Figure foreground and calculation problem
Zhang Jiang (Email:
Jakezj@163.com)
Since the 1930s, the map spirit, calculating these important concepts have been flashing in the scientific sky. Especially in recent years, innovation work in quantum computers, biological computers, and DNA calculations has aroused widespread concern. We can't help but ask such a problem, why can foreign computers can be invented? What does this mean? In fact, this source is from the calculation theory. Although there are many textbooks in the introduction of calculation theory, it is generally more difficult to understand. So I think it is necessary to conduct popular sciences. So try to write such an article, I hope that my article will make you clearer, thorough understanding of the basic and important concepts of the map spirit, calculations, etc., and insight into the essence and profound sense of these concepts.
This article can generally be divided into four parts: First, give you a story about Tuling, Gotel and other scientists; then officially introduced into the concept of the map, in order to have a more intuitive understanding of this concept, I use a manual Life: The metaphor of "bug" is described. Next, the article introduces the concept of the map spirit: What is analog, what is "universal computer", etc.; In-depth understanding of the problem of Tuling shutdown. In the process of writing, I have introduced some existing basic concepts in my own way (in order to express the clear understanding of it, I have to give up the strictness of the theoretical argument), and I also explore a lot I think that others have no discussion. These problems are mostly my own thinking results, and they have not passed scientific verification. In this part I labeled *, I hope you can choose these questions and opinions.
First, story
Any scientific idea, the birth of the science concept has its background, often has a lot of charming stories in the background. Regarding the calculation theory, it dted back to 1900, at that time, the famous MTH's Mathematian General Assembly made a famous 23 mathematics issues at the Mathematian General Conference of the Century. One of the tenth issues is this: there is no limited, mechanical step, can determine if the "lost map equation" is solved? Here, there is a limited problem with the proof step of the machine, saying that today's words is the algorithm. But at the time, people still don't know what "algorithm" is. In fact, there have been many problems in the field of mathematics are closely related to the "algorithm", and thus, the scientific "algorithm" is defined. In the past 30 years, there are finally two people to provide a method of accurately defining an algorithm. One person is a map spirit, a person is a hutcy. And the map of the map spirit is intuitive, so soon, it will soon be universally accepted.
I don't know if you have heard of the name of Tuling. Some people may know Newton, know Einstein, and even know Feng Niman, but I don't know the map spirit. However, the contribution of Tulex is definitely not asia. The biggest contribution of Tuling is to make a basic, profound concept such as the algorithm. It is because of the theoretical basis of the map spirit, people may invented the greatest invention in the 20th century: computer. Therefore, people call the spirit as: the father of computer theory.
The era of Tuling lives in the Second World War. During World War II, he once successfully decipher the German password for the British government, and thus made a prominent contribution to the UK. In fact, it is precisely because of World War II. The British government is only willing to make Tuling to make the most original computer. Of course, this computer is specifically used to decipher the password, not our general purpose computer. (There is a film called "password faint" English name is "enigma" is based on the story of the German password according to Tuling, and everyone is interested in finding.)
This person is very weird. I only like to study myself, I don't like to communicate with others. And it is said that he is a homosexual. It is necessary to know that the British, homosexual behavior is in the case. Finally, when he had just reached the wind, he committed suicide. In order to commemorate this great scholar, the computer industry has established the highest honor award: ACM Trim. On the one hand, the production of the map is the foundation of modern digital computers (to know that after Feng Niman is based on Tuling's idea), the first computer is designed. On the other hand, according to the basic concise concept of the map, we can also see what the calculated limit is. In other words, the skills of the computer are limited in principle. Please note that the limit of the computer is not to say that it can't eat, sweep the ground, etc., but only from the information processing this angle, the computer still has a limit. This is the troubleshooting problem of the map forever. This problem is even more important in Tuling. In his past paper, in fact, he is in order to demonstrate the problem of Tu Leung's shutdown.
It is a series of big things to mention the Tuling shutdown problem. I can't help but take a series of big things to mention Tibedel theorem, Russell Paradox. As early as the end of the 19th century, Condur made a foundation study for the collection. To know, although mathematics is eight, but people find that the concept of using the collection can summarize all mathematics, that is, the collection is the basis of all mathematics. Therefore, if the aquary is laid the basis of the publication, it is equal to the foundation for mathematics. Condal is the contribution of this. In addition, in order to prove that the number of real numbers is more than the natural number, a proof method called "diagonal deletion" is invented. Unexpectedly, this method has a very deep influence until the later Turing stop problem, the Gö der Theorem is actually the different extensions of the method.
