After listening to Zhang Yuan’s story, Lin Xuanxuan was silent for a while, and suddenly said, “The feelings between you boys are often more pure. If I were you, I would have cried a lot long ago…”

A star drifted from the light ball behind, drawing a complex curve, and moving to the light ball ahead. This is because the spacecraft is sailing at high speed.

"The relationship in our dormitory is not very harmonious. You know, there are always small frictions between girls. If a girl has a chaotic private life, the entire dormitory will be chaotic. Everyone forms their own small groups, and I don't know how complicated it is."

"I haven't heard of this."

Lin Xuanxuan said: "Actually nothing, everything is over... Finally, as graduation approaches, everyone had a breakup meal and then it dispersed, and all the new and old hatreds disappeared. There is no chance to get together again."

Zhang Yuan said: "It's no pity. In fact, the connection between people is not as close as you imagined. Sometimes you are too lazy to go to parties. In your life, having one or two friends is enough."

Lin Xuanxuan pondered for a while, "Hey, yes, I can't remember their names anymore! What's more regrettable is that I can't even remember my mother's appearance."

"I can't remember what my father looks like... I can only recall it by looking at the photos." Zhang Yuan sighed.

The two of them were silent for a while.

Lin Xuanxuan asked again: "...If I suddenly die, will you cry?"

"Why are you crying?" Zhang Yuan said with a smile: "Death is the new beginning. This cycle of reincarnation is over, and a new life will begin again. Missing the past has no meaning."

"I can only wish you happiness and happiness in the new world and a good life for your next life!"

Lin Xuanxuan was surprised at first, then smiled: "I wish you a bright future in the future world!"

...

In the last few years, Zhang Yuan stayed at the observatory and was mainly responsible for teaching elementary and junior high school students how to use astronomical telescopes, how to distinguish planets in the universe, including the direction of the sun, and the direction of Glitzer 581. These are the former parent planets, where human beings were born, or where they developed here.

"If one day you become captains, if you can't find the way home, it will be miserable!"

This job is easy, not much workload, and I am very fulfilling and happy every day.

A clever little girl asked: "Grandpa Zhang, how should we locate the navigation in the universe? The Milky Way is moving, everything is moving, how should we determine the position of our spaceship?"

"Even planes need navigation on planets, how do spacecraft navigate? Long-distance navigation must be accurate enough!"

Faced with this problem, Zhang Yuan pondered for a while and took another sip of water: "It's very simple, there are 3 good ways in total."

"First, use an accelerometer and a gyroscope, that is, an inertial navigation system. By measuring the acceleration and angular velocity at each moment, the speed and displacement of the aircraft can be calculated using integrals. However, the disadvantages of inertial navigation are also obvious: the longer the time, the greater the error, so it is only suitable for shorter ranges and auxiliary positioning."

"The second method is to use the relative positions of known celestial bodies to locate and observe the surrounding stars and systems of simultaneous equations. But as you said, everything is moving, and the distance measured by the spectrum changes at all times, and it is difficult to measure very accurately."

"Method 3: Navigation through a fixed radio signal source is also the method we use now. There are naturally a large number of pulsars in the universe, which periodically emit electromagnetic pulses. As long as multiple pulsars are observed to form a pulsar timing array, it is a natural deep space network, which is the so-called 'galactic positioning system'."

"If you think that pulsars inside the Milky Way are moving, causing a certain degree of error, you can even observe pulsars outside the Milky Way, 100 million light-years away!"

"A planet so far away, we can directly think it is still."

Zhang Yuan played several images of pulsars on the screen, which were equivalent to artificial satellites that were constantly sending signals to the outside world.

These students were stunned when faced with real complex knowledge.

The girl asked again: "If we walk out of the Milky Way and sail across the river, how should we locate it?"

Zhang Yuan replied: "There is a phenomenon called fast radio burst. These high-energy millisecond flashes are speculated that their signal sources are very huge, and they may come from outside the Milky Way. Maybe one day in the future, they will become a beacon for humans to travel across galaxies. These high-energy millisecond flashes are speculated that their signal sources are very huge, and they may come from outside the Milky Way. Maybe one day in the future, they will become a beacon for humans to travel across the rivers."

“Spanning the river?!”

When all the students thought of the universe, they were eager for so many natural lighthouses, and they couldn't help looking out the window.

Crossing the river is too far away!

"Grandpa Zhang, there is another question, why are there as many integers as even numbers?"

After a while, a fat man who had just entered junior high school asked again.

His name is Wang Tiantian. I don’t know where I heard about this knowledge, whether it is astronomy, geography, mathematics and chemistry, I ask almost everything.

Children all worship power, and knowledge is power. In their eyes, Zhang Yuan can be regarded as the person with the most extensive knowledge. He is also an old captain in the past, with a gentle temper and can basically answer all the content. He can even play computers here, so there are always many children gathering at the observatory.

"This question is too complicated!" Zhang Yuan laughed. It was too difficult to talk to a child of this age about the issue of "infinity".

After thinking for a while, he said, "Do you think there are too many points on the 1 cm line segment or more points on the 2 cm line segment?"

"Of course...there are more dots on the 2 cm line segment! 2 cm is longer than 1 cm. Shouldn't there be more dots on it!" The little fat man looked nervous. This is not a very simple question...

