数字，算学与文明

人工智能测试比较希腊拉丁与中国数字加法运算

李兆良（2023-8-30）

摘要

用Windows10与微软人工智能IT对话，比较希腊，拉丁，中国数字和算盘的加法运算 。希腊、拉丁数字系统计算严重错误。IT用中国数字系统给出比较正确答案, 一个数字出错，可能是图文辨识之误，也可能是其他操作错误，经作者指出，IT马上认错更正。

用希腊、拉丁数字计算错误，不只是辨识的问题，没有十进法，没有位值，是系统性问题。所有自然科学，社会科学均基于数据，希腊罗马数字不能准确运算，说明不能支持科学研究。欧洲文艺复兴起于15世纪以后，即放弃拉丁数字，接受中国传到阿拉伯的数字与计算系统以后。结论是欧洲文艺复兴并非源自希腊罗马。中国发明的数字，十进法，位值，几千年来一直是现代科学研究基础。

测试1 – 希腊数字How to calculate 15+38+784 with Greek numbers？

AI：

Here’s how you can add 15, 38, and 784 using Greek numerals:

• The Greek numeral for 15 is ιεʹ (iota-epsilon).

• The Greek numeral for 38 is ληʹ (lambda-eta).

• The Greek numeral for 784 is ωοδʹ (omega-omicron-delta).
        (李注：这里AI错了，ωοδʹ 是874。784是ψπδ)

To add these numbers, we can use the psephismos method that the Greeks used for addition and subtraction. We start by placing the pebbles or shells on different lines on the board to represent the numbers and then move them around to perform calculations ¹².

Here’s how we can add these numbers:

ιεʹ

ληʹ

ωοδʹ

---

Copy

We start by adding the units (the rightmost digits) of each number:

ιεʹ

ληʹ

ωοδʹ

---

δʹ

Copy

The Greek numeral for 3 is δʹ (delta), which we write in the units place. We then move to the next column and add the tens:

ιεʹ

ληʹ

ωοδʹ

---

πηʹ   （李注：80+8=88）

Copy

The Greek numeral for 5 is πηʹ (pi-eta), which we write in the tens place. We then move to the next column and add the hundreds: （李注：错了，5 是ε epsilon）

ιεʹ

ληʹ

ωοδʹ

---

κμγʹ  （李注：20+40+3=63）

Copy

The Greek numeral for 1,000 is χιλιάς (chilias), which we write in the hundreds place. Therefore, the sum of 15, 38, and 784 in Greek numerals is κμγπηδ’ (kappa-mu-gamma-pi-eta-delta) .

I hope this helps!

- 微软对话结束 –

IT的答案κμγπηδ’是20+40+3+80+8+4=155，是错误的。 正确答案是837，ωλζ omega-lambda-zeta. AI引入1,000 is χιλιάς (chilias) 是没有任何意义的，也不出现在答案。整个运算错得一塌糊涂。

测试2：第二次希腊数字算法。How to calculate 15+38+784 with Greek numbers？

微软AI回答：In ancient Greece, numbers were represented using letters of the Greek alphabet. The original Greek number system was developed in ancient Greece and included the use of alphabet letters instead of numbers. As centuries passed by, the use of ancient Greek numbers faded away and Greeks started to use the Hindu-Arabic numeral system, which is still used today.

The following table shows the Greek numerals from 1 to 9:

Greek Numeral Pronunciation

α’           άλφα

β’           βήτα

γ’           γάμμα

δ’           δέλτα

ε’           έψιλον

ϛ’           στίγμα

ζ’           ζήτα

η’           ήτα

θ’           θήτα

To calculate 15+38+784 with Greek numerals, we need to convert each number to its corresponding Greek numeral. The Greek numeral for 15 is δεκαπέντε (dekapénde), for 38 it is τριάντα και οκτώ (triánda kai októ), and for 784 it is επτακόσια ογδόντα τέσσερα (eptakósia ogdónta tésera) .

Now we can add these numbers using the same rules as we do with Hindu-Arabic numerals. We get:

δεκαπέντε

+ τριάντα και οκτώ

+ επτακόσια ογδόντα τέσσερα

---------------------------

= επτακόσια εξήντα επτά

Therefore, the result of 15+38+784 in Greek numerals is επτακόσια εξήντα επτά (eptakósia exínta eptá) .

李问：What is Greek number επτακόσια εξήντα επτά in modern number？

 - 微软对话结束 –

 AI 这次用希腊数字运算：15+38+784=767 的答案也是错误。正确答案 = 837， ωλζ omega-lambda-zeta。

AI 说的Hindu-Arabic numeral system 其实是8-9世纪中国通过丝绸之路传到阿拉伯的数字系统。

测试3。拉丁数字算法。How to calculate 15+38+784 with Roman Latin numbers?

