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VNU Jo jm a l of Science, Sociol Sciences a n d H um anities 25, No.5E (2009) 1-11 Word foimation in the C a r d i n a l number systems across languages (Mathematical problems in numbers) Hoang Thi Chau* College o f Socìtil Sciences and Humanities, VNU 336 Nguy en Trai, Thanh Xuan, Hcỉtìoi, Vietnam Rcceived 15 December2009 A b s tr a c t T h e C ardinal n u m b e r sy s te m is a d d re sse d in th is p a p e r a s a sm a ll y e t ty p ic a l sig n sy stc m in its larger sign super-system - language The biíaceted nature of signs is clearly demonstratcd: m o s t n u m b e r s h a v e d o u b l c m c a n i n g s , o n e is s t r u c t u r a l \v h ile th e o t h e r is l e x i c a l F o r i n s t a n c e , in Vietnamcse, the numbcr “ ỉbrty four" lexically denotes “the next number ìer 43 in natural numbcr chains'\ and structuralỉy means 4x10+4 Meamvhile, irv Prench, numbcr “ 80" is quatre-vingt (4x20) vvith ihc lexical nicaning o f “eighty” while it structuralỉy means “4x20”; and number “70” soixaní-dix has the structure “60+10" Deep undcr thc addition and multiplication problems mentioned abovc are mathcmatical thoughts and ỉanguages of thcse nations: thc Vietnamese is based on the dccinial numeration wlìile the French use the degisemal numeration The data used in this analysis are rcstricted vvithin languages of ethnic minoritics in Vietnam and tvvo major language families in Southcast Asia, namely Austroasiatic and Austronesian, or to be more precisc, Austro-Tai, which are closely reỉated to the Vietnamesc ỉanguage In order to clearly identify featurcs of word formation in the numbers of isolating, analytic ỉanguages in Vietnam and Southeast Asia, comparative and contrastive analyses have becn made against the number systcms o f Ỉndo-Europcan languagcs representative of the synthctic typoỉogy and familiar to us, incluđing French, English and German, beíore the following conclusions arc made: Numbers are thc most basic vvords among the basic, i.e the most ancicnt The number system of each nation has been developed through a long process of thousands o f years The 10 basic vvords have transíormcd into 100 others by employing one or morc of thcse: morphological changc, aíTixation, word combination, and word order change The numbcr systcms are highly systematic vvith fixed structure However, partial or totaỉ borrovvings of an cntirc system are still possiblc This is an inỉtial structural investigation of the linguistic íbrm of the numeration systcms with a vievv to identifying the steps in the íormation of language and thought in a narrovv sensc The investigation of the number systcms in diíĩerent European and Asian regions, across v a rio u s la n g u a g e fa m ilie s, h c lp s re v e a l th e ir u n iv e rsa litie s a s w e ll a s ty p ic a litic s in th e ir lan g u ag c formulation and development process The Cardinal numbcr system is addressed in this paper as a small yet typical sign system in its largcr sign super-system - language The bifaceted nature o fsig n s is clearly demonstrated: Tel : 84-4-8531855 H.T Chau / V N U ịournnì o f Science, Social Sciences and H um arities 25, No.5F (2009) 1-11 most numbers havc double mcanings, one is structural(1) while thc other is lcxical For instance: - In Vietnamese, the numbcr “ forty four” lexically denotes "th ỏ icơ m ": " th ổ i" changed ils m eaning into "náu " blow fire hoiI ricc > blovv rice “Cook rice.” 2.3 Number 10 - "one te n " in M ôn - Khmer languages Number 10, witl) the cxception o f đổp in Khmer, and “ mười” in Viet-Muong group, is the same “ muôi chit” (“one ten” ) in all other languages with such phonetic variants as: mi chi! / m ươi chiet / m òi chai m ói jé l / m já t / m oi j t / mát "One ten” is a critical number o f the decimal system marking a novel progrcss from finger counting, and forming the basis for continuation: In Bru for instance: " I I " : m uôi clnrt la m uôi (one ten a n done) "12 m uôi chirt la bar (une ten a n d two) "20 bar chirt (two ten) Also ‘one ten ’ is used as a basis to count larger numbcrs like ‘onc liundred, one thousand’, and 'o n e million’ In other lanauaaes, Indo-Europcan ones, for example, just ‘hundred thousand, miliion’, etc., are used \\ithout the preceding w ord ‘o n e’ In Chrau languagc (Bahnar South), “ 10” is m át, shortcned from m uôi j â l - “ one ten” ; “ 12” is m át var; but “20” is var jđ t, “ 30” is p e já t [6, p.76-77] It is possiblc to hypothesize tha! in Vietnamese in the past, “ 10" vvas m chât/jât, \vhich was repcatcd in various combinations I ! (one ten and onc), 12 (one ten and two), etc., and íinally reduccd to only tw o words - the initial and the final oncs; “ mươi” stands at the íront to bear the lexical meaning o f the whole combinalion and takcs on a new meaning ‘one ten" This is similar to the lcxical semantic change o f "đu n ” and “thổi” lo “ nấu” in modern Vietnamese: “đun cùi nấu n c " > "đun nư ớc": "đun" changed ils m eaning into "nấu ” push vvood boil watcr > push water “boil vvatcr.” Today, electricity is used to cook rice and boil water, but thc language remains "thổi cơm’' and "đun nước” Forming numbers with addition and multiplication is diffcrcntiated in Victnamese by changinii thc tones and vvord orders: mười hai mựời ba mười bốn hai mưoi ba mươi ten tvvo ten three ten four two ten three ten 10+2 10+3 10+4 2x10 3x10 or by phonetical change, reduction or blending: "hai m i" > “hâm "; "ba m i" > "băm " hăm mốt băm hai hăm lăm/nhăm bốn tư twenty one thirty two twcnty five forty four 20+1 30+2 20+5 40+4 and “một trăm tư” (one hundred four - 140) distinct from “ trăm linh bốn” (one hundred and four - 104) Thesc investigations reveal that vvord formation in thc numbcr systems in Vietnamese as vvell as other isolating languages does not only involve the combination o f word and word order change, as wc ve so far believed, but also phonetical transíormation similar to morphological change of Indo-Buropean languages, and this phonetical change has been used in a very ílexible way 2.4 K hm er numbers Khmer number systern is a perfect model of ứie combination o f íinger counting and the decimal system, o f basic Khmer words and loans from ancient Sino It is interesting that /7.7 Chau / VN U lourtuĩl o f Science, Social Sciences and Humanities 25, No.5E (21)09) 2-27 ancient Sino borrowings are uscd as íoundation for upper ordcrs o f the decimal system, and function as the basic word in vvord Ibrmation What vvcrc borrovved were the materials to build up Khmer number system, vvhiclì diỉTers from Thai languagcs that borrovvcd the whole ancient Sino numbcr system The usc o f alien loan words to make the 'ten* likc sam sấp - “30”, s e sấ p - “40" vvould have rcsultcd in their loss o f \vord-forming meaning, leaving only thc lcxical