Deep Space Fleet

After listening to Zhang Yuan's narration, Lin Xuanxuan was silent for a while, and suddenly said: "The relationship between you boys is often more pure. If I were you, I would have cried a long time ago..."

A star drifted over from the light cluster in the rear, drew a complicated curve, and transferred to the light cluster in front. This is because the spaceship is traveling at high speed.

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

"I haven't heard you say that before."

Lin Xuanxuan said: "Actually, it's nothing. Everything is over... Finally, when graduation was approaching, everyone had a breakup meal and then dispersed. All old and new hatreds disappeared. There is no chance to get together again."

Zhang Yuandao: "It's nothing to regret. In fact, the connection between people is not as close as imagined. Sometimes you are asked to go to parties, and you don't bother to go. In a lifetime, one or two friends are enough."

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

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

The two were silent for a while.

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

"Why are you crying?" Zhang Yuan smiled and said, "Death is a new beginning. This cycle is over, and a new life will start again. It doesn't make much sense to miss the past."

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

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 has been working at the observatory, mainly responsible for teaching elementary school and junior high school students how to use astronomical telescopes, how to identify planets in the universe, including the direction of the sun and Gliese 581. It was the former mother star, where human beings were born or developed here.

"If one day you become captains, it will be a disaster if you can't find your way home!"

This job is easy, there is not much workload, and every day is full and happy.

A clever little girl asked: "Grandpa Zhang, how should we position our spaceship? The Milky Way is in motion, and everything is in motion. How should we determine the position of our spaceship?"

"Even the planes on the planet need to navigate, how can the spacecraft navigate? Long-distance navigation must be accurate enough!"

Facing 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 accelerometers and gyroscopes, that is, inertial navigation systems. 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, it is only suitable for shorter voyages and auxiliary positioning.”

"The second method is to use the relative positions of known celestial bodies to locate, observe the surrounding stars, and combine equations. But as you said, everything is moving, and the distance measured by the spectrum changes all the time. It's hard to measure very precisely."

"Method three, navigation through a fixed radio signal source, is also the method we are using now. There are a large number of pulsars naturally in the universe, which periodically emit electromagnetic pulses. As long as multiple pulsars are observed to form a pulsar timing array, It's a natural Deep Space Network, the so-called 'Galactic Positioning System'."

"If you feel that the 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!"

"Such a distant planet, we can directly consider it to be stationary."

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

These students, facing the real complex knowledge, are all stunned.

The girl asked again: "If we go out of the Milky Way 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, it is speculated that their signal sources are very huge, and they may come from outside the Milky Way. Maybe someday in the future, they will become human beings. Lighthouses for galaxy travel. These high-energy millisecond flashes are speculated to have a very large signal source and may come from outside the Milky Way. Maybe someday in the future, they will become human lighthouses for traveling across the galaxy."

"Crossing the river system?!"

Thinking that there are so many natural lighthouses in the universe, all the students were fascinated, and they couldn't help but look out the window.

It's too far to cross the river system!

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

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

His name is Wang Tiantian, and he didn't know where he heard about this aspect of knowledge. Whether it was astronomy, geography, mathematics or chemistry, he asked almost anything.

Children worship power, and knowledge is power. In their eyes, Zhang Yuan can be regarded as the person with the most extensive knowledge, and he is also a former veteran captain with a very gentle temper. He can basically answer all the questions. . You can even play computer games here, so there are always many children gathering at the observatory.

"This question is too complicated!" Zhang Yuan laughed loudly. It is still too difficult to talk about "infinity" with children of this age.

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

"Of course... there are too many points on the 2cm line segment! 2cm is longer than 1cm, shouldn't there be more points on it!" The little fat man looked nervous. This is not a very simple problem...

Get it wrong and you'll lose face.

The surrounding students also agreed, and there were a few more clever ones who tilted their heads and did not speak.

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

"Of course I have."

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

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

Zhang Yuan intercepted 1 cm on the x-axis of the abscissa, and the corresponding oblique section was exactly 2 cm. He said with a smile: "According to this function image, the point on the abscissa and the point on the oblique line are not the same. Is there a one-to-one correspondence, from (0, 0) to (1, √3), exactly 2 centimeters. Every x-axis coordinate can be one-to-one correspondence."

"You said that there are 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 as many points on the 1 cm line segment as there are on the 2 cm line segment, right?."

The little fat man searched for those missing points with an expression of disbelief, but it was impossible for him to find them...

