Chapter 333: Single-handedly, as good as the gods!
""
After writing the word ‘solution’.
Xu Yun put down his pen and stood aside with his hands folded.
Well behavedjpg.
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.
Every time Gauss took a step, his spirit was lifted up.
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 vitality that 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 energy 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 formulas
d2u/dθ2 =g/h2 (3g/2)u2
△Φ=6π2/2
d2x^a/d2=-￡ai(dx^i/d)(dx^/d).
Students with good memories must have noticed it.
These three formulas are exactly the second-order asymptotic solution of general relativity, the precession angle equation and the theoretical geodesic equations of 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 only remains 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-order 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 orbit of trans-Neptunian objects.
Then the next second.
Gauss then wrote another formula
d2u/dθ2 u2=-2aθ(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 did not know how far Gauss had been derived 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.
It's a bad thing to say.
If the study of Gauss only stops at the asymptotic solution given by Xu Yun
So tonight's star-hunting mission can be washed away and replaced by the analysis machine seller's show.
Another reason why Xu Yun is not sure is that Planet X is too far away, and even if he calculates the formula, he may 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, apologized to Prince Albert, and walked quickly towards the venue.
This person is called
Augustine Louis Cauchy.
Then there is the second person, from the UK.
called arthur kelly
then the third
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 excited he can't help himself at this time.
Among these people, Xu Yun also met an important guest who should have passed away through Aveline's mouth.
Simone Denis Poisson.
That's right, he was the unlucky guy who was slapped in the face by Fresnel in the original timeline and had to leave his name in history.
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 the pen again and continued writing.
"Let u=u0 xu1 x2u2..."
This chapter is not over yet, please click on the next page to continue reading the exciting content! "d2u0/dθ2 u0="
"Then d2u1dθ2 u1=2ain(θ h)"
"When u=5, ignore 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
His eyes were widened, and the word "fuck" came to his lips subconsciously, 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 really too amazing!
After regaining consciousness.
He rubbed his eyes in a funny way 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, who was trembling slightly.
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 Spanish astronomer Ortiz’s team in 2017 through occultation observations with the assistance of the Barcelona Supercomputing Center (b)!
The d//nature of that article was published in the magazine "Nature", and it is also the most accurate general formula as of September 14, 2022! (I used this paper plus the jp precision ephemeris of dgv
This version of de421 is calculated. The basic idea is to use Kepler's square root number to analytically extrapolate, taking into account the change of the root number over time, and approximating it to the t2 term, which is as reasonable as possible.)
It is also worth mentioning that.
The supercomputer of b is called din, which is the name in Nordic 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 who was slowly writing on the paper, Xu Yun's mind came back to Gauss's original words.
"I don't create 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, you guys 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 question marks appeared on their faces.
"?"
Oh my god?!
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 the long-standing bottleneck of some people, 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 Bedell 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 were all written by Gauss and Faraday after the Pluto night ended, instructing observatories in various countries to take starry sky observation records.
In return or as a price.
Gauss and others 'paid' the structural drawings of the Schmidt telescope to major observatories.
Xu Yun had no opinion on 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.
At Lao Su's time, the most common telescopes had not yet appeared, so being able to observe the starry sky was of great significance.
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 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. Coupled with the full-scale observation of our Greenwich Observatory, the image records in the box total more than 25,000."
"Good guy, are there so many?"
Xu Yun was slightly startled when he heard this, and after coming back to his senses, he quickly thanked George Bedell Ally.
"Thank you very much, Mr. Airy."
This chapter is not over yet, please click on the next page to continue reading! These days, unlike in 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 £0.1.
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.
As a result, I didn’t expect that these observatories were so powerful and took so many observation records in one year.
These observation records are coupled with the analytical engine, Gauss's formula and the latest tool team.
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 to perform least squares calculations.
The magnitude used by Gauss on Pluto's night is the 8th power, which is
=(0 1*t 2*t^2 3*t^3 4*t^48*t^8)/10^8.
But this time with the help of the Analytical Engine, Gauss went directly to
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 01-04.
For example, 0412 raised to the 17th power is 0000000.
013 raised to the 17th power is 00000000000000000.
Although these numbers are large, they are within the order of magnitude of the Analytical Engine.
