The Science Fiction World of Xueba

"How about it, Mr. Pang, are you sure you can solve this problem?"

Shu Lao on the side looked at Pang Xuelin with a half-smile.

Pang Xuelin smiled lightly and said, "I can try."

Of course, Pang Xuelin and Murphy were unwilling to be controlled by this seemingly benevolent, but actually very scheming old monster.

After all, no matter whether he is looking for high-dimensional human civilization or for the sake of the safety of the Eternal Night, he must get out of Shu Lao's control.

But in a short time, he couldn't think of a good way to get out of the predicament, so he could only stay here temporarily, and make a fool of himself with Shu Lao.

As for helping Shu Lao solve some math and physics problems, Pang Xuelin didn't resist much.

Living in this tree hole for a long time, studying mathematics problems is undoubtedly the best way to pass the time.

Shu Lao smiled and said: "Okay, Mr. Pang, then I won't disturb your research. But while working hard on research, I hope you and Ms. Murphy can work harder to create humans, after all, this is your main job .”

Pang Xuelin said lightly: "Don't worry, Old Shu, of course I understand this."

"That's good."

The old tree disappeared instantly.

...

In the following time, Pang Xuelin devoted all his attention to the research of Hodge's conjecture.

Since the birth of Galois' group theory, modern mathematics has become more and more inclined to extract an abstract understanding of the nature of things.

For more than a hundred years, mathematicians have continued to build deeper abstractions on the basis of abstraction, and each level of abstraction is farther away from our daily empirical world.

Taking group theory as an example, our general "addition, subtraction, multiplication, and division" are abstracted into four algorithms.

The Hodge conjecture is a difficult problem born under the extremely abstract system of modern mathematics.

As a highly specialized problem, the object it deals with is far from people's intuition, so that not only is it difficult to judge whether the conjecture itself is right or wrong, but even the formulation of the problem itself seeks to establish a real consensus.

Therefore, for the definition of the Hodge conjecture,

We have to start talking about the birth of geometry.

In ancient Greece, Pythagoras proved by deduction that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the two sides, that is, the Pythagorean theorem.

Since then, humans have associated shapes with mathematics.

Two hundred years later, Euclid listed some recognized facts as definitions and axioms, and used these definitions and axioms to study the properties of various graphics with the method of formal logic, thus establishing a set of axioms and definitions, Argumentative propositions get theorems of geometric argumentation methods, forming a strict logical system - geometry.

After thousands of years of changes, people's research on shapes has become more and more complicated, and at this time, Hodge's conjecture came into being.

Before the 1770s, both geometry and algebra had developed considerably, but they were two separate disciplines.

Descartes compared the geometric methods and algebraic methods at that time. He advocated reducing the problems of geometry to problems in algebraic form, and using algebraic methods for calculation and proof, so as to achieve the ultimate goal of solving geometric problems.

In this way he created what we now call "analytic geometry".

Descartes' mathematical thought proves that if you abstract one step further, geometry is actually the same as algebra, geometry can be transformed into algebraic equations, and algebraic equations can also be transformed into geometric figures.

If you want to see where a certain line intersects a certain circle, you can draw shapes geometrically, or just compare equations algebraically.

Both methods will give the same answer.

In the 19th century, mathematicians tried to generalize Descartes' method.

They started with some algebraic equations and defined the solutions of these equations as "geometric" objects.

Objects generated from algebraic equations in this way are called "algebraic varieties".

Thus, algebraic varieties are a generalization of geometric images.

Any geometric correspondence is an algebraic variety, but there are many algebraic varieties that cannot be visualized.

However, just because a particular algebraic variety cannot be visualized doesn't mean you can't do (algebraic) geometry with it.

You can do it, but it's geometry without shapes.

Afterwards, mathematicians soon discovered that more complex equations, or even systems of equations working together, could produce astonishing shapes in a variety of dimensions.

Mathematicians have discovered a very practical way to get more complex shapes, the basic idea is to what extent we can take the shape of a given object by gluing together simple geometric building blocks of increasing dimensionality form.

This technique works so well that it can be promoted in many different ways.

