After Yoshida's death, his disciples continued to fight and gradually became the leaders of the Choshu Domain, and eventually the four powerful feudal domains of the late Shogunate merged and united with other feudal states to overthrow the shogunate by force and establish the Meiji Restoration.

It is said that there are more than 80 disciples of Yoshida, most of whom have become successful talents, among which the more famous ones are Kusaka Genrui, Takasugi Shinsaku, Kido Takayoshi, Irie Kuichi, Yoshida Minoru, Inoue Shin, Maehara Kazukomi, Ito Hirobumi, Yamada Akitomo, Nogi Noshinori, Masuda Uemon Monsuke, Shinagawa Yajiro and others, among which Takasugi Shinsaku is listed as the "Top Three Masters of the Restoration", Kido Takayoshi is listed as the "Three Masters of the Restoration", Ito Hirobumi and Yamaguchi Aritomo served as the Prime Minister of Fuso, and many students have held important positions, and Yoshida himself is also among them" The first three heroes of the Restoration", Yoshida is a powerful one.

Naohide thanked Shiraishi again and respectfully asked Yoshida to come to the ashram to ask him about the art of war, and Yoshida also gave a brief explanation in the ashram.

Among the many schools of military science in the Edo period, the seven schools that had a far-reaching influence and spread widely were Koshu, Hojo, Yamaga, Echigo, Naganuma, Kazeyama, and Kojo. In Naoxiu's heart, because of the progress of weapons, logistics, and organizational systems, these art of war are behind the times, but he can't explain it to these hard-working art artists, and he has a feeling of helplessness and powerlessness.

Naohide had an idea and told Yoshida about the Lanchester equation. The Lanchester equation, also known as the Lanchester battle theory or battle dynamics theory, is a branch of operations research that applies mathematical methods to study the process of destroying weapons and forces of opposing sides in battle.

In 1915, the British engineer F.W. Lanchester first proposed to use ordinary differential equations to describe the process of destroying the forces of the two opposing sides, and qualitatively explained the principle of concentrating forces. Initially used to analyze casualty ratios between the two sides in the course of an engagement, the use was gradually expanded.

The Lanchester equation includes Chester's linear law and Lanchester's square law.

When two sides of a battle are fighting at a distance of each other's gaze, the strength of either side is proportional to its own number, i.e., Lanchester's linear law.

When any combat unit on both sides of the battle is engaged within each other's field of view and firepower, the strength of either side is proportional to the square of its own number, i.e. Lanchester's law of squares.

Lanchester's combat effectiveness equation is: combat effectiveness = total number of units participating × combat efficiency of units. It shows that only when the quantity reaches the maximum saturation can the combat effectiveness of the troops be enhanced, and it is the most effective way to multiply the combat effectiveness.

Lanchester reduced combat to two basic situations: long-range firefights and close-range concentrated fire.

In a long-range firefight, the loss rate of one side is proportional to both the opponent's strength and the strength of one's own, expressed in differential equations

dy/dt=-a*x*y，dx/dt=-b*x*y 。

where x and y are the number of combat units of the Red Army and the Blue Army, a and b are the average unit combat effectiveness of the Red Army and the Blue Army, respectively, and T represents time.

When concentrating fire at close range, the loss rate of one side is only proportional to the number of combat units of the opponent, and has nothing to do with the number of combat units of the team.

dy/dt=-a*x，dx/dt=-b*y。

where x and y are the number of combat units of the Red Army and the Blue Army, a and b are the average unit combat effectiveness of the Red Army and the Blue Army, respectively, and T represents time.

With these two equations, the estimation of a battle is reduced from a military problem to a purely mathematical one, and several important military theories are clearly explained:

1. The mathematical basis for concentrating forces to fight a war of annihilation (in close combat), and explains the reasons why the actual losses of the superior side are smaller than those of the inferior side in this mode of warfare.

2. The mathematical explanation of the principle of "individual defeat" is also a mathematical explanation of the defeat of the army, because the typical characteristic of defeat is that each of them fights separately and ignores the end of the battle, which objectively strengthens the chance of being defeated by each other.

