"...."
After writing the word 'solution'.
Xu Yun put down his pen and stood aside with his hands folded.
Well behaved.JPG.
The protagonist of tonight's session on the Analytical Engine is not him, but Babbage and Gauss. This is their stage.
After Xu Yun got out of the way.
Gauss took Riemann and Mai and walked to the table step by step.
With every step Gauss took, his spirits lifted.
After arriving at the table.
This little old man who is over seventy years old has no trace of his earlier malaise.
The whole person was as energetic as if he had eaten a Snickers bar, and his whole body was filled with an energy he had never seen before.
He had been preparing for this day for a long time. In order to ensure that he had enough energy to perform calculations today, he even refused visits from outsiders a week ago.
Except for Xu Yun, Riemann, and Xiaomai, no one has seen the shadow of Gauss in the past week.
Do not know why.
Looking at Gauss at this time, Xu Yun suddenly thought of Tong Hu, Zilong's master in "Saint Seiya Lost".
The Libra Gold Saint was ordered by Athena to monitor the 108 underworld warriors, so he sat at the Wulao Peak in Lushan all year round.
At the same time, Tong Hu learned Athena's technique of feigning death from the gods in order to be able to unleash his strongest fighting power at the critical moment in the final battle.
At this time, Gauss has been cultivating his spirit for a year, just to have the most perfect state tonight!
And just when Xu Yun's imagination was widening.
Gauss also happened to walk to the table, picked up the pen without hesitation, and wrote down a line of formula:
d²u/dθ²+ u =GM/h²+(3GM/C²)u²
△Φ=6πM²/L²
d²x^a/dS²=-￡aik(dx^i/dS)(dx^k/dS).
Students with good memories must have noticed this.
These three formulas are the theoretical geodesic equations of the second-order asymptotic solution of general relativity, the precession angle equation, and the weak field low-speed approximation given by Xu Yun on Pluto's night.
After all, the scientific community's understanding of planets these days is only in the category of first-level asymptotic solutions.
Although Gauss, Laplace and others have established perturbation theory, there is still a certain distance from the concept of 'perturbation method'.
And even the first-level asymptotic solution given by the perturbation method is still somewhat inaccurate in planetary problems.
Therefore, Xu Yun had no choice but to take out the second-level asymptotic solution after Pluto's Night.
Without a second-order asymptotic solution, even Gaussian cannot calculate the orbits of trans-Neptunian objects.
Then the next second.
Gauss then wrote another formula:
d²u/dθ²+ u²=- k²Aθcos(θ+h).
x=u-1+2e^（-2u+2）-10ve^（-4u+4）
Xu Yun was stunned for a moment.
Mentioned earlier.
In the past year, although Gauss had no reservations about Xu Yun in terms of teaching, he sincerely regarded him and Mai as close disciples.
But on the other hand.
Gauss never informed anyone of his progress in second-order asymptotic solutions.
Even Riemann, who was responsible for taking care of Gauss's daily life, was completely blank about this.
This is one of the two reasons why Xu Yun is not sure whether he can find Planet X:
He had no idea how far Gauss had come to derive mathematically.
The second-level asymptotic solution can be divided into four stages. Each stage has different assistance to the star search work, and the final probability resulting from different progress is also different.
To put it bluntly.
If the study of Gauss only stops at the asymptotic solution given by Xu Yun...
So tonight’s star-hunting mission can be done with some sleep, and it’s time to show off to the seller of the analytical machine.
Another reason why Xu Yun was unsure was that Planet X was too far away, and even if he calculated the formula, he might not be able to find the target.
But now it seems...
Gauss has calculated the special solution of small accumulation for many times?
This is good news.
This formula was quickly spread to the old audience at the side.
Today's guests cover a wide range of majors, including physicists, chemists, biologists and even writers. Not everyone can understand the content of this formula.
Therefore, when faced with this formula, everyone's reaction is different.
Some people looked confused.
Some pretend to be reserved and show disdain.
Some people are shocked!
About half a minute later.
Finally, a guest from abroad couldn't sit still.
He stood up and apologized to Prince Albert, then walked quickly towards the venue.
This person is called...
Augustin Louis Cauchy.
Then came the second person, from England.
His name is Arthur Kelley...
Then the third one....
the fourth.....
