Into Unscientific

untie.

This is a very special word in mathematics, with entanglement in the macroscopic sense.

There may be nothing behind this word, or there may be eloquent content all over the page.

At the same time, even if the content is all over the page, the final result is likely to be the same as nothing.

In addition, it has nothing to do with the appearance and stationery of the solver.

Of course.

As the initiator of this observation, Xu Yun is naturally not the former.

So after writing down a solution, he continued to draw the initial calculation.

As for the initial entry point of the calculation.

Naturally, it is the Titius-Bode rule.

well known.

As an important branch of the history of civilization, the history of human science can be described as a galaxy of stars.

These great people are basically geniuses, but there are also rising stars who have become superstars by virtue of unimaginable and shocking conjectures.

For example, Faraday, such as Eldar Alikan who wrote the 5G standard channel coding at the age of 51.

Another example is a certain German secondary school teacher named John Titus.

John Titius lived in the 18th century. At that time, it was known that there were six planets in the solar system.

Namely Mercury, Venus, Earth, Mars, Jupiter, Saturn.

Titius is an amateur astronomer. After long-term observation, he wrote down such a sequence in 1766:

a=0.4+0.3X2^k.

The a in it refers to the average distance from the planet to the sun, which is 150 million kilometers.

Among them, k=0, 1, 2, 4, 8, 16, and numbers after 0 are 2 to the nth power.

If the distance between the sun and the earth is 150 million kilometers as an astronomical unit, then the ratios of the distances from the six planets to the sun are:

0.4, 0.7, 1.0, 1.6, 5.2, 10.0.

And the actual value is:

0.39, 0.71, 1.0, 1.52, 5.2, 9.8.

Are you surprised?

That's right.

In the reference system of the starry sky, the two results can be said to be infinitely close to the same.

In 1781, Herschel discovered Uranus at a position close to 19.6 (the eighth in the sequence).

Since then, people have believed in this certainty.

According to this rule.

The fifth item in the sequence, that is, the position of 2.8 should also correspond to a planet or asteroid, but it was not discovered at that time.

So many astronomers and astronomy enthusiasts embarked on a journey to find this new planet with great enthusiasm.

This asteroid is Ceres, and the discoverer is Gauss at the scene.

Later, this law was summarized by Bode, the director of the Berlin Observatory, and summarized into an empirical formula to express it, which is called the Titius-Bode rule.

Having said that, it's time to flog the corpse again.

If you search for the Titius-Bode rule on Baidu, you will see a sentence in the detailed introduction:

[Because Neptune discovered in 1846 and Pluto discovered in 1930 deviate greatly from this formula, many people still hold negative attitudes”]

Among them, the calculation data of Neptune given by Encyclopedia is 38.8 AU, and the actual distance is 30.2 AU.

The calculated data of Pluto is 77.2 AU, and the actual distance is 39.6 AU.

Yes, seeing this, students majoring in astronomy should have discovered a problem:

A certain editor calculated the data of Pluto as 77.2—this is the distance of the inner boundary of the solar system

Actually.

In the calculation process, due to the existence of k-degree polynomials, Pluto and Neptune share n=8 for calculation.

Therefore, according to the Titius-Bode rule, the error rate of Pluto is 2%, not 200%.

This is the content that will be clearly marked in the textbook in the second semester of astrophysics and astrometry. As an encyclopedia column, it is quite helpless to make such a mistake.

In his previous life, Xu Yun happened to use the Titius-Bode rule in a certain episode. When he harassed Keke and consulted a friend who worked at the Phoenix Mountain Observatory, the other party once expressed some extremely cordial greetings to Baike with blessings.

Of course.

A large part of the reason for this situation is due to the unpopularity of knowledge. The Titius-Bode rule itself is a minority knowledge, let alone Pluto, a minority among the minority.

all in all.

Later generations basically have no opinion on the numerical value of the Titius-Bode rule in mathematical calculations.

Its main controversy is that its physical meaning is vague, and it is a purely empirical formula, which is difficult to explain in principle.

Other measurement methods such as an+1:an=β are basically mathematically accurate, but the physical meaning is unclear.

Then Xu Yun wrote down two more formulas, which are the function of polynomial of degree k and the minimum error value:

f(x)≈g(x)=a0+a1x+a2x2+a3x3++akxk.

loss=i=0∑10(g(i)f(i))2.

Thus.

As long as the appropriate coefficient is found, the error value can be minimized.

While Xu Yun was optimizing the function.

