カクトビック数字 - 人間と文化にあわせた多様な表現の可能性 / Kaktovik Numerals

by Sorami Hisamoto

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ΧΫτϏοΫ਺ࣈ ਓؒͱจԽʹ͋Θͤͨଟ༷ͳදݱͷՄೳੑ )*4".0504PSBNJ $P45&1ϓϨθϯԋश ը૾%"--u&Ͱੜ੒ 𝋅 𝋁 𝋃 𝋊 𝋒

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਺ࣈ ਺Λදݱ͢ΔͨΊͷه߸

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インド‧アラビア数字

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ʓҰೋࡾ࢛ ޒ࿡ࣣീ۝ ेඦઍສԯ 漢数字

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*******77 7*7**7****9 9-$%. ローマ数字

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ੈքʹ͸༷ʑͳ਺ࣈʢͦͯ͠จԽʣ͕͋Δ https://en.wikipedia.org/wiki/List_of_numeral_systems

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東アジア ௚ײతͳදݱըઢ๏ʢ͔ͤ͘Μ΄͏ʣ 欧州, 北⽶, 豪州などスペイン, 南⽶など

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ΠϯυɾΞϥϏΞ਺ࣈਓྨ্࢙ɺ࠷΋ීٴͨ͠ه๏ ेਐ๏ ҐऔΓه਺๏ ेछྨͷه߸Λ༻͍Δ ྫ͑͹ʮʯ͸ϩʔϚ਺ࣈͰʮ.$$999*7ʯ ه߸ͷҐஔʹΑΓʮܻʯΛද͢ Y 1 2 3 4 Y Y Y

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ΠϯυɾΞϥϏΞ਺ࣈਓྨ্࢙ɺ࠷΋ීٴͨ͠ه๏ ेਐ๏ ҐऔΓه਺๏ ेछྨͷه߸Λ༻͍Δ ྫ͑͹ʮʯ͸ϩʔϚ਺ࣈͰʮ.$$999*7ʯ ه߸ͷҐஔʹΑΓʮܻʯΛද͢ େ͖ͳ਺ࣈ΋؆ܿʹදݱ ࢉज़͕༰қʢzࢉ༻਺ࣈzʣ Y 1 2 3 4 Y Y Y

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͜Ε͚͕ͩ ࠷దͳ΍Γํͳͷ͔ʁ

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"Arctic Shore at Barrow Alaska”, Andrei , CC BY 2 . 0 https://commons.wikimedia.org/wiki/File:Arctic_Shore_at_Barrow_Alaska.jpg ΞϥεΧ࠷๺෦ /PSUI4MPQF#PSPVHI "MBTLB

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ΠψϐΞοτ*ÑVQJBU ΞϥεΧ๺෦ͷ๺ۃւԊ؛஍ҬʹॅΉઌॅຽ଒ "Inupiat Family from Noatak, Alaska, 1 929 ”, Edward S. Curtis, Public Domain https://commons.wikimedia.org/wiki/File:Inupiat_Family_from_Noatak,_Alaska,_ 19 2 9 ,_Edward_S._Curtis_(restored).jpg

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Floyd Davidson, CC BY SA 4 . 0 https://commons.wikimedia.org/wiki/File:Genuine_kunik.jpg ΠψϐΞοτ*ÑVQJBU ΞϥεΧ๺෦ͷ๺ۃւԊ؛஍ҬʹॅΉઌॅຽ଒

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ΧΫτϏοΫ ๺Ң౓ ๺ۃݍͷொ ਓޱʢ೥ʣ , B L U P W J L

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"Kaktovik, Alaska, DEW Line Site”, U.S. Fish and Wildlife Service, Public Domain https://commons.wikimedia.org/wiki/File:Kaktovik,_Alaska,_DEW_Line_Site.jpg

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https://www.cityofkaktovik.org/

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https://www.ktoo.org/ 20 18 / 0 9 / 03 /in-kaktovik-sea-ice-loss-means-a-boom-in-polar-bear-tourism/

