人工智能測試西學東漸:歐幾里得幾何究竟幾何?_風聞
李兆良-科学正史,美洲郑和学会荣誉会长10-26 22:41
希臘數字與歐幾里得幾何
下面用微軟的ChatGPT 測試希臘數字計算圓周。
李:Can you show me how to calculate, using Greek numbers, the circumference of a circle with a radius of 40 m?
Chat GPT**:** Certainly! The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π is the mathematical constant pi, which is approximately equal to 3.14159265… 1. (ChatGPT 的希臘數字主要參考是Wikipedia。)
Substituting the given value of radius (40 m) in the formula, we get:
C = 2πr C = 2π(40) C = 80π
Therefore, the circumference of a circle with a radius of 40 m is 80π meters.
In Greek numerals, this would be written as “80π μέτρα”.
李: You are using the modern numbers 2 and 80. I am asking for the calculation using Greek numbers.
Chat GPT**:** I apologize for the confusion. In Greek numerals, the number 2 is represented by the symbol β (beta) and the number 80 is represented by the symbol πο (pi-omicron) (李注:錯誤。80應為π, pi; 70為ο, omicron)
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π is the mathematical constant pi, which is approximately equal to 3.14159265…2.
Substituting the given value of radius (40 m) in the formula, we get:
C = 2πr C = βππο
Therefore, the circumference of a circle with a radius of 40 m in Greek numerals is βππο.
(李注:正確答案是ππ,或 80π, 換算為251.327, 但是希臘數字80與圓周率是同一符號,所以電腦無法分辨。人工智能邏輯與希臘數字邏輯不相容。)
李:No, you are still using 40, which is not****aGreek number.
Chat GPT**:** I apologize for the confusion. The Greek numeral for 40 is μξ (mu-xi)1. (錯誤)
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π is the mathematical constant pi, which is approximately equal to 3.14159265…2.
Substituting the given value of radius (40 m) in the formula, we get:
C = 2πr C = βπμξ
Therefore, the circumference of a circle with a radius of 40 m in Greek numerals is βπμξ.(錯誤!)
李:Thanks, how do you say the answer in Greek?
Chat GPT**:** In Greek numerals, the circumference of a circle with a radius of 40 m is βπμξ. (錯誤!)
李:I mean how to pronounce it in Greek?
Chat GPT**:** In Greek, the pronunciation of βπμξ is “vita-pi-mi-xi”.
李:Please calculate with modern numbers of the same formula for the circumference of a circle with radius 40 m.
Chat GPT**:** Certainly! The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π is the mathematical constant pi, which is approximately equal to 3.14159265…1.
Substituting the given value of radius (40 m) in the formula, we get:
C = 2πr C = 2π(40) C = 80π
Therefore, the circumference of a circle with a radius of 40 m is approximately 251.3274 meters.(李注:人工智能用中國發明的現代數字可以算出正確答案。)
李:How do you express 3.14159265 in Greek numbers not using pi?
Chat GPT**:** In Greek numerals, the number 3 is represented by the symbol γ (gamma) and the number 1 is represented by the symbol α (alpha)1. The number 5 is represented by the symbol ε (epsilon) and the number 9 is represented by the symbol θ (theta)1. The number 2 is represented by the symbol β (beta) and the number 6 is represented by the symbol ϛ (stigma)1. Finally, the number 5 is represented by the symbol ε (epsilon) and the number 6 is represented by the symbol ϛ (stigma)1.
Therefore, in Greek numerals, 3.14159265 can be expressed as γαεθβϛεϛ.To express the same answer in modern numbers, 3.14159265 can be rounded to 3.1416.
(李注:Chat GPT漏掉小數點,數字4)
李:You did not include the decimal place (.)
Chat GPT**:** I apologize for the oversight. In Greek numerals, the number 3 is represented by the symbol γ (gamma) and the number 1 is represented by the symbol α (alpha)1. The number 5 is represented by the symbol ε (epsilon) and the number 9 is represented by the symbol θ (theta)1. The number 2 is represented by the symbol β (beta) and the number 6 is represented by the symbol ϛ (stigma)1. Finally, the number 5 is represented by the symbol ε (epsilon) and the number 6 is represented by the symbol ϛ (stigma)1. The decimal point is represented by a dot, which in Greek is called a τελεία (teleía)2.
Therefore, in Greek numerals, 3.14159265 can be expressed as γαεθβϛεϛ τελεία γα.
李:what does ϛ mean in here?
Chat GPT**:** In Greek numerals, ϛ (stigma) is a special numeral symbol that represents the number 61. It is derived from the Phoenician letter waw, which represented the sound /w/1. The symbol was used in ancient Greece to represent the sound /st/ in some words, such as στρατός (army)1.
(李注:根據ChatGPT的解釋,答案γαεθβϛεϛ τελεία γα換算為31592656.31,不知所謂。)
總結:
ChatGPT的基礎是二進法,一般數學的基礎是十進法,位值。希臘數學沒有二進法,沒有十進法,沒有位值,數字與字母用同一套符號,不能運算圓周,認為幾何學來自希臘人歐幾里得是沒有根據,不能成立的。只有用中國發明,從結繩記事開始一萬多年傳承有序的數字符號才能得出正確答案。中國數字是數學計量之源,是科學研究之祖。
歡迎大家測試,糾錯。
李兆良 2023-10-25 (另發《科學網》)