Their names are:
De Morgan…
Poncelet...
Hamilton...
...
If you observe carefully, you will find that these mathematicians who can't help but walk into the scene are all well-known in the local timeline.
You may not be able to name their specific contributions or achievements, but you must have heard their names more or less.
In fact, this is not difficult to understand.
The second-level asymptotic solution written by Gauss is an advancement of perturbation theory. If you are not a mathematician at the time, you will never understand its meaning.
Therefore, the more top-notch the boss is, the more he cannot help but feel excited at this time.
Among these people, Xu Yun also met an important guest who should have passed away through Aveline:
Simone Denis Poisson.
That's right, he was the unlucky guy who had to leave his name in history because he was slapped in the face by Fresnel in the original timeline.
In the original history, Poisson became depressed after being slapped in the face by Fresnel, and eventually died of mental illness in 1840.
But now in this timeline, the discoverer of Poisson's spot has become Maverick, and this spot has been renamed Newton's spot.
Poisson escaped the disaster without knowing it, but he has survived successfully until now...
After coming to Gauss.
These elders had a tacit understanding and did not talk loudly, but quietly watched Gauss write the calculations.
Gauss, as if he didn't notice anyone coming around, picked up his pen again and continued writing:
"Let u=u0+Xu1+X2u2+…"
"d²u0/dθ²+u0=k....."
"Then d²u1dθ²+u1=2kAsin(θ+h)..."
"When u=5, ignore O in the asymptotic solution and substitute it into the correction term as a first-order approximation..."
The open space on this side was silent at the moment, except for the rustling sound of the Gauss pen tip rubbing against the calculation paper.
All the top mathematicians stood aside respectfully and listened to the lectures like ordinary students.
More than ten minutes later.
Gauss took a deep breath and wrote a final formula on the calculation paper:
u*²= u*21+ u*22=49kA³cos²(θ+h)+13kA³θsin²(θ+h)-k³A/4θcos(θ+h)-k³A/4θ²sin(θ+h)+θ〔a1cos(θ+ h)+ b1sin(θ+h)〕.
Look at this final form.
Xu Yun's heart skipped a beat for a moment.
His eyes were widened, and the word "f*ck" subconsciously came to his lips, and he almost couldn't help but blurt it out.
This is not because of his lack of determination, but because of the equation written by Gauss...
It’s so amazing!
After coming back to his senses.
He rubbed his eyes funny and looked at the formula again.
The content remains unchanged.
Seeing this, Xu Yun opened his mouth and put his right hand in front of him.
I saw my girlfriend, trembling slightly at this time...
Xu Yun actually has no impression of the specific numerical value of this formula, but the expression form of this formula is not unfamiliar to him:
The form of this formula is surprisingly consistent with the general formula of the ring system deduced by the Spanish astronomer Ortiz's team in 2017 through occultation observations and with the assistance of the Barcelona Supercomputing Center...that is, the BSC!
The d/10.1038/nature24051 of that article was published in the magazine "Nature". It is also the most accurate formula as of September 14, 2022! (I calculated it using this paper plus the version DE421 in the jpl precision ephemeris of sd..gov. The basic idea is to use Kepler's square root numbers to analytically extrapolate, taking into account the changes in the radical numbers over time, approximately When it comes to item t², it’s as reasonable as possible.)
It is also worth mentioning that.
The BSC supercomputer is called Odin, which is the character in Norse mythology...
God King Odin.
In other words...
In 1851.
Gauss, a 74-year-old man who is dying...
With a mortal body, he rivaled the gods!
Looking at Gauss writing slowly on the paper, Xu Yun's original words reappeared in Xu Yun's mind:
"I don't perform miracles because I am a miracle."
Xu Yun didn't know how much effort Gauss put into calculating this formula. There was no need to mention it at this moment.
All descriptions of his efforts are not as intuitive as this fifteen-centimetre-long formula at this moment.
this moment.
The light of humanity on the ground shines brighter than the thousands of stars in the sky.
After writing this formula.
Gauss handed the piece of paper to Riemann and ordered:
"Bornhard, give it to Mr. Charles - by the way, Kexi and Kai are here just in time. Let's help recheck the data together."
Cauchy, Kai Lai and several other mathematicians looked at each other after hearing this, and a question mark appeared on their faces:
"?"