The others were not idle, and they were acting according to their predetermined plans.

For example, Lao Tangzheng and the technicians from the Greenwich Observatory took pictures of today's star map, and Gauss sorted out the unique observation records left by the Bradley family:

"0.000660450.010722610.126845380.43146853"

well known.

If it is necessary to calculate planetary orbit data only through mathematics, then Kepler's three planetary laws must be used:

First law:

Each planet orbits the sun in its own ellipse, with the sun at one focus of the ellipse.

Second law:

In equal time, the areas swept by the line connecting the sun and the moving planets are equal.

That is Sab=Scd.

The third law is:

The square of the revolution period of each planet around the sun is proportional to the cube of the semi-major axis of their elliptical orbits.

That is, T/a=K, T is the planetary period, and K is a constant.

In addition, the elliptic curve in the Cartesian coordinate system needs to be used, namely:

Ax+Bxy+Cy+Dx+Ey+F=0.

With these, calculations can be performed as long as a certain tool is added.

With the development of science and technology in later generations, the tool for calculating orbits is generally numpy, and the results can be calculated in a few seconds.

Although there is no numpy assistance at the moment, the calculation logic of this thing is actually the least square method.

The inventor of the least squares method is none other than Gauss

"g(x)=0.43146853+0.12684538x0.01072261x+0.00066045x"

"The next set is 0.314685310.215384620.12960373"

"0.053379950.017249420.32307692" (Note: All data comes from NASA's open database, not fabricated)

After about ten minutes.

Riemann, who was in charge of the final calculation, wiped the sweat from his forehead and wrote a number on the paper:

0.4857342657342658.

Although it is still impossible to know the specific position of Pluto, let alone its weight.

But it was mentioned before.

After deducting the gravity of Neptune, the orbit of Uranus is still somewhat abnormal.

This abnormal data is the entry point of the calculation, which is the number calculated by Riemann and the others.

Gauss took the paper and glanced at it, then shook his head.

The observation records they gathered at the scene this time can be traced back to 1012, with nearly 32,000 hand-drawn drawings and about 2,700 black-and-white photos.

In the face of these data, the results calculated by the cubic polynomial obviously cannot be accurately fitted.

However, this situation was already expected by Gauss and Xu Yun, and the cubic polynomial was just a wave of low-cost temptations.

If the accuracy of the result obtained is high enough, then you can save a lot of effort, if the accuracy is low, you will lose a little time.

Seeing that Gauss' complexion did not change at all, he turned his head and said to Riemann:

"Bernhard, turn on the high power."

Riemann nodded, hesitated for a moment, and asked:

"Teacher, should we still use Huang Jing?"

Gauss thought for a while, waved his hand, and said:

"Continue to use Huang Jing, go to the eighth power!"

Hearing the word eighth power, Riemann's expression suddenly became serious:

"clear!"

Students who are rare in this life should not know.

in planetary orbit calculations.

x' is the true position of the planet and x is the mean position.

The orbital longitude is γN + NX', and these two angles are on two different orbits.

Draw a celestial longitude vertically through the true position x' of the planet, intersect at x" on the ecliptic, then γx" is the celestial longitude L.

Then Gauss looked at Sylvester at the side and asked:

"James, have you counted your time yet?"

Sylvester swallowed when he heard the words, frowned and said:

"The result has been calculated, and it is in the third round of verification, it will be ready soon!"

Previously, Xu Yun divided the entire team into several modules, and Sylvester was responsible for time correction.

This is also a very critical part-because there is an error between the Julian number of days and the number of thousands of years.

Assume that at a given time JDE is the standard Julian number of days and τ is the number of millennia.

Then the expression for τ is τ=(JDE - 2451545.0)/ 365250.

In today's calculations of this magnitude, even a single decimal can make a huge difference.

five minutes later.

Sylvester raised his head abruptly, and said to Gauss:

"The verification is correct, τ is 0.00834422!"

Gauss turned his head and said to Riemann:

"Bernhard, do you remember?"

Riemann quickly filled in the numbers, and only had time to utter an 'um'.

At this point in the calculation, the next thing is very simple, only the calculation is left.

The whole formula is L=(L0+L1*τ+L2*τ^2 +L3*τ^3+L4*τ^4 L8*τ^8)/10^8.

L'= L - 1°.397*T - 0.00031*T^2.

Corrected value of ΔL=-0.09033 + 0.03916*( cos(L')+ sin(L'))*tan(B).