3. Mathematical explanation of (rapid breakthrough from long-distance to close-range combat by a large number of troops) Courageous breakthrough and close combat annihilation of the enemy to overcome the enemy's long-range firepower superiority.

It's a pity that Yoshida also pities Naohide, Yoshida understands that this is an important military theory as soon as he listens to the explanation, but Naohide wants to explain the mathematical formulas in it to Yoshida, but it will cost him a small life, basically the more he talks about it, the more confused he becomes.

Shiraishi was stunned and drowsy as he watched from the sidelines—he was afraid that Yoshida would be tricked out by Naohide when he was young, so he kept an eye on the sidelines. Finally staying up until lunchtime, he took the opportunity to pull Yoshida to another room, "What did Hori-kun say, is it useful?" ”

"White Stone Palace, what Hori-kun said is the avenue of the art of war, but it only involves Lanxue, which is really incomprehensible."

Shiraishi was anxious, "Can it be finished as soon as possible and let Hori-kun leave for Nagasaki as soon as possible?" He said in his heart that this might be a shogunate agent, so he just sent it away.

"Shiraishi, I don't think Hori-kun is actually interested in the art of war of Yamaga-ryu, and he probably wants to see me because of the prodigy's false name and curiosity. But the Lanchester Art of War he talked about, if I knew about it, and dedicated it to the Imperial Front (the name of the time was called), it would be a great achievement, and the White Stone Hall should be the first merit! ”

"But the longer he stays, the more dangerous it is to my house."

"It's okay, the White Stone Hall is worry-free, this kind of secret transmission of the art of war is not something that can be learned by the selfish and unscrupulous. Besides, Shiraishi had to find a ship to Nagasaki for him, and for only two days, I was pestering Hori-kun all the time, and he didn't have time to investigate information. In addition, as a master of war, if he is not interested in such a secret transmission of the art of war, I am afraid that it will arouse his suspicions. ”

Shiraishi knew that the head of the family had high hopes for Yoshida, and several important ministers also admired Yoshida, so he stomped his foot, "Okay, I will definitely find a boat to Nagasaki in two days, but you must pester him for these two days." ”

"A gentleman's word", "the horse is difficult to chase", the two high-fived and swore an oath.

Naoxiu's current feeling is to be cocooned and self-bound.,Originally, I saw celebrities.,There's a good bragging in the future.,I didn't expect to pretend to be that nothing.,Yoshida Injiro's eyes are shining.、Respectful attitude.,Naoxiu feels that it's my fault that I don't understand.,But what's wrong with me?

After talking for a day, Yoshida was fine, Naohide was sick with food, and he directly asked Shiraishi to help arrange a boat to Nagasaki, and Shiraishi also happened to find a merchant who had recently shipped goods to Nagasaki - he didn't want to use his own ship to make trouble again. So he said that two days later, Naohide and the three of them would take a boat to Nagasaki.

As soon as Yoshida heard about it, he was anxious, and he asked to die on the eve of the road, but before the Tao arrived, the teacher who taught the Tao was about to run, and he couldn't die, right? He chased directly to Zhixiu's brigade cage at night and asked to pick up the lamp to study. Naohide took a huge historical figure in Yoshida, so he didn't dare to put one, so he had to rack his brains to explain for half the night, he couldn't bear the sleepiness, Naohide held back an idea, "Yoshida, I think this way of learning mathematics and physics is really not something that can be understood in a day or two, but we can use examples as an analogy, grasp the essence first, and then naturally integrate it after the profound study of the noble orchid", Yoshida can't help it, how can he make people sleep, he is also tired, so Yoshida also made do with the room of the three of Naohide for a night.

The next day, he didn't eat breakfast, so Yoshida took Naohide to Shiraishi's mansion - Shiraishi's house has everything for easy recording and deduction. Naohide asked Shiraishi for Go to make a model for the armies of both sides.