Mom? !
We just came here to watch the calculation process, how come we were caught in the blink of an eye?
But a few seconds passed.
Kexi still sighed slightly and accepted his fate:
"That's all, Friedrich, we'll just do some hard work for you."
Kai Lai, Peng Serie and others also nodded.
Gauss's deduction process brought them many new ideas, and even broke some people's long-standing bottlenecks, giving them enlightenment.
To describe it in fantasy terms, it is enlightenment!
Therefore, it is reasonable and reasonable to let these elders be tool men for once. There is no problem.
Riemann quickly handed this formula to Babbage, and Ada, the first programmer in human history, entered the relevant content.
at the same time.
George Beadle Airy, then director of the Greenwich Observatory, also came to Xu Yun with his men and opened boxes of observation records one by one.
These observation records are all starry sky observation records taken by observatories in various countries after Gauss and Faraday wrote letters personally and asked observatories in various countries to take pictures after the night of Pluto.
In return....or price.
Gauss and others 'paid' the structural drawings of the Schmidt telescope to major observatories.
Xu Yun had no objection to this.
After all, the Schmidt telescope is different from other equipment he brought out. This thing actually does not have a particularly significant role in promoting the level of science and technology - at most it allows humans to observe some stars in advance.
This year is not the year 1100 AD that Old Su used to be.
Lao Su's most common telescopes didn't exist at that time, so it was of great significance to be able to observe the starry sky.
At this point in time in 1851, the Schmidt telescope was at most useful under certain circumstances.
For example, Da Shen and Eris were discovered decades in advance. To put it bluntly, the meaning is just that. At most, Pluto will be removed from the nine planets earlier.
Pluto doesn’t have any objections anyway, right?
Once the space radio telescope comes out, the status of the Schmidt telescope will quickly decrease.
Unless the astronomical community can rely on this thing to discover aliens, it will be the least helpful thing in promoting the history of science and technology among all the technologies Xu Yun has come up with.
"Classmate Luo Feng."
After arriving at Xu Yun's side, George Beadle Airy pointed at the box and introduced to him:
"In the past year, in addition to major European observatories, we have also persuaded five observatories in the Americas to collaborate, bringing the total number of participating institutions to 22."
"Each observatory takes at least three photos every day, and coupled with the full-scale observation of our Greenwich Observatory, the image records in the box total more than 25,000."
"Good guy, so many?"
Xu Yun was slightly startled when he heard this, and after coming back to his senses, he quickly thanked George Bedell Ally and said:
"Thank you very much, Mr. Airy."
These days, unlike later generations, the cost of photos...or film is very high.
Even for an official institution like the Observatory, the cost of a photo is around £0.10.
According to the previous exchange rate, it is equivalent to between 90 and 100 yuan in later generations.
Therefore, in Xu Yun’s previous estimate.
It is very rare for an observatory to be able to take one record every day.
Unexpectedly, these observatories were so powerful, and they took so many observation records in one year.
These observational records are coupled with the Analytical Engine, Gauss's formulas, and the latest team of toolmakers.
Basically, it can be said that the 'personnel' aspect has been done to the extreme.
All that's left is...
I know my destiny.
.......
The boxes of observation records were quickly distributed on the table, and the tool team began to perform coordinate conversions.
The converted coordinates are input into the analysis engine and the least squares calculation is performed.
The magnitude used by Gauss on Pluto's night is the 8th power, which is:
L=(L0+L1*τ+L2*τ^2 +L3*τ^3+L4*τ^4... L8*τ^8....)/10^8.
But this time with the help of the Analytical Engine, Gauss went directly...
Seventeenth power!
Of course.
A large part of the reason for achieving this kind of accuracy is that the maximum change in orbital longitude does not exceed 1, and generally fluctuates around 0.1-0.4.
For example, 0.412 raised to the 17th power is 0.000000283957.
0.13 raised to the 17th power is 0.00000000000000008650415919381338.
Although these numbers are large, they are within the order of the Analytical Engine.
If you change it to other larger or smaller numbers, then the 17th power operation will exceed the computing power.
In later generations, calculations on planetary orbits generally use 50-70th power. More professional teams, such as Pluto killer Mike Brown, basically use the order of magnitude 120+.
See here.
Some students may feel strange:
its not right.
