Chapter 68 Category Theory [3rd Update]

Although that is what I say, but...

To be honest, Wang Qi actually has little confidence in calculator theory.

In fact, from the perspective of any earthling, the field of calculator theory in this world is very strange.

First of all, the concepts of "computer" in the two worlds are actually subtly different.

There has always been only one classic route on earth, from George Boole, to Frege, Russell, to Gödel, Church, and Turing. It is actually a continuous and progressive route. But this is just the development route of Turing machines.

In fact, the earth's electronic computer has another origin that almost everyone has forgotten.

In 1943, a neurobiologist, Warren McCulloch, and a mathematician, Walter Pitts, created an abstract diagram of the human brain's divine system by simulating the ideas of the human brain. It is a simplification based on the human nervous system. But this achievement proves that a system that can think can be built with wires, and the connections of the wires play the role of neurons. The flow or non-flow of electric current represents the presence or absence of a synaptic response.

What these neural networks implement is exactly a set of "predicate logic".

However, at that time, human beings' understanding of the brain and electronic technology was very shallow and narrow.

When most people think about "neural networks," they think of the achievements of the 21st century.

Because the materials science and engineering of the 1940s could not support the ideal neural network of those two scholars at all.

The real significance of this experiment is to give the "Turing machine" an implementable structure.

And it is further optimized in engineering, which is the von Neumann architecture.

However, the Aura Universe, the entire universe is a huge black box.

Qianji Pavilion itself has the idea of ​​​​"using mechanisms to imitate all things". Here, creating artificial intelligence, the so-called "acquired will" is actually very simple, just a ray of divided soul, or even using magic to imprint the soul's activities. Magical weapons and true spirits can be barely counted among them.

Turing's earliest calculator prototype was also based on the idea of ​​"simulating the process of soul movement."

As for the prerequisite mathematics research that was originally used for the development of computers, that is, part of the achievements of Church and Turing, and the pursuit that is closely related to Charles Babbage’s dream, in this world, it is not for “creating computable computers”. "Machine" itself is born.

They are by-products of the critical questions raised by Simon’s twenty-three questions.

If not viewed in the context of the Aura Universe, this period of technological history would be simply crazy.

Artificial intelligence existed before computers. Then, computers were invented and the “yin and yang” lines were used to represent the basis of change. Then, the monks extracted high-level language from the spells and controlled the calculator with the ideas of "refining weapons" and "controlling objects". Then, in the field of pure mathematics next door, the incompleteness theorem appeared, which in turn led to the development of computers.

No matter how you talk to any Earthling, that Earthling will not believe that there is such nonsense in the history of technology.

As for Suanjun's "chaos topological network structure", after the first line developed to its extreme, another line parallel to the calculator was opened.

If Suanjun hadn't already figured it out, Wang Qi wouldn't have believed that such technology existed.

The reason why Wang Qi gradually handed over this matter to Su Junyu after forming the elixir was not only because he was busy exterminating the remnants of the ancient magic on Linghuang Island, but also because he was afraid that he would delay this work due to the intellectual barriers he would create on the earth. A line of development.

Earth's common sense is of limited use in this area. He also withdrew from some of the "motivating forces" for the rapid advancement of computer technology on Earth - such as open source, and the like. Even if he creates Alpha Dog, it actually doesn't matter.

China no longer needs "the acquired will to play chess better than the national players with limited computing power", they have this kind of thing. Instead, they are more concerned about, "Why is there such a thing?"

This is considered his weakness.

However, I can’t care anymore now.

Wang Qi thought so.

You have to learn this well to feel at ease.

It's not that he thinks that Suanjun will really harm him by means other than mathematical methods, let alone that he hopes that he can overtake Suanjun within a foreseeable time.

It's just closing a possible loophole.

"Furthermore, it is also very important to find a solid foundation for your virtual phase body.",

Wang Qi encouraged himself, and then looked at the other two people in the quiet room.

Zhao Qingtan and Wei Cang are both the main force in writing "Original Calculation".

"Our task in the next stage is to continue to study the structure. With the previous "original calculations", we have established the brand of "structure". However, this is not the end yet, we need to continue to delve deeper."

Zhao Qingtan frowned: "Is this purely arithmetic? But didn't you say that saving lives is important..."

"Without this step, how can I save myself?" Wang Qi spread his hands: "Senior Brother Zhao, did I make it clear yesterday?"

