"Disasters continue to occur year after year, and they will be sensed by heaven and man. Your Majesty is naturally right when you say that people help themselves and heaven helps them, but we must not forget to worship the gods of heaven and earth......"

"The words of the saints, worship the ghosts and gods and stay away... How to explain this, is to be like Your Majesty, respectful and fearless. The ancients had clouds, and man will conquer the sky......"

"Datong Monthly" also had a great influence among scholars.

The most typical manifestation is that the content of the court meeting published in the newspaper will also be discussed by the folk scholars. You know, this is a court meeting, and only the emperor and ministers knew about it before. Now ordinary readers can also see it, how can they not follow the trend?

And no matter how outrageous the dispute is, it is all concerned about national affairs, and there is a sense of satisfaction that worries about the world.

Listening to the dispute outside, Chen Zisheng couldn't help but shake his head: "These guys, they don't do business, they follow the country scholars all day long. ”

Xiao Shixuan said: "Let them talk about it, and it will be quiet after the quarrel." ”

The planetarium in Qintianyuan was noisy, and the math hall next door was full of crackling abacus.

"Bang bang bang!"

After a meal, Kuang Hong wrote down the data and said: "The calculation of Huang Zhong in "Historical Records" is really wrong, and the value given in "Mengxi Pen Talk" is correct. ”

"I said that Taishi Gong was wrong, maybe he didn't count it, but he made a mistake when copying historical materials." Chen Zisheng said.

Xiao Shixuan has a super abacus in front of him, and he has been beating for more than half a month, and at this time, he finally came to the result: "Zhu Zaiyu is right, He Chengtian is slightly deviated." ”

He Chengtian lived during the Northern and Southern Dynasties and tried to calculate the twelve equal laws, and the value he came up with was: 1.060070671.

And Zhu Zaiyu of the Ming Dynasty also calculated the twelve equal laws, and the value obtained was: 1.059463094.

He Chengtian's calculation method was very rough, and he also used this method to calculate pi, which was used by Zu Chongzhi when calculating pi.

And Zhu Zaiyu is even more rude, making his own eighty-one big abacus, which can open more than 20 square roots and cubic roots.

Xiao Shixuan looked at the results of the two mathematical sages, pondered their calculation methods, and said with emotion: "Although Zhu Zaiyu's numbers are correct, the mathematical methods he uses are too backward. Although He Chengtian was wrong, his mathematical method was more advanced. Whether it is Shen Kuo or Zhu Zaiyu, in terms of mathematical methods, they are not as good as this He Chengtian! ”

Chen Zisheng said: "But Zhu Zaiyu is also very powerful, he has also deviated from the traditional three-point profit and loss method, and has standardized and revised the law (twelve laws). ”

Xiao Shixuan said: "Your Majesty taught us the method of analytic geometry, and we already have the concept of variables. He Chengtian talked about 'the amount of micro-accumulation', and Shen Kuo talked about 'the art of micro-making', can the combination of the two get the law of twelve equals? ”

Chen Zisheng said: "I'm afraid the two have nothing to do with each other. ”

Xiao Shixuan shook his head: "The shape is not similar but the god is similar, our thoughts have to jump out and reformulate a mathematical method to calculate the law." I had this idea two years ago and have already figured something out. ”

Zhao Han's previous major did not require mastery of advanced mathematics, so he could not teach calculus. But the analytic geometry he taught could be used as a precursor to the invention of calculus.

In fact, Xiao Shixuan has already figured out the differential, and another mathematician has figured out the integral. And they guessed the relationship between differentiation and integration, but for the time being, they have not really demonstrated it, and they are on the verge of creating calculus, but there is always a layer of window paper that has not been pierced.

Everyone else was blasted out, and Xiao Shixuan was the only one left in the room, quietly facing the super abacus of 100 gears.

This kind of super abacus was invented by Zhu Zaiyu, the king of Xiao Zheng, and comes with a new set of abacus usage methods, which can be primitive and crude to open the root operation. For example, in calculating the 12 equal laws, the core problem is to open the 12th power root of 2, and Zhu Zaiyu really used an abacus to knock it out.

In front of the abacus, standing from morning to evening, Xiao Shixuan suddenly felt a little hungry.

The integral and differential points swirled in his mind, as if the two tendons could never be connected, and he walked towards the cafeteria like sleepwalking. What is eating tonight, Xiao Shixuan doesn't know at all, he only knows how to put the food in his mouth, and his eyes are not focused on the table.

"Poof...... Ahem, ahem! ”

Xiao Shixuan suddenly thought of something, as if a lightning bolt crossed his mind. He squirted out a mouthful of food, coughed several times in quick succession, and suddenly ran back to his office.

……

A few days later, Xiao Shixuan begged to see the emperor.

Zhao Han has always treated the researchers of Hanlin and Qintian Academy very favorably. As long as you have a master's title or above, you can ask for a meeting at any time, and you will definitely arrange to meet within three days.

"Great mathematician, what new discoveries have you made?" Zhao Han asked with a smile.

