After listening to Zhang Yuan's story, Lin Xuanxuan was silent for a long time, and suddenly said: "The feelings between you boys are often more pure. If I were you, I'd be crying a long time ago......"

A star drifted from the light cluster behind it, drawing a complex curve and transferring to the light cluster in front of it. This is because the ship is traveling at high speed.

"We don't have a very good relationship in the dormitory, you know, there's always little friction between the girls. If there is a girl whose private life is chaotic, then the whole dormitory will be in a miasma. Everyone formed their own small groups, and I don't know how complicated it was. ”

"I haven't heard you talk about it."

Lin Xuanxuan said: "Actually, it's nothing, everything has passed...... Finally, when graduation was approaching, everyone had a casual meal and then dispersed, and all the old and new hatreds disappeared. There will be no chance to get together again. ”

Zhang Yuan said: "There's nothing to be sorry about. In fact, the connection between people is not as close as imagined, and sometimes you are too lazy to go to a party. One or two friends in a lifetime is enough. ”

Lin Xuanxuan pondered for a while, "Hey, yes, I can't even remember their names!" Unfortunately, I can't even remember what my mother looked like. ”

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

The two were silent for a moment.

Lin Xuanxuan asked again: "...... Would you cry if I died suddenly? ”

"Crying for what?" Zhang Yuan smiled and said, "Death is a new beginning. This reincarnation is over, and a new life will start again, nostalgic for the past, and there is not much meaning. ”

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

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

……

In the last few years, Zhang Yuan stayed at the observatory, mainly responsible for teaching elementary and junior high school students how to use astronomical telescopes and how to identify the planets in the universe, including the direction of the sun and the direction of Gliese 581, which were once the home planet, where human beings were born or developed here.

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

It's an easy job, there's not much work, and every day is fulfilling and enjoyable.

A smart and clever little girl asked, "Grandpa Zhang, how should the voyage in the universe be positioned?" The galaxy is in motion, everything is in motion, how should we determine the position of our ship? ”

"Even airplanes on the planet need to be navigated, so how can a spaceship navigate it? For long distances, you have to be accurate enough! ”

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

"First, the use of accelerometers and gyroscopes, which are inertial navigation systems. By measuring the acceleration and angular velocity at each moment, the velocity and displacement of the aircraft can be calculated using the integral. 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, using the relative positions of known celestial bodies to locate them, observe the surrounding stars, and establish a system of simultaneous equations. But as you said, everything is in motion, and the distance measured by the spectrum is constantly changing, and it is difficult to measure it very accurately. ”

"Method three, navigating through a fixed radio source, is also the method we use now. There are a large number of pulsars in the universe, which periodically emit electromagnetic pulses to the outside world. 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 that we can just think of it as stationary."

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

These students, faced with really complex knowledge, are stunned one by one.

The girl asked, "If we go out of the galaxy and sail across the river system, how should we position ourselves?" ”

Zhang Yuan replied: "There is a phenomenon called fast radio bursts. These high-energy millisecond flashes, presumably from a very large source, may have come from outside the Milky Way. Maybe one day in the future, they will become a beacon for human transgalactic travel. These high-energy millisecond flashes, presumably from a very large source, may have come from outside the Milky Way. Perhaps one day in the future, they will become a beacon for human travel across river systems. ”

"Across the river system?!"

The thought of so many natural lighthouses in the universe made all the students yearn for it, and they couldn't help but look out the window one by one.

It's too far to cross the river system.

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

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

His name is Wang Tiantian, and he doesn't know where he heard about it, whether it's astronomy, geography, mathematics, chemistry, or almost anything.

Children worship power, knowledge is power, in their eyes, Zhang Yuan can be regarded as the most knowledgeable person, and he is also the old captain in the past, and his temper is very gentle, and he can basically answer all the contents. You can even play with the computer, so there are always a lot of children gathered at the observatory.

"That's a complicated question!" Zhang Yuan laughed, it was still too difficult to talk about "infinity" with a child of this age.

After pondering for a while, he said, "Do you think there are more dots on a 1 cm line segment, or more dots on a 2 cm line segment?" ”

"Yes, of course...... There are many dots on the 2 cm line segment! 2 centimeters is longer than 1 centimeter, shouldn't there be more dots on the top! The little fat man looked nervous, this is not a very simple question......

If you get it wrong, you'll be embarrassed.

The surrounding classmates also thought so, and a few were a little smarter, tilting their heads and not speaking.

Zhang Yuan smiled: "You have learned functions once, right?" ”

"Of course I did."

"So, the image of y=√3x, can you draw it?"

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

Zhang Yuan intercepted 1 centimeter on the axial x-axis, and the corresponding oblique section was exactly 2 centimeters, and he said with a smile: "According to this functional image, the points on the abscissa correspond to the points on the oblique line, from (0,0) to (1,√3), exactly 2 centimeters." The coordinates of each x-axis can be corresponded to one by one. ”

"You have more dots on the 2-centimeter segment, but where are the extra dots?"

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

The little fat man looked unconvinced and went to look for the missing dots, but he couldn't find them......

In the end, a mass offensive was launched, and crooked reasoning was launched, such as "whether the cycle of 0.9 is equal to 1", but in the end it could only be defeated very unwillingly.

