ꯔꯨꯂꯦꯠ ꯁꯤꯁ꯭ꯇꯦꯝꯁꯤꯡꯒꯤ ꯄꯨꯋꯥꯔꯤ
ꯊꯝꯂꯕ ꯁꯦꯜ ꯍꯣꯡꯗꯣꯛꯅꯕ ꯅꯤꯌꯝꯁꯤꯡ ꯏꯔꯝꯕ ꯃꯤꯑꯣꯏꯁꯤꯡꯒꯤ ꯆꯍꯤ ꯆꯥꯃꯥ ꯑꯅꯤ꯫
ꯃꯥꯔꯇꯤꯟꯒꯦꯜ ꯆꯍꯤ ꯆꯥꯃꯥ 18ꯁꯨꯕꯒꯤꯅꯤ; ꯗꯥꯂꯥꯝꯕꯦꯌꯔ ꯃꯗꯨ ꯄꯥꯝꯗꯕ ꯃꯦꯊꯃꯦꯇꯤꯁꯤꯌꯟ ꯑꯃꯒꯤ ꯃꯃꯤꯡꯗ ꯊꯣꯅꯈꯤ; ꯂꯥꯕꯨꯁꯦꯌꯔ ꯚꯤꯛꯇꯣꯔꯤꯌꯥꯒꯤ ꯃꯇꯃꯒꯤ ꯔꯥꯖꯅꯤꯇꯤꯒꯤ ꯃꯤꯑꯣꯏ ꯑꯃꯒꯤ ꯍꯕꯤꯅꯤ꯫ ꯃꯈꯣꯌ ꯑꯃꯠꯇꯅ ꯃꯇꯝ ꯑꯗꯨꯗꯁꯨ ꯊꯕꯛ ꯇꯧꯈꯤꯗꯦ꯫
ꯃꯥꯔꯇꯤꯟꯒꯦꯜ
ꯃꯤꯡ ꯑꯁꯤ ꯄ꯭ꯔꯣꯚꯦꯟꯁꯥꯜ ꯖꯨꯌꯥꯒꯤ ꯁ꯭ꯂꯦꯡꯗꯒꯤ ꯂꯥꯀꯏ (à la martegalo, “ꯃꯥꯔꯇꯤꯒꯒꯤ ꯃꯤꯁꯤꯡꯒꯤ ꯃꯑꯣꯡꯗ”, ꯃꯈꯣꯌꯁꯤꯡ ꯑꯁꯤ ꯋꯥꯐꯝ ꯑꯣꯏꯅ ꯋꯥꯈꯜ ꯂꯧꯅꯗꯕ ꯍꯥꯌꯅ ꯃꯃꯤꯡ ꯂꯩꯈꯤ), ꯃꯁꯤ ꯑꯅꯤ ꯊꯥꯛ ꯍꯥꯄꯆꯤꯟꯕ ꯕꯦꯠ ꯑꯃꯒꯤꯅꯤ, ꯑꯃꯁꯨꯡ 1760ꯒꯤ ꯆꯍꯤꯁꯤꯡꯗꯒꯤ ꯐ꯭ꯔꯦꯟꯆ ꯗꯤꯛꯁꯅꯔꯤꯁꯤꯡꯗ ꯏꯔꯝꯃꯤ꯫ ꯊꯣꯔꯄꯅ (1984), American Heritage Dictionaryꯕꯨ ꯇꯨꯡ ꯏꯟꯗꯨꯅ, ꯑꯇꯣꯞꯄ ꯃꯤꯌꯥꯃꯒꯤ ꯋꯥꯈꯜꯂꯣꯟ ꯑꯃꯥ ꯄꯤꯔꯤ: ꯃꯥꯔꯇꯤꯒꯒꯤ ꯃꯤꯁꯤꯡꯕꯨ ꯑꯉꯛꯄ ꯆꯠꯅꯕꯤꯁꯤꯡꯒꯤꯗꯃꯛ ꯅꯣꯛꯅꯔꯝꯃꯤ, ꯃꯈꯣꯌꯒꯤ ꯃꯅꯨꯡꯗ ꯐꯤꯔꯦꯛ ꯃꯇꯨꯡꯗꯒꯤ ꯊꯣꯡꯕꯁꯨ ꯌꯥꯎꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯋꯥꯍꯩ ꯄꯔꯦꯡ ꯑꯁꯤ “ꯅꯣꯛꯅꯤꯡꯉꯥꯏ ꯑꯣꯏꯕ ꯃꯑꯣꯡꯗ” ꯍꯥꯌꯕ ꯑꯔꯊ ꯑꯣꯏꯔꯀꯈꯤ꯫ ꯆꯍꯤ ꯆꯥꯃꯥ 18ꯁꯨꯕꯒꯤ ꯄꯦꯔꯤꯁꯇ ꯃꯁꯤ ꯍꯥꯟꯅꯗꯒꯤ ꯆꯦꯀꯁꯤꯟꯍꯟꯕꯒꯤ ꯋꯥꯔꯤ ꯑꯃꯥ ꯑꯣꯏꯔꯦ: ꯀꯥꯁꯥꯅꯣꯚꯥꯅ 1750ꯒꯤ ꯆꯍꯤꯁꯤꯡꯗ ꯚꯦꯅꯤꯁꯇ ꯐꯦꯔꯣꯗ ꯑꯅꯤ ꯊꯥꯛ ꯍꯥꯄꯆꯤꯟꯗꯨꯅ ꯂꯟ-ꯊꯨꯝ ꯌꯥꯝꯅꯥ ꯃꯥꯡꯈꯤꯕ ꯃꯍꯥꯛ ꯏꯁꯥꯅ ꯏꯔꯝꯃꯤ꯫ ꯃꯁꯤ ꯀꯔꯤꯒꯤ ꯃꯥꯏꯊꯤꯕꯒꯦ ꯍꯥꯌꯕꯒꯤ ꯃꯦꯊꯃꯦꯇꯤꯛꯁ, ꯇꯦꯕꯜꯒꯤ ꯉꯝꯈꯩꯇꯦꯕꯜꯇꯦꯕꯜꯒꯤ ꯉꯝꯈꯩꯌꯥꯍꯜꯂꯤꯕ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯦꯝꯕ ꯑꯃꯁꯨꯡ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯕ ꯕꯦꯠ꯫ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯋꯥꯡꯕ ꯉꯝꯈꯩ ꯑꯗꯨꯅ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯟꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯊꯤꯡꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯁꯨꯡ ꯂꯣꯏꯁꯤꯟꯕ ꯂꯩꯕ ꯕꯦꯡꯀꯔꯣꯜꯁꯦꯜꯕꯦꯡꯀꯔꯣꯜꯁꯥꯟꯅꯅꯕ ꯇꯣꯉꯥꯟꯅ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ꯫ ꯕꯦꯡꯀꯔꯣꯜ ꯃꯦꯅꯦꯖꯃꯦꯟꯠ ꯍꯥꯌꯕꯁꯤ ꯃꯗꯨꯒꯤ ꯀꯌꯥ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯁꯨꯡ ꯁꯦꯁꯟ ꯈꯨꯗꯤꯡꯗ ꯈꯨꯗꯣꯡꯊꯤꯕꯗ ꯊꯃꯒꯗꯒꯦ ꯍꯥꯌꯕ ꯋꯥꯔꯦꯞ ꯂꯧꯕꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →, 1770ꯒꯤ ꯆꯍꯤꯁꯤꯡ ꯐꯥꯑꯣꯕꯗ ꯈꯉꯂꯦ꯫ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯒꯤꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯊꯤꯑꯣꯔꯤꯗ “ꯃꯥꯔꯇꯤꯟꯒꯦꯜꯊꯧꯔꯥꯡꯃꯥꯔꯇꯤꯟꯒꯦꯜꯃꯥꯏꯊꯤꯕ ꯈꯨꯗꯤꯡꯒꯤ ꯃꯇꯨꯡꯗ ꯕꯦꯠ ꯑꯗꯨ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯟꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ꯫ ꯃꯁꯤꯅ ꯀꯔꯤ ꯇꯧꯕꯒꯦ ꯑꯃꯁꯨꯡ ꯀꯔꯤ ꯇꯧꯗꯕꯒꯦ ꯍꯥꯌꯕ ꯊꯧꯔꯥꯡꯒꯤ ꯁꯦꯛꯁꯅꯗ ꯌꯦꯡꯕꯤꯌꯨ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →” ꯍꯥꯌꯕ ꯑꯁꯤ 1930ꯒꯤ ꯆꯍꯤꯁꯤꯡꯗ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯁꯥꯟꯅꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯆꯨꯝꯃꯤꯟꯅꯕ ꯁꯥꯟꯅꯕꯀꯅꯥꯒꯨꯝꯕ ꯃꯥꯏꯀꯩ ꯑꯃꯠꯇꯗ ꯑꯦꯖ ꯂꯩꯇꯕ ꯁꯥꯟꯅꯕ: ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯖꯤꯔꯣꯅꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯒꯤ ꯇꯦꯛꯅꯤꯀꯦꯜ ꯋꯥꯍꯩ ꯑꯣꯏꯔꯀꯈꯤ, ꯃꯁꯤꯗꯤ ꯔꯨꯂꯦꯠꯀꯤ ꯃꯥꯔꯇꯤꯟꯒꯦꯜ ꯑꯃꯅ ꯑꯣꯏꯗꯕ ꯄꯣꯠ ꯑꯃꯈꯛꯇꯅꯤ꯫
ꯗꯥꯂꯥꯝꯕꯦꯌꯔ
ꯖꯥꯟ ꯂꯦ ꯔꯣꯟ ꯗꯥꯂꯥꯝꯕꯦꯌꯔꯅ Encyclopédie (1754)ꯗ ꯍꯦꯗ ꯃꯈꯥ ꯆꯠꯅꯅ ꯊꯣꯀꯈꯤꯕꯥ ꯃꯇꯨꯡꯗ ꯇꯦꯜ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯍꯦꯟꯅꯥ ꯋꯥꯡꯏ ꯍꯥꯌꯅ ꯋꯥꯌꯦꯜ ꯄꯤꯈꯤ, ꯃꯁꯤ ꯃꯔꯨꯑꯣꯏꯕ ꯃꯦꯊꯃꯦꯇꯤꯁꯤꯌꯟ ꯑꯃꯅ ꯍꯥꯌꯈꯤꯕ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯑꯔꯥꯟꯕ ꯋꯥꯈꯂꯒꯤ ꯑꯍꯥꯅꯕ ꯋꯥꯐꯝ ꯑꯃꯅꯤ꯫ ꯃꯥꯏꯊꯤꯕꯒꯤ ꯃꯇꯨꯡꯗ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯥ ꯍꯥꯄꯆꯤꯟꯕ ꯑꯃꯁꯨꯡ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯃꯇꯨꯡꯗ ꯑꯃꯥ ꯂꯧꯊꯣꯛꯄ ꯕꯦꯇꯤꯡ ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯁꯤ ꯊꯥꯖꯕ ꯑꯗꯨꯃꯛ ꯂꯩꯔꯕ ꯃꯇꯨꯡꯒꯤ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯃꯍꯥꯛꯀꯤ ꯃꯃꯤꯡꯗ ꯊꯣꯅꯈꯤ꯫ ꯃꯍꯥꯛꯅ ꯃꯁꯤ ꯄꯥꯎꯇꯥꯛ ꯄꯤꯈꯤꯗꯦ, ꯑꯃꯁꯨꯡ ꯃꯍꯥꯛꯀꯤ ꯐꯕ ꯅꯨꯃꯤꯠꯁꯤꯡꯗ ꯃꯁꯤ ꯌꯥꯅꯤꯡꯂꯃꯂꯣꯏ꯫
ꯂꯥꯕꯨꯁꯦꯌꯔ
ꯍꯦꯟꯔꯤ ꯂꯥꯕꯨꯁꯦꯌꯔꯊꯧꯔꯥꯡꯂꯥꯕꯨꯁꯦꯌꯔꯀꯛꯊꯠꯄꯒꯤ ꯁꯤꯁ꯭ꯇꯦꯝ: ꯃꯁꯤꯡꯒꯤ ꯂꯥꯏꯟ ꯑꯃꯥ ꯏꯕꯤꯌꯨ, ꯃꯊꯛ ꯑꯅꯤꯒꯤ ꯄꯨꯟꯁꯤꯟꯅꯕ ꯕꯦꯠ ꯊꯝꯕꯤꯌꯨ, ꯃꯥꯏꯄꯥꯛꯂꯕꯗꯤ ꯃꯈꯣꯌ ꯀꯛꯊꯠꯄꯤꯌꯨ, ꯃꯥꯏꯊꯤꯔꯕꯗꯤ ꯃꯥꯡꯈꯤꯕ ꯊꯝꯂꯕ ꯁꯦꯜ ꯑꯗꯨ ꯍꯥꯄꯆꯤꯟꯕꯤꯌꯨ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → (1831–1912), ꯖꯔꯅꯥꯂꯤꯁ꯭ꯠ, ꯊꯤꯌꯦꯇꯔꯒꯤ ꯃꯄꯨ ꯑꯃꯁꯨꯡ ꯂꯤꯕꯔꯦꯜ MPꯅ 1870ꯒꯤ ꯆꯍꯤꯁꯤꯡꯗ ꯂꯟꯗꯟꯒꯤ ꯈꯨꯟꯅꯥꯏꯗ ꯀꯦꯟꯁꯦꯂꯦꯁꯟ ꯁꯤꯁ꯭ꯇꯦꯝ ꯃꯤꯌꯥꯃꯗ ꯆꯠꯍꯅꯈꯤ ꯑꯃꯁꯨꯡ ꯃꯣꯟꯇꯦ ꯀꯥꯔꯂꯣꯗ ꯁꯤꯖꯤꯟꯅꯈꯤ ꯍꯥꯌꯅ ꯍꯥꯌꯔꯤ꯫ ꯃꯑꯣꯡ ꯑꯗꯨ, ꯃꯁꯤꯡꯒꯤ ꯂꯥꯏꯟ ꯑꯃꯥ ꯏꯕ ꯑꯃꯁꯨꯡ ꯑꯔꯣꯏꯕ ꯑꯅꯤꯒꯤ ꯄꯨꯟꯁꯤꯟꯕꯗ ꯕꯦꯠ ꯊꯝꯕ, ꯃꯍꯥꯛꯀꯤ ꯃꯃꯥꯡꯗꯒꯤ ꯂꯩꯔꯦ꯫ ꯃꯍꯥꯛꯀꯤ ꯃꯃꯤꯡ ꯂꯦꯞꯂꯀꯈꯤꯕꯁꯤ ꯃꯍꯥꯛ ꯑꯇꯣꯞꯄ ꯊꯕꯀꯁꯤꯡꯅ ꯃꯃꯤꯡ ꯂꯩꯕꯅꯤ ꯑꯃꯁꯨꯡ ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯁꯤꯅ ꯌꯥꯝꯅꯥ ꯊꯤꯛꯅꯥ ꯊꯕꯛ ꯇꯧꯕ ꯍꯥꯌꯕ ꯈꯟꯅꯕ ꯃꯒꯨꯟ ꯑꯃꯥ ꯂꯩꯕꯅꯤ, ꯃꯁꯤꯅ ꯃꯁꯤꯕꯨ ꯆꯥꯛ ꯆꯥꯕ ꯃꯇꯃꯗ ꯋꯥꯔꯤ ꯁꯥꯅꯕꯒꯤ ꯄꯣꯠ ꯑꯃꯥ ꯑꯣꯏꯍꯅꯈꯤ꯫
ꯀꯥꯁꯥꯅꯣꯚꯥꯅ ꯐꯦꯔꯣꯗ ꯑꯅꯤ ꯊꯥꯛ ꯍꯥꯄꯆꯤꯟꯗꯨꯅ ꯃꯥꯡꯈꯤ꯫ ꯃꯥꯔꯇꯤꯟꯒꯦꯜ ꯍꯥꯟꯅꯗꯒꯤ ꯑꯔꯤꯕ ꯑꯣꯏꯔꯦ꯫
ꯗꯥꯂꯥꯝꯕꯦꯌꯔꯅ ꯃꯇꯨꯡꯗ ꯃꯍꯥꯛꯀꯤ ꯃꯃꯤꯡꯗ ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯃꯥ ꯑꯣꯏꯔꯀꯄ ꯑꯔꯥꯟꯕ ꯋꯥꯈꯜ ꯑꯗꯨ ꯐꯣꯡꯗꯣꯀꯈꯤ꯫
“ꯃꯥꯔꯇꯤꯟꯒꯦꯜ” ꯍꯥꯌꯕ ꯋꯥꯍꯩ ꯑꯁꯤ ꯖꯨꯌꯥꯒꯤ ꯁ꯭ꯂꯦꯡ ꯑꯣꯏꯅ ꯐ꯭ꯔꯦꯟꯆ ꯗꯤꯛꯁꯅꯔꯤꯁꯤꯡꯗ ꯌꯥꯎꯈꯤ꯫
ꯂꯥꯕꯨꯁꯦꯌꯔꯅ ꯂꯟꯗꯟꯗ ꯀꯦꯟꯁꯦꯂꯦꯁꯟ ꯃꯤꯌꯥꯃꯗ ꯆꯠꯍꯅꯈꯤ꯫
ꯐꯤꯕꯣꯅꯥꯆꯤ ꯑꯃꯁꯨꯡ ꯄꯥꯔꯣꯂꯤ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯖꯨꯌꯥꯒꯤ ꯂꯥꯏꯔꯤꯀꯁꯤꯡꯗ ꯊꯣꯔꯀꯈꯤ꯫
ꯆꯛꯔꯒꯤ ꯂꯦꯑꯥꯎꯠꯇ ꯌꯨꯝꯐꯝ ꯑꯣꯏꯕ “ꯁꯦꯛꯇꯔ” ꯁꯤꯁ꯭ꯇꯦꯝꯁꯤꯡ ꯆꯤꯊꯤꯒꯤ ꯑꯣꯔꯗꯔꯅ ꯌꯣꯟꯈꯤ꯫
ꯗꯨꯕꯀꯤ ꯁ꯭ꯇꯨꯗꯦꯟꯇ ꯍꯥꯜꯃꯣꯁꯅ ꯀꯔꯤꯒꯨꯝꯕ ꯕꯦꯇꯤꯡ ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯃꯠꯇꯅ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯂꯩꯕ ꯁꯥꯟꯅꯕ ꯑꯃꯕꯨ ꯃꯍꯥꯛꯀꯤ ꯀꯥꯟꯅꯕ ꯑꯣꯏꯕ ꯁꯥꯟꯅꯕ ꯑꯃꯗ ꯑꯣꯟꯊꯣꯀꯍꯟꯕ ꯉꯝꯗꯦ ꯍꯥꯌꯕ ꯎꯠꯈꯤ꯫
