Cyber ​​Heroes

Chapter 11 Penetrating the Phantom Sword

Yuki applauds.Among the applause, there were three points of coping and three points of sincerity: "But Xiang Shan, what does this have to do with the 'internal strength' we are talking about..."

"Yuki," Xiang Shan didn't answer directly, but asked a question instead: "Do you think computers are powerful?"

Yuki nodded.Control prosthesis.In fact, most of the work is done by computers.As long as there is a computer, even complex construction machinery can operate.

Yuki also knows that computers can calculate things at incredible speeds, and that rich people can do more with them, like... like...

Anyway, it is very powerful.

"Indeed. If the performance of the human biological brain is based on symbolic operations, the computing resources can be compared with supercomputers—well, in this era, most of the parameters in my memory are not considered 'supercomputers'." .However, the optimization of the software that matches this hardware is really poor. If you simply compete in calculations and pursue performance, the biological brain is no match for the computer."

This is a very normal thing.Biological evolution has always followed the principle of "enough is enough".Evolution does not pursue "extreme performance".An unfavorable trait, as long as it does not affect "live to reproductive age to have children", it will not be eliminated by natural selection.

There are a lot of mentally handicapped designs on natural people that can cause various injuries.

But there is only one thing, the computer cannot compare with the human brain.

"Computers, at least as far as I know, are still bound by 'computational problems'."

Yuki was a little confused: "'Calculation problem'..."

"The computational problem is to explore whether all mathematical problems can be solved by the same calculation method. On this basis, a genius named Alan Turing designed the 'Turing Machine', and then...he denied It meets the human ideal of 'computability'. Not all mathematical problems can be solved by machines."

There are many problems that a Turing machine cannot understand in the first place.Not "insufficient computing resources, unable to calculate" but "there is no possibility of even starting to calculate".

The simplest one is, for example, some geometry—note that "part of geometry" is not "all".In mathematics, concepts such as "number", "geometry" and "equation" can be transformed into each other to a certain extent.

But in the beginning, there were many problems that the computer could not calculate or even recognize.

In the early days of the birth of computers, a professor sent one of his graduate students to solve the problem of "computer image recognition" - he was optimistic that it only took two months for his graduate students to completely overcome this problem .

But the truth is, it's impossible.

Until the 21st century, "identifying verification codes with naked eyes" was also the standard for some network programs to judge "whether the loger is a human being".

"Computer Graphics Recognition" is a scary subject.Countless scholars all over the world are fighting for it, but programmers still use "visual recognition verification code" as a means to prevent malicious login of machines.

The reason why computer graphics recognition is so difficult is largely because...

"Problems that computers can understand are called 'polynomial time problems', Polynomial time—that is, the abbreviated P problem. Computers can quickly solve the P problem. The more difficult problem than the P problem is the non-deterministic polynomial time. Nondeterministic Polynomial time - NP problem."

Most geometric problems lie within NP.The Turing machine can quickly verify whether the answer is correct, but it cannot quickly give the answer.And some geometric problems are even harder than NP.

"There used to be a mathematician who wanted to prove 'P=NP', to prove that all NP problems can be transformed into P problems, and take the first step to make computers go to the gods. I still don't remember if I succeeded..."

When the Turing machine was born, it was delimited - because it proved that "mathematics has absolute Turing computability".

The great ideal of Mr. David Hilbert failed.

——If it wasn't for the war, perhaps Anatoly would have been able to... what...

—And who is Anatole?How did I know so many inexplicably powerful characters?

After a while, the man added desolately: "Probably not. There are things that computers are 'destined not to be able to do'. NP problems are destined to be things that electronic computers are unable to solve. And NP problems are not even possible. The ultimate in complexity."

"In addition to the NP problem, there is also the polynomial hierarchical structure problem [PH]. In addition to the polynomial hierarchical structure problem, there is also the polynomial space problem [PSPACE problem]. In addition to the polynomial space, there is also an exponential time problem [EXPTIME problem]."

"In this regard, quantum computers are one dimension stronger than electronic computers. But the theoretical capability limit of quantum computers is called the finite error quantum polynomial time problem [BQP]. And the BQP category only includes part of the PSPACE problem— —Even a quantum computer cannot touch EXPTIME. This is near the realm of Tao..."

Yuki nodded in awe: "Although I don't understand, it seems very powerful. Then Xiangshan... what is EXPTIME? Can you give me an example?"

"The simplest example is fine." Xiang Shan nodded: "You are using an electronic program, and you feel that the program is running a bit slow. At this time, you have to make a choice, which is to judge 'let it just lag like this' It will be fine in a while', or 'how long can I endure, and I will restart'? This 'judgment' is the EXPTIME judgment."

Yuki was silent for a while: "Huh?"

"This 'judgment' is EXPTIME judgment."

"what?"

"This 'judgment' is really an EXPTIME judgment."

"That's not right..." Yuki wondered if his biological brain was broken: "Isn't this... something that children can understand?"

