Chapter 29: Arithmetic (Part 2)

  The biggest difference between calculating with Arabic numerals and Chinese characters is that when carrying over, Arabic numerals only need to add one more column. To people after the 1800s, this might seem like a very minor issue, but in ancient China, this problem became a key factor in the complexity of ancient Chinese calculations.

  To know that ancient China used Chinese characters to record numbers, there is also a distinction between uppercase and lowercase. For example, "?" is lowercase, and its uppercase is "?". The latter is often used for records of tens, hundreds, and above, while the former is for units. Of course, the distinction between uppercase and lowercase was also made by later generations, and there was no such saying in ancient China.

  While using Chinese characters to record, simple calculations such as units and tens are still manageable. However, once the numbers reach hundreds or thousands, it becomes troublesome. Especially for people like Xun Yu and Mao Jie, who were responsible for calculating the food and grass supplies for an entire army, the numbers they dealt with were not just in the thousands or hundreds, but in the tens of millions. Although the use of counting rods helped, the larger the numbers, the more complicated the Chinese characters used to record them became. In contrast, using Arabic numerals made calculations much simpler, as only one column was needed, and whether it was addition, subtraction, multiplication, or division, as long as the units were aligned, calculations could be performed.

  When Cao Zhi finished introducing the Arabic numerals, he didn't waste any words and directly demonstrated a calculation involving addition, subtraction, multiplication, and division of numbers with more than six digits. The Chinese were very clever and had already developed the multiplication table of nine nines during the pre-Qin period, which saved Cao Zhi even more time as he simply recited the multiplication table, and everyone could understand it.

  When they saw that Cao Zhi could easily calculate the answer with this heap of symbols, all four of them were stunned and amazed. After their initial shock, Xun Yu and Mao Jie were the most excited, as Cao Zhi's method had rescued them from extremely tedious calculations, although they still needed to do some calculations in the end.

  Xun Yu's face also rarely showed a smile of appreciation, and Mao Jie murmured: "Genius! Absolutely genius! The complexity of arithmetic will be easily solved from now on!"

  While the four were surprised, Cao Zhi secretly congratulated himself: "It turns out that the evil filling duck education is not without its benefits. Although I am a liberal arts student and did not seriously listen to higher mathematics during my university days, but relying on middle school math, it was more than enough to deal with these."

  Ancient people relied on poetry and rhapsody to excel in classical learning. Cao Zhi finally discovered that he had one aspect where he could surpass them, and his heart was filled with pride.

  "By the way, Fourth Brother," asked Mo Jie in a low voice, "I have something I don't understand. When using the exclusion method to calculate, what if there is an integer that cannot be obtained?"

  Cao Zhi listened and was taken aback for a moment, thinking to himself: "Wow, the Chinese are really clever, they've already noticed the existence of decimals in this era."

  If someone else were to ask this question, they would truly be unable to answer it. But for Cao Zhi, it was as easy as turning over his hand. He picked up a branch and casually wrote out a bunch of numbers, doing a division calculation. For these clever people, explaining the theory is tiring and wastes time. It's better to just demonstrate directly; with their intelligence, even if they don't understand at first glance, they should quickly comprehend.

  As expected, Cao Zhi had not yet finished his third calculation when the four of them noticed the importance of that little decimal point. Liu Ye smiled faintly and said: "This decimal point actually has such an effect, wonderful! Fourth Master's ingenuity is remarkable, Ye admires!"

  Cao Zhi humbly said, "Mr. Yang's praise is excessive. In fact, this method is not difficult at all. I just changed the numerical symbols to make it more convenient for myself. Once these numbers are out, others will naturally follow suit." Cao Zhi told a small lie to avoid explaining too much. He was not afraid that this lie would be exposed, as Arabic numerals were invented in the 3rd century AD, and no one knew about them at that time. Cao Zhi could be considered the originator.

  Although this move was intentional on Cao Zhi's part, it was also for convenience. After all, looking at the large pile of numbers composed of Chinese characters and the math problems composed of Chinese characters, Cao Zhi felt extremely dizzy. The introduction of Arabic numerals not only made calculations more convenient for scholars, but even if they were passed down to civilians in the future, it would be extremely easy for ordinary people to learn.

  At this time, Guo Jia pointed to the large pile of numbers on the ground and laughed loudly: "This symbol was created by the Fourth Master, we should name it after him. Why not call it 'Si Shu' (Four Master's Number)?"

  The three of them burst out laughing and applauded: "Wonderful!"

  Cao Zhi's face turned slightly red, and he scratched his head, saying: "This Zhi does not dare to accept."

  Xun Yu smiled and said, "Since it was created by the Fourth Master, how can I not dare to use it? Yu will immediately go to report to the master, and in the future when the master governs, he will use this method to calculate and record."

  "Uh... Gong Da, you and Xiao Xian are still in charge of hiding the grain and fodder. As for reporting to Master, let Jia take care of it." Just hearing this, one can tell that it's definitely that lazy rascal who spoke up.

  However, Xun Yu was in an extremely good mood today and waved his hand casually, saying: "You rogue, go. Now that we have the Fourth Master's method of calculation, it saves a lot of time for recording."

  Guo Jia burst out laughing three times, then bowed to the three of them and said: "In that case, I'll take my leave first." After finishing speaking, Guo Jia immediately turned around and exited the large tent, as if afraid that Xun Yu would change his mind.

  Looking at Guo Jia who had already disappeared from sight, Xun Yu shook his head helplessly and said: "This rogue..." After finishing speaking, Xun Yu turned around to look at Cao Zhi, smiling and saying: "Fourth Master is proficient in arithmetic, why not stay and help me? This set of planting numbers we have just learned, I'm afraid there will be mistakes. At that time, Fourth Master can also point it out."

  Cao Zhi heard this and hastily bowed his hands, saying: "How dare I? If Master Gongda has given an order, then I will certainly obey it."

  Xun Yu was a man of action, and since Cao Zhi had agreed, and they had also wasted a lot of time just now, he immediately entered the work. Cao Cao's order to cover the grain and grass well to prevent them from being soaked by rainwater, in addition to doing these things, also required making a rough count of the grain and grass after covering, to see how much was left, and how many days it would be enough for the army. This kind of counting can be said to be a daily necessity, so Xun Yu, Mao Jie and others who handled logistics affairs were busy every day, after all, the consumption of a large army of 100,000 people every day is not trivial. However, now that Cao Zhi has contributed this set of super-era calculation methods, it has greatly reduced the workload of Xun Yu and others.

  The use of the plant number was so good that it didn't take long for Cao Cao's order to spread throughout the army. Those accountants would always look at Cao Zhi with shining eyes, and their admiration was evident. After the plant number named by Guo Jia spread under Cao Cao's rule, many other names emerged, but the most commonly used one was the "Gongzi number" coined by someone unknown. This name was easy to remember and not awkward to pronounce, so it quickly replaced the original "plant number" thought of by Guo Jia. And Cao Zhi's counting method also came to be known as "Gongzi arithmetic".