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https://natgeo.nikkeibp.co.jp/nng/article/news/ 1 4 / 6834 /

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ΧΫτϏοΫ਺ࣈ ೥୅ʹൃ໌͞Εͨ

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋋 𝋌 𝋍 𝋎 𝋏 𝋐 𝋑 𝋒 𝋓

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋋 𝋌 𝋍 𝋎 𝋏 𝋐 𝋑 𝋒 𝋓 छྨͷه߸

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𝋀

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𝋀 𝋁 𝋂 𝋃 𝋄

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 ͱͷ ૊Έ߹Θͤ 𝋁 𝋅

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋏

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋏 ͕ೋͭɺࡾͭ

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋏 ͕ ౓ճస↪͔ͨͨͪ͠ Ͱ΋͋Δ ͕ೋͭɺࡾͭ

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋏 𝋋 𝋌 𝋍 𝋎 𝋐 𝋑 𝋒 𝋓

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𝋄 𝋓 Y Y ೋेਐه਺๏ೋेΛఈͱ͢ΔҐऔΓه਺๏

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𝋁 𝋁 Y ೋेਐه਺๏ೋेΛఈͱ͢ΔҐऔΓه਺๏ 𝋁 𝋁 Y Y Y

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Akrasia 2 5 , CC BY SA 4 . 0 https://commons.wikimedia.org/wiki/File:Abacus_Inuit.jpg ΧΫτϏοΫ਺ࣈͷͦΖ͹Μ

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Akrasia 2 5 , CC BY SA 4 . 0 https://commons.wikimedia.org/wiki/File:Abacus_Inuit.jpg ΧΫτϏοΫ਺ࣈͷͦΖ͹Μ

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋏 𝋋 𝋌 𝋍 𝋎 𝋐 𝋑 𝋒 𝋓

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ࢹ֮తͳੑ࣭

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𝋂 + 𝋂 = ଍͠ࢉ

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𝋂 + 𝋂 = 𝋄 ଍͠ࢉ

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Ҿ͖ࢉ - 𝋍 𝋍 𝋅 =

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Ҿ͖ࢉ - 𝋍 = 𝋅 𝋍 𝋅

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𝋃 ׂΓࢉ 𝋃 𝋏 𝋓 Y Y Y ʸ

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𝋃 ׂΓࢉ 𝋃 𝋏 𝋓 Y Y Y 𝋁 Y

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𝋃 ׂΓࢉ 𝋃 𝋏 𝋓 Y Y Y 𝋁 Y 𝋃 ͕ ݸ 𝋁 3 1 ʸ

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𝋃 ׂΓࢉ 𝋃 𝋏 𝋓 Y Y Y 𝋁 Y 𝋃 ͕ 3 ճసͨ͠ܗ

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𝋃 ׂΓࢉ 𝋃 𝋏 𝋓 Y Y Y 𝋁 𝋅 Y Y 𝋃 ͕ 3 ճసͨ͠ܗ ͕ 𝋁 1 ճసͨ͠ܗ ʸ

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𝋁 𝋅 𝋃 ׂΓࢉ 𝋃 𝋏 𝋓 Y Y Y 𝋁 𝋅 Y Y Y 𝋃 𝋏 ʸ

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𝋁 𝋅 𝋃 ׂΓࢉ 𝋃 𝋏 𝋓 Y Y Y 𝋁 𝋅 Y Y Y 𝋃 𝋏 ༨Γ 𝋁 1 ʸ༨Γ

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𝋆 𝋃 ׂΓࢉ 𝋃 𝋏 𝋓 Y Y Y 𝋁 𝋅 Y Y Y ʸ༨Γ 𝋃 𝋏

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AquitaneHungerForce , Public Domain https://en.wikipedia.org/wiki/File:Kaktovik_long_division_(chunked).svg ʸ

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ͳͥ ͱ ͳͷ͔ʁ

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ΠψϐΞοΫޠͰ ltallimatz͸ z࿹taliqlʹ༝དྷ ࿹ʹ͸ຊͷࢦ

