<div>Waruno - Quote: </div> <div> </div> <div>"I cannot imagine what may have been the </div> <div>source of having '4' as a base for numeration." </div> <div> </div> <div>The 1-4 numeral system is not so baffling when you consider </div> <div>that virtually all numbering systems began with </div> <div>finger-counting. (Harald Hammarstrom will surely put me </div> <div>right if I'm exaggerating).</div> <div> </div> <div>It just comes down to whether you consider the thumb part of </div> <div>the finger-count or not. </div> <div> </div> <div>Different ways (and directions) in totting up fingers seem </div> <div>to have quite perceivable effects on the resulting number </div> <div>words. Either way.</div> <div>You might even emphasise it:</div> <div>Bargam (Papuan) uses abainakinta (thumb) for 5.<BR>---------------------------------------------------------<BR>The 'Papuan' Kewa of the PNG Southern Highlands have two </div> <div>number
systems, a full body part tally (hand, up arm, over, </div> <div>and down the other side) giving a 47-cycle number system, </div> <div>used mainly by elders for massive gift exchanges, and a 1-4 </div> <div>cycle system for everyday stuff.</div> <div> </div> <div>They're described at:<BR><A href="http://www.uog.ac.pg/PUB08-Oct-03/franklin1.htm">http://www.uog.ac.pg/PUB08-Oct-03/franklin1.htm</A></div> <div> </div> <div>(The strange bit, that I still can't fathom, is how 7 = hand </div> <div>+ 3 thumbs).<BR>---------------------------------------------------------<BR>There's even a Papuan language (Kote, from Morobe Prov) that </div> <div>has a 22 cycle system, because they count both nostrils as </div> <div>well as their fingers and toes. (Wouldn't want to buy a </div> <div>dozen bread rolls from them, though).<BR>----------------------------------------------------------</div> <div> </div> <div>There are more than a few Austronesian numeral
systems that </div> <div>show vestiges of an archaic 4 cycle system, with 8 at the </div> <div>end of the 2nd cycle, but most are now overlaid with a 10 </div> <div>cycle.</div> <div> </div> <div>In fact, they are rarer in New Guinea, with its multiple </div> <div>language families, and quite absent in Papuan languages west </div> <div>of there. They're not so very common elsewhere. (Except in </div> <div>California - where else?)</div> <div> </div> <div>And there is even a suggestion of a vestigial trace of a 4 cycle </div> <div>system in Indo-European, in that *oktô is apparently the </div> <div>dual form of *kwetwores - Beeler (1964, p. 1). Common </div> <div>counting in dozens may be another vestige.</div> <div>----------------------------------------------------------<BR></div> <div>If the 6-9 numbers are simple 5+1, 5+2, etc, then 8 would </div> <div>include, somewhere, 3. If it's subtractive from 10, it would </div> <div>include 2. If
it includes 4 then that indicates something </div> <div>quite different. </div> <div> </div> <div>If 9 includes a 1 morpheme, then it might be like 'sembilan' </div> <div>in Indonesian, or 'salapan' in Sunda, ie 1 from 10, or it </div> <div>could 'start again' from 8, which it would seem to do in </div> <div>the cases where 8 involves 4. </div> <div> </div> <div>The next cycle, to 12, seems to have been mostly overlaid </div> <div>now by 10/teen systems.</div> <div>Except, perhaps, in English, where 11 and 12 are 'irregular'.<BR>----------------------------------------------------------<BR></div> <div>Austronesian 4 cycles:</div> <div> </div> <div>Formosa: Siraya, Thao, Favorlang/Babuza, Taokas, Saisiyat, </div> <div>Atayal, Sedeq - all show no. 8 inclusive of 4, then start </div> <div>again with 'something different', often including a 1 </div> <div>morpheme. </div> <div> </div> <div>Enggano (which may not be An at all) -
has an 8 related to 4.</div> <div> </div> <div>Simba: Gaura Nggaura and Lamboya have 8 = pondopata ='x'.4 </div> <div>(or cognate) and banda' iha (or cognate) for 9.</div> <div> </div> <div>Flores: Ende, Rongga, Lio and Nghada - have 8=2x4 and 'ta </div> <div>esa' (or cognate) for 9</div> <div> </div> <div>Aru: Kola, Dobel, Ngaibor, Barakai, Tarangan West, Ujir - 8= </div> <div>karua and 9= ser, or tera (or cognates)</div> <div> </div> <div>Keule, Wogeo, and Biem, offshore of E Sepik Prov, PNG, have </div> <div>straightforward and obvious 1-4 systems: Boiken, a </div> <div>neighbouring Papuan language shares this, but only in one </div> <div>offshore island dialect, near the An speakers. But the </div> <div>system may be related to nearby Vanimo, Rawo and Mountain </div> <div>Arapesh, Papuan languages, also with 1-4 number systems.</div> <div> </div> <div>Ormu, Tobati/Yotafa and Kayupulau near Jayapura, have </div>