ꯀꯝꯞꯌꯨꯇꯔꯁꯤꯡꯅ ꯁꯤꯁ꯭ꯇꯦꯝ ꯈꯨꯗꯤꯡꯃꯛ ꯁꯤꯃꯨꯂꯦꯠ ꯇꯧꯈꯤ꯫ ꯄꯨꯝꯅꯃꯛꯅ ꯇꯔꯅꯑꯣꯚꯔꯒꯤ −1/37 ꯎꯠꯈꯤ꯫
ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯗꯨꯃꯛ ꯃꯍꯩ ꯑꯗꯨꯃꯛꯀꯥ ꯂꯣꯌꯅꯅ ꯑꯣꯟꯂꯥꯏꯟꯗ ꯌꯣꯟꯂꯤ, ꯃꯐꯝ ꯑꯁꯤꯗ ꯕ꯭ꯔꯥꯎꯖꯔ ꯑꯃꯗ ꯁꯤꯃꯨꯂꯦꯠ ꯇꯧꯔꯤ꯫
ꯆꯍꯤ ꯆꯥꯃꯥ 20ꯁꯨꯕ
ꯐꯤꯕꯣꯅꯥꯆꯤꯊꯧꯔꯥꯡꯐꯤꯕꯣꯅꯥꯆꯤ1, 1, 2, 3, 5, 8, 13… ꯁꯤꯛꯋꯦꯟꯁ ꯃꯇꯨꯡ ꯏꯟꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ: ꯃꯥꯏꯊꯤꯔꯕꯥ ꯃꯇꯨꯡꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯃꯥ ꯃꯃꯥꯡꯗ, ꯃꯥꯏꯄꯥꯛꯂꯕꯥ ꯃꯇꯨꯡꯗ ꯈꯣꯡꯊꯥꯡ ꯑꯅꯤ ꯃꯇꯨꯡꯗ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯁꯨꯡ ꯄꯥꯔꯣꯂꯤꯊꯧꯔꯥꯡꯄꯥꯔꯣꯂꯤꯄꯣꯖꯤꯇꯤꯕ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯟ: ꯃꯥꯏꯄꯥꯛꯂꯕꯥ ꯃꯇꯨꯡꯗ ꯑꯅꯤ ꯊꯥꯛ ꯍꯦꯅꯒꯠꯍꯜꯂꯤ, ꯃꯥꯏꯊꯤꯔꯕꯥ ꯃꯇꯨꯡꯗ ꯅꯠꯔꯒ ꯃꯈꯥ ꯆꯠꯅꯅ ꯑꯃꯨꯛ ꯑꯍꯨꯝ ꯃꯥꯏꯄꯥꯛꯂꯕꯥ ꯃꯇꯨꯡꯗ ꯑꯍꯧꯕꯗ ꯍꯜꯂꯀꯏ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯔꯤꯚꯔꯁ ꯃꯥꯔꯇꯤꯟꯒꯦꯜ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 1900 ꯃꯔꯛꯇ ꯖꯨꯌꯥꯒꯤ ꯂꯥꯏꯔꯤꯀꯁꯤꯡꯗ ꯌꯥꯎꯈꯤ꯫ ꯆꯍꯤ ꯆꯥꯃꯥꯒꯤ ꯃꯌꯥꯏꯗ ꯆꯤꯊꯤꯒꯤ ꯑꯣꯔꯗꯔꯒꯤ ꯁꯤꯁ꯭ꯇꯦꯝꯁꯤꯡ ꯂꯥꯀꯈꯤ, ꯈꯨꯗꯤꯡꯃꯛꯇ ꯇꯦꯁ꯭ꯇꯤꯃꯣꯅꯤꯌꯦꯜ ꯑꯃꯥ ꯑꯃꯁꯨꯡ ꯁꯦꯜ ꯍꯜꯂꯛꯄꯒꯤ ꯒꯦꯔꯦꯟꯇꯤ ꯑꯃꯥ ꯌꯥꯎꯏ, ꯑꯃꯁꯨꯡ ꯑꯍꯥꯅꯕ ꯀꯝꯞꯌꯨꯇꯔ ꯁꯤꯃꯨꯂꯦꯁꯅꯁꯤꯡ ꯂꯥꯀꯈꯤ, ꯃꯈꯣꯌꯅ ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯅ ꯍꯥꯟꯅꯗꯒꯤ ꯍꯥꯌꯔꯕ ꯑꯗꯨꯃꯛ ꯎꯠꯈꯤ꯫ ꯀꯔꯤꯒꯨꯝꯕ ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯃꯠꯇꯅ ꯊꯕꯛ ꯇꯧꯕ ꯉꯃꯗꯕꯒꯤ ꯄ꯭ꯔꯨꯐ ꯑꯗꯨ ꯍꯥꯟꯅꯗꯒꯤ ꯂꯩꯔꯦ: ꯖꯣꯁꯦꯐ ꯗꯨꯕ (1936) ꯑꯃꯁꯨꯡ ꯄꯣꯜ ꯍꯥꯜꯃꯣꯁ (1939)ꯅ ꯀꯗꯥꯏꯗ ꯑꯃꯁꯨꯡ ꯀꯌꯥ ꯕꯦꯠ ꯊꯝꯒꯗꯒꯦ ꯈꯅꯕꯒꯤ ꯀꯔꯤꯒꯨꯝꯕ ꯅꯤꯌꯝ ꯑꯃꯠꯇꯅ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯂꯩꯕ ꯁꯥꯟꯅꯕ ꯑꯃꯒꯤ ꯐꯪꯒꯗꯕ ꯃꯍꯩ ꯍꯣꯡꯗꯣꯛꯄ ꯉꯝꯗꯦ ꯍꯥꯌꯕ ꯎꯠꯈꯤ, ꯑꯃꯁꯨꯡ ꯊꯣꯔꯄꯀꯤ 1969ꯒꯤ ꯁꯔꯚꯦꯅ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯊꯦꯡꯅꯔꯤꯕ ꯃꯑꯣꯡꯗ ꯐꯤꯚꯃꯁꯤꯡ ꯑꯗꯨ ꯇꯥꯛꯈꯤ꯫ ꯃꯗꯨꯗꯒꯤ ꯍꯧꯅ ꯁꯤꯁ꯭ꯇꯦꯝꯁꯤꯡ ꯍꯣꯡꯈꯤꯗꯦ; ꯃꯥꯔꯀꯦꯇꯤꯡꯗꯤ ꯄꯦꯝꯐ꯭ꯂꯦꯠꯁꯤꯡꯗꯒꯤ ꯚꯤꯗꯤꯑꯣꯗ ꯆꯠꯈ꯭ꯔꯦ꯫
ꯑꯔꯥꯟꯕ ꯊꯥꯖꯕ: ꯃꯇꯝ ꯄꯨꯝꯕꯗ ꯃꯥꯏꯄꯥꯛꯄ ꯔꯨꯂꯦꯠ ꯊꯧꯔꯥꯡꯐꯤꯕꯣꯅꯥꯆꯤ ꯔꯨꯂꯦꯠ ꯊꯧꯔꯥꯡ
ꯃꯈꯣꯌ ꯀꯔꯤꯒꯤ ꯍꯤꯡꯂꯤꯕꯒꯦ
ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯃꯅ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯗ ꯇꯧꯒꯗꯕ ꯊꯕꯛ ꯑꯃꯥ ꯑꯃꯁꯨꯡ ꯍꯥꯌꯒꯗꯕ ꯋꯥꯔꯤ ꯑꯃꯥ ꯄꯤ꯫ ꯁꯤꯁ꯭ꯇꯦꯝ ꯌꯥꯝꯅꯥ ꯀꯌꯥꯒꯤ ꯃꯈꯥꯗ ꯁꯦꯁꯟ ꯌꯥꯝꯅꯥ ꯀꯌꯥ ꯑꯄꯤꯀꯄ ꯀꯥꯟꯅꯕꯗ ꯂꯣꯏꯏ, ꯃꯁꯤ ꯃꯁꯤꯡ ꯁꯤꯡꯕꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯐꯕ ꯋꯥꯔꯤꯅꯤ꯫ ꯃꯥꯏꯊꯤꯕ ꯁꯦꯁꯟꯁꯤꯡ ꯍꯦꯟꯅꯥ ꯌꯥꯝꯗꯦ ꯑꯃꯁꯨꯡ ꯂꯥꯛ ꯐꯠꯇꯕ ꯑꯣꯏꯅ ꯅꯤꯡꯁꯤꯡꯏ꯫ ꯃꯥꯔꯀꯦꯇꯤꯡꯅ ꯑꯣꯗꯁꯀꯤ ꯃꯇꯥꯡꯗ ꯂꯥꯟꯅ ꯍꯥꯌꯕ ꯃꯊꯧ ꯇꯥꯗꯦ; ꯃꯥꯏꯄꯥꯛꯄ ꯁꯦꯁꯟ ꯑꯃꯥ ꯎꯠꯄ ꯈꯛ ꯃꯊꯧ ꯇꯥꯏ, ꯑꯃꯁꯨꯡ ꯃꯗꯨ ꯌꯥꯝꯅꯥ ꯂꯩ꯫ ꯃꯥꯌꯣꯛꯅꯕ ꯋꯥꯌꯦꯜ, ꯇꯔꯅꯑꯣꯚꯔꯒꯤꯁꯦꯜꯇꯔꯅꯑꯣꯚꯔꯁꯦꯁꯟ ꯅꯠꯔꯒ ꯃꯇꯝ ꯑꯃꯒꯤ ꯃꯅꯨꯡꯗ ꯕꯦꯠ ꯊꯝꯂꯕ ꯁꯦꯜ ꯄꯨꯝꯅꯃꯛ, ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯝꯂꯕ ꯃꯥꯏꯄꯥꯛꯇꯨꯅ ꯐꯪꯂꯕ ꯁꯦꯜꯁꯨ ꯌꯥꯎꯅ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯍꯦꯟꯗꯜ, ꯑꯦꯛꯁꯟ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 2.70%, 1843ꯗꯒꯤ ꯐꯪꯕ ꯌꯥꯔꯦ ꯑꯃꯁꯨꯡ ꯂꯥꯛ ꯐꯕ ꯅꯨꯃꯤꯗꯥꯡ ꯑꯃꯒꯨꯝꯅ ꯊꯥꯖꯍꯅꯕ ꯉꯝꯕ ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯑꯣꯏꯈꯤꯗꯦ꯫
ꯌꯣꯟꯅꯕ ꯁꯤꯁ꯭ꯇꯦꯝꯁꯤꯡ
ꯆꯍꯤ ꯆꯥꯃꯥ 20ꯁꯨꯕꯒꯤ ꯂꯩꯅꯥꯏꯅꯥ ꯃꯁꯥꯒꯤ ꯊꯧꯔꯥꯡꯁꯤꯡ ꯍꯥꯄꯆꯤꯟꯈꯤ, ꯈꯨꯗꯤꯡꯃꯛ ꯃꯥꯏꯅꯁ ꯕꯦꯠ ꯑꯗꯨꯃꯛꯀꯤ ꯑꯅꯧꯕ ꯁꯦꯃꯖꯤꯟ ꯁꯥꯖꯤꯅꯕ ꯑꯃꯅꯤ꯫ ꯐꯦꯖ ꯋꯥꯟ $25 ꯑꯃꯁꯨꯡ ꯂꯧꯔꯤꯕ ꯃꯤꯑꯣꯏꯒꯤ ꯃꯥꯏꯄꯥꯛꯇꯨꯅ ꯐꯪꯂꯕ ꯁꯦꯜꯒꯤ 10%ꯗ ꯌꯣꯟꯈꯤ, $500 ꯄꯤꯔꯕꯥ ꯃꯇꯨꯡꯗ ꯐꯦꯖ ꯇꯨ ꯑꯃꯥ ꯑꯃꯁꯨꯡ $5,000ꯗ “ꯏꯅꯔ ꯁꯔꯀꯜ” ꯑꯃꯥ ꯋꯥꯁꯀꯄꯤꯈꯤ꯫ ꯃꯈꯣꯌ ꯑꯃꯠꯇꯅ ꯃꯁꯤꯡ ꯁꯤꯡꯕ ꯑꯗꯨ ꯍꯣꯡꯗꯣꯀꯄ ꯉꯝꯗꯦ: ꯕꯦꯠ ꯀꯌꯥꯒꯤ ꯁꯤꯔꯤꯖ ꯑꯃꯒꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯦꯊꯃꯦꯇꯤꯛꯁꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯇꯝ ꯁꯥꯡꯅ ꯌꯦꯡꯂꯕꯗ ꯕꯦꯠ ꯑꯃꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩ꯫ ꯃꯔꯨꯑꯣꯏꯕ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯃꯈꯣꯌꯒꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯁꯤꯡꯒꯤ ꯄꯨꯟꯁꯤꯟꯕꯅꯤ꯫
ꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯇꯕ ꯑꯗꯨ
ꯂꯦꯞꯄꯒꯤ ꯅꯤꯌꯝꯁꯤꯡ: ꯀꯌꯥ ꯃꯥꯡꯒꯅꯤ ꯅꯠꯔꯒ ꯃꯥꯏꯄꯥꯛꯀꯅꯤ ꯍꯥꯌꯕ ꯃꯃꯥꯡꯗ ꯂꯦꯞꯊꯣꯛꯇꯨꯅ ꯊꯣꯔꯛꯀꯗꯕꯅꯤ꯫ ꯃꯈꯣꯌꯁꯤꯡ ꯑꯁꯤ ꯌꯥꯝꯅꯥ ꯀꯌꯥ ꯁꯤꯁ꯭ꯇꯦꯝ ꯑꯃꯒꯤ ꯁꯔꯨꯛ ꯑꯃꯥ ꯑꯣꯏꯅ ꯌꯣꯟꯏ ꯑꯃꯁꯨꯡ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯥ ꯇꯧꯕ ꯁꯔꯨꯛ ꯑꯃꯈꯛꯇꯅꯤ, ꯃꯔꯃꯗꯤ ꯃꯈꯣꯌꯅ ꯇꯔꯅꯑꯣꯚꯔ ꯍꯟꯊꯍꯜꯂꯤ꯫ ꯃꯈꯣꯌꯒꯤ ꯃꯃꯤꯡ ꯊꯣꯅꯈꯤꯕ ꯃꯤꯑꯣꯏ ꯑꯃꯠꯇ ꯂꯩꯇꯦ, ꯃꯁꯤ ꯃꯥꯟꯅꯩ꯫
