Chapter 142 The world’s strongest numeracy team in the 11th century! (6.6k)
"Oh? Mr. Yang Huai?"
inside the house.
I heard the name reported by Mr. Xie.
Lao Jia, who was studying ink, suddenly put down the ink stick, raised his head, and asked Lao Su:
"Brother Zirong, could Mr. Yang Huai be the Han Gonglian and Han Wenyi who calculated the wheel scales in Yuanyou's armillary sky?"
"Yes, it is this person."
Lao Su nodded and confirmed what he said.
At the same time, there was a hint of apology on his face, and he explained:
"The lens matter is of great importance, so I shamelessly invited a few masters of mathematics to come and help. I also ask Mr. Tongyu not to be offended."
Lao Jia waved his hand indifferently and said:
"Brother Zirong, it's a trivial matter, how can you blame it?
It just so happens that Wen Yi and I haven't seen each other for several years, so I happened to get together with him at your house to see what this kid has become.
Wouldn't it be nice to save a few bucks to spend on your meal? ”
What Lao Jia said was quite calm and without any hypocrisy.
You can tell.
He really didn't think there was anything wrong with what Lao Su did.
After all, he was a former Zuoban official, and after being transferred to Daizhou, he also participated in several engineering designs organized by the state government.
So he knew it.
In the face of some practical projects, a person's ability is quite limited, and the official will not just put eggs in one basket.
At most, it is to prioritize in terms of status, but in fact, the final calculation result is still the main one.
Although he still doesn't know what kind of big thing Lao Su or Xu Yun are going to use the lens principle to do this time.
But it is not difficult to judge just from the formulas Xu Yun wrote previously. This is undoubtedly a project that requires a lot of tools, people, and computing power.
Therefore, not only did he not resent the arrival of Han Gonglian and others, he even welcomed them.
After a while.
Under the leadership of Mr. Xie Duguan.
Six men of different heights, fatness, thinness, and ages walked in outside the house.
"Mr. Tongyu, come on, let me introduce you."
After six people entered the house, Lao Su pointed at a few people and said:
"This is An Shisong, whose courtesy name is Yingtong. He is currently Zuo Lang of the Ministry of Personnel and is known as Mr. Dongping."
An Shisong is a little old man in his fifties, a little thinner than Lao Jia, and has a goatee.
But what attracted the most attention was not his beard, but the fact that he was wearing a black mandarin jacket even in summer.
After Lao Su finished his introduction, the man bowed respectfully to Lao Jia:
"Junior An Shisong has met Mr. Tongyu."
Although Lao Jia seems to have a bad temper, he is still relatively polite when facing his colleagues.
After all, mathematicians these days are as rare as genuine readers in later generations. I saw him returning the same gift:
"Mr. Dongping is polite."
When Lao Su saw this, he continued to introduce:
"This is Xiong Huanzhi."
"This is Song Ke"
"This is Lin Huainan."
When he came to the fifth young man, Old Su mentioned a few more words:
"This is Liu Yi, whose courtesy name is Leyi and whose nickname is Mr. Jinqu.
He is the youngest math teacher in Jigu Academy. He is a scholar and a man of heaven, and he has a promising future. ”
I heard the name Liu Yi.
Lao Jia didn't react much, but Xu Yun on the side couldn't help but look at this person a few more times.
Liu Yi.
This is one of the mathematicians who was mentioned during the selection process and whose name has been slightly left in the history books.
However, there are not many records about Liu Yi in history books. He is only mentioned as a figure in the late Northern Song Dynasty.
Around the third year of Yuanfeng, that is, 1080, he completed a work "On Ancient Roots" and proposed a method for finding the roots of quadratic equations.
Judging from the fact that Yang Hui later compiled it into "Shortcuts for Multiplication and Division of Field Ratios", his ability should be a little stronger than that of ordinary mathematicians.
After all, Yang Hui was born in the Middle Ages in the 13th century, just over a hundred years behind the Northern Song Dynasty.
It is equivalent to modern research on characters from the Opium War period. In theory, there won't be many mistakes or omissions.