<div>'symptoms' of a 4 cycle. Adjacent to them is Nafri, the only </div> <div>member of the Sentani family to have a 4 cycle system.</div> <div> </div> <div>Of all these, it seems only the Wogeo/Biem and Ormu/Yotafa </div> <div>groups may have existing neighbouring non-An languages with </div> <div>1-4 systems. But those Papuan languages are very much in the </div> <div>minority themselves, so without more information there is no </div> <div>way of telling which way the influence went.</div> <div> </div> <div>There are other languages that have a 4 morpheme in 8, but </div> <div>they seem to have a multiplicative system, with 6=2x3, etc, </div> <div>rather than a 1-4 cycle:</div> <div> </div> <div>Wuvulu-Aua, in the Admiralties, has a strange (and very </div> <div>lonely) number system, analysed by Dempwolff (1905) as:<BR>1 aiai : 1 - 1<BR>2 gu-ai : 2 - 1<BR>3 odu-ai : 3 -
1<BR>4 gui-ne-roa : 2 - 2<BR>5 ai-pan : : 1 hand<BR>6 ode-roa : : 3 - 2<BR>7 ode-ro-miai : 3 - 2 +1 <BR>8 vai-ne-roa : 4 - 2<BR>9 vai-ne-ro-miai : 4 - 2 +1 </div> <div>(Almost all other Admiralties numerals show the unique Manus </div> <div>subtractive system).</div> <div> </div> <div>'Motu' languages (under the 'tail' of Papua New Guinea) also </div> <div>(mostly) have a number 8 related to 4 (taura hani), and </div> <div>9=8+1, but these also have 6='2'x3 (taura toi) with 7 = a </div> <div>'regular' hitu, or ima ua =5/2 or 6/1 (karakoi ka pea). </div> <div>Quite mongrel systems.</div> <div> </div> <div>Some of the Formosan number systems may be similar to this.</div> <div> </div> <div>Or something else:<BR>Makassarese: 8=7+1 - mystery in Sulawesi, but many languages </div> <div>in Borneo have 7= tudju (or cognate) and 8 = aya, hanga, or </div> <div>mai, followed by 9 =
piah, jalatien, riqi (or cognates), </div> <div>which look as if they might just be 'start-agains'.</div> <div> </div> <div>Cognates of 'hanga' for 8 also appear in the Solomons. </div> <div> </div> <div>(I have no translations or even speculative etymologies for </div> <div>any of them, having 'discovered' them only yesterday, thanks </div> <div>to Anthony Jukes giving me the link to his excellent new Makassarese </div> <div>Grammar at: <A href="http://www.sendspace.com/file/2ps9y0">http://www.sendspace.com/file/2ps9y0</A>).</div> <div>----------------------------------------------------------</div> <div> </div> <div>This evidence, plus several quite scattered and different </div> <div>'subtractive from 10' systems, suggests that Austronesian </div> <div>number systems may have evolved individually through </div> <div>separate stages in many different areas, ,just as 'Papuan' , and </div> <div>many other languages appear to have done.</div>
<div> </div> <div>They could then have invented or borrowed new words for </div> <div>increasing needs to count exchangeable agricultural or </div> <div>fishing surpluses, and later again adopted very widespread </div> <div>loanwords with more contact and real trade, perhaps long </div> <div>after proto-Austronesians or proto-Oceanics were actually </div> <div>speaking those languages.</div> <div> </div> <div>(Perhaps, like the Kilivila (Trobriand) chief who got to </div> <div>9000 and 10000, for counting shells, and ran out of options, </div> <div>they just invented new words on the spot).</div> <div> </div> <div>Going through New Guinean language records, it's very </div> <div>obvious that the new decimal Tok Pisin has influenced modern </div> <div>speakers very quickly, obliterating earlier recorded </div> <div>systems, at least in the higher numbers. The overlaying </div> <div>process is ongoing, and very visible.</div> <div> </div>
<div>In my Filipino village, everyone now uses Spanish numbers </div> <div>for trade, and nobody can tell me the 'real Surigaonon' for </div> <div>10, any teens, or 20 up, except 'gatus'=100, which is still </div> <div>used in fishing and agriculture. But the 'native' system was </div> <div>decimal anyway, so there's no radical system change.<BR>----------------------------------------------------------</div> <div>It should be quite possible, then, to infer multiple </div> <div>overlays of newer systems on old. </div> <div> </div> <div>Tongan may be an example: <BR>10 = hongofulu<BR>20 = tekau<BR>50 = nai rima avuru (why has hongofulu become avuru?)</div> <div> </div> <div>The only An languages that seem to have preserved </div> <div>traces of apparent original number systems are out of the </div> <div>mainstream: </div> <div><BR>Formosa, Ilongot, Borneo, Sumba, Flores, Timor, SW Maluku, </div> <div>Micronesia, and all of Melanesia south of a
fairly definite </div> <div>line.</div> <div> </div> <div>regards</div> <div> </div> <div>Richard<BR></div>