ᐸᓯᑲᓪ: ᕉᓚᑦ ᐊᒃᓴᓗᐊᖓᑕ ᐅᓂᒃᑳᑐᐊᖓ
ᓈᓴᐃᓂᓕᕆᔨ ᐊᒃᓴᓗᐊᕐᒥᒃ ᓴᓇᓯᒪᔪᑦ ᐅᖃᐅᓯᐅᒐᔪᒃᑐᖅ, ᐊᓯᐊᓂᒃ ᓴᓇᓇᓱᒃᑐᓂ.
ᐸᓯᑲᓪ (Pascal, 1623–1662) 1650-ᖏᓐᓂ ᓄᖅᑲᖅᑐᐃᓐᓇᖏᑦᑐᓂᒃ ᐊᐅᓚᔪᓂᒃ ᓴᓇᐅᒐᓂᒃ ᖃᐅᔨᓴᖅᓯᒪᔪᖅ. ᑲᐃᕙᖅᑐᖅ ᐊᒃᓴᓗᐊᖅ ᐊᒥᖅᑯᓗᐃᓐᓇᖅ ᑕᓯᓂᖃᖅᑐᖅ, ᐸᓯᑲᓪᒧᑦ ᑐᕌᖅᑕᐅᒐᔪᒃᑐᖅ, ᕉᓚᑦ ᑲᐃᕙᖅᑐᖓᑕ ᓯᕗᓕᐊᕆᓯᒪᔭᖓ ᐱᔪᓐᓇᖅᑐᖅ; ᐅᓂᒃᑲᐅᓯᑐᖃᐅᔪᖅ, ᑎᑎᕋᖅᓯᒪᓂᒃᑯᑦ ᓇᓗᓇᐃᖅᑕᐅᓯᒪᙱᑦᑐᖅ.
ᓈᓴᐃᓂᓕᕆᔨ
ᐳᓚᐃᔅ ᐸᓯᑲᓪ (Blaise Pascal) ᖁᓕᑦ ᐊᕐᕕᓂᓖᑦ ᐱᖓᓱᓪᓗ ᐊᕐᕌᒍᓕᒃ ᓈᓴᐅᑎᓕᐅᕈᑎᒥᒃ ᓴᓇᐅᒐᒥᒃ ᓴᓇᔪᖅ, ᐃᑉᐱᒋᓱᒃᑐᓂ ᐊᓪᓚᕈᓯᕐᓂᒃ ᓈᓴᐃᓂᕐᒥᒃ ᓇᓗᓇᐃᖅᓯᔪᖅ, ᓇᑎᖅᑯᑎᒧᑦ ᐃᓗᐃᑦᑑᔪᒧᓪᓗ ᑐᙵᕕᐅᔪᓂᒃ ᐱᓕᕆᔪᖅ, 1654-ᒥᓗ, ᐱᐅᕆ ᑐ ᕙᕐᒫᒧᑦ (Pierre de Fermat) ᑎᑎᖅᑲᓂᒃ ᐊᐅᓪᓚᑎᑦᓯᓪᓗᓂ, “ᐱᙳᐊᕈᑎᑦ ᐊᕕᒃᑕᐅᓂᖏᑦ ᐊᐱᖅᑯᑎ” ᑭᐅᔪᖅ: ᖃᓄᖅ ᓄᖅᑲᖅᑎᑕᐅᓯᒪᔪᒥ ᐱᙳᐊᕐᓂᕐᒥ ᐱᙳᐊᕈᑏᑦ ᓈᒻᒪᒃᑐᒃᑯᑦ ᐊᕕᒃᑕᐅᓂᐊᕐᒪᖔᑕ. ᑭᐅᔾᔪᑏᖏᑦ, ᐱᙳᐊᖅᑏᑦ ᐊᑐᓂ ᐊᔪᒐᕐᓂᕐᒧᑦ ᐱᔪᓐᓇᕐᓂᖏᑦᓈᓴᐃᓂᖅᐱᔪᓐᓇᕐᓂᖅᐱᓐᓂᐅᑉ ᐱᔪᓐᓇᕐᓂᖓ, 0-ᒥᑦ 1-ᒧᑦ ᐅᕝᕙᓘᓐᓃᑦ 0%-ᒥᑦ 100%-ᒧᑦ. ᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ: 1/37 = 2.70%.