People at the end of the 19th century are busy establishing a axiological system building based on collections. However, when the building is about to be completed, a terrible thing happened that Russell's paradox was smashed with the dream of mathematician. A popular version of Russell paracheic is: "There is a hairdresser in the village. He gave himself a rule: 'Don't give all the articles giving you to myself'. Now I have to ask, this hairdresser should not What should I happen? " If you try to answer this question, you will find weird things: this problem itself seems impossible! It is because of this strange logic, philosopher Russell has subverted the basis of the entire mathematical building!
Because there is contradiction in the collection, there is a fundamental contradiction throughout the mathematical system, but ironically, mathematics has been strictly known! This feeling seems to be just when you are proud, someone suddenly flashes you a slap! In a panic, I started to gradually stabilize the way to find the way to avoid Russell paradox, and I always hope that the monsters like Russell paradox will be excluded from the exact math system. This is the reason why Hilbert has raised a mathematical program. He hopes to find a pro-system to rule out the paradox and save pure and beautiful math. Although Hilbert did not complete his dreams, he firmly believed that his dream is right.
However, how many years didn't have, a young logistician Gottel, a nameless, was completely smashed with Hilbert's dream. This is the later famous Gothic theorem! This theorem roughly: any of the mathematical system is not "perfect". In order to change, any mathematics system is dead. It has always needed to inject new axioms from the outside world to make it increasing, and it does not completely automatically avoid contradiction. The Gödel Theorem can say that the whole reversed people's worldview. Because it is considered to be the most "perfect" mathematics is incomplete, then the purely perfect world should not exist. The Gödel Theorem also pointed out the limit of "rationality" and "analysis" methods. This is the reason that later people entered the "comprehensive" era. More interesting is that Gotel uses the method of prove his theorem and Cantone proves that the real number is much more than natural, the method of Tulex shutdown and the paradox of Russell is a pulse. All of this is a big event in the first half of the 20th century, what happened later? The computer appeared, the information age is coming, it seems that science technology is universal, and they will always improve our lives and meet our desire. Gradually, people seem to have forgotten the idea of Masters, such as Tuling, Gendel, Condur. However, with the study of complexity in recent years, people have signs of regaining these relatively old and fundamental issues!
Second, the map spirit
The following is a matter of return, we start talking about the concept of the map. I first give you the model of the map spirit. Although it is a bit boring, please insist on seeing, I will use everyone to reinterpret the form. Here you just need to know its outline. A charter is a device like the following:
This device consists of several parts: an infinite tape, a read writing. (That big box in the middle), internal state (blocks on the box, such as A, B, E, H), and another program controls this box. This device is read and written, moved according to the command of the program and its internal state.
It is this time when it works: reads a checkered message from the read writing on the paper tape, and check the program based on its current internal state, then draw an output action, that is, whether it is paper With write information, or move the read and write to the next checkered. The program will also tell it which one is transferred to the internal state next time.
The specific program is a list, also called rule table, which is like this:
Current internal state S input value i output action o Next time internal state S '
B 1 forward C
A 0 written onto the paper tape 1 B
C 0 rear
... ...
Therefore, the map spirit can determine the internal state and output operation of the next time according to the information read by the writing head and the current internal state, according to the information read by each time and the current internal state.
The map spirit is so simple! Incredible? As long as you change its procedure (that is, the above rule table), it may work for any computer to do any computer. So it can be said that the map spirit is a simplest computer model!
Maybe, you will feel that the map spirit model is too simple, how can it complete the complicated task of the computer? The key to the problem is how to understand this model.
Third, how to understand the map spirit?
1, the metaphor of the bug
We may wish to consider such a problem. Suppose a bug climbed on the ground, then how should we build its model from the perspective of the bug information?
First, we need to model the environment in which the bug is located. We may wish to assume that the world in which the worm is in an infinite paper strip. This paper belt is divided into a number of small squares, and each checkered is only black and white color. Obviously, this bug has to have the eyes or nose or ears, etc. I feel the information of the world to get the world, and we may wish to simplify the model, assume it just a feeling of feeling: eyes, and its vision is pitiful, that is, It is only able to feel the color of the checkered in it. Therefore, the black or white information in this checkered position is the input information of the worm. In addition, we must of course also need to establish an output device for a worm, which means it can move. We still consider the simplest case: the output action of the bug is to climb a checkered or back to the paper tape.
Only the input device and the output device are not movable. The reason is simple, it does not know how to choose its output action in a variety of situations. So we need to give it to specify the rules of action, this is the program! Suppose we record the input information of the beewwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwfish, white}, its output of possible action is: o = {front movement, rear shift}, then the program is to tell it to input, such as black In case, it should choose what output. Thus, a program is a mapping from i collection to the O collection. We can also use the list of procedures, such as:
Program 1:
input Output
Black forward
White post-shift
This program is very simple, it tells the beewbit to take a chewwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwworms, and then retreated one after reading a white checkered.