Why can the calculator on my mobile phone and any calculator randomly searched on Baidu calculate results of dozens of powers?
Is this all the power of supercomputing?
This involves a concept, which is scientific notation.
Most computers currently on the market have a calculation upper limit. Once this level is exceeded, a certain number will be expressed as a multiplied by the nth power of 10.
For example, 19971400000000=1.99714×10^13. When a calculator or computer expresses the power of 10, it is usually E or e.
That is 1.99714E13 and so on...
The power multipliers used in modern supercomputing calculations are basically accurate to 10 decimal places or more.
For example, 0.4556456112 raised to the 50th power and so on.
If this kind of calculation is not suitable for supercomputing, it will be difficult for ordinary computers or calculators to produce accurate results, which are basically approximate numbers.
Useless knowledge has been added.JPG.
The calculation performers of the star search project were Gauss and Babbage, so after the calculation started, Xu Yun moved to today's 'second venue'.
That is, the clearing where Michelson-Morley's experiment took place.
At this moment.
Influenced by Cauchy et al.
Many physicists couldn't help but leave the stands and came to the interferometer to watch the excitement.
Compared to the quietness over there at the analysis machine, the area around the interferometer was much more lively.
However, this excitement is not festive, but...
Extremely intense hostility.
"Hey, Oriental boy!"
As soon as Xu Yun showed up, a young man ran up to him aggressively and looked at him with unkind eyes:
"Damn Eastern boy, I heard that you have been preaching that ether does not exist recently?"
Looking at this young man who seemed to be saying "God, I will kick your ass hard" in the next second, Xu Yun blinked:
"Yes, it's me. What can I do, sir?"
The young man was stunned for two seconds, and then shouted:
“God, I’m going to kick your ass!
"
Xu Yun:
"?"
Are you really coming?
However, before the young man could make a move, he was stopped by the people around him and quickly taken aside.
After a while.
Another middle-aged man who looked a bit like Charlie Liu in "Detective Detective Dee" walked up:
"Classmate Luo Feng, right...Although Anderson's behavior is a bit rude, as a student at Cambridge University, your remarks are a bit too shocking."
"especially......"
As he spoke, the middle-aged man turned his head and glanced at Aveline not far away:
"You have also led the descendants of Sir Newton to this wrong path. How will you face Sir Newton and your fat fish ancestors after your death?"
It is clear.
This is also a stressful person...or should I say a stressful person?
Then Xu Yun thought for a while and asked him:
"Sir, don't you know what to call me?"
The middle-aged man puffed up his chest and announced a name:
"Rudolf Julius Emmanuel Clausius."
"Clausius?"
Xu Yun repeated the name and quickly locked the target in his mind.
Rudolf Julius Emmanuel Clausius.
The German is one of the main founders of thermodynamics. To be honest, he is considered a 3/4 boss.
The concept of 'entropy' that often appears in later science fiction was proposed by him a few years later.
Even at the end of the 19th century, the unit of entropy was the "Clausius", with the symbol Cl.
This person is also a well-known Mavericks fan in history, but he is a bit more normal than Doppler and can be considered a figurehead.
Among the existing autograph letters of Mavericks in the Newton Personal Museum at Cambridge University, more than 30 were donated by Clausius after his death.
In 1857, a corner of Maverick's former residence collapsed, and Clausius donated 500 pounds the next day.
at the same time.
Clausius is also a standard classical nobleman:
His father was a primary school principal in Keslin, Pomerania, with a title of baronet, and his family's business spanned Europe.
Although he studied at the University of Berlin, he even was a classmate with Dirichlet for a period of time.
But out of support for the classical disciplines, he ultimately chose to go it alone.
no doubt.
This is a standard dogmatist - at most more capable than other keyboard warriors.
However, considering that the gas motion model that Clausius later studied introduced a variety of concepts and non-subjectively derived the development of modern science, Xu Yun decided to maintain some respect for him:
"I Have a Picture Book of Ghosts and Gods"
"Mr. Clausius, how do you know that matter like ether must exist?"
Clausius looked at him seriously and answered without hesitation:
"Because this is the concept proposed by Sir Isaac Newton."
"...."
Xu Yun opened his mouth but stopped talking.
What are we talking about...