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᒪᓕᒡᓗᒋᑦ ᐊᕕᒃᓗᒋᑦ ᐱᙳᐊᕐᓂᖅ ᑲᔪᓯᓚᐅᖅᐸᑦ, ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓᓈᓴᐃᓂᖅᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓᐱᙳᐊᕈᑎ ᐊᑐᓂ ᐊᑯᓂᐅᓂᖅᓴᒥ ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ ᐱᓐᓂᖓ. ᐃᐅᕌᐸ ᐱᙳᐊᕈᑎ ᑕᒪᐃᓐᓂ −1/37 ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᓂᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᓇᑭᙶᕐᕕᐅᔪᖅ. EV ᓈᓴᐃᓂᐅᔪᑦ ᑕᒪᕐᒥᒃ ᑖᓐᓇ ᐃᑦᑕᕐᓂᓴᓕᕆᕝᕕᒻᒥ ᑎᑎᖅᑲᓐᓂᑦ ᑖᒃᑯᓇᙵᑦ ᐱᕝᕕᖃᖅᑐᑦ.
ᐸᓯᑲᓪ ᕉᓚᑦ ᓴᓇᐅᒐᖓᓂᒃ ᓴᓇᓯᒪᕙ?
1650-ᖏᑦ ᑕᑦᑎᓂᖓᓂ ᐸᓯᑲᓪ ᓄᖅᑲᖅᑐᐃᓐᓇᖏᑦᑐᒥᒃ ᐊᐅᓚᔪᒥᒃ ᓴᓇᐅᒐᒥᒃ ᐱᓕᕆᔪᖅ, ᐅᖃᐅᓯᐅᒐᔪᒃᑐᖅᓗ ᐊᒃᓴᓗᐊᒥᒃ ᓇᓪᓕᒌᑦᑎᐊᖅᑐᒥᒃ ᓴᓇᓯᒪᓂᖓᓂᒃ, ᐊᑯᓂ ᑲᐃᕙᒃᑐᒥᒃ ᐊᒥᖅᑯᓗᐃᓐᓇᖅ ᑕᓯᓂᖃᖅᑐᓂ. ᑖᓐᓇ ᐊᒃᓴᓗᐊᖅ ᕉᓚᑦ ᑲᐃᕙᖅᑐᖓᐊᑐᖅᑕᐅᔪᑦᑲᐃᕙᖅᑐᖅᐊᒃᓴᓗᐊᑉ ᑲᐃᕙᖅᑐᖅ ᐃᓚᖓ ᐃᓂᓂᒃ ᐃᓗᓕᓕᒃ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐅᓕᖅᑐᖅ ᐅᓂᒃᑳᖅ ᐊᒥᓱᓂ ᐱᐅᓯᑐᖃᓕᕆᓂᕐᓂ ᐅᓂᒃᑳᖅᑕᐅᑲᐃᓐᓇᖅᑐᖅ, ᓯᕗᓪᓕᐅᔪᓂᓪᓕ ᐱᕝᕕᒋᔭᐅᔪᓂ ᓇᓗᓇᐃᖅᑕᐅᓯᒪᙱᑦᑐᖅ. ᐱᔪᓐᓇᖅᑐᖅ 18-ᖓᓂ ᐊᕐᕌᒍᐃᑦ ᑕᑕᑎᒐᖏᓐᓂ ᐃᒥᖅᑕᕐᕕᐅᑉ ᓄᓇᓕᖓᓂ ᑳᓯᓄᓕᕆᔩᑦ ᐊᑎᖓᓂᒃ ᓂᐅᕕᖅᑎᑦᓯᓇᓱᐊᕈᑎᒃᓴᒥᒃ ᐊᑐᖅᓯᒪᓂᖏᑦ. ᖃᐅᔨᓴᕐᕕᒃ ᑖᔅᓱᒥᖓ ᓇᓗᓇᐃᖅᓯᒪᐅᑏᑦ ᒪᓕᒡᓗᒋᑦ ᐊᖏᕈᓐᓇᙱᑕᖓ.
