ꯕ꯭ꯂꯦꯖ ꯄꯥꯁ꯭ꯀꯦꯜ: ꯔꯨꯂꯦꯠ ꯆꯛꯔꯒꯤ ꯋꯥꯔꯤ
ꯆꯛꯔ ꯁꯦꯃꯈꯤꯕ ꯃꯤꯑꯣꯏ ꯑꯣꯏꯅ ꯌꯥꯝꯅꯥ ꯀꯌꯥ ꯃꯤꯡ ꯊꯣꯅꯕ ꯃꯦꯊꯃꯦꯇꯤꯁꯤꯌꯟ, ꯃꯍꯥꯛꯅ ꯑꯇꯣꯞꯄ ꯄꯣꯠ ꯑꯃꯥ ꯁꯦꯝꯕ ꯍꯣꯠꯅꯔꯝꯃꯤ꯫
ꯄꯥꯁ꯭ꯀꯦꯜ (1623–1662)ꯅ 1650ꯒꯤ ꯆꯍꯤꯁꯤꯡꯗ ꯂꯣꯏꯕ ꯅꯥꯏꯗꯕ ꯆꯠꯄꯒꯤ (perpetual motion) ꯈꯨꯠꯂꯥꯏꯁꯤꯡꯒ ꯂꯣꯌꯅꯅ ꯑꯦꯛꯁꯄꯦꯔꯤꯃꯦꯟꯠ ꯇꯧꯈꯤ꯫ ꯃꯍꯥꯛꯀꯤꯅꯤ ꯍꯥꯌꯅ ꯍꯥꯌꯔꯤꯕ ꯐ꯭ꯔꯤꯛꯁꯟ ꯌꯥꯝꯅꯥ ꯅꯦꯝꯕ ꯀꯣꯏꯔꯤꯕ ꯆꯛꯔ ꯑꯗꯨ ꯔꯨꯂꯦꯠ ꯔꯣꯇꯔꯒꯤ ꯏꯄꯥ-ꯏꯄꯨ ꯑꯃꯥ ꯑꯣꯏꯕ ꯌꯥꯏ; ꯑꯗꯨꯕꯨ ꯃꯁꯤ ꯆꯠꯅꯕꯤ ꯑꯣꯏꯅ ꯍꯥꯌꯔꯤꯕꯅꯤ, ꯏꯔꯝꯕꯒꯤ ꯈꯨꯗꯝ ꯂꯩꯇꯦ꯫
ꯃꯦꯊꯃꯦꯇꯤꯁꯤꯌꯟ
ꯕ꯭ꯂꯦꯖ ꯄꯥꯁ꯭ꯀꯦꯜ (Blaise Pascal)ꯅ ꯆꯍꯤ ꯇꯔꯥꯃꯥꯄꯟ ꯑꯣꯏꯔꯀꯄꯗ ꯃꯦꯀꯥꯅꯤꯀꯦꯜ ꯀꯦꯜꯀꯨꯂꯦꯇꯔ ꯑꯃꯥ ꯁꯦꯃꯈꯤ, ꯅꯍꯥ ꯑꯣꯏꯔꯤꯉꯩꯗ ꯄ꯭ꯔꯣꯖꯦꯛꯇꯤꯕ ꯖꯤꯑꯣꯃꯦꯠꯔꯤꯒꯤ ꯃꯍꯩꯁꯤꯡ ꯎꯠꯈꯤ, ꯄ꯭ꯔꯦꯁꯔ ꯑꯃꯁꯨꯡ ꯚꯦꯛꯌꯨꯃꯒꯤ ꯃꯇꯥꯡꯗ ꯌꯨꯝꯐꯝ ꯑꯣꯏꯕ ꯊꯕꯛ ꯇꯧꯈꯤ, ꯑꯃꯁꯨꯡ 1654ꯗ ꯄꯤꯌꯦꯔ ꯗꯤ ꯐꯔꯃꯥꯒ ꯆꯤꯊꯤ ꯊꯥꯅꯖꯤꯟꯗꯨꯅ “ꯄꯣꯏꯟꯇꯀꯤ ꯁꯃꯁ꯭ꯌꯥ” ꯁꯣꯜꯕ ꯇꯧꯈꯤ: ꯃꯌꯥꯏꯗ ꯂꯦꯞꯂꯕ ꯂꯥꯛꯀꯤ ꯁꯥꯟꯅꯕ ꯑꯃꯒꯤ ꯊꯝꯂꯕ ꯁꯦꯜ ꯆꯨꯝꯅꯥ ꯀꯔꯝꯅ ꯌꯦꯟꯁꯤꯅꯒꯗꯒꯦ꯫ ꯃꯈꯣꯌꯒꯤ ꯄꯥꯎꯈꯨꯝ, ꯁꯥꯟꯅꯕ ꯑꯗꯨ ꯃꯈꯥ ꯆꯠꯊꯔꯝꯂꯕꯗꯤ ꯁꯥꯟꯅꯔꯤꯕ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯥꯏꯄꯥꯛꯀꯗꯕꯒꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯒꯤꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯇꯨꯡ ꯏꯟꯅ ꯌꯦꯟꯁꯤꯟꯕ, ꯑꯁꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯒꯤꯃꯦꯊꯃꯦꯇꯤꯛꯁꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯇꯝ ꯁꯥꯡꯅ ꯌꯦꯡꯂꯕꯗ ꯕꯦꯠ ꯑꯃꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩ꯫ ꯃꯔꯨꯑꯣꯏꯕ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯍꯧꯔꯛꯐꯝꯅꯤ꯫ ꯃꯐꯝ ꯑꯁꯤꯗ ꯂꯩꯕ EV ꯃꯁꯤꯡ ꯁꯤꯡꯕ ꯈꯨꯗꯤꯡꯃꯛ ꯆꯤꯊꯤꯁꯤꯡ ꯑꯗꯨꯗꯒꯤ ꯂꯥꯀꯄꯅꯤ꯫
ꯕ꯭ꯂꯦꯖ ꯄꯥꯁ꯭ꯀꯦꯂꯒꯤ ꯔꯨꯂꯦꯠ ꯃꯦꯁꯤꯟ ꯑꯃꯥ ꯂꯩꯔꯝꯕꯔꯥ?
1650ꯒꯤ ꯆꯍꯤꯁꯤꯡꯒꯤ ꯃꯌꯥꯏꯗ ꯄꯥꯁ꯭ꯀꯦꯂꯅ ꯂꯣꯏꯕ ꯅꯥꯏꯗꯕ ꯆꯠꯄꯒꯤ ꯃꯦꯁꯤꯟ ꯑꯃꯗ ꯊꯕꯛ ꯇꯧꯈꯤ ꯑꯃꯁꯨꯡ ꯐ꯭ꯔꯤꯛꯁꯟ ꯌꯥꯝꯅꯥ ꯅꯦꯝꯅꯥ ꯃꯇꯝ ꯁꯥꯡꯅ ꯀꯣꯏꯕ ꯌꯥꯕ ꯆꯥꯡ ꯆꯞ ꯃꯥꯟꯅꯅ ꯁꯦꯝꯕ ꯆꯛꯔ ꯑꯃꯥ ꯁꯦꯃꯈꯤ ꯍꯥꯌꯅ ꯍꯥꯌꯔꯤ꯫ ꯆꯛꯔ ꯑꯁꯤ ꯔꯨꯂꯦꯠ ꯔꯣꯇꯔꯈꯨꯠꯂꯥꯏꯔꯣꯇꯔꯄꯣꯀꯦꯠꯁꯤꯡ ꯄꯨꯔꯛꯄ ꯆꯛꯔꯒꯤ ꯀꯣꯏꯕ ꯁꯔꯨꯛ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯣꯏꯔꯀꯈꯤ ꯍꯥꯌꯕ ꯋꯥꯔꯤ ꯑꯁꯤ ꯄꯨꯋꯥꯔꯤ ꯀꯌꯥꯗ ꯍꯟꯊꯕ ꯍꯟꯊꯕ ꯏꯔꯤ ꯑꯗꯨꯕꯨ ꯑꯍꯥꯅꯕ ꯁꯣꯔꯁ ꯑꯃꯠꯇꯗ ꯏꯔꯝꯗꯦ꯫ ꯆꯍꯤ ꯆꯥꯃꯥ 18ꯁꯨꯕꯒꯤ ꯁ꯭ꯄꯥ ꯁꯍꯔꯁꯤꯡꯒꯤ ꯑꯣꯄꯔꯦꯇꯔꯁꯤꯡꯅ ꯃꯤꯡ ꯑꯁꯤ ꯌꯣꯟꯅꯕꯒꯤ ꯈꯨꯠꯂꯥꯏ ꯑꯃꯥ ꯑꯣꯏꯅ ꯁꯤꯖꯤꯟꯅꯈꯤꯕ ꯌꯥꯏ꯫ ꯃꯁꯤ ꯂꯦꯕꯅ ꯂꯩꯔꯤꯕ ꯈꯨꯗꯃꯁꯤꯡꯒꯤ ꯃꯈꯥꯗ ꯌꯥꯕ ꯄꯣꯠ ꯅꯠꯇꯦ꯫
ꯈꯨꯗꯣꯡꯆꯥꯕ, ꯃꯍꯥꯛꯀꯤ ꯋꯥꯍꯩꯗ ꯑꯃꯁꯨꯡ ꯑꯩꯈꯣꯌꯒꯤ ꯋꯥꯍꯩꯗ
1654ꯒꯤ ꯆꯤꯊꯤꯁꯤꯡꯅ ꯔꯨꯂꯦꯠꯀꯤ ꯃꯔꯃꯗ ꯋꯥ ꯉꯥꯡꯗꯦ, ꯃꯔꯃꯗꯤ ꯃꯇꯝ ꯑꯗꯨꯗ ꯃꯁꯤ ꯍꯧꯖꯤꯛ ꯐꯥꯑꯣꯕ ꯂꯩꯔꯃꯗ꯭ꯔꯤ꯫ ꯃꯈꯣꯌꯅ ꯍꯪꯏ: ꯁꯥꯟꯅꯔꯤꯕ ꯑꯅꯤꯅ ꯄꯣꯠ ꯃꯥꯏꯄꯥꯛꯅꯕ ꯄꯣꯏꯟꯇ ꯑꯍꯨꯝ ꯃꯊꯧ ꯇꯥꯏ; ꯃꯈꯣꯌꯅ 2–1ꯗ ꯂꯦꯞꯂꯦ; ꯄꯣꯠ ꯑꯗꯨ ꯀꯔꯝꯅ ꯌꯦꯟꯁꯤꯅꯒꯗꯒꯦ? ꯄꯥꯁ꯭ꯀꯦꯂꯒꯤ ꯄꯥꯎꯈꯨꯃꯅ ꯍꯧꯖꯤꯛ ꯑꯩꯈꯣꯌꯅ ꯀꯟꯗꯤꯁꯅꯦꯜ ꯑꯦꯛꯁꯄꯦꯛꯇꯦꯁꯟ ꯍꯥꯌꯅ ꯀꯧꯔꯤꯕ ꯑꯗꯨ ꯑꯃꯁꯨꯡ ꯊꯣꯀꯄ ꯌꯥꯕ ꯃꯈꯥ ꯆꯠꯄꯁꯤꯡꯒꯤ ꯎꯄꯥꯜ ꯃꯈꯥ ꯊꯥꯗꯨꯅ ꯆꯠꯄ ꯔꯤꯀꯔꯁꯤꯕ ꯋꯥꯌꯦꯜ ꯑꯃꯥ ꯁꯤꯖꯤꯟꯅꯩ꯫ ꯍꯣꯏꯒꯦꯟꯁꯅ ꯆꯤꯊꯤ ꯊꯥꯅꯖꯤꯟꯕ ꯑꯗꯨ ꯄꯥꯈꯤ ꯑꯃꯁꯨꯡ 1657ꯗ ꯑꯦꯛꯁꯄꯦꯛꯇꯦꯁꯅꯒꯤ ꯃꯇꯥꯡꯗ ꯑꯍꯥꯅꯕ ꯇꯦꯛꯁꯕꯨꯛ ꯐꯣꯡꯗꯣꯀꯈꯤ꯫ “ꯑꯦꯛꯁꯄꯦꯛꯇꯦꯁꯟ” ꯍꯥꯌꯕ ꯋꯥꯍꯩ ꯑꯁꯤ ꯃꯍꯥꯛꯀꯤꯅꯤ꯫
ꯄꯥꯁ꯭ꯀꯦꯜ ꯑꯃꯁꯨꯡ ꯐꯔꯃꯥꯅ ꯄꯣꯏꯟꯇꯀꯤ ꯁꯃꯁ꯭ꯌꯥ ꯁꯣꯜꯕ ꯇꯧꯈꯤ: ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯑꯁꯤ ꯐꯤꯚꯝ ꯑꯃꯒꯤ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯃꯃꯜ ꯑꯣꯏꯅ꯫
ꯍꯣꯏꯒꯦꯟꯁ, De Ratiociniis in Ludo Aleae: ꯑꯦꯛꯁꯄꯦꯛꯇꯦꯁꯅꯒꯤ ꯃꯇꯥꯡꯗ ꯑꯍꯥꯅꯕ ꯐꯣꯡꯗꯣꯀꯈꯤꯕ ꯂꯥꯏꯔꯤꯛ꯫
ꯌꯥꯀꯣꯞ ꯕꯔꯅꯨꯂꯤ, Ars Conjectandi: ꯑꯆꯧꯕ ꯃꯁꯤꯡꯒꯤ ꯅꯤꯌꯝ꯫
ꯄꯦꯔꯤꯁꯇ ꯔꯨꯂꯦꯠ ꯏꯔꯝꯈꯤ꯫ ꯄꯦꯑꯥꯎꯠ ꯈꯨꯗꯤꯡꯃꯛ 36/n − 1ꯅꯤ: EV = −1/37 (ꯅꯠꯔꯒ −2/38)꯫