In the end, a mass offensive was launched, making fallacies, such as "whether the cycle of 0.9 is equal to 1" came out, but in the end they 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 method. There are as many points on a one-centimeter line segment as there are points on a two-centimeter line segment; according to one method, one There are as many centimeter points as there are points on a piece of paper, that is, on a plane.

"Even a point of one centimeter, there are as many points on a curved surface as large as the Kunlun Mountain spacecraft, or even points in the entire universe...even any point in a high-dimensional space, and they can be corresponded one by one by certain methods .”

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

"Ah?" Not only this little fat man, but also a large group of students behind him also exclaimed.

They never imagined that such a small section can be compared with the entire universe, isn't this incredible?

It has become a great joy for Zhang Yuan to let these children show surprised expressions and marvel at the mystery of the universe.

Zhang Yuan smiled and said: "But infinity also has a size. The set of natural numbers is called Aleph 0 in mathematics, and it is the smallest infinity."

"The smallest infinity?"

"The number of points on a line segment, that is, the infinite set of real numbers, is called Aleph 1."

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

"I see, there's Aleph 3, Aleph 4, and Aleph 5!" the little fat man yelled loudly, as if he had discovered something full of power.

Students of this age are always in the second grade, and after gaining a little knowledge, they can show off in front of their peers.

Zhang Yuan smiled and said: "Yes, it can be extended upwards infinitely... However, it is difficult for you to find the specific meaning of infinity in higher dimensions, and it can only become a string of symbols on paper. Moreover, mathematics The hard part is, is there an infinity with a number larger than Aleph 0 and smaller than Aleph 1? This problem is called the continuum hypothesis."

"Although the continuum hypothesis is a hypothesis, it can never be proven, nor can it be denied. It has been put there alone for nearly four thousand years, and it has not been resolved until now."

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

A problem that has not been solved for four thousand years. He's getting a little restless inside

Zhang Yuan laughed again: "That's...another story, it's called Gödel's incompleteness theorem! The history of mathematics is another magnificent journey. There are so many problems that cannot be solved in the world. Woolen cloth!"

...

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

Even the journey to the observatory will feel very exhausting, but he still insists on working and answering the children's doubts. This can be said to be the greatest joy after friends die one by one.

On this day, the doctor who examined his body showed a very regretful expression, and she said very cautiously: "Old Captain, your physical condition has reached the standard for entering the virtual world."

"I'll make a report for you, and your wife has already met the standard. At the end of this month, if you want..."

"Is that so... I really lived long enough." Zhang Yuan nodded and sighed, "There's nothing you don't want, let me bid farewell 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 lighted 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 specially. The remaining 10% of the sober population all spontaneously carried out this farewell ceremony.

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

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

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 their tears. This time, he is not the last one to leave.

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

Several staff helped him out of the wheelchair and lay him down.

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

One after another, former friends and colleagues are saying goodbye to him.

It seems that there are not many.

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——

When he was very young, the moment he understood what death was all about, he squatted by the corner and cried loudly.

"Can I not die?" Zhang Yuan asked tearfully.

"What do you mean by not dying?" His father Zhang Qiming replied.

"It's just...alive."

"Oh, you mean...you want to live forever." Faced with this question, Zhang Qiming pondered for a long time, and said with a serious face: "I think it's better to die. People can't live forever."

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

Zhang Qiming said: "I think you may imagine the time period of eternal life too short. Immortality means infinity, one hundred years, ten thousand years, one hundred million years, or even ten billion billion years, compared with infinity , is indistinguishable from zero."

"In the eyes of the truly immortal, the universe may be heat-dead in a second, that is, all the happiness you experience on earth only exists for a very short time. After that, it will be a long time, in the boundless A time that exists alone in an empty universe. Without any substance and without any companionship."

"Until waiting for that tiny little big bang in the sea of ​​quantum, restarting a new era. But how much time will it take?"

"Human beings may not be able to bear this kind of loneliness, or their thinking form has changed into another species, or they have stopped thinking... I think it is better to stop thinking and choose to die." Zhang Qiming looked at the blue sky, touched Zhang Yuan's head, said solemnly.

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

For some reason, Zhang Yuan remembered this conversation before leaving this world.

Maybe, dead heroes are good heroes.

It's just... so lonely...

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

Confused, he soon lost consciousness.

...

One era ended, and another began immediately after.

Human beings will not stop their footsteps because of this, this great journey is still going on...

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