"I can't find it, haha!"

Zhang Yuan gloated and said: "Actually, according to our theory, one-to-one correspondence is a very important means. There are as many dots on a one-centimeter segment as there are as many dots as there are two-centimeter dots; According to one method, there are as many dots as a centimeter on a piece of paper, that is, on a flat surface.

"Even a centimeter of point, a point on such a large curved surface as the Kunlun Mountain spacecraft, and even a point in the entire universe...... Even any point in the high-dimensional space is the same, and it can be corresponded to one by one in some way. ”

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

"Huh?" Not only the little fat man, but also a large number of students behind him exclaimed.

They couldn't have imagined that such a small section could be compared to the entire universe, which is incredible, right?

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

Zhang Yuan smiled: "But infinity also has a size, and the set of natural numbers, mathematically called Alev 0, 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 Aleph 1."

“…… The number of all possible mathematical functions: continuous and discontinuous functions, is called Alev2. ”

"I see, and Alev 3, Alev 4, Alev 5!" The little fat man shouted loudly, as if he had discovered something full of power.

Students at this age are always in secondary 2, gaining a little bit of knowledge, and being able to show off in front of their peers.

Zhang Yuan smiled: "Yes, it can be extended infinitely...... However, it is difficult for you to find the concrete meaning of the higher dimension infinity in reality, and it can only become a string of symbols on paper. Moreover, the mathematical difficulty is, is there an infinity whose number is greater than Alev 0 and smaller than Alev 1? This problem is known as the continuum hypothesis. ”

"Although the continuum hypothesis is a hypothesis, it can never be proved or denied, and it has been sitting there for nearly four thousand years, and it has not been solved until now."

"Why?" Wang Tiantian asked again, this world is too strange, isn't it?

A problem that has not been solved for 4,000 years. He was a little nervous inside

Zhang Yuan laughed again: "That's ...... again Another story, known as Gödel's incompleteness theorem! The history of mathematics is another magnificent process, and there are many impossible problems in the world! ”

……

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

Even the journey to the observatory would be very tiring, but he still insisted on working and answering the children's questions, which can be said to be the greatest joy after his friends withered one by one.

On this day, the doctor who specially examined his body showed a very regretful look, and she said very carefully: "Old captain, your physical condition has reached the standard of entering the virtual world. ”

"I'll make a report for you, and your wife is up to par. At the end of this month, if you will......"

"Is that so...... Really lived long enough. Zhang Yuan nodded and sighed: "There's 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 lit up briefly in the starry sky, and then disappeared silently.

At present, 90% of the population is in hibernation, and there is no need to wake up. The remaining 10% of the sober population all spontaneously carried out this farewell ceremony.

Many production activities in the Kunlun Mountains have also stopped, and there is a day off in school, and Zhang Yuan deserves such an honor.

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

Countless juniors who saw him off were looking at him, expecting him to say something, or encouragement, or something else. There are also some old people, who are constantly wiping tears, and this time, he is not the last person to go.

"No, everybody's fine, let's move on." Zhang Yuan said with a smile: "The future still depends on you." ”

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

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

A former friend, a colleague, is saying goodbye to him.

It doesn't seem to be a few anymore.

This feeling is very subtle, Zhang Yuan is not a person who is afraid of death, but at this moment, there is still a feeling of being out of breath.

He suddenly remembered—

At a very young age, the moment he understood what death was all about, he crouched in the corner and cried.

"Can I not die?" Zhang Yuan asked with teary eyes.

"What does it mean to be immortal?" His father, Zhang Qiming, replied.

"That's it...... I've been alive all the time. ”

"Oh, you mean...... You want eternal life. Faced with this question, Zhang Qiming pondered for a long time, and said with a serious face: "I think it's better to die." There is no way to live forever. ”

The young Zhang Yuan couldn't accept this answer for a while, although many of his father's answers were very inexplicable.

Zhang Qiming said: "I think you are likely to imagine the time period of eternal life too short. Eternal life means infinity, a hundred years, ten thousand years, ten million years, or even ten billion billion years, and there is no difference between infinity and zero. ”

"In the eyes of the truly eternal, the universe may die in a second, that is, all the pleasures you feel on Earth will only exist for a very short time. What followed was a long time of solitude in the vast empty universe. There is no substance, and there is no companionship. ”

"Until waiting for the quantum sea, that little bit of the Big Bang of the universe, to restart a new era. But how much time will it take? ”

"This kind of loneliness may not be endured by human beings, or the thinking form may become another species, or the thinking form may stop thinking...... I think it's better to stop thinking and choose death. Zhang Qiming looked at the blue sky, touched Zhang Yuan's head, and said seriously.

Even if the young Zhang Yuan didn't understand what his father was talking about......

I don't know why, Zhang Yuan remembered this conversation before leaving this world.

Perhaps, a dead hero is a good hero.

It's just that...... How lonely it is......

Among the flowers, Zhang Yuan faintly heard bursts of crying. I don't know who is crying.

Confused, he quickly lost consciousness.

……

One era is over, and another begins right after.

Humanity will not stop itself because of this, and this great journey is still continuing......

、