Ethno-mathematics Ethno-mathematics in Amarasi: how to count 400 ears of corn „ multiple counting systems in 60 seconds „ loan systems „ associated with different contexts Heronimus Bani, SPd & „ may not be known by all speakers Charles E. Grimes, PhD „ English “stone” (+Commonwealth;-American) „ Psalm 90:10 (KJV) Language & Culture Unit (UBB), „ The days of our years are three score and ten… „ Abraham Lincoln: Gettysburg Address

„ Four score and seven years ago, our fathers…

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Sociolinguistic profile

„ ISO: aaz

„ ±60,000 speakers

„ Main dialects: Kotos and Ro'is

„ Part of Uab Meto language/dialect chain

„ ISO: aoz

„ people referred to as ‘’

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Word shapes: metathesis Word shapes: truncation

„ asu ‘dog’ [PMP *asu ‘dog’] „ an-fani ‘3-turn, return’ [PMP *balik ‘turn’] aus metan ‘black dog’ [metathesis] n-fani ‘3-turn, return’ [truncation of prefix] na-fani’ ‘3-turn s.t., return s.t.’ „ umi ~ ume ‘house’ [PMP *Rumaq ‘house’] [transitive; prefix na- vs. an-] uim onen ‘house of prayer’ [metathesis] n-fain ‘3-turn, return’ umi skoor ‘school building’ [metathesis] [truncation of prefix; metathesis of root] n-fani-n‘3-turn, return-3p’ [truncation of prefix] an-fani-n ‘3-turn, return-3p’

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Bani-Grimes Amarasi corn-ICLDC 2011 1 Word shapes: truncation (2) Head-marking: infl of prep

„ an-taam ‘3-enter’ [metathesis of root] „ a'bi ~ 'bi ‘1s-at’ n-taam ‘3-enter’ ambi ~ mbi ‘2-at’ [truncation of prefix; metathesis of root] anbi ~ nbi ‘3s-at’ na-taam ‘3-put in s.t.’ atbi ~ tbi ‘1pi-at’ [transitive; metathesis of prefix] ambi ~ mbi ‘1px-at’ n-tama-n ‘3-enter-3p’ [truncation of prefix] anbin ~ nbin ‘3p-at’

an-tama-n ‘3-enter-3p’ „ ma ~ am ~ m ‘and (conjunction)’

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Basic Amarasi numbers numerals follow head noun

PAN or PMP Amarasi gloss Comment „ tua-f nua ‘two people’ 1 es, mese' one, a, single *isa, *əsa usi-f niim ‘five kings’ 2 nua two *DuSa *D Æ /n/ 3 teun ~ tenu three *təlu *l Æ /n/; metathesis neno nee ‘six days’ *p Æ /h/; metathesis; lose 4 haa four *apat final C 'poni hiut ‘seven baskets’ 5 niim ~ nima five *lima *l Æ /n/ 6 nee six *ənəm metathesis; lose final C 7 hiut ~ hitu seven *pitu *p Æ /h/; metathesis *w Æ /f/ (#_); *l Æ /n/; 8 faun ~ fanu eight *walu metathesis 9 seo / sea nine *siwa dialect differences 10 bo'es ten (one ten) 9 10

Teens: bo'es, plus ma ‘and’ Multiples of ten

Amarasi gloss Amarasi gloss 20 bo' nua twenty 11 bo'es am mese' eleven 21 bo' nua m-mese' twenty one 12 bo'es am nua twelve 22 bo' nua m-nua twenty two 13 bo'es am teun thirteen 23 bo' nua m-teun twenty three 14 bo'es am haa fourteen 24 bo' nua m-haa twenty four 15 bo'es am niim fifteen 25 bo' nua m-niim twenty five 16 bo'es am nee sixteen 26 bo' nua m-nee twenty six 27 twenty seven 17 bo'es am hiut seventeen bo' nua m-hiut 28 bo' nua m-faun twenty eight 18 bo'es am faun eighteen 29 bo' nua m-seo / sea twenty nine 19 bo'es am seo / sea nineteen 11 12