Looking at Clausius with a determined look on his face, Xu Yun inexplicably thought of some fans of Fengfeng and Fanfan whom he met on the Internet in his previous life.
Idiot fans really can't communicate...
So Xu Yun sighed and decided to change his mind.
I saw him spread his hands and said crisply:
"Mr. Clausius, whether you believe that ether does not exist or not, the current situation is not suitable for fighting or oral pleasure."
"There are so many elders and Prince Albert watching outside. If you want to stop me, why don't you go talk to them?"
"Besides, the idea of this experiment is simple and clear. If the interference fringes really shift, doesn't it mean that the ether exists and I am wrong?"
"In that case, what are you afraid of?"
Clausius was silent for a long time and did not speak.
The second half of Xu Yun's sentence really touched his point of contradiction.
As an ardent fan of the Mavericks, Clausius naturally unconditionally believes in the existence of ether, and the Mavericks can never be wrong.
But on the other hand.......
The formation Xu Yun created during this period is indeed quite scary:
Although Xu Yun himself felt nothing, as Faraday and others published papers that shocked the scientific community, he, a descendant of fat fish, naturally appeared in the public eye.
In history, Fat Fish once corrected Maverick's misunderstanding of optics, which directly led to the introduction of the concept that light has wave-particle duality.
In addition, the same is true for the absolute view of time and space.
So including Clausius.
Many Mavericks fans have a subconscious idea that even they themselves do not believe, but at the same time it is real:
just in case........
Has Xu Yun really inherited some knowledge from Fei Yu and can he really overturn the ether theory?
So what will the Mavericks do then?
Think of this.
Goosebumps appeared on Clausius's arms.
However, as Xu Yun said.
Right now, Prince Albert is sitting in the auditorium not far away. The presence of the uncrowned king of the British Peninsula can to some extent ensure the normal conduct of tonight's experiment.
I don’t know if he came here on a whim to see the excitement, or if he came here deliberately to sit in Cambridge?
Looking at Clausius who remained silent, Xu Yun breathed a sigh of relief.
The hurdle of being a fanatical fan is over for the time being.
So he crossed Clausius and walked quickly to Lao Tang who was standing near the light source:
"Mr. Thomson, is everything okay?"
Lao Tang gave him a thumbs up, indicating that the situation was good:
"Well, everything is normal, no one came to interfere."
Xu Yun nodded and looked at the auditorium in the distance playfully:
"OK, let's start testing."
Upon hearing this, Lao Tang immediately turned around and shouted in several directions not far away:
"Maxwell! Stanley! Airy! Werner! Everyone is in position! The interferometer experiment is ready to begin!"
brush--
Mai and others, who had been waiting at their respective positions for a long time, quickly stood up and stood at several corners of the interferometer according to the pre-arranged positions.
The interferometer is large in size, and underneath the main body is a closed pool that looks like a sink.
This pool is filled with mercury to ensure the balanced rotation of the interferometer.
After everything is ready.
Xu Yun pressed the start button of the light source.
stop--
In an instant.
The sodium lamp in the light source container is activated.
A bright light shot out quickly and hit the spectroscope directly.
Under the action of the spectroscope, the light is quickly divided into two.
Xu Yun was doing a flat demonstration on the blackboard.
The light source shoots from left to right, and the direction of light travel is to the right and above.
But now that we have changed to a real situation, the directions have become west, east, and north.
The two beams of light quickly return to the beam splitter after passing through the reflector.
Less than a few seconds.
A clear interference pattern was displayed on the observation screen in the south.
at the same time.
Voices announcing the point were quickly heard from several directions:
"Senior Thomson, the M1 reflection is completed and the rotation angle is 0!"
"President, the M2 reflex has been completed, the arm length is 12.3!"
"The interference fringes have appeared, and the optical path is straight and correct!"
After this step is completed.
Xu Yun was not in a hurry to proceed to the next step, but instead invited several stressed men, including Clausius, to the observation screen.
He pointed at the interference fringes on the edge of the observation screen and asked about these pressures:
"Guys...ah, gentlemen, do you have any objections to the experimental procedure?"
Upon hearing this, Clausius turned around, looked at Doppler who had just arrived at the interferometer, and both shook their heads:
"No."
The experimental plan Xu Yun came up with was very mature, and they really couldn't find any loopholes.
