Friday, January 25, 2008

Indo-European Numbers 1-10

I've only just discovered that Eugenio Ramón Luján Martínez, in ‘The Indo-European system of numerals from ‘1’ to ‘10’’, makes detailed proposals on exactly how they came about, and how they were formed (the words' etymology). This is from notes reviewing a paper by him:

The proto-Indo-European 1-10 numerals are:
*oynos/*sem *duwo: *treyes *kwetwores *penkwe *sweks *septm *okto: *newn *dekm

Indo-European ‘6’ ‘may best be explained as a loan from Semitic’, as does ‘7’.
(This is not at all unlikely; the Akkadian 6 and 7 were shishshu and sebe - RP)
- ‘1’ through ‘3’ were deictic in origin
- ‘4’ relates to the four fingers or the width of the palm,
- *okto ‘8’ resolves to a dual marker (-o) and ‘4’
‘best related to Av. ašti ‘width of four fingers, palm’;
- ‘5’ is generally related to ‘fist’ and ‘finger’, but is also related to ‘all’;
- ‘10’ the I-E root underlies *deks- ‘right [hand]’; and
- ‘9’ is generally related to ‘new’.

The proto-Indo-European 1-10 numerals are:
*oynos/*sem *duwo: *treyes *kwetwores *penkwe *sweks *septm *okto: *newn *dekm

M concludes that achieving units for ‘1’ through ‘10’ remains far from demonstrating an original decimal system, as the grouping of ‘1’ through ‘3’ as deictic in origin, ‘4’, 5’, ‘8’, and ‘10’ as involving fingers or hands, and ‘9’ as ‘new’, suggests. Thus, we see can bases for at least two, and possibly four distinct counting systems prior to the development of the decimal system.
From: Notes on: Numeral Types and Changes Worldwide.

Martinez' full doctoral thesis on Indo-European numbers is available online but is entirely in Spanish, and 24MB in size, which I shall endeavour to read some time. It deals with Indo-European numbers from 1 to 100.

This find certainly reinforces my conviction that numerals do not come into existence by immaculate conception, but evolve from very small, simple beginnings set in place many thousands of years ago, perhaps when humans first began to speak and estimate quantities.

1 - 3 are deictic, which means they rely on context. Early on, speakers in many languages made a distinction in pronouns: I (singular), we two (dual), we three (trial) and we (more than 3 - plural), and this also extended to the very low numbers, that used the same roots. Number markers related to these were added to many different kinds of words, not just pronouns and the lower numerals.

The dual still exists in the English distinctions both vs. all, either vs. any, twice vs. x times (an archaic thrice also exists, meaning "three times"), and so on, but the dual and the trial no longer occur in our pronouns.

Those very numbers (in fact 1-4) are also the most easily subitisable; that, is you can estimate the number very quickly by sight, without counting. Most people can estimate number by sight up to 7 or 8, but this takes a bit longer.

You can also, of course, easily subitise 1 hand, 2 hands, 1 foot, 2 feet once you start 'bunching' numbers into groups (mostly based on counting 5 digits, and then making that 1 unit, usually related to 'hand'). A digit, of course, was literally, a finger or toe.

But some number systems rely on just the four fingers, so you get one bunch of 4 fingers, then the next stage is 2 bunches of 4 fingers = 8.
This seems to have happened in proto-Indo-European, or in a counting system that preceded that. (See above: *okto ‘8’ resolves to a dual marker (-o) and ‘4’,
‘best related to Av. ašti ‘width of four fingers, palm’).
9 would then be the start of a new cycle, or if 10 had become a new base, it might be a completely new word (‘9’ is generally related to ‘new’).

This kind of '4,8 cycle' number system occurs in isolated areas in a few Austronesian languages around New Guinea, and in Papuan number sytems as well.
A more 'advanced' system, with a 5,10 cycle, but with 'relicts' of a base 4 system, is more common in Austronesian. In these cases, the '9' is usually constructed something like X1.

This puzzled me for a long time, but the problem begins to clarify itself with the knowledge that proto-Indo-European is confirmed to be probably more of a messy accumulation of different counting systems than the miraculously fully-blown decimal system it appears to be.
Of all Indo-European 1-10 numeral systems, only Vedda has a system that counts 6-9 as 5+1, 5+2, etc. But there are more than 250 of those constructions in Austronesian languages, and in many quite unrelated languages, as well.

For that reason, I believe that the "proto" Austronesian numerals words *enem=6, *pitu=7, *walu=8, and *Siwa=9, appeared latest in the majority of Austronesian of An 1-10 systems.
*sa puluq=1 x puluq*, has nothing to do with hands, but probably appeared before 6-9, because many systems with 5+1, 5+2 constructions use *sa puluq. Furthermore, thei particular word seems to appear quite late in Austronesian languages, suggesting they were borrowed by languages that still preserved older systems in whole or in part.