Cyber Heroes

Yuki applauded. The applause was partly coping and partly sincere: "But Xiangshan, what does this have to do with what we call 'internal strength'..."

"Yuki," Xiangshan did not answer directly, but asked a question: "Do you think computers are powerful?"

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

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

Anyway, it’s pretty awesome.

"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, the few parameters in my memory are probably not considered 'supercomputers' . However, the software that matches this hardware is really poorly optimized. If we simply compete in calculations and pursue performance, biological brains cannot compete with computers."

This is normal. Biological evolution has always followed the principle of "enough is enough". In such things as evolution, we will not pursue "the ultimate in performance." An unfavorable trait will not be eliminated by natural selection as long as it does not affect "living to childbearing age and having children".

Natural people have a lot of mentally retarded designs that can cause various injuries.

But there is only one thing that computers cannot compare with the human brain.

"At least as far as I know, computers still can't escape the confines of 'computational problems.'"

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

"Computational problems are exploring whether all mathematical problems can be solved with 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 Turing machines cannot understand in the first place. It's not "Insufficient computing resources, unable to calculate" but "There is no possibility of even starting calculation".

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

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

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

But the truth is, this is impossible.

Until the 21st century, "naked verification code" was also the standard used by some network programs to determine "whether the login person is a human being."

"Computer graphics recognition" is a terrifying subject. Countless scholars around the world are struggling with this problem, but programmers still use "naked verification codes" as a means to prevent malicious logins from 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 - also known as the abbreviated P problem. Computers can quickly solve the P problem. What is more difficult than the P problem is non-deterministic polynomial time. Nondeterministic Polynomial time—that is, NP problem.”

Most geometric problems are located in NP. The Turing machine can quickly verify whether the answer is correct, but it cannot give the answer quickly. And some geometric problems are even more difficult than NP.

"There was once 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 towards making computers reach the realm of gods. I still don't remember whether he succeeded..."

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

Mr. David Hilbert's great ideal failed.

——If it weren’t for the war, maybe Anatole would have been able to do... something...

——Who is Anatole? How do I know so many inexplicably awesome characters?

After a moment, the man added lonely: "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 The ultimate in sophistication.”

“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 the exponential time problem [EXPTIME problem].”

"In this regard, quantum computers are one dimension better than electronic computers. However, 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 a realm close to Tao..."

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

"The simplest example is enough." Xiang Shan nodded: "You are using an electronic program and feel that the program is a little stuck. At this time, you have to make a decision, which is to judge, 'Let it just be stuck like this. It will be fine after a while', or 'I'll just wait for a while longer and then I'll restart it'? This 'judgment' is the EXPTIME judgment."

Yuki was silent for a moment: "Huh?"

"This 'judgment' is the EXPTIME judgment."

"What?"

"This 'judgment' is really EXPTIME judgment."

"Isn't it right..." Yuki doubted whether his biological brain was broken: "Isn't this something that... a child can understand?"

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

"Perhaps this is a limitation. The human brain cannot build a more advanced computational model than its own at the mathematical level? Maybe it can, but humans have not yet touched this field? But I am sure that humans still have not solved this problem. ——Because the warrior I met today still retains his biological brain."

Xiang Shan took out two iron strips and drilled holes in them with his hands.

"This is the secret of internal strength. Use your brain...use your innate wisdom to control the huge resources brought by computers to form the 'internal force' to resist external evils."

"Since the Turing machine is used to control the prosthetic body, the Turing machine is used to record the information, and even everything in this world is subordinate to the Turing machine. Therefore, when you can use your internal power to control the Turing machine, you are superior to all tools. On. The one in power won’t be able to stop you from getting information, and he won’t be able to steal anything from you. He won’t be able to control you anymore.”

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

He inserted the iron strip into one of the input ports of the machine.

This iron strap is the memory. The presence or absence of holes on it represents the machine language of "yes" and "no". This is the original soul of computers.

Even without electronic structure, it has all the functions required by a computer.

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

Yuki turned as he was told. The steel drill continues to fall driven by the gear. Some of them are blocked by the iron sheet, and some pass through the holes in the iron sheet, transmitting kinetic energy to the gears below. The iron sheet moves inward with the movement of the gear.

Xiangshan stared at the exposed machinery and observed its operation.

There was a "ding" sound. Yuki was a little surprised.

"Stuck, Xiangshan..."

"Very good." Xiang Shan nodded: "The world has not disappeared, the machine has not disappeared - this is a good sign, kid. This shows that I am real and you are real. We are not in a simulator."

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

The Turing Halting Problem is a problem of determining whether any program can end its operation within a limited 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 within a limited time or loop endlessly.

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

Alan Turing gave his judgment before the birth of computers.

The Turing Halting problem is logically unsolvable.

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

If we can construct a structure that is mathematically isomorphic to the Turing machine in the illusion formed by the calculation of a Turing machine, and then use it to determine the shutdown problem, then this Turing machine will exhaust the resources of the matrix. The ability to penetrate layers of matrices.

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 inside the body.

An instruction that can crash a virtual Turing machine can crash the Turing machine of this virtual Turing machine.

——Of course, there is also a situation where "the virtual world that you exist in 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 is far beyond human understanding. In this case, 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 origins of internal power.

This is why Xiangshan would rather put aside rebuilding his prosthetic body temporarily and complete this mysterious ritual 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 think that the hallucinations around him are "real".

So he has to verify it.

Although the biological brain is extremely advanced in mathematical structure, it is such an easily deceived thing. It cannot compete with artificial objects in terms of "functionality".

How can something created by nature based on the principle of "just use it" be better than a method designed by wisdom with the purpose of "deceiving"?

Only wisdom can counter wisdom.

After confirming the "reality" around him, the world seemed to come alive in Xiangshan's eyes.

He gently rubbed Yuki's head: "That's good. 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 ( # laughs)