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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

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

CoSTEP「科学技術コミュニケーター養成プログラム」プレゼン演習, 第1回
https://sorami.dev/costep/2023-11-02/

Sorami Hisamoto

October 18, 2023
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  1. ΧΫτϏοΫ਺ࣈ
    ਓؒͱจԽʹ͋Θͤͨଟ༷ͳදݱͷՄೳੑ

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

    View full-size slide

  2. ਺ࣈ
    ਺Λදݱ͢ΔͨΊͷه߸

    View full-size slide



  3. インド‧アラビア数字

    View full-size slide

  4. ʓҰೋࡾ࢛
    ޒ࿡ࣣീ۝
    ेඦઍສԯ
    漢数字

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  5. *******77
    7*7**7****9
    9-$%.
    ローマ数字

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

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  7. 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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  8. 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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  9. 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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  10. ͜Ε͚͕ͩ
    ࠷దͳ΍Γํͳͷ͔ʁ

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  11. "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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  12. 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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  13. 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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  14. ΧΫτϏοΫ
    ๺Ң౓ ๺ۃݍͷொ
    ਓޱʢ೥ʣ
    , B L U P W J L

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  15. "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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  16. https://www.cityofkaktovik.org/

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

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  19. ΧΫτϏοΫ਺ࣈ
    ೥୅ʹൃ໌͞Εͨ

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  20. 𝋀 𝋁 𝋂 𝋃 𝋄

    𝋅 𝋆 𝋇 𝋈 𝋉

    𝋊 𝋋 𝋌 𝋍 𝋎

    𝋏 𝋐 𝋑 𝋒 𝋓

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  21. 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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  22. 𝋀

    𝋁

    𝋂

    𝋃

    𝋄

    View full-size slide

  23. 𝋀

    𝋁

    𝋂

    𝋃

    𝋄

    𝋅

    View full-size slide

  24. 𝋀

    𝋁

    𝋂

    𝋃

    𝋄

    𝋅

    𝋆

    View full-size slide

  25. 𝋀

    𝋁

    𝋂

    𝋃

    𝋄

    𝋅

    𝋆

    ͱͷ
    ૊Έ߹Θͤ
    𝋁
    𝋅

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  26. 𝋀

    𝋁

    𝋂

    𝋃

    𝋄

    𝋅

    𝋆

    𝋇

    𝋈

    𝋉

    View full-size slide

  27. 𝋀

    𝋁

    𝋂

    𝋃

    𝋄

    𝋅

    𝋆

    𝋇

    𝋈

    𝋉

    𝋊

    View full-size slide

  28. 𝋀

    𝋁

    𝋂

    𝋃

    𝋄

    𝋅

    𝋆

    𝋇

    𝋈

    𝋉

    𝋊

    𝋏

    View full-size slide

  29. 𝋀

    𝋁

    𝋂

    𝋃

    𝋄

    𝋅

    𝋆

    𝋇

    𝋈

    𝋉

    𝋊

    𝋏

    ͕ೋͭɺࡾͭ

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  30. 𝋀

    𝋁

    𝋂

    𝋃

    𝋄

    𝋅

    𝋆

    𝋇

    𝋈

    𝋉

    𝋊

    𝋏

    ͕
    ౓ճస↪͔ͨͨͪ͠
    Ͱ΋͋Δ
    ͕ೋͭɺࡾͭ

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  31. 𝋀

    𝋁

    𝋂

    𝋃

    𝋄

    𝋅

    𝋆

    𝋇

    𝋈

    𝋉

    𝋊

    𝋏

    𝋋

    𝋌

    𝋍

    𝋎

    𝋐

    𝋑

    𝋒

    𝋓

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  32. 𝋄
    𝋓
    Y Y

    ೋेਐه਺๏ೋेΛఈͱ͢ΔҐऔΓه਺๏

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  33. 𝋁
    𝋁
    Y

    ೋेਐه਺๏ೋेΛఈͱ͢ΔҐऔΓه਺๏
    𝋁
    𝋁


    Y


    Y


    Y

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  34. Akrasia
    2
    5
    , CC BY SA
    4
    .
    0

    https://commons.wikimedia.org/wiki/File:Abacus_Inuit.jpg
    ΧΫτϏοΫ਺ࣈͷͦΖ͹Μ

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  35. Akrasia
    2
    5
    , CC BY SA
    4
    .
    0

    https://commons.wikimedia.org/wiki/File:Abacus_Inuit.jpg
    ΧΫτϏοΫ਺ࣈͷͦΖ͹Μ


    View full-size slide

  36. 𝋀

    𝋁

    𝋂

    𝋃

    𝋄

    𝋅

    𝋆

    𝋇

    𝋈

    𝋉

    𝋊

    𝋏

    𝋋

    𝋌

    𝋍

    𝋎

    𝋐

    𝋑

    𝋒

    𝋓

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  37. ࢹ֮తͳੑ࣭

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  38. 𝋂
    +
    𝋂
    =

    ଍͠ࢉ

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  39. 𝋂
    +
    𝋂
    =
    𝋄

