人工智能测试西学东渐：欧几里得几何究竟几何？

希腊数字与欧几里得几何

下面用微软的ChatGPT 测试希腊数字计算圆周。

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 的希腊数字主要参考是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：错误。80应为π, pi; 70为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：正确答案是ππ，或 80π,　换算为251.327, 但是希腊数字80与圆周率是同一符号，所以电脑无法分辨。人工智能逻辑与希腊数字逻辑不相容。）　

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.　（错误）

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.（错误！）

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.　(错误！)

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：人工智能用中国发明的现代数字可以算出正确答案。）

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漏掉小数点，数字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 6 ¹. 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：根据ChatGPT的解释，答案γαεθβϛεϛ τελεία γα换算为31592656.31，不知所谓。）

总结：

ChatGPT的基础是二进法，一般数学的基础是十进法，位值。希腊数学没有二进法，没有十进法，没有位值，数字与字母用同一套符号，不能运算圆周，认为几何学来自希腊人欧几里得是没有根据，不能成立的。只有用中国发明，从结绳记事开始一万多年传承有序的数字符号才能得出正确答案。中国数字是数学计量之源，是科学研究之祖。

欢迎大家测试，纠错。

李兆良 2023-10-25 （另发《科学网》）