Corrected value of ΔB=+0.03916*( cos(L')- sin(L')).

swipe swipe——

The scene where hundreds of people gathered was silent at this time, and everyone's eyes were on the 43 math tool people.

Xu Yun took this opportunity to walk to the other side of the shed.

He first glanced at Mai Mai who was calculating their respective tasks, and then said to a yellow-skinned young man beside Mai Mai who was assisting in the calculation:

"Brother Hao, how do you feel?"

"Oh, it's Brother Luo Feng."

Tian Haosuo was frowning and thinking about how to write, but when he heard this, he quickly raised his head, smiled wryly and shook his head:

"It's a bit difficult, but I can barely keep up with the train of thought. I have to say that there are people beyond people, and there is a sky beyond the sky."

Tian Haosuo's expression was a little emotional. This was the first time he had come into contact with such a high-standard computing activity.

Xu Yun patted him on the shoulder with a smile, and comforted him:

"It's okay, we mainly want to broaden our horizons, and we don't necessarily have to pursue results."

"I've seen it all the way, and your performance is already better than many sophomore seniors."

Tian Hao is one of the computing power members that Xu Yun invited to join yesterday. After all, this Oriental is also a student of the Department of Mathematics.

However, Xu Yun did not give him a specific task, mainly hoping to improve his vision and thinking pattern.

Anyway, this approach has no cost, and it is even less likely to be a bad thing. What surprises can we reap in the future if we don't guarantee it?

Then Xu Yun and Tian Hao said goodbye, and came to Lao Tang in the center of the venue, and asked him in a low voice:

"How is the visibility tonight, Mr. Thomson?"

Lao Tang glanced around a few times, and said in a low voice:

"God bless, the visibility is very high, almost all of Hevelius' star map is visible."

Xu Yun breathed a sigh of relief and nodded.

Black-and-white photographs were invented in 1839. Before that, all observation records of planets relied on words or star maps.

For example, the Big Dipper positioning method in Huaxia's "Historical Records Tianguan Shu", that is, the star bridge method:

The dipper carries the dragon's horn, weighs Yin Nandou, and the chief pillow participates in the head.

What does it mean?

It is the four stars from the right of the seven stars that form the mouth of the spoon, which is called "Qui".

The three straight stars in the middle form the longer straight handle of the spoon, which is the "balance".

The angle of the connecting line of the two leftmost pieces is deflected, forming the part of the handle of the spoon, which is what Sima Qian called "dipper".

"Diao carries the dragon's horn" means that the connecting line of two stars (dippers) comes out and points directly to a very bright star.

The ancients believed that it was the dragon horn of the oriental blue dragon in the sky, that is, the Arcturus of later generations.

"Heng Yin Nan Dou" refers to the connection line of the long handle represented by "Heng", pointing directly to the Nandou stars in the twenty-eight constellations.

The last "Kui Zhen Shenshou" means that the "Kui" representing the mouth of the spoon is facing the Xi Su in the twenty-eight mansions.

In the Han Dynasty, Zisu and Sansu were added together and regarded as a tiger.

Zisu represents the head of a tiger, so "Shenshou" is "Zisu".

In addition, in Su Shi's "Red Cliff Fu", "the moon rises above Dongshan, hovering between the bullfights", which is also a positioning method in poetry.

Besides the text, the rest is the star map.

The most famous star map in ancient China is the Suzhou stone inscription astronomical map, which was drawn by Huang Chang, the teacher who taught him astronomy when Zhao Kuo, Emperor Ningzong of Song Dynasty, was the prince.

This star map is centered on the North Pole, and the three concentric circles represent the constant apparent circle, the equatorial circle and the constant hidden circle.

As the name suggests.

The stars in the constant display circle never set; while the stars outside the constant hidden circle are invisible to the ancients.

This star map was later engraved on a stone tablet with a height of 2.16 meters and a width of 1.06 meters, which is currently preserved in Changshu.

In addition, there are the Dunhuang star map, and the Su Song star map drawn by Lao Su, etc. - the star map drawn by Lao Su is also the one with the most recorded celestial bodies in all ancient civilizations.

As for the more famous one in Europe, it is the Hevelius star map, which is extremely vivid in shape and has a very high artistic value. (If you are interested, you can search it, it is really beautiful.)

These days, the Hevelius star map is also used to judge visibility, which is a default method.

The more observed objects in the Hevelius map, the better the observation environment.

be honest.

Not an easy thing to come across such a nice night around London in 1850.

While Xu Yun was chatting with Thomson.

