Into Unscientific

  Chapter 281 I found you, Conan! (middle)

untie.

   This is a very special word in mathematics, which has a macroscopic sense of entanglement.

   There may be nothing behind the word, or there may be eloquent content covering 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 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 their 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 middle school teacher named John Titus.

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

   That is 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, that is, 150 million kilometers, is taken 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.

   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 (that is, the eighth item in the sequence).

  Since then, people have firmly believed in this rule.

  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 rule 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.

  Speaking of this, it's time to flog a certain encyclopedia again.

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

  【Since Neptune discovered in 1846 and Pluto discovered in 1930 deviate greatly from this formula, many people still hold a negative attitude”]

   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.

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

  So calculated 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 Encyclopedia 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 lies in the fuzzy physical meaning, it is a purely empirical formula, and it is difficult to explain it in principle.

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

   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 laws of planets must be used:

  First Law:

  Each planet circles the sun along its own elliptical orbit, and the sun is at one focus of the ellipse.

  Second Law:

  In equal time, the areas swept by the line connecting the sun and the moving planet 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, an elliptic curve in the Cartesian coordinate system is also needed, namely:

  Ax+Bxy+Cy+Dx+Ey+F=0.

   With these, just add a tool to calculate.

  Later generations have advanced technology, and 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)

   About ten minutes passed.

  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 the exact location of Pluto is not yet known, 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.

   Faced with 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. The cubic polynomial is just a low-cost trial.

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

   "Bornhard, open 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?"

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

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

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

  This is also a very critical link—because there is an error in the Julian number of days and the number of thousands of years.

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

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

  In today's calculations of this magnitude, even a single decimal can be a thousand miles away.

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:

   "Bornhard, have you written it down?"

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

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

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

  L\'=L-1°.397*T-0.00031*T^2.

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

  The corrected value of ΔB=+0.03916*(cos(L\')-sin(L\')).

  Swipe, 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, 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 God beyond the sky."

  Tian Haosuo's expression was a little emotional. This was the first time he had been exposed to such a high-standard computing activity.

  Xu Yun smiled and patted him on the shoulder, comforting him:

   "It's okay, we mainly want to broaden our horizons, and don't necessarily 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. He mainly hoped that he could 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 get in the future if we don't keep it all together?

  After Xu Yun and Tian Hao parted, he came to Lao Tang in the center of the field again, and asked him in a low voice:

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

  Old Tang looked 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 photos 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·Tianguanshu", that is, the star bridge method:

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

What does it mean?

  It is the mouth of the spoon formed by the four stars from the right among the seven stars, which is called "Qui".

  The three straight stars in the middle form the longer straight handle of the spoon, which is "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 line connecting 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 Southern Dipper in the twenty-eight mansions.

  The last "Kui Zhen Shenshou" means that "Qui", which represents the mouth of the spoon, is facing the scorpion in the twenty-eight mansions.

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

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

  In addition, in Su Shi's "Red Cliff Fu", "the moon rises above Dongshan, wandering 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 Shang, the teacher who taught him astronomy when Song Ningzong Zhao Kuo was the prince.

  This star map takes the North Pole as the center, and the three concentric circles represent the constant apparent circle, the equatorial circle and the constant hidden circle respectively.

   As the name suggests.

  The stars inside the constant visible circle never set; while outside the constant hidden circle, the ancients could not see the active area.

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

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

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

be honest.

   It's really not easy to meet such a good night near 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 quick 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 macroscopic feedbacks of Pluto’s gravitational effect on Uranus.

  One is the orbit of Uranus.

  The second is the ecliptic angle of Uranus.

  Has already calculated Huang Jing L before, so there is only one task left for the calculation team:

   Compare the difference in orbital offset.

What does it mean?

  Assume that a magnet A moves on a horizontal plane, and its trajectory is a straight line in the absence of other external forces.

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

  Uranus is magnet A, and Pluto is magnet B.

  The trajectory of magnet A after 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 without being 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 goes on a trip. He was supposed to go to Shanghai today, but ended up in Jinmen instead.

  And no matter what happens 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 .

   In other words.

  The so-called 'difference in contrast to orbital offset', to put it bluntly, is just that.

   Compare observation records!

Precisely.

   is to compare 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 reports the coordinates, and the other person starts 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 set the formula, so it takes about four hours in total.

  Xu Yun and Lao Tang were not idle, 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.

   Some data from the Bradley family statistics, dusty for many years, appeared in front of the world for the first time.

  Many of the data have even surpassed similar documents from the Greenwich Observatory in terms of accuracy.

  For example, Daniel Bradley's father, Conton Bradley, recorded the trajectory of Makemake twenty 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.

  Maybe it was because I 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.

  Looking at Earl Eisley not far away with an ugly expression, Xu Yun was inexplicably moved.

  This may be the charm of science.

  Many times, its appeal is invisible.

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

  750 years ago.

  He once worked day and night with a group of Chinese sages to conquer the sky.

  750 years later.

   It was also a night without snow.

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

   how lucky

Note:

  Now things are too expensive. Ten years ago, the tofu at the mobile stall in my hometown was 50 cents. Today I want to drink and buy a bowl. It costs 3.5 yuan.

  (end of this chapter)