人工智能測試西學東漸：歐幾里得幾何究竟幾何？_風聞

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》）