onc, i.e total elimination o f niultiplication (3x10), \vhich leaves only the result (30) The entire system merely uses simplc addition, as simple as vvord combination For instancc sam sáp m i “ 31” (three ten - one) It sTiccs for the user just to add the ‘ten’ digit lo the unit digits in Khmcr language to count till 100,S) đỏp “ 10” muôi môphey “20" pi s a m s â p “ ” bây se sáp “40” bn sáp "50" prâm hót sảp “60" prăm muỏi chétsâp pét sâp kảusâp muôi roi ti Ị 11 môphey muôi = “2” 4*2 I ” sam sáp buôn = “34” “4 se sàp prãtìĩ “5 mi = “46” *‘6" (5+1) sản prăm “7" (5+2) hây Ị 5g,, u3 ” “70" pram pi “80" Pfăm “90" prăm buôn “9” (5+4) f,ui-)n*=p“69" “ 100” prămbây I8IÍ5+Ĩ** Anothcr comparison o f the numbcrs from to 100 in Indo-European languages can provide us vvith an impressive and comprehensive view o f the íormation and content o f the language substance and tens in French, Victnamcsc: English, Prcnch 3.trois 4.quatrc I3.treize 14.quatorze 30.trente 40.quarantc English 3.thrcc four 13.thirleen 14.fourtcen 30.thirty 40.forly Gcrman drei 4.vicr 13.dreizehn 14.vierzchn 30 dreizig 40.vicr/jg Victnamcse 3.ba 4.bốn 13.mười ba 14.mười bốn ba m i b ố n m i German an 5.cinq 15.quinzc so.cinquante 5.five I5.fifteen 50.fifty 5.fủnf 15.fúnfzchn 50.fiinfzig 5.năm I5.mưòi làm 50.năm mươi 3.2 Through íhe p re se n te d exơmples, it i possihle lo conclude as fo llo w s In French and all the thrcc Indo-Iìuropcai languagcs undcr comparison, thc numbers lesi than 10 are common roots, wlìile thc numberi above 10 and the ‘tens’ arc dcrivatives in botl ways: inorphological change and suiTixation c.g trois > treize trente English and German mostly use worc combinaiion, vvith slight phonetical change likt “ mười” and “ mươi” in Vietnamese In addition Vielnamese changes the word ordcrs, followinj the ordcrs o f the numbcr, i.c the unit standí aftcr thc tcn “ 13” “30” mưòiba Ba mưoi thirlccn thirty drci/ehn dreizig In d o -E u ro p c an 3.3 Apart fro m the afore-mentionec similariíies, the com pared num ber systems show íhe fo llo w in g differences: 3.1 The follow ing table can providc a useful comparison o f the numbers lcss than 10, over 10 3.1 In German thc ordcr o f the odc numbcrs above 10 (from 21 to 99) is reversed the unit is place before the ten N u m b c r languagcs systems in (8) Spccial thanks lo L)r Nguyễn Văn Chién for providing us vvilh invaluablc corpus in Khmcr "21 ” - em im dz\vanzig (one a n d twenty) "9 " - neun utidneum ÌỊỊ (nine andìùìiety) II T Chrnt / VN U lournnl o f Science, Social Sciences and Humanities 25, No.5E (2009) 1-11 ?.3 In Frcnch, the num bcrs lcss than 70 rc íb rm c d on th e b a sis of th c d ccim al umcralion, vvhile those above 70 use thc igesimal numeration: "60 - soixante (sixty) Oriỉer 3: Form num bers 16 to 19 on the basis o f 15 "1 " - un a r bym lheg (one a n d fìfteen + 15) (p > h) "1 " - peihvar a r hym theg (fuur andfifteen "70 - soixante-dix (sixty-len) 4+15) "71 - soixante-otìie (sixty-eleven) O rder 4: Start to build up numbers using thc degisemal num eration taking 20 as thc most basic num bcr for thc vvhole system: “20" ugain (changcd into vinỊỊt in P r e n c h ) From novv on, ugain alw ays takes the Hnal position, cxccpt for num ber 50 The ncxt basic numbers include: "80 " - quatre-vìngt (four-tw enly)'JI "9 " - quatre-vingt-dix cfour-twenty-ten) "99 - quatre-vingt-dix-neụ\f ựour-twenty- en-nine) Such uniqueness and originality o f the ìcrnian and French num ber system s vverc iriginatcd from the ancicnt languagc o f Celtic lass, particularly G auls"0), the language o f the ndigcnous inhabitants who uscd to dwell upon he tcrritoiy o f present-day France and Gcrmany housands o f years B.C.E until the Roman ■mpirc cxpanded to all over Europe "4 " - deugain (lwo - tw o len, 2x20) "6 " - Irigain (three - tw o ten, 3x20) "80 " - pechvar ugain (four - [MO len 4x20) Betvveen these landmark numbers are com binations with I to 19 e.g "2 " - un ar hugain (one a n d two len, +20) The G aul num ber system is wonderful rvidcnce whicli enables us to visualisc a pattern ‘or building up the num bcrs from to 100 using hc degisemal num cration w hich is carricd out irdcr by orđer like this: tìrd er 1: Use 10 basic num bers, ju st likc Mhcr Indo-European languagcs: l.u n dau tri p e d w a r p u m p chvvech sa ith w y th n a w 10 d e g O rder 2: Combine num bers to make 11 to 15 in a consistent m anner throughout the iystem: the basic num bcr 10 - (ieg always ỉssum es the final position "22 " - (ìau a r hugain (two a n d two len, 2+20) This inversc order w as im ported German to form num bcrs from 21 to 99 into e.g "2 " - ein u n d zwartzig (one and twenly, 1+20) "9 " - n e m u n d neuraig (nine and ninety, 9+90) N um bcrs 30, 70 and 90 are not marked basic num bers like those in the decimal num eration; rather, they are merely ordinary numbcrs, c.g in Gauls "3 " - (ỉeg ar hugain (ten a n d tw o len, " I I " - undeg (one ten) 10 +20) "12 " - daudeg (two ten) “7 " - ileg a Irigain (len an d íhree - lwo ten 10+3x20) "15 " - pu m lheg (five ten) (p d > ih) "9 " - deg a p ed w a r ugain (ten a n d fo u r*' In English, for a tim e, score w as also uscd as num bcr 20, and numbcr w as also form cd by com bining ‘four scorcs’, vcry much like French I0’ The languagc o f the G auls is slill uscd as a living languagc (local longue) in W ales, Soulhw csl o f the UK Scc refcrcncc 28 two ten, 10+4x20) in French: "70 ” - soixante-dix (sixty-ten, 60 + ì 0) "71 ” - soìxante-onze (sixty-eleven, 60+11) 10 /7.7* Chau / VN U Ịoum aỉ of Science, Sociaỉ Sâences and ỉỉurtuĩrtities 25, No.5F (2009) 1-71 “9 " - quatre-vingt-dix (four-twerưy-ten, 4x20+10) 4491 ” - quatre-vingt-om e eleven 4x20+11) (four-twenty- It is clear that French uses the degisem al numeration o f the Gauls to build up the latter part o f their number system (from 70 to 99) (see 3.2.2) From numbcr 100 - canỉ, a common number am ong Indo-European languages, the Gauls people crcatcd num bcr 50 - hưnner cant, i.e Vi o f 100 This is probably a ncw number 50 in substitution for an oldcr onc íorm cd by using the degiscm al numeration 3.5 The universality o f the num ber system structure 3.5.1 The struclure o f the G auls numeration system enables us to visualize an impressive five-storey ancient castlc, witlì the foundation and upper tloors, which diffcrs ỉronì modern squarish high-rise blocks, i.e the decimal system which is becoming increasingly popular and allovvs onc to count until infinity thanks to its sim plicily and conveniencc in massive assemblies The structure o f thc dcgisemal numeration ju st cxam ined in G auls is selfeviđent wilh regards to its age It starts from counting parts o f the human body: the two hands, and then the tvvo feet Suclì counting may possibly have cxisted long am ong the primitive tribes living on hunting and gathering When humans