Bani-Grimes Amarasi corn-ICLDC 2011 2 Multiples of ten (2) Hundreds & thousands

30 bo' teun thirty Amarasi gloss 35 bo' tenu m-niim thirty five 100 natun mese' one hundred (PMP *Ratus) 40 bo' haa forty 200 natun nua two hundred 50 fifty bo' niim 300 natun teun three hundred 53 bo' nima m-teun fifty three 365 natun tenu m-bo' nee m-niim three hundred sixty five 60 bo' nee sixty 1,000 nifun mese‘ / niufn es one thousand (PMP *Ribu) 70 bo' hiut seventy 2,000 nifun nua two thousand 72 bo' hitu m-nua seventy two 8,000 nifun faun eight thousand 2010 nifun nua m-bo'es two thousand ten 80 bo' faun eighty 1945 nifun mese' m-natun seo / nineteen forty five 86 bo' fanu m-nee eighty six sea m-bo' haa m-niim 13 14 90 bo' seo / sea ninety 2,000,000 hoto nua two million

How to count? Gendered behaviour

Male knot Female knot (around) (through)

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Corn: which way to count? Individual ears of corn

Amarasi gloss „ soi' tain nima (based on 5s and 10s, x10) 1 one ear, a single ear „ rean es = 400 puin es 2 puni' nua two ears (*buliR ‘grainhead’) „ soi' tain ne'e (based on 4s and 8s, x12) 3 puni' teun three ears „ rean es = 384 4 puni' haa four ears 5 puni' niim five ears „ tu’us bo’es am nua (5s and 10s, x12) 6 puni' nee six ears „ rean es = 480 7 puni' hiut seven ears 8 puni' faun eight ears „ Different from TTS, TTU 9 puni' seo / sea nine ears 10 puni' bo'es ten ears 17 18

Bani-Grimes Amarasi corn-ICLDC 2011 3 tu'us (2 ties of five) tanin ‘two tu'us bundles' gloss Amarasi Amarasi equivalent Amarasi gloss 20 tu'us nua tain es one tanin (20) 10 tuu's es one bundle (of 10 ears) one tanin (20) 30 tu'us teun tain es am roit haa and a roit haa (10) 20 tu'us nua two bundles (of 10) 40 two tanin (40) 30 tu'us teun three bundles (of 10) tu'us haa tanin nua 2 tanin (40) 40 tu'us haa four bundles (of 10) 50 tu'us niim tanin nua m-roit haa and a roit haa (10) 50 tu'us niim five bundles (of 10) 60 tu'us nee tanin teun three tanin (60) 60 tu'us nee six bundles (of 10) three tanin (60) 70 tu'us hiut tanin teun m-roit haa 70 tu'us hiut seven bundles (of 10) and a roit haa (10) four tanin (80) 80 tu'us faun eight bundles (of 10) 80 tu'us faun tanin haa 90 nine bundles (of 10) four tanin (80) tu'us seo / sea 90 tu'us seo/sea tanin haa m-roit haa and a roit haa (10) 100 tu'us bo'es ten bundles (of 10) five tanin (100) 19 100 tu'us bo'es tanin niim 20

10 tu'us = 5 tanin = 1 suku Counting 400 ears of corn

Amarasi gloss „ . „ rean es ‘1 rean (=400)’ „ 100. suuk goes one suku = 'kouf goes 'kofu haa ‘4 'kofu (=400)’ 200 suku nua two suku = 'kofu nua suku haa ‘4 suku (=400)’ „ . 300 suku teun three suku = 'kofu teun tanin bo' nua ‘20 tanin (=400)’ „ 400. suku haa four suku = 'kofu haa tu'us bo' haa ‘40 tu'us (=400)’ „ 4 suku (4 'kofu) = rean es puni' natun haa ‘400 puni' (=400)’ „ bundle of 400 ears of corn

