Cyber Heroes

Yuki applauds. Among the applause, there are three points to deal with, and three points to be sincere: "But Xiang Shan, what does this have to do with the'internal strength' we call..."

"Yuki," Xiang Shan did not answer positively Instead, he asked a question: "Do you think computers are powerful?"

Yuki nodded. Control the prosthesis. In fact, most of the work is done by computers. As long as there is a computer, no matter how complex construction machinery is, it can run.

Yuki also knows that computers can calculate things at incredible speeds, and rich people can use it to do more things, such as...for example...

Anyway, it is very difficult to deal with.

"Indeed. The performance of the human biological brain, if the symbolic calculation is the benchmark, the computing resources can be compared with the supercomputer-well, in this era, most of the parameters in my memory are also considered It’s not super-computing anymore. However, the software that matches this hardware is too poorly optimized. If you simply compare calculations and pursue performance, biological brains can’t compare to computers."

This It's a normal thing. Biological evolution has always followed the principle of "sufficient use". The evolution of this kind of thing will not pursue the "extreme performance". An unfavorable trait will not be eliminated by natural selection as long as it does not affect "live to reproductive age to have a child".

Natural persons have a lot of mentally handicapped designs that can cause various injuries.

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

"At least in the times I know, computers still can't escape the limitation of'computational problems'."

Yuki is a little confused: "'computational problems'..."

"Calculation problems are exploring whether all math 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 the human ideal of'computability'. Not all mathematical problems can be solved by machines."

Turing Machine at first cannot understand many problems. It is not "computing resources are insufficient to calculate" but "the probability of starting calculation does not even exist".

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

But at first, there are many problems, the computer cannot calculate or even recognize.

At the early stage of the birth of computers, a professor sent a graduate student under him to solve the problem of "computer image recognition"-he was optimistic that it would only take two months. Graduate students can completely overcome this problem.

But the fact is, this is impossible.

Until the 21st century, the "naked eye identification verification code" was also the criterion for certain network programs to determine whether the login was a human.

"Computer graphics recognition" is a terrifying subject. There are countless scholars all over the world who are fighting for it, but programmers still use the "naked eye identification verification code" as a means to block the malicious login of the machine.

Computer graphics recognition is so difficult, and the reason is largely because...

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

One Most geometric problems are located within NP. Turing Machine can quickly verify whether the answer is correct, but it cannot give the answer quickly. Some geometric problems are even more difficult 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, stepping out of the 1st Step that allows the computer to move towards the gods. I still don’t remember success Isn't it..."

When 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 weren’t for the war, maybe Anatoly could do...what...

——Who is Anatoly? How do I know so many powerful characters of unfathomable mystery?

After a while, the man added lonely: "Probably not. Computers are'destined to be impossible'. NP problems are destined to be something that electronic computers cannot solve. And the NP problem is not even the extreme complexity."

"In addition to the NP problem, there are 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 the exponential time problem [EXPTIME problem]."

"In this regard, quantum computers are one dimension stronger than electronic computers. However, the theoretical capacity limit of quantum computers is It is called the finite error quantum polynomial time problem [BQP]. The BQP category only includes part of the PSPACE problem-even quantum computers cannot touch EXPTIME. This is a realm close to Tao..."

Yuki looked nodded in awe: "Although I don't understand it, it looks like very difficult to deal with. Then Xiang Shan...what is EXPTIME? Can you give me an example?"

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

Yuki was silent for a moment: "Huh?"

"This'judgment' is EXPTIME judgment."

"What?"

"This'judgment' is really EXPTIME judgment."

"That's not right..." Yuki doubts whether his biological brain is broken: "Isn't this... something that a child can understand?"

"From the perspective of mathematics See, the level of difficulty of this question is EXPTIME. Biological brains can make this judgment simply, but computers cannot even'understand'. Among the known calculation models, there is only one that can touch this Domain..." Xiang Shan pointed to his head: "The human biological brain."

"Perhaps this is a limitation. The human brain cannot build a more advanced mathematical Computational models? Maybe, 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 encountered today still retains the biological brain."