Through this method, mathematicians hope to expand step by step in various types of ways, and finally establish a set of powerful algebraic equations or/and geometric tools to classify various complex objects into some specific simple geometric objects and combinations thereof.

This has allowed mathematicians to make huge strides in classifying the wide variety of objects they encounter in their research.

Unfortunately, in this generalization the geometric starting point becomes blurred.

Which simple geometric objects should be combined?

What is the combined procedure/sequence?

Therefore, some "non-geometric" basic modules without any geometric interpretation must be added.

Based on this dilemma, in 1958, Professor Hodge, a British mathematician and chairman of the 13th International Mathematical Congress, proposed: For the space of projective algebraic varieties, any Hodge class can express Rational linear (of geometric components) combinations for the class of algebraically closed chains.

This sentence is expressed in a popular mathematical language, that is:

Let x be a projective algebraic manifold and p be a positive integer. Let H^2p(X, Q)afg??(X, Q) be the subspace of algebraically closed chain, that is, the Q vector space generated by the basic class of algebraic subcluster with codimension p in X. The Hodge conjecture asserts that the subspace H^2p(X, Q)afg can be "calculated" using Hodge's theory, specifically, H^2p(X, Q)afg=H^p, p∩H^2p( X, Q).

Here, the so-called "non-singular projective algebraic variety" refers to the "surface" of a smooth multi-dimensional object generated by the solution of an algebraic equation.

...

In the real world, Perelman once chatted with Pang Xuelin. He found the inspiration to prove Hodge's conjecture in the study of Ponzi geometry.

After that, Perelman entered a state of retreat, and Pang Xuelin didn't know where his research progress was.

However, intuitively speaking, Pang Xuelin feels that there is an inseparable close relationship between Ponzi's geometric theory and Hodge's conjecture.

Therefore, during the past six months, Pang Xuelin did not focus on the Hodge conjecture itself, but has been looking for some internal connections between Ponzi geometry and algebraic geometry, analysis and topology.

This kind of work is very boring and requires some thinking about the nature of mathematics.

Although half a year is far from being able to solve Hodge's conjecture.

But the study of analysis and topology gave Pang Xuelin a deeper understanding of Ponzi's geometric theory.

As for Shulao, at first, Shulao didn't care much about Pang Xuelin's research.

After all, in his opinion, no matter how powerful a small human being is, it is impossible to easily solve problems of this level.

But as time passed, after reading Pang Xuelin's research notes one by one, Shu Lao was shocked, but at the same time began to have a little expectation for Pang Xuelin's research.

This morning, when Pang Xuelin opened his eyes, he saw Murphy sleeping comfortably on his chest with a slight smile on his lips.

In the past six months, the two have been together day and night, and they have long been intimate with each other.

Especially with the old tree watching from the sidelines, except when Murphy's relatives visited once a month, the two would applaud and make people almost every night.

It's just that for some reason, half a year later, Murphy's stomach still hasn't moved.

Pang Xuelin and Murphy were not in a hurry, but Shu Lao was a little anxious.

Thinking of this, a faint smile appeared on Pang Xuelin's face.

He stroked Murphy's smooth back with his hand, lowered his head, and pecked lightly on her red lips.

In the past six months, with Murphy by his side, Pang Xuelin's research life is not so boring.

Apart from spending eight hours a day thinking about Hodge's conjecture, Pang Xuelin spends the rest of the time with Murphy.

Play computer games brought from the earth in the shuttle, watch early film and television dramas, and occasionally cook together with the two of them, making earth age delicacies.

Life is very peaceful and warm.

Perhaps Pang Xuelin's actions just now disturbed Murphy. Murphy opened his eyes in a daze, and a pair of blue eyes touched Pang Xuelin. A bright smile appeared on the girl's face, and she raised her head and offered a sweet kiss.

Then this move caused another storm.

By the time everything calmed down, it was already after nine o'clock.

After the two of them got dressed, they got out of the shuttle and saw that Shu Lao was already waiting outside.

Pang Xuelin smiled and said, "Old Shu, good morning."

"Good morning."

Shu Lao nodded and looked at Murphy, his eyebrows imitated by vines frowned again.

Murphy said, "Old Shu, I still don't have one?"