ᐱᔪᓐᓇᕐᓂᖅ, ᐅᖃᐅᓯᖏᑎᒍᑦ ᐅᖃᐅᓯᑦᑎᒍᓪᓗ
1654-ᒥ ᑎᑎᖅᑲᐃᑦ ᕉᓚᑦᒥᒃ ᐅᖃᐅᓯᖃᙱᑦᑐᑦ, ᓴᖅᑭᓚᐅᓐᖏᓐᓂᖓᓄᑦ. ᐊᐱᖅᑯᑎᖏᑦ ᐅᑯᐊ: ᐱᙳᐊᖅᑏᒃ ᒪᕐᕉᒃ ᐱᖓᓱᓂᒃ ᐊᔪᒐᕐᓂᓂᒃ ᐱᔭᕆᐊᖃᖅᑐᑯᒃ ᑮᓇᐅᔭᓂᒃ ᐱᓂᐊᕐᓗᑎᒃ; 2–1-ᒥ ᓄᖅᑲᖅᑐᑯᒃ; ᖃᓄᖅ ᑮᓇᐅᔭᑦ ᐊᕕᒃᑕᐅᓂᐊᖅᐸᑦ? ᐸᓯᑲᓪ ᑭᐅᔾᔪᑎᖓ ᒫᓐᓇ ᐱᔾᔪᑎᓕᒃ ᓂᕆᐅᒋᔭᐅᔪᒥᒃ ᑕᐃᒎᓯᖃᖅᑕᑦᑎᓐᓂᒃ ᐊᑐᖅᑐᖅ, ᐅᑎᖅᑕᖅᑐᒥᓪᓗ ᐃᓱᒪᓕᐅᕈᓯᕐᒥᒃ ᐱᔪᓐᓇᖅᑐᑦ ᑲᔪᓯᓂᖏᑦ ᓄᑭᖏᑎᒍᑦ ᐊᑖᓄᑦ ᐊᐅᓪᓚᖅᑐᒥᒃ. ᕼᐊᐃᒡᔅ (Huygens) ᑎᑎᖅᑲᓕᐅᕐᓂᖏᓐᓂᒃ ᐅᖃᓕᒫᖅᑐᖅ 1657-ᒥᓗ ᓯᕗᓪᓕᖅᐹᒥᒃ ᓂᕆᐅᒋᔭᐅᔪᒧᑦ ᐃᓕᓐᓂᐊᕈᑎᒥᒃ ᐅᖃᓕᒫᒐᒥᒃ ᓴᖅᑭᑦᑎᔪᖅ. “ᓂᕆᐅᒋᔭᐅᔪᖅ” ᐅᖃᐅᓯᖅ ᐅᐊᑦᑕ ᐅᖃᐅᓯᖓ.
ᐸᓯᑲᓪ ᕙᕐᒫᓗ ᐱᙳᐊᕈᑎᑦ ᐊᕕᒃᑕᐅᓂᖏᑦ ᐊᐱᖅᑯᑎᒥᒃ ᑭᐅᔪᑦ: ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓ ᐃᓂᒋᔭᐅᔪᐃᑦ ᓈᒻᒪᒃᑐᖅ ᐊᑭᖓᑎᑐᑦ.
ᕼᐊᐃᒡᔅ, De Ratiociniis in Ludo Aleae: ᓂᕆᐅᒋᔭᐅᔪᒥᒃ ᓯᕗᓪᓕᖅᐹᖑᔪᖅ ᐊᓪᓚᖅᑕᐅᓯᒪᔪᖅ ᓇᓗᓇᐃᖅᓯᓂᖅ.