ꯄꯤꯌꯔꯁꯅꯒꯤ ꯀꯥꯏ-ꯁ꯭ꯛꯕꯦꯌꯥꯔ ꯇꯦꯁ꯭ꯠ, ꯔꯨꯂꯦꯠ ꯁ꯭ꯄꯤꯟꯁꯤꯡꯗ ꯎꯠꯈꯤ꯫
ꯃꯊꯛꯇ ꯂꯩꯕ ꯄꯨꯝꯅꯃꯛ, ꯃꯐꯝ ꯑꯁꯤꯗ, ꯕ꯭ꯔꯥꯎꯖꯔ ꯑꯃꯗ꯫
ꯋꯦꯖꯔ
ꯕꯦꯠ ꯊꯝꯕꯒꯤ ꯃꯇꯥꯡꯗ ꯄꯥꯁ꯭ꯀꯦꯂꯒꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯃꯃꯤꯡ ꯂꯩꯕ ꯋꯥꯌꯦꯜ ꯑꯁꯤ ꯔꯨꯂꯦꯠꯀꯤ ꯃꯇꯥꯡꯗ ꯅꯠꯇꯦ, ꯏꯁ꯭ꯕꯔꯒꯤ ꯃꯇꯥꯡꯗꯅꯤ: Pensées ꯗ ꯂꯩꯕ “ꯋꯦꯖꯔ”, ꯃꯁꯤꯅ ꯊꯥꯖꯕ ꯑꯁꯤ ꯂꯣꯏꯕ ꯅꯥꯏꯗꯕ ꯐꯜ ꯂꯩꯕ ꯕꯦꯠ ꯑꯃꯥ ꯑꯣꯏꯅ ꯎꯏ꯫ ꯃꯁꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯒꯤ ꯋꯥꯌꯦꯜ ꯑꯃꯅꯤ, ꯑꯃꯁꯨꯡ ꯀꯅꯥꯒꯨꯝꯕ ꯑꯃꯅ ꯄꯣꯠ ꯑꯃꯒꯤꯗꯃꯛ ꯋꯥꯌꯦꯜ ꯄꯤꯅꯕ ꯗꯤꯁꯤꯖꯟ ꯊꯤꯑꯣꯔꯤ ꯑꯍꯥꯅꯕ ꯑꯣꯏꯅ ꯁꯤꯖꯤꯟꯅꯈꯤꯕꯅꯤ꯫ ꯆꯛꯔꯒꯤꯗꯃꯛ ꯄꯥꯁ꯭ꯀꯦꯂꯒꯤ ꯃꯃꯤꯡ ꯂꯧꯔꯤꯕ ꯔꯨꯂꯦꯠ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯑꯔꯥꯟꯕ ꯄꯥꯁ꯭ꯀꯦꯜ ꯑꯗꯨꯒꯤ ꯃꯃꯤꯡ ꯂꯧꯔꯤꯕꯅꯤ; ꯃꯔꯨꯑꯣꯏꯕ ꯑꯗꯨꯗꯤ ꯖꯨꯌꯥ ꯑꯃꯒꯤ ꯃꯃꯜ ꯀꯔꯝꯅ ꯂꯦꯞꯀꯗꯒꯦ ꯍꯥꯌꯕ ꯎꯠꯈꯤꯕ ꯑꯗꯨꯅꯤ꯫
ꯑꯉꯛꯄ ꯑꯗꯨ
ꯄꯥꯁ꯭ꯀꯦꯂꯅ ꯑꯍꯥꯅꯕ ꯔꯨꯂꯦꯠ ꯆꯛꯔ ꯁꯦꯃꯈꯤꯕ ꯑꯣꯏꯔꯕꯁꯨ ꯑꯣꯏꯗ꯭ꯔꯕꯁꯨ, ꯁꯥꯟꯅꯕ ꯑꯁꯤ ꯃꯍꯥꯛꯀꯤ ꯑꯁꯦꯡꯕ ꯊꯕꯛꯀꯤ ꯐꯖꯕ ꯈꯨꯗꯝ ꯑꯃꯅꯤ: ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯠꯇ ꯅꯠꯇꯕꯗꯒꯤ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯥ ꯐꯪꯕ ꯉꯝꯗꯦ ꯍꯥꯌꯕ ꯎꯠꯈꯤꯕ ꯃꯤꯑꯣꯏ ꯑꯃꯒꯤ ꯈꯨꯠꯂꯥꯏ ꯑꯃꯥ (ꯂꯣꯏꯕ ꯅꯥꯏꯗꯕ ꯆꯠꯄ ꯃꯥꯏꯊꯤꯏ; ꯑꯦꯛꯁꯄꯦꯛꯇꯦꯁꯟ ꯍꯣꯡꯗꯦ), ꯆꯍꯤ ꯈꯨꯗꯤꯡꯒꯤ ꯁꯥꯟꯅꯔꯤꯕ ꯃꯤꯂꯤꯌꯟ ꯈꯔꯗ ꯋꯥꯐꯝ ꯑꯗꯨꯃꯛ ꯎꯠꯅꯕ ꯁꯤꯖꯤꯟꯅꯔꯤ꯫
ꯋꯥꯍꯪꯁꯤꯡ
1650ꯒꯤ ꯆꯍꯤꯁꯤꯡꯒꯤ ꯍꯧꯔꯛꯐꯃꯗ ꯃꯍꯥꯛ ꯄꯦꯔꯤꯁꯀꯤ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯒꯤ ꯃꯔꯛꯇ ꯆꯠꯃꯤꯟꯅꯈꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯄꯣꯏꯟꯇꯀꯤ ꯁꯃꯁ꯭ꯌꯥ ꯁꯦꯚꯥꯂꯤꯌꯦ ꯗꯤ ꯃꯦꯔꯦꯒꯤ ꯈꯨꯠꯊꯥꯡꯗ ꯃꯍꯥꯛꯀꯤ ꯃꯅꯥꯛꯇ ꯌꯧꯈꯤ꯫ ꯃꯍꯥꯛꯅ ꯁꯦꯜꯒꯤꯗꯃꯛ ꯃꯤꯅꯨꯡꯁꯤ ꯂꯩꯅꯥ ꯁꯥꯟꯅꯈꯤ ꯍꯥꯌꯕꯒꯤ ꯔꯦꯀꯣꯔꯗ ꯑꯃꯠꯇ ꯂꯩꯇꯦ꯫
ꯃꯔꯃꯗꯤ ꯃꯁꯤ ꯐꯖꯕ ꯋꯥꯔꯤ ꯑꯃꯅꯤ ꯑꯃꯁꯨꯡ ꯆꯍꯤ ꯆꯥꯃꯥ 19ꯁꯨꯕꯒꯤ ꯀꯦꯁꯤꯅꯣ ꯄ꯭ꯔꯣꯃꯣꯇꯔꯁꯤꯡꯅ ꯃꯁꯤ ꯄꯥꯝꯕꯤꯈꯤ꯫ ꯃꯁꯤ ꯍꯥꯌꯔꯕꯗ ꯐꯨꯠꯅꯣꯠ ꯑꯃꯒ ꯂꯣꯌꯅꯅ ꯍꯥꯌꯕꯤꯌꯨ꯫
ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ
ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯠꯇ ꯅꯠꯇꯕꯗꯒꯤ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯥ ꯐꯪꯕ ꯉꯝꯗꯦ ꯍꯥꯌꯕ ꯃꯍꯥꯛꯅ ꯎꯠꯈꯤ꯫ ꯃꯗꯨꯒꯤ ꯃꯇꯨꯡꯗ ꯀꯅꯥꯒꯨꯝꯕ ꯑꯃꯅ ꯃꯗꯨꯒꯤ ꯃꯊꯛꯇ ꯀꯦꯁꯤꯅꯣ ꯑꯃꯥ ꯁꯦꯃꯈꯤ꯫
ꯍꯧꯔꯛꯐꯃꯁꯤꯡ
- 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.