"From a mathematical point of view, the difficulty level of this problem is EXPTIME. The biological brain can easily make this judgment, but the computer can't even 'understand'. Among the known calculation models, only One, can touch this field..." Xiang Shan pointed to his head: "Human biological brain."

"Maybe this is a limitation. The human brain cannot build a more advanced computing model than itself at the mathematical level? Maybe it is possible, but humans have not yet touched this field? But I am sure that humans still have not solved this problem. ——Because the martial artist I met today still retains a biological brain."

Xiang Shan took out two iron strips and drilled holes in them by hand.

"This is the mystery of internal strength. Use your brain...use your innate wisdom to control the huge resources brought by the computer, and form an 'internal force' that resists external evils."

"Because the Turing machine is used to control the prosthetic body, and the Turing machine is used to record information, and even everything in this world is subordinate to the Turing machine. Therefore, when you can use your internal force to control the Turing machine, you are above all tools on. The people in power won’t be able to stop you from getting information, or steal anything from you. He can no longer control you.”

"Practicing martial arts without practicing kung fu will end in vain. If you focus on the cultivation of outer martial arts and ignore the inner martial arts, then any strong internal skill or any hacker can read your memory at will and take away your memory. Your martial arts algorithm, experience convolution, and even inputting wrong signals into your sensory organs will make you live in an illusion all your life. A martial artist without inner strength, no matter how strong he is, is just an oppressed person, and he can only achieve success. Only with superior internal strength can you have the strength to resist."

He slipped the tin strip into one of the machine's input ports.

This iron strip is the memory.The presence or absence of holes on the top represents the machine language of "yes" and "no".This is the original soul of the computer.

Even without the electronic structure, it has everything a computer needs.

"Now, let me teach you the first lesson. This may be your way to counterattack after falling into illusion." Xiang Shan pointed to the handle: "Now, turn him."

Yuki turned as he said.Driven by the gears, the steel drills kept falling down.Some of them are held back by the iron sheet, and some pass through holes in the iron sheet, transferring kinetic energy to the gears below.The iron sheet moves inwards with the movement of the gears.

Xiang Shan stared at the exposed machinery, observing its operation.

There was a "ding".Yuki was a little weird.

"Stuck, Xiangshan..."

"Very good." Xiang Shan nodded: "The world hasn't disappeared, and the machine hasn't disappeared—this is a good sign, kid. It shows that I am real, and so are you. We are not in a simulator."

"Remember this. This is called the 'Turing Stop', the sword that cuts through illusions."

The Turing Halting Problem is the problem of judging whether any program can finish running within a finite time.This problem is equivalent to the following decision problem: whether there is a program P, for any input program w, it can be judged that w will end in a finite time or an infinite loop.

This question can be simply stated as "Can a Turing machine simply determine that another Turing machine should stop".

And Alan Turing gave his judgment before the birth of the computer.

The Turing Halting Problem is logically unsolvable.

Therefore, this also gave people the sword to cut through the illusion.

If it is possible to construct a structure that is mathematically isomorphic to the Turing machine in the illusion formed by the Turing machine calculus, and then use it to determine the halting problem, then this Turing machine will exhaust the resources of the matrix. The ability to penetrate layer by layer matrix.

As long as the superior matrix is ​​still a "Turing machine".

The only way for a Turing machine to understand another Turing machine is to simulate the work of that Turing machine in vivo.

An instruction that can cause the virtual Turing machine to shut down can cause the Turing machine that virtualizes the Turing machine to shut down.

——Of course, there is also the situation that "the virtual world where you exist is not a Turing machine, but a super-Turing machine".But to be honest, a civilization that can take out a super-Turing machine as a brain in a vat has far surpassed human understanding.In this situation, there is no way to crack it within the scope of human cognition, so there is no need to think about it.

Turing machine, Turing halting problem, Hilbert plan...these are the origin of internal strength.

This is also the reason why Xiang Shan Ning temporarily put aside rebuilding the prosthetic body, and has to complete this mysterious ceremony first.

He is not sure now whether he is a "brain in a vat" - according to his understanding of technology, it is not difficult to soak a brain in culture fluid and make him mistakenly believe that the illusion around him is "real".

So he has to be verified.

Although the biological brain is extremely advanced in its mathematical structure, it is such an easily deceived thing.It is not comparable to man-made objects in terms of "functionality".

How can something that nature concocts based on the principle of "use it if it can be used" compare to the means designed by wisdom based on the purpose of "deception"?

Only wisdom can fight wisdom.

After confirming the "reality" of the surroundings, the world seemed to come alive in Xiang Shan's eyes.

He lightly stroked Yuki's head: "It's fine, you are real, and so am I."

　Regarding the inclusion relationship between P problem, NP problem, PH problem, PSPACE problem, EXPTIME problem, and BQP problem, you can see the author's avatar (#笑)

　　

　

(End of this chapter)