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Rean es (400) System 2: soi' tain ne'e

Amarasi gloss 8 tuu's es one bundle (of 8 ears) 16 tu'us nua two bundles (of 8) 24 tu'us teun three bundles (of 8) 32 tu'us haa four bundles (of 8) 40 tu'us niim five bundles (of 8) 48 tu'us nee six bundles (of 8) 56 tu'us hiut seven bundles (of 8) 64 tu'us faun eight bundles (of 8) 72 tu'us seo / sea nine bundles (of 8) 80 tu'us bo'es ten bundles (of 8) 88 tu'us bo'es am mese' eleven bundles (of 8) 23 96 tu'us bo'es am nua twelve bundles (of 8) 24

Bani-Grimes Amarasi corn-ICLDC 2011 4 12 tu'us = one suku 4 suku = 1 rean (384)

Amarasi gloss Amarasi gloss 384 rean es one rean (48 bundles of 8) 96 suuk goes one suku (12 bundles of 8) 768 rean nua two rean (96 bundles of 8) 192 suku nua two suku (24 bundles of 8) 1152 rean teun three rean (144 bundles of 8) 288 suku teun three suku (36 bundles of 8) 1536 rean haa four rean (192 bundles of 8) 1920 five rean (240 bundles of 8) 384 suku haa four suku (48 bundles of 8) rean niim 2304 rean nee six rean (288 bundles of 8) 384 rean es 2688 rean hiut seven rean (336 bundles of 8) 3072 rean faun eight rean (384 bundles of 8) 3456 rean seo / sea nine rean (432 bundles of 8) 3840 rean bo'es ten rean (480 bundles of 8) 25 26

Lots of corn to count & store Different systems

„ soi' tain nima „ suuk goes = tu'us bo'es (10 bundles x 10 =100) „ soi' tain ne'e „ suuk goes = tu'us bo'es am nua (8 x 12 =96)

„ (unnamed system) „ suuk goes = tu'us bo'es am nua (10 x 12 =120)

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Counting units Nearby systems

„ puni' ‘ear of corn’ „ TTS + TTU districts count by „ tu'us ‘tied bundle (8 or 10)’ kuda ‘(Malay) horse’ „ , , Amfo'an, Mollo, Miomafo, „ tanin ‘two bundles’ Insana, Biboki „ roit ‘four bundles’ „ 1 kuda = 8 tu'us bundles (80 ears) „ suku ‘10 or 12 bundles’ „ they do not use the rean units „ (tied for carrying) 'kofu = suku „ Tais Nonof (an Amarasi dialect) counts by nifu „ rean ‘four suku’ ‘thousand’

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Bani-Grimes Amarasi corn-ICLDC 2011 5 Cultural issues Why three counting systems?

„ Amarasi grow corn for food and seed „ soi' tain nima (rean = 400) is neutral; „ In general, they do not sell their corn the norm

„ TTS and TTU do sell corn „ soi' tain ne'e (rean = 384) is a way „ Once the corn is stored, only the mother has to hide laziness or misfortune of bad crop rd the right to retrieve it „ 3 system tu'us bo'es am nua (rean = 480) is

„ rations out for food over a year a way to hide hard work and bounty

„ ensures enough seed corn left for planting „ not just modest, but also self-protecting „ Amarasi stored in the ceiling; other regions in the „ How much? Everyone can claim “10 rean”; ‘round house’ „ 4,000 vs. 3,840 vs. 4,800 ears of corn 31 32

Current developments

„ excessive rains in 2011 st „ 1 planting died; 2nd planting died (borrowed seed)

„ some are planting tomatoes instead of corn

„ to sell for cash, to buy rice to eat

„ some investigating switching to candlenut (‘kukui nut’ in Hawai'i); st „ 3-4 years for 1 yield

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Bani-Grimes Amarasi corn-ICLDC 2011 6