If you change it to other larger or smaller numbers, then the 17th power operation will exceed the computing power.
Later calculations of planetary orbits generally use 50-70 powers. More professional teams, such as Pluto killer Mike Brown, basically use the order of 120.
See here.
Some students may find it 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 10 raised to the nth power.
For example =x10^13, when a calculator or computer expresses the power of 10, e or e is generally used.
That is e13 cloud
The power multipliers used in modern supercomputing calculations are basically accurate to 10 decimal places or more.
For example, 0 raised to the 50th power, etc.
If this kind of calculation is not suitable for supercomputing, it will be difficult for ordinary computers or calculators to achieve accurate results, which are basically approximate numbers.
Useless knowledge has been added to jpg.
The calculation executors 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 empty space where Michelson-Morley experiment was conducted.
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 with the quietness over the analytical machine, the area near the interferometer is much more lively.
However, this excitement is not festive, but brings
Extremely intense hostility.
"Hey, Dongfang boy!"
As soon as Xu Yun showed up, a young man ran up to him aggressively and looked at him with unkind eyes.
"Damn Dongfang boy, I heard that you have been preaching that ether does not exist recently?"
Looking at this young man who seemed to be ready to say 'God, I will kick your ass' 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 he screamed
"God, I'm going to kick your ass!
"
Xu Yun
"?"
Are you really coming?
However, before the young man made any 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.
Is this also a stressed man or a stressed man?
Then Xu Yun thought about it and asked him
"Sir, don't 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 to be 3/4 of the boss.
The concept of 'entropy' that often appeared 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 .
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 classical disciplines, he ultimately chose to go it alone.
no doubt.
This is a standard dogmatist - at most more capable than other keyboard warriors.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! However, considering that the gas motion model that Clausius later studied introduced a variety of concepts and deduced the development of modern science non-subjectively, Xu Yun still
Decided to have 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 a 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 having sex."
"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 this mean that the ether exists. Am I 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 believed unconditionally in the existence of ether, and the Mavericks could 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 that includes 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
Did Xu Yun really inherit some of Feiyu's knowledge, and could 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 a certain 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 stay in Cambridge?
Looking at Clausius who remained silent, Xu Yun breathed a sigh of relief.
The stage 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 tamper with it."
Xu Yun nodded and looked at the auditorium in the distance playfully.
",Then 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--
Wheat and others who had been waiting at their respective positions quickly stood up and stood at several corners of the interferometer according to the pre-arranged positions.
The interferometer is very large, 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 emits 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.
In just a few seconds.
A clear interference pattern was displayed on the observation screen in the south.
at the same time.
The sound of calling the time soon sounded from several directions.
"Senior Thomson, the reflection of 1 is completed and the rotation angle is 0!"
"President, 2 reflexes completed, arm length 123!"
"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 invited several pressure 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.
"Hey, 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 when 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 1 and returning from 1 is different.
This chapter is not over, please click on the next page to continue reading! 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 -v and v respectively.
Equivalent to headwind and tailwind.
The round trip time between the two is
d/(-v) d/(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/√(2-v2).
This way.
The optical path difference between beam 2 and beam 1 reaching the observation screen is
(d/(-v) d/( v)-2d/√(2-v2)).
△ is 2dv2/2.
With this data, the next step is simple mathematical calculations.
The number of moving stripes is
2x11x(1x10^-4)2/(59x10^-7), that is
"037."
Looking at the value calculated by everyone, Xu Yun emphasized again
"Everyone, that means if aether exists, then the stripes will move 037 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 05%, which means that the movement change of 1/200 stripes can be measured."
"037 is converted into a percentage, which is 37%. There is a huge difference between the two values."
"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 restless audience in the distance, raised the corner of his mouth slightly, and then said to Lao Tang
"Mr. Thomson, start changing seats!"
"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 turning the angle 90 degrees!"
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 with dull eyes, and then at the spectroscope.
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 guys must have made a mistake somewhere, it must be true!
"
The sound of Doppler 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 scholars in the audience who were already restless and impatient could not sit still at all.
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 was as if people were 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 is an update of 10,000 words. I will continue coding all night tonight. Please vote for me!