After introducing Liu Yi.
Lao Su pointed to the fat man on the far right who looked quite tall:
"Mr. Tongyu, I don't need to introduce this person."
After hearing this, Lao Jia stepped forward, looked at the person slightly, and said with some emotion:
"Wenyi, we haven't seen each other for twenty years, right?"
The fat man, Han Gonglian, happily raised his hand to him:
"It has been twenty-three years. I haven't seen you for many years, sir, but he still looks like the same."
Lao Jia gave him a simple greeting, and then asked curiously:
"Wen Yi, when I first met you, it seemed like you didn't even have enough to eat, and you had to do small jobs to make ends meet after your break.
Why haven't I seen you in these years, but you have gained a lot of weight?
And these clothes. Let me take a look. Tsk, tsk, are they from Tianxinxuan? ”
Tianxinxuan.
Just by hearing the name, you know that this store has an extraordinary background.
After all, in ancient China, it was easy to name people, but there were not many shops with the word "天" in their shop names.
Not to mention that under the feet of an emperor like Bianjing, the people behind such shops are at least ordinary relatives of the emperor.
Looking at the surprised old Jia, Han Gonglian still looked cheerful:
"Mr. Tongyu, you don't know something. In the seventh year of Yuanyou, my junior Boju won 700 yuan, bought several acres of land, and harvested some grain in the autumn.
At the beginning of the new year, the Qingtang Dynasty regained power, and the price of food soared, making us rich all at once."
Lao Jia and Xu Yun:
"."
have to.
Another little mystery was solved.
Anyone who knows the history of the Song Dynasty knows that the Song Dynasty was a period when the gambling industry was very, very developed.
The more common ones are throwing money and Guan Pu, and the more advanced ones are Cuju and horse racing.
What's even more outrageous is to bet on which concubine the emperor will favor today - can you believe that sometimes the emperor is still the one behind the scenes?
Basically, except for the ownership of the throne, anything can be a subject of gambling.
therefore.
A very magical thing happened:
Until 1023 in the Northern Song Dynasty, the names of European emperors who won the big prize every year were recorded.
In the seventh year of Yuanyou, that is, in 1092 AD.
There was a European Emperor in Bianjing who won more than 700 yuan, and his registered name was Han Gonglian.
Therefore, some people in the mathematical community of later generations firmly believe that Han Gonglian is the mathematician, and the two are the same person.
After all, the name Han Gonglian can be said to be quite rare, and the probability of coincidence is not high.
However, for other people, they refused on the grounds that they did not have accurate information.
Although on the surface it was for the sake of so-called rigor, in fact, Xu Yun was more interested in the anger coming from the non-chiefs.
His gaze returned to its original position.
After introducing each other, Xu Yun briefly repeated the content of the question.
After a while.
Several mathematicians, the last of whom are also among the first-class contemporary mathematicians, officially began their calculations.
Take a look at this configuration:
Jia Xian, Han Gonglian, and Liu Yi are just three mathematicians recorded in history books.
Although the remaining three people are unknown, there are not many records in history books.
But it is not difficult to see from a simple conversation that these people have quite good mathematical literacy, but their status as mathematicians has been ignored.
It can even be said that.
In this current era, in AD 1100.
These six people are the strongest calculation team in the world!
True limited edition lineup.
In fact, from the perspective of future generations.
The question raised by Xu Yun is actually not very difficult:
This is a threshold for Fresnel approximation. Strictly speaking, it is a type of geometric optics, and the solutions can be said to be diverse.
The simplest one is, of course, the geometric optical mapping method.
However, simplicity is simplicity, and the information that the drawing method can give is very limited. It can only give the imaging properties of a lens with a known focal length.
It cannot relate the focal length to the properties of the lens itself, and is the simplest method mathematically.
Going one step further, you can use the basic principle of geometric optics, which is Fermat's principle.
Using Fermat's principle, the influence of lens shape and material on imaging under geometric optics approximation can be given, which is mathematically more troublesome than the previous one.
The third stage is the Huygens-Fresnel principle, which is the scalar wave diffraction theory of light.
Using this theory to analyze imaging problems can also give more information - such as the impact of lens aperture, etc. This is why the larger the aperture of an astronomical telescope, the better.
The more rigorous ones are naturally Maxwell's equations, which solve the wave equation under given boundary conditions.
But in the end this method was too troublesome.
To give the most intuitive example:
Have you seen the blackboards in university lecture halls in later generations?
If you use the fourth method, you will need at least six such blackboards - and it may not be possible to calculate the analytical solution.
So unless the previous approximation theory does not apply, generally no one does this.
Because of this, Xu Yun was planning to take the third approach.
Although the third method is much more complicated in theoretical mathematics, calculating a lens requires two double integrals.
But first of all, its practical effect is the best. When the theoretical system lags behind seriously, the importance of practical effect needs no introduction.
The second is
Lao Jia, he is the real inventor of Yang Hui Triangle.
Yang Hui's triangle is one of the most suitable ancient tools for solving integrals, so for Lao Jia to take that step, there is actually a lot of practicality in theory.
Of course.
Taking a step here does not refer to the invention of calculus, but a temporary application of ideas.
After all, it is impossible to tinker with calculus using Yang Hui's triangle alone. It requires a certain amount of mathematical accumulation.
More importantly.
This kind of mathematical accumulation does not refer to personal accumulation, but to the accumulation of the entire mathematical community and the entire era. It is a kind of sublimation of qualitative change.
Therefore, Xu Yun had no intention of becoming a fat man in one go, not to mention that he had a good relationship with Mavericks, and they were fair-weather friends after all.
His gaze returned to its original position.
After suddenly discovering a new field, Lao Jia, Han Gonglian and others showed great interest.
After all, these days, it is too rare for this kind of team to tackle key problems.
I saw only a few people discussing ideas or directly taking data measurements.
For example, a very primitive tool appeared in Liu Yi's hands:
Curved ruler.
When talking about the curved ruler, we have to talk about another concept first:
angle.
In their long scientific and technological practice, the ancient Chinese actually formed the concept of abstract angle very early - the word "zao" here can even be traced back to three or four thousand years ago.
But sadly.
They did not develop from this to establish the corresponding accurate measurement of angles.
Notice.
It is an accurate measurement.
This situation lasted until the Ming Dynasty, when the concept of perspective brought by the missionary Matteo Ricci broke this situation:
The "Elements of Geometry" he and Xu Guangqi co-translated gave a general definition of angles, described the classification and various situations of angles, how to express angles, and how to compare angles with angles.
Since then, the 360-degree division method has officially appeared in the cognition of the Chinese mathematics community.
And before that.
There are generally only two rough ways of measuring angles in China.
The first one is very simple, it is divided only according to obtuse angles and acute angles, and the words used are arrogant and hook.
Arrogant means blunt, hook means sharp.
The middle moment is a right angle.
The second one is more complicated.
It is somewhat similar to measuring orientation:
Using the twelve earthly branches Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen, You, Xu, and Hai, add A, B, B, D, Geng, Xin, and Ren among the ten thousand. , Gui and Qian, Kun, Gen and Xun in Bagua form twenty-four specific names to express angles.
That means each name is about fifteen degrees.
But it’s very strange. It can even be said to be an unsolved mystery.
The ancient Chinese sages actually knew the concept of 360:
When our ancestors conducted astronomical observations, the celestial body circle they used was actually a graduation system of 365+1/4 degrees.
In a sense.
This is infinitely close to the 360-degree approach.
What a pity.
In other situations other than astronomy when measuring angles, our ancestors did not use this system at all.
therefore.
This indexing method cannot play any role in the establishment of Chinese angle measurement.
So in some marketing slogans you will see the statement "China is actually the first nation to define 360 degrees", which uses the celestial body graduation system.
It's a pity.
The last half of the sentence is fine, but the whole sentence is wrong.
Or give a modern example, and you should be able to better understand where the blame lies:
This is probably similar to the 21st century. A scientist correctly analyzed the concept of high-dimensional space, but he did not use this concept in scientific research. Instead, he used it to create certain basic settings for novels and movies.