Xiao Shixuan said: "Please Your Majesty correct the law." ”

Zhao Han was puzzled: "It's good, why do you want to fix the law?" ”

Xiao Shixuan explained: "Since the pre-Qin period, the twelve laws have not been equal. Those who are happy are the major affairs of the country. The uneven twelve rhythms will be discordant to play. Generations of astronomical scholars know that the yellow bell cannot be restored, and for more than 2,000 years, they are looking for a way to restore the yellow bell. Zhu Zaiyu, the king of Xiao Zheng in the previous dynasty, has found a method of restoration, and the ministers have recently verified it, and Xiao Zheng Wang has calculated that it is indeed the law of twelve equals. ”

Zhao Han was even more confused when he heard it: "Lu Lu is music, how can it have anything to do with astronomy?" ”

Xiao Shixuan said: "The Book of Changes is the first of the hundred classics, and everything in China originates from the Book of Changes, and the Book of Changes comes from astronomical research. The twelve laws are corresponding to the twelve qi, and if you want to calculate the twelve laws, you must first seek the yellow bell, just like formulating the calendar to calculate the winter solstice. Huang Zhong can get a guest when he opens the root, just like formulating a calendar to calculate the summer solstice. Your Majesty, whether it is a sacrifice or a court meeting, the music played is in harmony with astronomy. If you don't revise the law, you don't revise the calendar. ”

Huang Zhong is the key of C in Western music, and Rui Bin is the key of F# in Western music.

In terms of music, the East and the West are actually the same, and for thousands of years they have been finding the correct value of the twelve equal laws, just as everyone is looking for a more accurate pi.

Gong, Shang, Yu, Change, Sign, Sign, Angle, Change, corresponds to the seven piano white keys such as Dolai Mi Instigation.

The twelve laws are also completely corresponding: Huang Zhong (C key), Lin Zhong (G key), Tai Kou (D key), Nan Lu (A key), Gu Xi (E key), Ying Zhong (B key), Rui Bin (F# key), Da Lu (C # key), ......

There are subdivisions of the twelve laws, for example, the yellow bell also divides the clear yellow bell, that is, the high octave of the yellow bell.

The theoretical value of the Qing Yellow Bell should be half of the Yellow Bell, so that the Yellow Bell can be restored when the tone is set. If the twelve equal laws cannot be calculated, the yellow bell cannot be restored, and there must be errors in the rhythm, and musicians in both the East and the West have discovered this situation.

Xiao Zheng Wang Zhu Zaiyu is a bug, in the absence of calculus, he used an abacus to open the 12th root of 2 and forcibly calculated the correct value. This value was transmitted to the West, and the modern piano was born, and the modern music theory system was born.

Of course, music is only a subsidiary meaning when calculating the twelve equal temperaments, and it can also be applied to many fields such as astronomy.

After Xiao Shixuan's detailed explanation, Zhao Han finally understood that the music of the East and the West is the same, and Chinese music is not a simple pentatonic scale. The chimes of the pre-Qin dynasty used the twelve laws, and the names of the yellow bell, the yingzhong, and the lin bell are likely to be related to the chimes of the pre-qin.

As for how important the Twelve Laws are, it can be seen from the Records of the Historians that Sima Qian recorded the data of the Twelve Laws in detail—although there are still errors in the records.

Books such as "Zhou Li" and "Book of Rites" also record the twelve laws in detail, but ordinary people can't understand them at all, because they are all relevant numbers of the law. Only those who are proficient in mathematics can truly read the Book of Rites thoroughly.

Zhao Han said to Li Xiangjun: "Draft the edict, order the Mathematics Hall of the Qintian Academy to assist the Ministry of Rites in revising the law." The revised Lu Lu was published in the "Datong Monthly". The errors in the record of Lu Lu in the "Historical Records" were also published in the "Datong Monthly" for correction. ”

"Yes."

While Li Xiangjun was preparing the edict, he couldn't help but look at Xiao Shixuan twice. She has been studying music since she was a child, but she learned it wrong and was changed back by a math person.

Zhao Han asked: "During this time, you have verified Zhu Zaiyu's results?" ”

Xiao Shixuan replied: "Back to Your Majesty, not only has it been verified, but also a new set of mathematical methods has been formulated. Zhu Zaiyu used the big abacus to forcibly open the roots, and the new method used by the minister was temporarily named 'calculus'. ”

"Ahem, ahem!"

Zhao Han choked on saliva and coughed when he heard this, and made a calm appearance: "Calculus? ”

Xiao Shixuan said: "It's calculus. Xunzi has a saying, the small one is big, and the small one is written. Later generations of people who studied mathematics originated from Xunzi's theory of the amount of micro-accumulation and the technique of creating micro-snails. ”

Zhao Han actually wanted to say, you are so awesome, you don't even change your name.

Zhao Han asked, "How did you create calculus?" ”

Xiao Shixuan said: "This method benefits from the analytic geometry taught by His Majesty. In the past ten years, with the help of analytic geometry, those who study mathematics have created two sets of methods, which can be called differentiation and integration. The more I researched, the more I found a connection between the two methods. The day before yesterday, I verified the twelve equal laws, and found the method used by He Chengtian, a scholar of the Northern and Southern Dynasties, when calculating the twelve laws, in the Book of Sui. He Chengtian's mathematical work "Legislative System" has been lost, but the "Book of Sui" records only a few words. Later, I checked other classics, and I could probably guess what method he used. Although it is not really calculus, it gives Chen a kind of inspiration. ”

"Thank you for your hard work."

Zhao Han can only say that this group of mathematicians actually studied the rhythm of music, but to study the rhythm of music, they had to read the "Records of the History" and "Book of Sui", and then got the inspiration to create calculus.

What is this?

It's too much of a cross-professional leap.

Zhao Han thought for a while and said, "You can use the twelve equal temperaments to invent a musical instrument, and you can play all the melodies by hitting the strings with a button." ”

Xiao Shixuan was stunned and muttered, "Minister...... No. ”

"Then forget it, I'll find someone else to get it." Zhao Han thought to himself, you can't do it, I thought you could invent the piano.

(Thanks to Joe Jiu's alliance leader for the reward.) ）

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