ꯋꯥꯍꯪꯁꯤꯡ
ꯃꯥꯔꯇꯤꯟꯒꯦꯜ, ꯆꯍꯤ ꯆꯥꯃꯥ ꯑꯃꯥ ꯅꯠꯔꯒ ꯃꯗꯨꯗꯒꯤ ꯍꯦꯟꯅꯥ꯫ ꯃꯥꯏꯊꯤꯕꯒꯤ ꯃꯇꯨꯡꯗ ꯑꯅꯤ ꯊꯥꯛ ꯍꯥꯄꯆꯤꯟꯕ ꯑꯁꯤ ꯃꯤ ꯈꯨꯗꯤꯡꯃꯛꯅ ꯑꯍꯥꯅꯕ ꯈꯟꯕ ꯋꯥꯈꯜꯂꯣꯟꯅꯤ꯫
ꯗꯥꯂꯥꯝꯕꯦꯌꯔꯅ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯛꯅꯥ ꯌꯧꯈꯤ, ꯆꯥꯏꯔꯥꯛ ꯑꯣꯏꯅ꯫ ꯄꯥꯁ꯭ꯀꯦꯜ, ꯐꯔꯃꯥ, ꯍꯣꯏꯒꯦꯟꯁ, ꯕꯔꯅꯨꯂꯤ ꯑꯃꯁꯨꯡ ꯂꯥꯞꯂꯥꯁ ꯄꯨꯝꯅꯃꯛꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯤ ꯃꯥꯏꯊꯤꯕꯒꯦ ꯍꯥꯌꯕ ꯇꯥꯛꯈꯤ꯫
ꯃꯔꯃꯗꯤ ꯁꯦꯁꯟ ꯌꯥꯝꯕꯥ ꯃꯥꯏꯄꯥꯀꯏ, ꯑꯃꯁꯨꯡ ꯃꯥꯏꯄꯥꯛꯄ ꯁꯦꯁꯟ ꯑꯃꯒꯤ ꯚꯤꯗꯤꯑꯣ ꯁꯦꯝꯕ ꯌꯥꯝꯅꯥ ꯌꯥꯝꯕ꯫
ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ
ꯆꯍꯤ ꯆꯥꯃꯥ ꯑꯅꯤꯒꯤ ꯃꯃꯤꯡꯁꯤꯡ꯫ ꯃꯁꯤꯡ ꯑꯃꯈꯛ꯫
ꯍꯧꯔꯛꯐꯃꯁꯤꯡ
- Thorp, E. O. “Optimal gambling systems for favorable games.”
- Thorp, E. O. The Mathematics of Gambling.
- Doob, J. L. “Note on probability.”
- Halmos, P. R. “Invariants of certain stochastic transformations: the mathematical theory of gambling systems.”
- d’Alembert, J. “Croix ou pile.”
- Schwartz, D. G. Roll the Bones: The History of Gambling.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.
- Bollman, M. Mathematics of the Big Four Casino Table Games: Blackjack, Baccarat, Craps, & Roulette.