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ΠψϐΞοΫޠͰ liñuiññaqz͸ lਓؒͷશମz ྆ख྆଍Ͱຊͷࢦ

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ൃ໌ͷܦҢ ೥୅ॳ಄ɺ ΧΫτϏοΫͷֶߍ)BSPME,BWFPMPPLTDIPPMͰߟҊ ʮΠψϐΞοΫޠͰͷ਺͑ํʯΛ ʮจࣈʯͰදه͢Δतۀ՝୊ͱͯ͠։࢝ ڭࢣ8JMMJBN#BSUMFZࢦಋͷ΋ͱɺ ౰࣌ͷதֶߍɺશߍੜె໊Ͱ࡞੒

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ΧΫτϏοΫ਺ࣈͷ ීٴͱӨڹ

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https://www.unicode.org/L 2 /L 2 02 1 / 2 1058 r-kaktovik-numerals.pdf ΞϥεΧ๺෦ֶ۠ͷΧϦΩϡϥϜʹಋೖ

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https://www.unicode.org/L 2 /L 2 02 1 / 2 1058 r-kaktovik-numerals.pdf

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https://www.unicode.org/L 2 /L 2 02 1 / 2 1058 r-kaktovik-numerals.pdf

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2008 Jun 12 03:54:25 2008 Jun 12 04:45:24 Qawiaraq Inupiatun Inupiatun Inuinnaqtun Siglitun Natsilingmiutut Aivilimmiutut Nunavimmiutitut Nunatsiavummiutut Qikiqtaaluk nigiani Kalaallisut Kalaallisut Tunumiit Tunumiit oraasiat oraasiat Avanersuaq Qikiqtaaluk Qikiqtaaluk uannangani uannangani Kivallirmiutut Kivallirmiutut Asybaris 01 , CC BY SA 3 . 0 https://commons.wikimedia.org/wiki/File:Inuktitut_dialect_map.svg ๺ۃ஍ํʹ͓͚Δ ΠψΠοτޠมछͷ෼෍

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ڭҭ΁ͷӨڹ ೥ɺΧΫτϏοΫͰ ਺ֶ౷Ұࢼݧ$BMJGPSOJB"DIJFWFNFOU5FTU ͷ ੒੷͕ඈ༂తʹ޲্ ͦΕ·Ͱ͸ԼҐͩͬͨͷ͕ɺ ΧΫτϏοΫ਺ࣈͷߟҊޙɺ ฏۉΛ௒͑Δ·Ͱʹͳͬͨ

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भ֎͔Βͷڭࢣͷྲྀೖ΍ɺඪ४ςετͷ૿ՃͳͲͷӨڹ ·ͨɺ࿈๜੓෎ʹΑΔʮམͪ͜΅Ε๷ࢭʯ੓ࡦͷ΋ͱɺಉ஍Ҭͷֶߍ͸ ࠃͷج४Λຬ͍ͨͯ͠ͳ͍ͱͯ͠ݫ੍͍͠ࡋΛड͚ɺ ด࠯ʹ௥͍ࠐ·Εͨ͜ͱ΋͋ͬͨɻ ͦΕʹΑͬͯੜͨ͡ʮڪා৺ʯ͔Βɺಋೖ͕᪳᪯͞Ε͍ͯΔ ݱࡏɺ࣮ࡍʹ࢖ΘΕ͍ͯΔͷ͸ΠψϐΞοΫޠͷڭࣨͷΈ ͔͠͠ ͦͷޮՌ͕࣮ূ͞Ε͍ͯΔʹ΋ؔΘΒͣɺ ಋೖͷن໛͸ॖখ͞Ε͍ͯΔ

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σδλϧͷੈք΁ ීٴ΁޲͚ͯ

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Ϣχίʔυ ੈքதͷจࣈ΍ه߸Λࣝผ͢ΔͨΊͷࠃࡍن֨

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೥݄ɺΧΫτϏοΫ਺ࣈɺ࠷ॳͷఏҊ ೥݄ɺϢχίʔυͰಋೖ https://www.unicode.org/charts/PDF/Unicode- 15 . 0 /U 150 - 1 D 2 C 0 .pdf