Riemann in the shed whispered a few words to the people around him, and then raised his head happily:

"The eighth root is opened, and the parameter of the deviation is 0.001273499338486!"

0.001273499338486.

Compared with the previous 0.4857342657342658, it is hundreds of times more accurate!

After all, one is the third power and the other is the eighth power, so the difficulty and precision are equal.

But then again.

This value is almost the upper limit of human quick calculation.

The result calculated by the 17-person speed calculation contest organized by Oxford University in 1937 was about 8% lower than this figure.

This parameter represents the correction coefficient of Uranus, that is, the gravitational effect of Pluto on it.

With this coefficient, the next link is very clear.

As mentioned before, there are only two feedbacks from Pluto to the gravitational effect of Uranus on a macro level.

One is the orbit of Uranus.

The second is the ecliptic angle of Uranus.

The Huang Jing L has been calculated before, so there is only one task left for the calculation team:

Compare the difference in orbital offset.

What does it mean?

Assuming that a magnet A is moving on a horizontal plane, its trajectory is straight in the absence of other external forces.

If another weaker heteropolar magnet B is added during its movement—for example, placed ten meters to the left of A, then the trajectory of A will appear slightly while maintaining the original direction of motion. offset.

Uranus is magnet A, and Pluto is magnet B.

The trajectory of magnet A after the deflection is the trajectory of Uranus observed and recorded by the naked eye.

After deducting the correction coefficient calculated by Riemann and others, what is obtained is its theoretical original trajectory—that is, the trajectory that is not attracted by Pluto, that is, the "straight line".

In this way.

There will be a coordinate difference between these two trajectories.

It's like a person who went on a trip. He was supposed to go to Shanghai today, but ended up in Jinmen instead.

Regardless of what happened in the middle, at least the geographical difference in latitude and longitude can be determined.

Then compare those observation records, find out a large number of coordinate differences at different times and different locations, and use multivariate equations to calculate the position of Pluto—because according to the Titius-Bode rule, the distance of Pluto can be roughly determined of.

In other words.

The so-called 'compared to the difference in orbital offset', to put it bluntly is.

Compare observation records!

Precisely.

It is a comparison of tens of thousands of observation records.

Of course.

Due to the existence of perihelion and aphelion, and the reference significance of some early images is greater than the actual significance, the data that really need to be identified are not so exaggerated.

According to rough statistics, there are about 4,000 copies in total.

Afterwards, the counting members at the scene began to form pairs in pairs.

One person reported the coordinates, and the other began to calculate the deviation.

Among them, the ability of the tool people who report the coordinates is slightly lower, mainly those students in the Department of Mathematics.

It is Riemann, Jacobi, and Weierstrass who provide computing power.

On average, each person needs to calculate more than two hundred observation records.

The calculation and comparison of a record takes about one minute. After all, there are only two coordinates to formulate, so it takes about four hours in total.

Xu Yun and Lao Tang were not idle either, and took the initiative to undertake part of the computing tasks.

"4.66925686283.07585"

"462.6112.5661517"

"2.0371529.691"

"2.920.067"

Soon, the coordinate system parameters of different specifications were reported one by one.

For the first time, some data from the Bradley family's statistics and dusty years have appeared in front of the world.

In terms of accuracy, many of the data even surpassed similar documents from the Greenwich Observatory.

For example, Daniel Bradley's father, Conton Bradley, recorded the trajectory of Makemake 20 years ago.

Although it is only recording the trajectory rather than accurately discovering it, it is already very scary in nature-because according to historical development, this thing will not be discovered until 2005.

2005 and 1830.

From the perspective of the accuracy of observation equipment, it is basically two epochs

It can be seen from this that the Bradley family has held back a lot of energy in order to reverse the case for their ancestors.

Perhaps it was because he was touched by the atmosphere of the scene.

after awhile.

A few students from the mathematics department came out of the crowd and took the initiative to take over the work of the mathematicians who reported the numbers, allowing them to fully exert their abilities in the calculation process.

According to Lao Tang, one of them was a follower of Frederick Agar Ellis.

Seeing Earl Eisley with an ugly expression not far away, Xu Yun felt inexplicably moved.

Perhaps this is the charm of science.

In many cases, its appeal is invisible.

Then he thought of something, raised his head, and looked around.

750 years ago.

Together with a group of Chinese sages, he worked day and night to conquer the sky.

750 years later.

It was also a night without snow.

Xu Yun cooperated with another group of European mathematicians, looked across the sky, and looked at the vast starry sky.

how lucky