"Yes, I understand." Zhao Qingtan sighed slightly.

"It's better to say structure. Our 'structure' is still a new concept, but it is not powerful enough yet - I think it is powerful. It should be able to change the way of thinking of all Wanfa disciples."

Wang Qi originally proposed the incompleteness theorem, which almost destroyed half of Wanfamen.

But why is it only half? Why is there only "half" when the Master of Calculation is in the heyday and there are more people who leave the sect than join the sect?

Because logic is not so closely related to the whole of mathematics.

In other words, only logicians care about logic itself. Most mathematicians don't care about logic. There are contradictions in logic, and it does not affect any actual proof of mathematics.

The reason why many monks lost their faith is that the beautiful picture of the Master of Calculation "finding the unified foundation of mathematics" is too tempting, which leads many people to firmly believe in it.

Just like the atomic theory does not affect the normal people's perception of macroscopic things, the disciples of the Wanfa Sect will not imagine natural numbers as "classes of equipotential sets" when counting.

There are even many mathematicians who think that incompleteness and incompatibility are only problems of "logic" and "sets" themselves, not problems of mathematics.

The Master of Calculation is the representative of this kind of thinking. When the Master of Calculation practices his ideals, the Master of Calculation does not care at all, as if success or failure does not matter.

Incompleteness and incompatibility also have this tendency - the problem is only a logical problem, not a problem of mathematics itself.

They look more like obstacles on the road to mathematics.

The benefit of set theory with a universal door seems to be only "a unified language that is convenient for expressing various abstract concepts".

And "structure" is another level of things.

The Bourbaki school claimed that "structure" is "the mathematical foundation used by mathematicians" [not "the mathematical foundation used by logicians"]. They started from another way to unify the entire field of mathematics.

Before the Bourbaki school, the concept of "structure" already existed. They just pointed out that the concept of "structure" can be used for "integration" just like Hilbert hoped to use Cantor's set theory to dominate the mathematical world. This method has achieved great success, because on Earth, only a very small number of "mother structures" are needed to discuss a large number of typical and interesting examples.

The Bourbaki school even affected the division of mathematics. Mathematics is no longer divided into several major categories such as arithmetic, algebra, geometry, and analysis as in the classical period, but there are classifications such as "topological algebra" and "algebraic geometry".

This foundation can change the world.

The further sublimation of the concept of "structure" is "category".

The class of all possible examples of a certain type of structure, plus all functions that maintain this structure, is "category".

Category is a more flexible concept than structure.

Category can be identified as a special case of the concept of structure, while on the other hand, sets and their functions can be regarded as a special case of categories.

Sets and their functions, structures and their morphisms can all constitute categories.

It also has the potential to "become the foundation of the entire mathematics".

This is also another important supplement to the Bourbaki school.

On the other hand...

This thing is finally a little more down-to-earth than many previous theories.

At least, category theory can be applied to computer science - although Wang Qi has forgotten what it is specifically about.

After all, this is considered a relatively high-end and classy skill on Earth, and ordinary programmers may not understand it.

In addition, the technological history of Shenzhou, which is completely different from that of Earth...

It is really unsure.

But Wang Qi had no choice but to bite the bullet.

The basic theory has become an integral part of his law revision.

If there is a conflict in his skills, it is very likely that it is caused by the conflict between the virtual cultivation method of the Lord of Calculation and this part.

This kind of problem rarely occurred in the Immortal Alliance before. Because even if the "theory" is different, the "application" is not incompatible. The beast mechanism cluster is just "used" for him, and there should be no problem.

However, the Dragon Emperor's prophecy is beyond ordinary cause and effect, and it must be prevented.

Therefore, Wang Qi has no choice but to choose this path.

In this way, he can better combine his own mathematical level with the beast mechanism cluster and his own cultivation method.

Although it is also a dark road.

But he, Wang Qi, is going to find a way out.

After arranging for the two people, Wang Qi said again: "Brother Zhao, I plan to visit the Yu clan later and solve some...problems that may be mathematical problems in advance. I remember that you also plan to go there to deal with the education problems of the Yu clan, right? Let's go together. I have something else to do, and I will ask you for help alone."

"Okay, no problem." Zhao Qingtan said.

Wei Cang left first. Zhao Qingtan called Jiao Shuhaihua and walked towards the Yu tribe settlement with Wang Qi.