kncvv how to domcsticatc animals and did agricultural farming, the number systcm s vvere lopped up vvith lìigher floors vvith various vvays o f thinking on the basis o f degisem al or binary num eration in diíĩerent localities, as expressed in their languages 3.5.2 The num ber system s in Austroasiatic and Austroncsian (A ustro-Tai) families also d isp la y sim ilar structure in th c ío u n d a tio n - finger counts In A ustroasiatic languages only K hm cr retains this íìngcr-count m anner num bcr - p r ă m m uôi (5+ 1); “ ” - p r ă m J (5+2); “ 8” - p r ă m húy (5+3); “ 9” - p r ă m buc (5+ 4) as a kind o f m useum In o th er Moi K hm er languagcs, thcy arc replaced \vii num bcrs “six, seven, eig h t" and “ nine” , formin 10 basic num bcrs which servc as the íoundatio for thc decim al num cration, and a special iori is given to num ber 10: m i c h (one ten) 3.5.3 A ustro-Tai languages build up the num bcrs in tvvo ways: - L anguagcs o f the T hai branch b o rro u c the num bers from ancienỉ Sino vvhich used th decim al num eration - Kadai and M alayo-Polynesian languagc posscss a prim itivc num ber system : íinger coun (6 - + , , = 5+4), which is still retaincd ii several indigenous languages in Taivvan Thi contractcd results o f ihis addition problem (5+1 5+2, 5+3, 5+4) are the four num bers “6 ” ♦enem ; T - *pitu; “ 8” - *w alu; “9” - *siwa Ì! PM P, w hich arc bcing used in the remaininị T aiw anese languages and present-day Kada and M alayo-Polynesian languages Then thí system continues to build upon the decima systcm Kadai and M alayo-Polynesiaí languages in V ictnam also preserve such tracci in its ovvn vvay In sum , the dilTcrcnccs am o n c Austroasiati( and A ustroncsian languages in the bascs o f th( num bers lic in tlial A ustronesian use th( contractcd form s o f old num bers whilc A uslroasiatic use new rcplacem ents Conclusion I N um bers arc thc m ost basic vvords among the basic, i.c the most ancient The numbei system o f each nation has been developcd through a long process o f thousands o f ycars T he 10 basic w ords have transfonned into 100 othcrs in ihe follow ing manners: H.T Chau / VN U loum aỉ o f Science, Socinl Sciences and Humanities 25, No.5E (2009) 1-11 II [10] Bùi K hánh T h ế (ed ), “Việt - Chăm D ictionary'\ “C hâm - V iệt D ictionary,\ Social Sciences P ublisher, H anoi, 1996 - Morphological change - Affixation - W o rd c o m b in a tio n [11] B u rusphat s , “Eỉem entary Thai f o r fo reig n ers'\ M ahidol U nivcrsity, 1991 - Word order change The number system s are lìighly system atic 'ith fixed structure Hovvever, partial or total orrovvings o f an entire system arc still possible This is an initial structural investigation f the linguistic form o f the num eration system s /ith a view to identifying thc stcps in the m nation o f languagc and tliouglìt in a narrow ense The investigation o f the num ber system s diíĩcrent European and A sian regions, across arious languagể fam ilies, helps reveal their nivcrsalities as well as typicalities in their inguage formulation and dcvelopm ent process [12] Đ oàn V ăn P húc, “P honetics o f Ẻ đ ê '\ Doctoral D issertation, H anoi 1993 [13] E dm ondson, Jcrold A , D evid B Solnit (eds), “Comporaiive Kaclai lingiíistics studies beyond T a i'\ D allas: SIL /U T A Series in L inguistics [14] F uller, E., “C hru Vocabuỉary'\ SIL 1997 [15] G regerson, K enneth, Vocabuỉary", S IL , 1977 