 AI 回答：

- 微软对话结束 –

 IT用拉丁数字计算15+38+784=787是错误的。正确答案是837.

以上测试证明：

希腊数字需要记忆大量符号，很难做基本算术。15+38+784=837.  希腊数字的答案应该是ωλζ omega-lambda-zeta）。 人工智能的答案是κμγπηδ’，按照希腊数字是20+40+3+80+8+4=155。AI设定的3 is δʹ (delta) 是错的，3应该是γ。AI设定5 is πηʹ (pi-eta) 也是错的，5应该是ε.  莫名其妙引进根本不需要的1000 χιλιάς (chilias)，1000应该是（,α）hasta alpha。 以上我的更正数字是根据Greece.com，Wolfram MathWorld，TAMU Math和大量数学网站的希腊数字表。

拉丁数字也不能给出正确答案。

测试4  中国数字算法。Can you calculate in Chinese numbers?

AI:  Sure! The Chinese number system is based on the decimal system, and the numbers are represented using a combination of characters. The following table shows the Chinese numerals from 1 to 9:

To calculate 15+38+784 with Chinese numerals, we need to convert each number to its corresponding Chinese numeral. The Chinese numeral for 15 is 十五 (shíwǔ), for 38 it is 三十八 (sānshíbā), and for 784 it is 七百八十四 (qībǎi bāshísì) .

Now we can add these numbers using the same rules as we do with Hindu-Arabic numerals. We get:

十五

+ 三十八

+ 七百八十四

---------------------------

= 八百五十七   答案 857. （正确答案应该是837）

测试5:  中国算盘算法。Can you calculate with Chinese abacus?

Yes, I can help you calculate with a Chinese abacus. The Chinese abacus, also known as suanpan, is a calculating tool that has been used in China for centuries. It consists of a rectangular frame with vertical rods and beads that slide up and down the rods.

To calculate 15+38+784 with a Chinese abacus, we can follow these steps:

1. Move one bead on the bottom deck      of the first rod to the left and four beads on the top deck of the same      rod to the right to represent 15.

2. Move three beads on the bottom      deck of the second rod to the left and eight beads on the top deck of the      same rod to the right to represent 38.

3. Move four beads on the bottom deck      of the third rod to the left, eight beads on the middle deck of the same      rod to the left, and seven beads on the top deck of the same rod to the      right to represent 784.

4. Add up all the beads on each rod      from right to left. If there are more than nine beads on a single rod,      move one bead from that rod to the left and add it to the next rod on its      left .

The result of 15+38+784 with a Chinese abacus is 857.

李：You are wrong. It should be 837.

IT:

李注：根据微软IT叙说的步骤， 它用的可能不是中国算盘，演算步骤不对。为何用中国数字与算盘得出同样错误的结果，不得而知。

再重新发问同样算式，You calculated 15+38+784 with Chinese numbers and abacus. Your answer was 857. Can you calculate again?

李注：再发问时，IT Chat 不运行了， 可能在把刚才的错误纳进算法。经过重启，IT才给出下面的答案。这次IT给出正确答案837，也许是直接用现代公式计算，不是用中国数字和算盘：

15+38+784 is equivalent to 837 in decimal notation. The Chinese abacus is a mechanical device designed to make arithmetic calculations easier. It represents the evolution of our hands as tools used for counting. The abacus usually consists of a set of ordered beads that can be moved and positioned to represent numbers. Sometimes the beads are aligned horizontally, such as in the Russian abacus, or vertically, as in the Chinese and Japanese abaci ¹.

总结：

1.              人工智能基于二进制，四则算术基于十进法、位值，都是来自中国。希腊、拉丁数字结构不符合十进法，没有位值，整个数字系统架构不能支持算法，所以严重错误。

2.              用中国数字系统和算盘，十进法、位值，IT快速给出比较准确的答案。 但是两次把837误成857，错了一个数字，可能是图形辨识3三与5五之误，或其他原因，经作者指出，IT马上认错更正。

3.              希腊拉丁数字无法运算简单四则算术，应该不能测量天文地理数据，不能发展科技。

4.              8-9世纪，阿拉伯人通过陆上丝绸之路与中国通商，学到中国数字，10世纪后传到欧洲，经过300年，14世纪后普及，欧洲放弃拉丁数字，改用中国数字衍化的数字和数学系统，才有欧洲文艺复兴。

5.              现在世界科学研究基础源自几千年来中国使用的数字，数学系统，十进法、位值。