Unfortunately, this setting has been used in many movies, so almost every ordinary person on the planet has heard of this setting.
But in the scientific research community, everyone seems to have ignored this setting and only delved into various inefficient theories.
This is indeed a very strange situation:
Because the circumference of celestial bodies is also determined by the method of arranging circles, it is impossible for the ancestors to have thought of this with the wisdom of our ancestors.
Therefore, in some civil circles of later generations, some people put forward some nagging conjectures.
For example, the cognition of ancient ancestors has been blocked, fragments of relevant angles have been removed, etc.
There are even those who advocate 256 degrees for this reason, which is quite bizarre.
The topic returns to its original place.
No matter which method the ancestors used to divide the angle, after dividing the angle, another step must be carried out:
Measurement.
It is precisely because of this that the curved ruler appeared.
This is a right-angled ruler with one side long and one short. There are also special arc-shaped rulers.
In some places, this thing is also called a square ruler, commonly known as a turning ruler.
I only see this moment.
Liu Yizheng is holding a ruler and measuring the angle of the lens:
"The Harlequin is carved in the middle. The bottom of the Wu corner is carved. The top of the Hai corner is carved and the top of the Yin corner is carved."
Carve up and down.
This should be a classification that Liu Yi came up with himself, which is further refined compared to the 24-minute angle.
But even so.
It only achieved an accuracy of 72 points, which was a full five times worse than 360 points.
There is only one way to correct the five-fold difference:
By constantly adjusting the lens angle, a large amount of corresponding information is collected.
Next, we will use human calculations to filter out the most accurate answers step by step.
When Xu Yun saw this, a trace of unbearability flashed in his eyes.
To know.
This is the most basic link in the entire process.
Later generations only need three to five mapping data to lock a certain interval, but Lao Jia may need hundreds of sets.
After all, there is a square root process, which means that the amount of calculation has increased many times.
Thinking of this, Xu Yun couldn't help but open his mouth.
Subconsciously, he wanted to tell Liu Yi and Lao Jia about the concept of angle.
But after much hesitation, he gave up the idea.
After all, it was according to his original intention.
I really can’t participate too much in this derivation of convex lenses
If you tell Lao Jia the concept of angle.
What about the angle of incidence and angle of exit?
What about the waist radius?
What about screen function sampling?
What about the Fourier transform?
These are all connected concepts.
Although Xu Yun only spoke a few words, in order to break through these barriers, the sages (both Chinese and foreign) paid a huge price.
Therefore, no matter what, this hole must not be opened.
Just like women's clothing, there are only zero and countless openings.
To know.
Xu Yun's stay in this world was not long, only more than a year.
If the task is completed early.
It may even return to reality within a few months like the 1665 copy.
True.
He could make some big news during this period of time, which would shock these ancient people.
But if we just blindly instill finished knowledge without telling the deeper root causes and without establishing a system with self-thinking feedback.
Then after Xu Yun leaves, everything will only become a "black technology" that only knows the outside but doesn't know the inside.
The fate of this kind of rootless Ping was vividly reflected in the Chinese Jinyuan football in later generations:
when capital pours in.
Capital is used to introduce well-known foreign players and keep stars who have studied abroad or are expected to study abroad in the country.
They spend their youth and do not train new people.
The league remains the same for a while, the football market is gratifying, and it has achieved good results in the AFC Champions League and even the Club World Cup.
But when the gold dollar recedes.
Everything was restored to its original state, even worse than before.
Such as now.
National football fans can already look forward to losing to Myanmar.
This is what Xu Yun is worried about:
Knowing it but not knowing why is a very dangerous situation.
Therefore, Xu Yun would rather move slower and bring less changes to the world.
I also hope to create a vibrant soil for them.
And the first step in reclaiming land.
It fell on Lao Jia, Han Gonglian, Liu Yi and others.
Think of this.
Xu Yun couldn't help but take a deep breath and said to Lao Su:
"Master, let's go out and talk." (End of Chapter)