M arilyn, “Rengao [16] H o àn g L ơng, UA glim pse aí the Kadai ethnic com m unities o f Vietnam: an anthropological síu d y \ D iscussions in K adai and SE A sian L inguistics C oordinator: Jerold A Edm ondson IV , 10/1994 [17] H ồng T uệ, (ed), “Learning Pakơh - Tih languages” textbook, People’s Committcc of B ình Trị T hiên P rovince, 1986 [18] H oàng Văn M a, T V ăn T h ô n g , “The Language o f Bru - Ván K iều ” , Social Sciences Publishcr, H anoi, 1998 Leícrences [19] H o àn g Văn L anguage'\ [ ] I R einecke, A , N g u y ễn C h iề u , L âm T hị M ỹ D ung, “Ateu' Findings o f S a H uynh C u ltu re '\ L indcn S o íì, 2002 [2J T h o m as, D , Thồ Sàng Lục , “ C h u V o c a b u la ry ” , SIL 1966 [3] C o h en , p , "Jeh V o ca b u ỉa rỳ\ SIL, 1970 M a, V ũ B H ùng, “Pupeo Social Sciences Publisher, H anoi.1992 [20] K osaka R., “A Descriptive Study o f the Lachi Language - syntactic descripíion historical reconstructìon a n d geneíic reỉation ” , D octoral D issertation, U niversity o f Foreign Languages, T o k y o f 2000 [4] H ein e - G e ld e m , R , “ P rim itiv c G c o g p h ic a ỉ T errito ry and th e E a rlic st M ig tio n s o f th e A u stro n esian s,\ Anthropers, voỉ X X V II (1 ), 543-619 [21] Lâm Đồng Province, “Việt - Kơho Dictionary”, [5] N atio n al C e n te r fo r S o c ia l S c ie n c e s and H u m an ities, H istory ỉnstitute, "V ietnam H isíoric Evenís (from a n c ie n t lim e to 1858)” , E d u catio n P ub ỉish er, 2001 [23] N guyễn Phú P hong, T rần T rí D ồi, Fer!us M , “Lexique Vietnamien R uc-F rancais'\ Paris 1988 [6] S m ith, K D , “A phonological reconstruction o f P roío - N orth - Bahnaric L anguage D ata ” , A sian P a c iíic S eries N o , S IL , 1972 [7] A w i-h a th e , A v io n g , Rơglai C o ỉlcctio n o f V ietn am ese E thnic l.a n g u a g e s, vo ỉ , part 1, p 99 G lossary , M in o rity [8] Đ en ed ỉct, Paul K , “A ustro - Thai: L anguage a n d C uỉture , Nevv H eaven: H R A F [9] B en ed ict, Paul K “Thai - K adai a n d ỉndonesian: a new aiignm ení in Southeastern A m erican A n th o p o lo g ist, N o 4 , 1942 Asia"y 1983 [22] M ussay, G , “ D ictio n n aire Cảm - Vietnamien - Francais'\ Phan Rang, 1971 [24] R em ah, D el, u Việt - G iarai Dictionary ” , Social S ciences P ublisher, H anoi, 1977 [25] S agart L “T he H ig h er Phylogeny of A u stronesian and the P osition o f T - K adai”, O ceanic Linguisticsy V ol , N o.2 [26] S m ith, K D , “Sedang Vocabuỉary, Sedang - Viet E nglish ’è, SIL, S aig o n 1967 [27] V y T hị B é, Sauỉ, J.E , W ilso n , N F , “N ung Phan Síihng English D ic tio n a rỷ \ S IL , 1982 [28] W alter, H , L aventure des langues en Occidení, Roberí Laffonty S.A , P aris, 1994, pp 90-93 [29] W atsont R ichard, S aundra, “Pacoh - Viet English G ỉossary >SIL 1979 ... in existence until novv and built up the number system to in inity A closer investigation can shovv us the clear mismatch in the two combined parts in Roglai number system The mismatch lies in. .. closely rclatcd to the Victnamcse language In order to clearly identi fy featurcs of word formation in the numbers o f isolating, analytic languages in Vietnam and Southeast Asia, comparative and... roup uscs these numbers in the reverse ordcr, as number I in forming numbcr 8, and number in forming numbcr This could be temporarily explained that the Ede and Giarai peoplc, when borrowing numbcrs
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