ᔭᑲᑉ ᐸᕐᓄᓕ (Jakob Bernoulli), Ars Conjectandi: ᐊᒥᓱᑦ ᓈᓴᐅᑏᑦ ᒪᓕᒐᖓ.
ᕉᓚᑦ ᐸᐃᕆᔅᒥ ᓇᓗᓇᐃᖅᑕᐅᔪᖅ. ᐊᑭᓕᐅᑏᑦ ᑕᒪᕐᒥᒃ 36/n − 1: EV = −1/37 (ᐅᕝᕙᓘᓐᓃᑦ −2/38).
ᐲᔅᓴᓐ (Pearson) ᑲᐃ-ᔅᑯᐃᐅ ᖃᐅᔨᓴᕈᑎᖓ, ᕉᓚᑦ ᑲᐃᕙᕐᓃᑎᒍᑦ ᑕᑯᔅᓴᐅᑎᑕᐅᔪᖅ.
ᖁᓛᓂ ᑕᒪᕐᒥᒃ, ᑖᓐᓇ ᐃᑦᑕᕐᓂᓴᓕᕆᕝᕕᒻᒥ, ᖃᕆᑕᐅᔭᒃᑯᑦ ᑕᑯᓐᓇᐅᑎᒥ.
ᐱᙳᐊᕈᑎᖓ
ᐸᓯᑲᓪ ᐱᙳᐊᕈᑎᓕᐅᕐᓂᕐᒧᑦ ᑐᓴᐅᒪᔭᐅᓛᖑᔪᖅ ᐃᓱᒪᓕᐅᕈᓯᖓ ᕉᓚᑦᒥᒃ ᐅᖃᐅᓯᖃᙱᑦᑐᖅ ᒎᑎᒥᒃ ᐅᖃᐅᓯᖃᖅᑐᖅ: Pensées-ᒥ “ᐱᙳᐊᕈᑎ”, ᐅᑦᑕᕐᓂᖅ ᐱᙳᐊᕈᑎᑐᑦ ᑭᒡᓕᖃᙱᑦᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᑕᐃᒪᐃᑦᑐᒥᒃ ᐃᓱᒪᒋᔭᐅᔪᖅ. ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᑭᖓᓄᑦ ᐃᓱᒪᓕᐅᕈᓯᐅᔪᖅ, ᓯᕗᓪᓕᐅᔪᖅᓗ ᓇᓕᐊᑐᐃᓐᓇᖅ ᐃᓱᒪᓕᐅᕈᓯᕐᒥᒃ ᐊᑐᖅᓯᒪᒻᒪᑦ ᓇᓕᐊᑐᐃᓐᓇᕐᒥᒃ ᐱᔾᔪᑎᖃᕐᓗᓂ. ᕉᓚᑦᒥ ᐱᙳᐊᖅᑏᑦ ᐸᓯᑲᓪᒥᒃ ᐊᒃᓴᓗᐊᕐᒧᑦ ᐅᖃᐅᓯᖃᖅᑐᑦ ᐸᓯᑲᓪᒥᒃ ᑕᑯᓐᓇᖅᑐᑦ ᑕᐃᑦᑐᒥᒃ ᓱᓕᙱᑦᑐᒥᒃ; ᐱᒻᒪᕆᐅᔪᖅ ᑖᓐᓇ ᓇᓗᓇᐃᖅᓯᓯᒪᔪᖅ ᖃᓄᖅ ᐱᙳᐊᕈᑎᐅᑉ ᐊᑭᖓ ᓈᓴᖅᑕᐅᓂᐊᕐᒪᖔᑦ.
