of this type are known as ‘unrestricted numeral systems.’ We take this for granted in English but in smaller communities these are typically not that common. For example, in Marind a culturally dominant language spoken by around 9000 people in the same region as Ngkolmpu have words for one and two only. Counting is done by counting fingers and toes without any productive means for extending beyond that. Similar are the body part tallies of New Guinea such as the Oksapmin body part tally where one can count up to 27 by listing names for the places along the fingers, hands, arms and head for values up to 27 (Picture 4). This is very different to the Ngkolmpu system as we see in Table 1.

Pic 4 – Oksapmin body tally system

It was previously thought that unrestricted numeral systems could only develop in cultures which had sufficient organisational bureaucracy to warrant such a system. What the southern New Guinea situation shows is that the agrarian practices of yam cultivation under certain conditions also allow for the development of advanced counting systems. So, it looks like if people want to count something enough, they can develop the systems to do so which is remarkable.

The next time you have to count up something in multiples of six spare a thought for the Ngkolmpu and their wonderful counting system.


Reindeer = rein + deer?

Reindeer = rein + deer?

In linguists’ jargon, a ‘folk etymology’ refers to a change that brings a word’s form closer to some easily analyzable meaning. A textbook example is the transformation of the word asparagus into sparrowgrass in certain dialects of English.

Although clear in theory, it is not easy to decide whether ‘folk etymology’ is called for in other cases. One which has incited heated coffee-time discussion in our department is the word reindeer. The word comes ultimately from Old Norse hreindyri, composed of hreinn ‘reindeer’ and dyri ‘animal’. In present-day English, some native speakers conceive of the word reindeer as composed of two meaningful parts: rein + deer. This is something which, in the Christian tradition at least, does make a lot of sense. Given that the most prominent role of reindeer in the West is to serve as Santa’s means of transport, an allusion to ‘reins’ is unsurprising. This makes the hypothesis of folk etymology plausible.

When one explores the issue further, however, things are not that clear. The equivalent words in other Germanic languages are often the same (e.g. German Rentier, Dutch rendier, Danish rensdyr etc.) even though the element ren does not refer to the same thing as in English. However, unlike in English, another way of referring to Rudolf is indeed possible in some of these languages that omits the element ‘deer’ altogether: German Ren, Swedish ren, Icelandic hreinn, etc.

Another thing that may be relevant is the fact that the word ‘deer’ has narrowed its meaning in English to refer just to a member of the Cervidae family and not to any living creature. Other Germanic languages have preserved the original meaning ‘animal’ for this word (e.g. German Tier, Swedish djur).

Since reindeer straightforwardly descends from hreindyri, it may seem that, despite the change in the meaning of the component words, we have no reason to believe that the word was altered by folk etymology at any point. However, the story is not that simple. Words that contained the diphthong /ei/ in Old Norse do not always appear with the same vowel in English. Contrast, for example, ‘bait’ [from Norse beita] and ‘hail’ [from heill] with ‘bleak’ [from bleikr] and ‘weak’ [from veikr]). An orthographic reflection of the same fluctuation can be seen in the different pronunciation of the digraph ‘ei’ in words like ‘receive’ and ‘Keith’ vs ‘vein’ and weight’. It is, thus, not impossible that the preexistence of the word rein in (Middle) English tipped the balance towards the current pronunciation of reindeer over an alternative one like “reendeer”. Also, had the word not been analyzed by native speakers as a compound of rein+deer, it is not unthinkable that the vowels may have become shorter in current English (consider the case of breakfast, etymologically descending from break + fast).

So, is folk etymology applicable to reindeer? The dispute rages on. Some of us don’t think that folk etymology is necessary to explain the fate of reindeer. That is, the easiest explanation (in William of Occam’s sense) may be to say that the word was borrowed and merely continued its overall meaning and pronunciation in an unrevolutionary way.

Others are not so sure. The availability of “fake” etymologies like rein+deer (or even rain+deer before widespread literacy) seems “too obvious” for native speakers to ignore. The suspicion of ‘folk etymology’ might be aroused by the presence of a few mild coincidences such as the “right” vowel /ei/ instead of /i:/, the fact that the term was borrowed as reindeer rather than just rein as in some other languages [e.g. Spanish reno] or by the semantic drift of deer exactly towards the kind of animal that a reindeer actually is. These are all factors that seem to conspire towards the analyzability of the word in present-day English but which would have to be put down to coincidence if they just happened for no particular reason and independently of each other. Even if no actual change had been implemented in the pronunciation of reindeer, the morphological-semantic analysis of the word has definitely changed from its source language. Under a laxer definition of what folk etymology actually is, that could on its own suffice to label this a case of folk etymology.

There seems to be, as far as we can see, no easy way out of this murky etymological and philological quagmire that allows us to conclude whether a change in the pronunciation of reindeer happened at some point due to its analyzability. To avoid endless and unproductive discussion one sometimes has to know when to stop arguing, shrug and write a post about the whole thing.