Xiang Shan took out two metal strips and drilled holes on them by hand.

"This is the profound mystery of internal strength. Use your brain...Use the wisdom of your innate talent to control the huge resources brought by the computer to form an'Inner Strength' against external evils"

"Because the control body uses Turing Machine, the record information uses Turing Machine, and even everything in this World belongs to Turing Machine. Therefore, when you can use Inner Strength to control Turing Machine, you will Above all tools. Those in power will not be able to prevent you from obtaining information, nor can they steal anything from you. He can no longer control you."

"Practicing martial arts without practicing martial arts will end up futile. If you are focused Due to the cultivation of outer sect martial arts and neglecting the inner sect cultivation technique, then any internal strength powerhouse, any hacker, can read your memory at will, take away your Martial Dao algorithm, empirical convolution, and even Inputting wrong signals into your sensory organs will make you live in hallucinations for a lifetime. Martial Artists without internal strength, no matter how strong they are, they are nothing but oppressed. You can only have them if they have cultivated superior internal strength. The power of resistance."

He stuffed a metal strip into an input port of the machine.

This iron strip is the memory. The presence or absence of holes in the upper face represents the machine language of "yes" or "no". This is the original soul of the computer.

Even without an electronic structure, it has all the functions a computer needs.

"Now, I will teach you the first lesson. This may be Danger Land's counterattack after you fall into the Illusion Technique." Xiang Shan pointed to the handle: "Now, turn him."

Yuki turns according to words. The steel drill is continuously falling under the drive of the gear. Some of them are blocked by the iron sheet, and some pass through the holes in the iron sheet to transfer kinetic energy to the gears below. The iron sheet moves inward with the movement of the gear.

Xiang Shan stared at the naked machine, observing his operation.

"Ding". Yuki is a little weird.

"Stuck, Xiang Shan..."

"Very good." Xiang Shan nodded: "The world has not disappeared, the machine has not disappeared-this is a good phenomenon, child. This shows that I am real, and so are you. We are not in an emulator."

"Remember this. This is called'Turing Shutdown', and it is a sword that smashes illusions."

The Turing shutdown problem is the problem of judging whether any program can finish running within a limited time. This problem is equivalent to the following determination problem: whether there is a program P, for any input program w, it can be determined that w will end in a finite time or an endless loop.

This question can be simply expressed as "Can a Turing Machine simply determine whether another Turing Machine should stop".

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

The Turing shutdown problem is logically unsolvable.

So, this also gives people the sword to cut through the illusion.

If you can construct a structure that is mathematically isomorphic with Turing Machine in an illusion formed by Turing Machine calculus, and then use it to determine the shutdown problem, then this Turing Machine will have The ability to exhaust the resources of the matrix and break down the layers of the matrix.

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

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

The instruction that can make the virtual Turing Machine down, you can make the virtual Turing Machine down.

——Of course, there is also a situation in which "virtual you exist in the world, not Turing Machine, but super Turing Machine". But to be honest, the civilization that can take the Super Turing Machine out as the brain in the tank is far beyond human understanding. In this situation, there is simply no way to crack within the scope of human cognition, so there is no need to think.

Turing Machine, Turing halt problem, Hilbert plan...the origin of these all are internal strengths.

This is exactly why Xiang Shan would rather put aside for the time being to rebuild the prosthetic body, but also complete this mysterious ceremony first.

He is not sure if he is a "brain in a tank"—according to his understanding of technology, soaking a brain in the culture fluid makes him mistakenly believe that the surrounding hallucinations are "real" , It's actually not difficult.

So he must be verified.

Although the biological brain is extremely high level in mathematical structure, it is so easy to be deceived. It cannot be compared with man-made objects in terms of "functionality".

What is made by nature based on the principle of "just use it", how can it be better than the means designed by wisdom for the purpose of "deception"?

Only wisdom can fight against wisdom.

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

He gently rubbed Yuki’s head: "It’s nice, you are real, and I am real."

About P, ​​NP, PH, PSPACE, The relationship between the EXPTIME question and the BQP question can be found in the author's portrait (#笑)