In fact, these pressured people had discussed the relevant content before the experiment started, that is, during the break in the auditorium. If they could really find the bug, they would have jumped in the face before the experiment started.
Seeing that no one had any objections, Xu Yun waved to the side.
soon.
Aveline came over with the paper and pen she had prepared.
Xu Yun took the paper and pen, unscrewed the cap of the pen very considerately, and handed it to Clausius and others:
"In this case, can you please calculate the fringe deviation that will occur after the interferometer is rotated 90° based on the existence of ether?"
Clausius and others hesitated for a moment, took pens and paper, and started calculating on the spot.
Mentioned earlier.
According to the theory of ether theory.
When the earth revolves around the sun, there will be an 'ether wind' blowing towards it, with a speed of 30 kilometers per second.
Therefore, the propagation speed of beam 1 along the revolution direction when arriving at M1 and returning from M1 is different.
Assume that the speed of the earth is v, and the distance from the beam splitter to the reflector is d.
Then the past and return velocities are cv and c+v respectively.
Equivalent to headwind and tailwind.
The round trip time between the two is:
d/(cv)+d/(c+v).
Since Beam 2 is perpendicular to the direction of the Earth's rotation, it will encounter the ether wind whether it comes or returns.
Then the time is fixed:
2d/√(c²-v²).
This way.
The optical path difference between beam 2 and beam 1 reaching the observation screen is:
c(d/(cv)+d/(c+v)-2d/√(c²-v²)).
△l is 2dv²/c².
With this data in hand, it’s simple math.
The number of moving stripes is:
2x11x(1x10^-4)²/(5.9x10^-7), that is...
"0.37."
Looking at the value calculated by everyone, Xu Yun emphasized again:
"Everyone, that means if aether exists, then the stripes will move 0.37 stripe units, right?"
After everyone nodded.
Xu Yun pointed at the imaging screen again and said:
"As you can see, the accuracy of our instrument is 0.5%, which means it can measure the movement change of 1/200 stripes."
"0.37 is converted into a percentage, which is 37%. The difference between the two values is huge."
"That is to say, if the stripes move as they should, we will definitely be able to observe this change."
After saying that, Xu Yun suddenly stood up.
He looked at the agitated audience stand in the distance, raised the corners of his mouth slightly, and then said to Lao Tang:
"Mr. Thomson, start changing positions!"
"clear!"
Xu Yun just finished speaking.
Lao Tang turned off the light source, came to the closed water tank, and controlled the interferometer to start turning.
The mercury in the water tank holds the interferometer steadily, and no impact from the collision can be seen.
One minute later.
The interferometer rotated smoothly ninety degrees.
Wheat and others stepped forward to make corrections again:
"No problem, there is no error in the 90-degree angle!"
Xu Yun waved his hand again:
"Turn on the lights!"
Click——
Lao Tang decisively turned on the light source.
at the same time.
Clausius, Doppler and others suddenly turned their heads and looked at the imaging board beside them.
I only see this moment.
Interference fringes on the imaging plate...
Not moved an inch.
See this situation.
Snapped--
Clausius swayed heavily, lost his balance and fell to the ground.
He didn't care at all about the coldness in his disciple's heart, and looked at the photo plate and then the spectroscope with a dull look.
He wanted to try to find out the flaws in this experiment, but how could there be any loopholes in such a simple experiment?
Doppler even rushed to the imaging board, shaking his head crazily:
"Impossible, this is absolutely impossible, Sir Newton is invincible!
! "
"You...you must have made a mistake somewhere, it must be!
! "
Doppler's voice carried far and wide in the dark night, like a lost dog on the street who was hungover after failing to express his love.
Hear this.
Some of the already restless and impatient scholars in the audience could no longer sit still.
I saw them walking down from the auditorium one by one and running quickly towards the interferometer.
These people are not only physicists, but also include a large number of aristocrats - the ether theory is the core link of the classical system, and in a sense, it is also the key support of the aristocratic system.
In just half a minute.
Most of the seats in the auditorium were empty.
Looking from a distance.
It seemed as if someone was lining up to jump down from the top floor of a building in despair.
Accompanied by shouts and shouts, there was also the sound of the building collapsing...
.......
Note:
Here comes the update of 10,000 words. I will continue to code all night tonight. Please vote for me!
!
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