Vol 3 Chapter 875: "Sound of the Avenue" 【Next】

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After Wang Qi appeared, Feng Luoyi and Turing took the initiative to give up a seat at the edge of the table, beckoning him to sit down. This means that they have recognized Wang Qi's ability as an abacus and regarded him as an equal fellow rather than a junior. Turing also smiled at Wang Qi: "You can't drink tea with this manifested illusion, so I won't pour you."
Feng Luoyi first asked Wang Qi: "Is everything resolved?"
"Yes, Gou Dabao's hand and tail have been finished, there should be a report there. This time, there ..."
"You don't need to tell me specific things. I only need to know that nothing happened." Feng Luoyi said calmly. When Wang Qi and Gou Dabao began to testify, there were many Tianjian facing the secret place. Based on the situation at that time, even if Gou Dabao was able to break away from the space station-type small Tianchen magic weapon, he would only be caught up by Tianjian and then completely evaporated.
Feng Luoyi first briefly talked to Wang Qi about his conversation with Turing. First of all, Wang Qi was amazed by what Turing did, and even lamented the magic of this cosmic physical law.
In this universe, the concept of von Neumann machine appeared earlier than the Turing machine. This is a very magical thing. Feng Luoyi and Turing first relied on the imitation of the soul to standardize the Feng's framework, and then further mechanized it to get a less strict "Turing machine".
Only this universe, where the technological black box is particularly easy to form, can support this phenomenon.
Now, the monks of China recognize this between the calculator and the abacus. First, the calculator is undoubtedly an advanced version of the abacus. However, there is no excessive version between the calculator and the abacus?
no one knows.
And now, Turing real people have followed the rapid advancement of mathematical logic and filled this vacancy.
This research is not a scam project called "filling the gap". It clarifies the basis of the calculator and allows the development of the calculator to be
down to earth
.
Many calculator theories have a more solid foundation. There is more room for research on the direction of the calculator.
According to Turing, this is just a "by-product." He was thinking about how to bypass the "undecidable" and made improvements to the calculator theory.
What Turing real people really think about is what makes Wang Qi more interested.
"You mean, you were just trying to make a logical reasoning method to prove ... prove some problems?"
"I hope he can bypass your incompleteness, but it seems to have failed." Turing lively spread out his manuscript and pointed out: "First of all, we define Tianyuan, Diyuan, Yuanren in an unknown sky-changing style. As we often do in the Tianyuan style, use fictitious symbols to deal with the unknown variable sky style. Then, we assume that we have two variable sky styles
bucket
and
cow
-do n’t ask me for details What is it, assuming there is such a ... "
Feng Luoyi was somewhat interested. This kind of thinking of "hypothesis" is still very rare.
On the other side, Wang Qi grew his mouth.
"This ... this is clearly ..."
This is the lambda algorithm, another undecidable proof that has existed in the history of the earth.
That is the proof method of Alan Turing's mentor and mathematician Church.
Although Alan Turing finally proved that the lambda algorithm is equivalent to the Turing machine, both are proofs of undecidability. However, these two proofs have very different meanings in mathematics. In the subsequent development, the Turing machine proof and the λ algorithm proof have all gone out of an imperial road.
Thinking of this, Wang Qi looked at Turing Real's slightly clear face, and felt a little sigh in his heart.
Unexpectedly, unexpectedly. The Turing Machine Proof and the λ Algorithm Prove that each other is on the inside and out, which is the same but different. I used the "self-referential" Dongfeng to use the Turing machine to prove the undecidable, and then the real Turing man completed Church's idea.
The overhaul of Shenzhou, although there are shadows of some people on the earth, they still have their own lives after all.
Church is the mentor of Alan Turing. However, in this world, Turing real people are self-taught, which led them to the Qianji Pavilion and suppress the Fusang Wanyu.
However, Turing ’s thinking should not be as good as that of Church? How did Turing humans take this step?
The two happy monks are quick-minded and communicate very quickly. In the moment when Wang Qi was distracted, Turing Real Man had finished his new idea. He smiled and said, "This algorithm is also good. I tried it myself. He can prove almost all propositions and express almost all arithmetic systems-it is a complete system."
This is Turing real man's thinking about undecidability, and also his thinking about incompleteness.