ᐊᔾᔨᒋᙱᑦᑐᖅ ᐃᓱᒪᒋᔭᐅᓯᒪᔪᒥᒃ
ᐸᓯᑲᓪ ᓯᕗᓪᓕᖅᐹᒥᒃ ᕉᓚᑦ ᐊᒃᓴᓗᐊᖓᓂᒃ ᓴᓇᓚᐅᖅᐸᑦ ᐅᕝᕙᓘᓐᓃᑦ ᐋᒃᑲ, ᐱᙳᐊᕐᓂᖅ ᐱᓕᕆᐊᖓᓂᒃ ᓱᓕᔪᒥᒃ ᓇᓗᓇᐃᖅᓯᑦᑎᐊᖅᑐᖅ: ᓴᓇᐅᒐᖅ ᐊᖑᑎᒥᑦ ᓇᓗᓇᐃᖅᓯᓯᒪᔪᒥᑦ ᓇᓕᐊᑐᐃᓐᓇᕐᒥᒃ ᐱᔪᓐᓇᙱᓐᓂᑦᑎᓐᓂᒃ ᐱᖃᙱᑦᑐᒥᑦ (ᓄᖅᑲᖅᑐᐃᓐᓇᖏᑦᑐᖅ ᐊᐅᓚᓂᖅ ᐊᔪᖅᑐᖅ; ᓂᕆᐅᒋᔭᐅᔪᖅ ᐊᓯᑦᑐᖅᑎᑕᐅᙱᑦᑐᖅ), ᑕᐃᒪᐃᑦᑐᒥᒃ ᑕᑯᔅᓴᐅᑎᑦᓯᓂᕐᒧᑦ ᐊᑐᖅᑕᐅᔪᖅ ᐊᕐᕌᒍᑕᒫᖅ ᐱᙳᐊᖅᑎᓄᑦ ᐅᓄᖅᑐᓄᑦ ᒥᓕᐊᓐᓄᑦ.
ᐊᐱᖅᑯᑏᑦ
1650-ᖏᑦ ᐱᒋᐊᕐᓂᖓᓂ ᐸᐃᕆᔅᒥ ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᖅᑎᓂᒃ ᐃᓚᐅᖃᑎᖃᖅᐸᒃᑐᖅ, ᑕᐃᒪᓐᓇᓗ ᐱᙳᐊᕈᑎᑦ ᐊᕕᒃᑕᐅᓂᖏᑦ ᐊᐱᖅᑯᑎ ᑎᑭᑦᑐᖅ ᓯᕙᓕᐊ ᑐ ᒥᐊᕆᒃᑯᑦ (Chevalier de Méré). ᑮᓇᐅᔭᓂᒃ ᐱᙳᐊᓗᐊᕐᓂᖓᓂᒃ ᑎᑎᕋᖅᓯᒪᔪᖃᙱᑦᑐᖅ.
ᐅᓂᒃᑳᑦᑎᐊᕙᐅᒻᒪᑦ, 19-ᖓᓂᓗ ᐊᕐᕌᒍᐃᑦ ᑕᑕᑎᒐᖏᓐᓂ ᑳᓯᓄᓂᒃ ᓂᐅᕕᖅᑎᑦᓯᓇᓱᒃᑐᑦ ᓇᒡᓗᒋᒻᒪᑕᐅᒃ. ᐅᓂᒃᑳᕆᐊᖅᑭᑦᑐᒋᑦ ᐱᕝᕕᒋᔭᐅᔪᒥᒃ ᓇᓗᓇᐃᖅᓯᓗᑎᑦ.
ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ
ᓇᓗᓇᐃᖅᓯᔪᖅ ᓇᓕᐊᑐᐃᓐᓇᕐᒥᒃ ᐱᖃᙱᑦᑐᖅ ᐱᔪᓐᓇᙱᓐᓂᑦᑎᓐᓂᒃ. ᑭᖑᓂᖓᓂ ᐃᓄᒃ ᑖᔅᓱᒥᖓ ᑐᙵᕕᖃᖅᑐᒥᒃ ᑳᓯᓄᓕᐅᖅᑐᖅ.
ᐱᕝᕕᒋᔭᐅᔪᑦ
- Pascal, B. & Fermat, P. Correspondence on the problem of points.
- Huygens, C. De Ratiociniis in Ludo Aleae.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.