It is impossible to say when Go arrived in Fuso, but it became popular in the Fuso court during the Nara period (710-794 AD), and the Nara Shosoin Temple, which specializes in the preservation of antiquities, contains a game used by Emperor Shomu (724-948). There is also the following record in the Fuso history book "Continuation of Fuso Ji": In the Nara period, "there were two people in the palace named the Great Companion Ya and Rendongren, who played against each other in the leisure of government affairs, and in the middle of the argument, Suya slashed and killed the Dongren with a knife." If you lose a game of chess and then draw a knife and cut someone, there is no one else in this chess game.

In fact, at this time, Fuso's sum arithmetic (mathematics) also developed to a certain level. Harmony was developed under the influence of ancient Chinese mathematics. Guan Xiaohe was revered as a "sage" in Fusang, and in the late 17th and early 18th centuries, a school called "Guan Liu" was formed with him as the core, and the main achievements of this school were "point art" and "round theory". "Point Technique" is a change from the astronomy introduced from China to pen arithmetic, and the notation of the arithmetic formula is improved, which is unique to the pen algebra of the arithmetic. "Circular theory" can be regarded as a mathematical analysis unique to summath. Kenhiro Kenbe seeks the infinite series expression of the arc length, also known as the circular formula. Kurushima Yoshita popularized the formula of the circle theory, developed the pole number technique of the circle theory (extreme value problem), and discovered the Euler function and the determinant expansion theorem before Western mathematicians. Naoyuan Yasushima, the fourth-generation master of the Guan School, delved into the field of calculus and proposed a method for finding the arc length; This method is also extended to form a double integral, and the volume of the common part of the two intersecting cylinders is obtained. The mathematician of the Seki school in the late Edo period, Wada Ning, further improved the circle theory, simplifying the calculation of arc length, area, volume, and so on, and the method he used was similar to the principle of the current integral method.

But although the sum is good, Naohide and Yoshida are not proficient, so they have no choice but to deduce the Lanchester equation by example. Naohide wrote down the number of combat units on both sides at each step of each scene, the average unit combat effectiveness and time interval, and then didn't seek to understand first, first recorded the number changes clearly, and then Naohide fought a little life to explain mathematical concepts such as square and partial differentiation in vague language, and when he couldn't explain clearly, he asked Yoshida to replace the mathematical calculation with the number changes at each step, and after a busy day, it finally seemed to be able to explain - in fact, it can't stand scrutiny, "obvious", "it should be like this" and so on, If the number of people on both sides goes from 400 to 1,000, Naohide feels that poor Mr. Yoshida is obviously going to get sick.

In addition, what makes Naoxiu complain is the time measurement of Fuso - Fuso timing uses the irregular time method, to put it simply, the irregular time method is to divide the day into day and night, the day from sunrise to sunset is divided into six equal parts, and the time from sunset to sunrise is also divided into six equal parts, and then use the twelve earthly branches and the Chinese character numbers reduced from nine to four to call the good time. For example, there are nine quarters in the child's time, and the so-called ugly time is divided into four quarters of "ugly time with eight quarters", of which the third period is the ugly time and three quarters.

To put it simply, time is not equal! Fortunately, Fuso scholars have studied Sinology, and Naohide set the time interval unit as the Chinese hour and hour.

Scrapped the power of the two tigers.,At night, I finally changed the Lanchester equation magic to Sinology and Fuso.,Naohide invited Shiraishi Shoichiro over.,Let Yoshida explain it to Shiraishi at first.,Shiraishi said at first that he understood.,Frequently nodding his head.,But after listening, Shiraishi touched his chin and said, "I think I understand, but I always feel that there's something wrong". Naohide didn't care, and once again thanked Shiraishi for his care these days and presented a thank you gift, and then instructed Yoshida to "If you really want to figure it out, you can go to the Nagasaki Ranshokan to ask for mathematics and physics, and you are also welcome to have a long-term exchange with those who have time and clumsiness", and promised to give Yoshida a fixed address to welcome him after the study tour.

After saying goodbye politely, Naohide declined Shiraishi and Yoshida's request to say goodbye, and then returned to the travel cage and slept hard. Choshu achievements have been achieved, and tomorrow will be opened!