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೥݄ɺΧΫτϏοΫ਺ࣈɺ࠷ॳͷఏҊ ೥݄ɺϢχίʔυͰಋೖ https://www.unicode.org/charts/PDF/Unicode- 15 . 0 /U 150 - 1 D 2 C 0 .pdf ͜Ε·Ͱ͸ ʮखॻ͖ʯʮࣸਅʯͩͬͨͷ͕ɺ ίϯϐϡʔλʔͰѻ͑ΔΑ͏ʹͳͬͨ

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೥݄ɺΧΫτϏοΫ਺ࣈɺ࠷ॳͷఏҊ ೥݄ɺϢχίʔυͰಋೖ https://www.unicode.org/charts/PDF/Unicode- 15 . 0 /U 150 - 1 D 2 C 0 .pdf ৘ใͷ΍ΓͱΓ΍ɺ ڭࡐͷ࡞੒ͳͲ͕༰қʹͳΔ طଘͷܭࢉΤϯδϯ΋׆༻Ͱ͖Δ

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋋 𝋌 𝋍 𝋎 𝋏 𝋐 𝋑 𝋒 𝋓 𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋋 𝋌 𝋍 𝋎 𝋏 𝋐 𝋑 𝋒 𝋓 Noto Sans Symbol 2 Gentium Kaktovik ͋ΘͤͯϑΥϯτ΋։ൃ͞Ε͍ͯΔ https://languagetools- 153 41 9 .appspot.com/ik/downloads/

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https://github.com/notofonts/symbols/pull/ 67 https://fonts.google.com/noto/specimen/Noto+Sans+Symbols+ 2

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https://languagetools- 153 41 9 .appspot.com/ik/

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https://languagetools- 153 41 9 .appspot.com/ik/numerals/

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https://crates.io/crates/kaktovik

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https://en.wikipedia.org/wiki/Ethnomathematics ຽ଒਺ֶ&UIOPNBUIFNBUJDT ྫ͑͹ɺ ωΠς ΟϒɾΞ ϝϦΧϯͷ νΣϩΩʔ଒΋ ͦͷݴޠͷͨΊͷԻઅจࣈɾه਺๏Λ ൃҊ͠ ͍ͯΔ

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋋 𝋌 𝋍 𝋎 𝋏 𝋐 𝋑 𝋒 𝋓 ࠓͷ΍Γํ͚͕ͩ ࠷ྑͱ͸ݶΒͳ͍ ͦΕͧΕʹదͨ͠ ଟ༷ͳදݱ͕͋ΓಘΔ

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𝋀 𝋁 𝋂 𝋃 𝋄 𝋅 𝋆 𝋇 𝋈 𝋉 𝋊 𝋋 𝋌 𝋍 𝋎 𝋏 𝋐 𝋑 𝋒 𝋓

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参考⽂献 ‣ “イヌイットの算術”, ⽇経サイエンス 2023年10⽉号, p. 3 0 ‣ “A Number System Invented by Inuit Schoolchildren Will Make Its Silicon Valley Debut” Amory Tillinghast-Raby. Scientific American, 2 02 3 ‣ “Numerals invented by Kaktovik students can now be used digitally”, Alena Naiden. Anchorage Daily News, 202 2 ‣ “Unicode request for Kaktovik numerals” Eduardo Marín Silva, Kirk Miller, Catherine Strand. 2 0 21 ‣ Kaktovik numerals - Wikipedia ‣ Kaktovik Numerals (Unicode block) - Wikipedia ‣ “Why These Are The Best Numbers!”, Artifexian. YouTube, 2 01 9 ‣ “Why These Are The Best Numbers | FOLLOW UP”, Artifexian. YouTube, 2 0 1 9 ‣ “Kaktovic Numerals”, The Ferret. YouTube, 202 1 ‣ “A brief history of numerical systems - Alessandra King”, TED-Ed. YouTube, 2 0 1 7