Feng Luoyi said: "But Wang Qi has also proved before that completeness and compatibility will not exist at the same time. If this is a omnipotent algorithm, then ..."
"Then it must be a self-contradictory algorithm." Wang Qi's fingers flicked in the air, condensed the colorful light, and wrote the mathematics formula: "For a meaningful logical system, the powerful expression ability must be accompanied by indestructible restrictions. We Now substitute some obviously wrong algorithms ... you see, it makes sense. "
If it is a theory, it is right or wrong, both positive and negative can be explained. If you can say what makes sense, then there is no reason.
Real Turing watched Wang Qi respond quickly and nodded appreciatively: "You are indeed terrible. I also realized this at the beginning. But, at the time, I still thought that I can rely on more restrictions." 'To circumvent this paradox. "
"Impossible." Wang Qi shook his head and said: "Self-reference can't be bypassed."
Self-referential is also a hurdle that the λ algorithm cannot circumvent.
In this algorithm called λ, the prototype of λ is a function. When defining the λ term, it is allowed to process any one function into another λ term.
Since it is "any function term", it must contain the λ term itself.
So, can it handle itself?
"Self-referential, what a miraculous concept." Turing lively praised: "I feel that the core part of our work now is closely related to it."
"The distinction between" this is not true "has been around for tens of thousands of years, but no one before Wang Qi realized the horror in it." Feng Luoyi nodded and agreed with Turing.
So is incompleteness, as is undecidable. This "self-referential" seems to be a logical monument. It is a conspicuous monument on the boundaries of mathematics itself.
It seems that there is such a limit that firmly limits the development of logic.
Crossing this boundary, one can only face an endless and endless loop, or one can only contradict oneself and become unstable.
How to get around this limit was once the most concerned issue of mathematicians.
"This attempt was defeated." Turing said slowly: "This arithmetic that I became the Vientiane algorithm has other meanings. I will sort it out later. The next thing I talk about is me. A little personal thought. "
"If-just if." Turing Reality emphasized: "If we can really bypass that boundary-here we will ignore it for the time being, just say that we can do it. It has to be cheap. The spirit of the avenue "Fan Sheng Chan Singing" is between the heaven and the earth, and then we can easily build such a calculator, which directly connects to the avenue and can give any specific problems answer……"
Wang Qi knew it. What Turing said, is called "oracle machine" on earth.
"The oracle machine" is another Turing machine connected to "God" and a black box with the prophet closed. Let ’s say that there is an oracle machine with prime number judgment instructions. In addition to everything that ordinary Turing machines can do, it can also instantly determine whether a natural number written on a paper tape is a prime number without actually calculating it. .
Then, can some problems that originally involved self-referentiality and contradictions be solved?
For example, the contradiction caused by self-referential.
"This is another conjecture made recently. Can this" self-referentiality "go around?" Turing smiled bitterly: "Can the fictional Daosheng sound solve this problem?"
Mathematics often has this method of proof, which is to assume that something exists first, and then make various logical deductions based on this premise.
The essence of Turing's deduction is to find an omnipotent existence in my imagination, assume that it can solve the original undecidable problem, and then look at what problem it can solve.
"What can we imagine, can we accomplish this business?" Turing lively looked at Wang Qi and Feng Luoyi and asked quietly: "If it is feasible, there is still a silver lining for our road. But even if We ca n’t do everything in our illusions ... "
Feng Luoyi asked: "What's the result?"
Turing live-action reported with a bitter smile: "Not very good."
If there is a program A that judges the shutdown problem (the input required by A is a program), we construct a new program B, which calls A but the opposite of the output of A: If the input of B is judged to be shutdown by A Then B will not stop; if the input of B is judged by A to be non-stop, then B will stop.
Suppose there is an oracle machine with an oracle problem. If the
code
and input of an ordinary Turing machine are written on the paper tape of this machine, then it can be instantly known without calculation. Whether the smart machine will stop when it encounters the indicated input.
However, if we replace all three words of "Turing machine" in the proof with "oracle machine with" number theory problem "oracle," what about the other parts? Incomplete proof is still true!
Perhaps it is human thinking that limits their imagination, even if it is omnipotent in human imagination, it cannot cross this line.
Even Dao Shengyin can't knock on this door.
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