    ଍͠ࢉ

    View full-size slide

  40. Ҿ͖ࢉ
    -
    𝋍

    𝋍
    𝋅
    =

    View full-size slide

  41. Ҿ͖ࢉ
    -
    𝋍
    =
    𝋅

    𝋍
    𝋅

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  42. 𝋃
    ׂΓࢉ

    𝋃
    𝋏
    𝋓
    Y

    Y

    Y

    ʸ

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  43. 𝋃
    ׂΓࢉ

    𝋃
    𝋏
    𝋓
    Y

    Y

    Y

    𝋁
    Y

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  44. 𝋃
    ׂΓࢉ

    𝋃
    𝋏
    𝋓
    Y

    Y

    Y

    𝋁
    Y
    𝋃
    ͕ ݸ
    𝋁
    3
    1
    ʸ

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  45. 𝋃
    ׂΓࢉ

    𝋃
    𝋏
    𝋓
    Y

    Y

    Y

    𝋁
    Y
    𝋃
    ͕
    3
    ճసͨ͠ܗ

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  46. 𝋃
    ׂΓࢉ

    𝋃
    𝋏
    𝋓
    Y

    Y

    Y

    𝋁
    𝋅
    Y Y
    𝋃
    ͕
    3
    ճసͨ͠ܗ
    ͕
    𝋁
    1
    ճసͨ͠ܗ
    ʸ

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  47. 𝋁
    𝋅
    𝋃
    ׂΓࢉ

    𝋃
    𝋏
    𝋓
    Y

    Y

    Y

    𝋁
    𝋅
    Y Y Y

    𝋃
    𝋏
    ʸ

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  48. 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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  49. 𝋆
    𝋃
    ׂΓࢉ

    𝋃
    𝋏
    𝋓
    Y

    Y

    Y

    𝋁
    𝋅
    Y Y Y
    ʸ༨Γ
    𝋃
    𝋏

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  50. AquitaneHungerForce , Public Domain


    https://en.wikipedia.org/wiki/File:Kaktovik_long_division_(chunked).svg
    ʸ

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  51. ͳͥ
    ͱ
    ͳͷ͔ʁ

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

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  53. ΠψϐΞοΫޠͰ
    liñuiññaqz͸
    lਓؒͷશମz
    ྆ख྆଍Ͱຊͷࢦ

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

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  55. ΧΫτϏοΫ਺ࣈͷ
    ීٴͱӨڹ

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

    View full-size slide

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

    View full-size slide

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

    View full-size slide

  59. 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෼෍

    View full-size slide

  60. 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෼෍
    ΠψϐΞοΫޠ͚ͩͰͳ͘ɺ
    ଞͷΠψΠοτɾϢϐοΫݴޠͰͷ
    ਐ๏ʹ΋ద͍ͯ͠Δ

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  61. 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෼෍
    ΞϥεΧ Χφμ άϦʔϯϥϯυ ϩγΞͷ
    ډॅऀສਓΛ୅ද͢Δ
    ΠψΠοτۃҬධٞձʢ*$$ʣ΋ঝೝ

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

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  63. 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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  64. σδλϧͷੈք΁
    ීٴ΁޲͚ͯ

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  65. Ϣχίʔυ
    ੈքதͷจࣈ΍ه߸Λࣝผ͢ΔͨΊͷࠃࡍن֨

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

    View full-size slide

  67. ೥݄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

    View full-size slide

  68. ೥݄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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  69. 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/

    View full-size slide

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

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

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

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  73. https://crates.io/crates/kaktovik

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

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  75. 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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  76. 𝋀 𝋁 𝋂 𝋃 𝋄

    𝋅 𝋆 𝋇 𝋈 𝋉

    𝋊 𝋋 𝋌 𝋍 𝋎

    𝋏 𝋐 𝋑 𝋒 𝋓

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  77. 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

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