If you answer wrong, you will be embarrassed.

The students around me also agreed with each other, and there were a few smart ones who were tilted their heads and didn't speak.

Zhang Yuan smiled and said, "Have you learned the function once?"

"Of course I've learned it."

"Then, can the image of y=√3x be drawn?"

This image is very simple, it is a straight line with an angle of 60 degrees to the x-axis.

Zhang Yuan intercepted 1 cm from the x-axis of the horizontal coordinate, and the corresponding oblique section was exactly 2 cm. He smiled and said: "According to this function image, do not the points on the horizontal coordinate correspond to the points on the diagonal line, one by one? From (0,0) to (1, √3), it is exactly 2 cm. The coordinates of each x-axis can correspond to one by one."

"What you call more points on the 2 cm line segment, where are the extra points?"

"If we can't find it, we can only think that there are more points on the 1 cm line segment, as many points on the 2 cm line segment, right?"

The little fat man looked for the disappeared points with dissatisfaction, but he could not find them...

Finally, he launched a mass offensive and created a fallacy, such as "whether the cycle of 0.9 is equal to 1", but in the end he could only lose with great reluctance.

"Can't find it, haha!"

Zhang Yuan said gloatingly: "In fact, according to our theory, one-to-one correspondence is a very important means. The points on a one-centimeter line segment are as many as 2 cm points; according to one method, the points on a piece of paper, that is, the points on a plane are as many.

"Even a centimeter of points is the same as points on the curved surface of the Kunlun Mountain spacecraft, and even points in the entire universe... and even any arbitrary points in high-dimensional space, and they can be used to correspond one by one with certain methods."

"That is, there are as many points on a one-centimeter line segment as the points in the entire universe!"

"Ah?" Not only this little fat man, but a lot of students behind him also exclaimed. Computer::/

They never thought that such a small section could be compared with the entire universe, which was incredible, right?

Let these children show a shocking expression and sigh at the mystery of the universe, which has become a great pleasure for Zhang Yuan.

Zhang Yuan smiled and said, "But infinity can also be divided into sizes. The set of natural numbers is mathematically called Alev 0, which is the smallest infinity."

"The smallest infinity?"

"The number of points on a line segment, that is, the infinite set formed by real numbers, is called Alev1."

"…all possible mathematical functions: the number of continuous and discontinuous functions, called Alev 2."

"I understand, there are also Alev 3, Alev 4, Alev 5!" The fat man shouted loudly, and seemed to have discovered something full of power.

Students of this age are always so second-year-old, gaining a little knowledge, and being able to show off in front of their peers.

Zhang Yuan smiled and said, "Yes, it can extend infinitely upwards... However, it is difficult for you to find the specific meaning of higher dimensions. In reality, it can only become a string of symbols on paper. Moreover, the difficulty in mathematics is whether there is an infinity with a number that is larger than Alev 0 and smaller than Alev 1? This question is called the continuum hypothesis."

"Although the continuum hypothesis is a hypothesis, it can never be proved or denied. It is just left alone and has been there for nearly four thousand years and has not been resolved yet."

"Why?" Wang Tiantian asked again, this world is too strange.

A problem has not been solved for four thousand years. He is a little ready to move inside.

Zhang Yuan laughed again: "That's another story... another story, called Godel's incomplete theorem! The history of mathematics is another magnificent process, and there are many problems that cannot be solved in the world!"

...

Time passes day by day, and as aging continues, the body becomes worse day by day.

Even when he goes to the observatory, he feels very tired, but he still insists on working and answering questions for the children. This can be said to be the biggest joy of his friends after they withered one by one.

On this day, the doctor who specially checked his body showed a very regretful expression. She said very carefully: "Old Captain, your physical condition has reached the standard of entering the virtual world."

"I will give you a report and your wife has reached the standard. Just at the end of this month, if you want..."

"So... I really lived long enough." Zhang Yuan nodded and sighed: "There is nothing I don't want to do, let me say goodbye to this era."

On August 29, 5812, the first captain of the Kunlun Mountain Fleet, Zhang Yuan, was about to leave this world.

The salute briefly lit up in this starry sky and disappeared silently.

Currently, 90% of the population is in hibernation and there is no need to wake up specially. The remaining 10% of the sober population are all spontaneously conducting this farewell ceremony. Mobile::

Many production activities in Kunlun Mountains have also stopped, and the school has a day off, and Zhang Yuan can also deserve such honors.

"Do you have anything else to say?" said the doctor.

Countless juniors who saw him off were looking at him, looking forward to what he said, or encouragement, or something else. There were also some old people who were constantly wiping their tears. This time, he was not the last person to leave.

"No more, everyone is fine, keep moving forward." Zhang Yuan said with a smile: "It depends on you in the future."

Several staff members helped him up from his wheelchair and lay down.

The hibernation chamber is like a soft Simmons, which is very comfortable to lie down. Zhang Yuan turned his head and looked around.

A group of former friends and colleagues are saying goodbye to him.

There seem to be few more.

This feeling is very subtle. Zhang Yuan is not a person who is afraid of death, but at this moment, he still feels breathless.

He suddenly remembered

When he was very young and understood what death was like, he squatted in the corner of the wall and cried loudly.
To be continued...