Shu Lao shook his head and said, "It's strange, it's been half a year, your bodies are all normal, and you haven't taken any contraceptive measures, why isn't Murphy pregnant yet?"

Pang Xuelin and Murphy looked at each other and shrugged helplessly.

In fact, Pang Xuelin was not surprised by this.

At the beginning, the system told him that in the plane world, it is impossible to have children.

Therefore, when Pang Xuelin was in the plane world, he never took any contraceptive measures.

Then in the world of "Interstellar Crossing", he discovered that after this world merged with the world of "District Ninth", Chris actually gave birth to a child for himself.

He asked the system what was going on.

The system's answer is: "The plot needs it."

According to the system, in the world of "Interstellar Crossing", Pang Xuelin needs to be concerned about family affection, so some rules in the world of the ninth district have undergone strange changes, resulting in a daughter between him and Chris.

Although Pang Xuelin faintly felt that there were some key things hidden in the answer given to him by the system.

But Pang Xuelin also knew that as long as the system didn't cause trouble, it would be difficult for him to have offspring in the plane world.

Even in the main world, Pang Xuelin was not sure if he could really make Yao Bingxia and Qi Xin pregnant.

After all, the bottle of gene optimizer that the World of the Ninth District rewarded has made Pang Xuelin completely different from ordinary humans.

At this time, Shu Lao said: "Mr. Pang, Ms. Murphy, please extend your hands."

Pang Xuelin and Murphy looked at each other, and they stretched out their hands one after another.

Soon, the vine stretched out and wrapped around Murphy's wrist. The tip turned into a needle and pierced into Murphy's vein. After sucking some blood, the vine left Murphy's wrist.

Shu Lao closed his eyes, was silent for a while, and said, "Ms. Murphy's body is fine."

Then, he turned his gaze to Pang Xuelin: "Mr. Pang, it's your turn."

Pang Xuelin smiled lightly and said, "Old Shu, please."

Soon, the vines spread over and entangled Pang Xuelin's wrist, and the needle slowly pierced into Pang Xuelin's body.

Just the next second, the expression on Mo Lao's face suddenly changed, and the vines were pulled out from Pang Xuelin's veins in an instant, shrinking into a ball, Mo Lao's face showed disbelief, pointing at Pang Xuelin tremblingly said: "You... …you……"

Pang Xuelin and Murphy looked at each other, and looked at Mo Lao with some surprise: "Mo Lao, is there something wrong with my blood?"

With a complicated expression on Mr. Mo's face, he said, "Mr. Pang, can you take a step to speak?"

Pang Xuelin nodded, and said to Murphy, "Honey, you go back to the shuttle and stay in the shuttle, and I'll have a chat with Mr. Mo."

There was a hint of worry on Murphy's face, but he nodded obediently and said, "Honey, you...be careful..."

Pang Xuelin smiled slightly.

In the next second, he felt the scenery in front of him suddenly change. The tree hole where Murphy and the shuttle were located disappeared before his eyes, and he and Shu Lao appeared in another tree hole space.

Pang Xuelin said: "Old Shu, if you have any questions now, you can ask them."

Shu Lao on the side looked at Pang Xuelin with a complicated expression, and said, "Mr. Pang, you are not an ordinary human being, are you? You are not even a member of this civilization, are you?"

Pang Xuelin smiled lightly and said, "How can you see that?"

Shu Lao said: "The genes in your body have undergone the optimization of high-level genetic medicines. This kind of genetic medicines cannot be produced by an ordinary civilization that has mastered point power... This civilization has at least reached..."

Shu Lao suddenly seemed to realize something, so he didn't continue talking.

Pang Xuelin nodded, and said lightly: "I have indeed undergone a genetic optimization transformation, and I am indeed not from this world."

A look of excitement suddenly appeared on Shu Lao's face, and he said, "Pang...Mr. Pang, in the past six months, I have neglected Mr. Pang, and I ask Mr. Pang to forgive me. In addition, I also ask Mr. Pang to tell me how to leave this small universe. ...I am willing to give Mr. Pang a thousand years to transform more than ten terrestrial planets for Mr. Pang."

With that said, Shulao made a long salute to Pang Xuelin.

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