We may wish to assume that a piece of the world in the bug is: black black white and white ..., the bug starts from the left end.
So how will the small insects read this piece? It first reads black, then moves a checkered in front of the program, so it will get another black information. At this time it will move it again according to the program again, it is still black, then move forward, this time you read white Checkered, according to the procedure it should be retired, this time the input is black, forward, white, back shift ..., it can be presented that the bug will be infinitely loop.
However, the insects in the real world will definitely not be so stupid to loop there. We also need to improve this simplest model. First, we know that insects can be mechanically moving in the world.
......
Start
It is influential, thereby changing this world. For example, the bug has a food next to it, it will eat the thing. In our model, it is equivalent to we must assume that the insects can rewrite the information on the paper tape. Thus, the possible output set of bugs becomes: o = {front movement, post-shifting, black, coated. At this time, we can change the program 1 to such as:
Program 2:
input Output
Blackhead
White
The paper strip is black and white and white ... how will bugs act? The following figure shows the position of each step in this example (the square is marked with a dot is the current position of the worm), and the condition of the paper strip.
Start: The bug is on the leftmost square, according to the first line of the program, reading black should be forwarded.
Step 2: Still reading black, according to the first line of the program, forward movement.
Step 3: This time, it is white. According to the second line of the program, it should be black, and there is no other action. Assume that this picture is still unoccupied, and it is expressed in next time.
Step 4: The current square is already black, so the bug reads in black checkered and moves forward. Step 5: Read the white, black square, not movable.
Step 6: The current square has been black and continues to move forward.
Step 7: Read in black, forward movement
The movement of the bug will continue ... We see that the bug will continue to go forward, and will apply all the paper with all the paper strips.
Obviously, you can also design other programs, but no matter how complicated your program, no matter the paper
......
......
......
......
......
......
......
In the case of, the behavior of the bug will either stay in a square, or move forward forever in a direction, or in a few squares. However, no matter what, the worm is compared to the bug in the real world, there is a fatal weak point: that is if you give it a fixed input message, it will give you a fixed output information! Because we know that the program is solid, it is time to move once, no matter how it is just a checkered, without making other reactions. It seems really mechanical!
If we further change the bug model, it will improve, at least in the case of given the same input, there will be different outputs. This is the internal state of adding a worm! We can make such a metaphor: assume that the black checkered is food, the bug can eat it, and when you eat a food, the small bug will feel full. When the read information is white, although there is no food but it is still full, it will only feel hungry when it is read again. Thus, we said that the bugs have two internal states and the collection of the internal state is: s = {hunger, eat full. In this case, the insect behavior will not only be based on its input information, but also determine its output action according to its current internal state, and change its internal state. And this action still uses program control, but it is more complicated to the above program, and now the program is more complex, such as:
Program 3:
Enter the internal state of the current internal state output
Black hunger, white food
Black eating and hungry
White hunger
White eats full
This procedure is more complicated, there are four lines, because you not only need to specify the movement of inwomen to take in each input, but also specify how small worms should act in each of the input and internal states. Look at our bugs in reading black and white ... What will happen when this paper? Still using the following series of figures, gray dots indicate hungerous bugs, white dots indicate that it is full. For clarity, we wrote the underworm to the state to be changed to the next line.
Assume that it is still starting from the left end, and the insect is hungry when the start is started. This is read in black, currently hungry, according to the first line of the procedure, put the checkered white, and become eating (this is equivalent to eating the food, pay attention to the insects).
Step 2: The current square has become white, and thus reading white, and the current state is full, then according to the fourth predecessor in the program, it is still full.
Step 3: Reading white, the current state is eating, and thus the second step of the second step is repeated.
......
Coated and white, become full
......
Front movement, still eat full
......
Top movement, keep eating
Step 4: Still repeat the last action.
Step 5: After reading black, the current state is full, this time according to the second line of the program, it should be subjected to the square, and transfer to the hunger; six step: read in white, current hunger, according to the third The line should be disintegrated, and keep the hunger (pay attention, this buzz seems to spit out food!);
In the seventh step, read black, current hunger, so put the checkered white, and transferred to a full state (huh, the bug has eaten the things you just spit out!).
In the eighth step, read it in white, you are now saturated, so forward movement, keep the eating state.
At this time, the situation is exactly the same as the fourth step, so the insect will repeat the action of 5, 6, 7, and 8 steps and will loop forever. It seems that the last black checkered is a threshold, and the blade does not have passed.
The behavior of bugs is complicated than previous procedures. Although from a long time, it still falls into the mechanical cycle or endless repetition. However, this is essentially completely different from the previous procedure, because when you enter the white information to the bug, it is not to predict! It is possible to apply black square. Of course, the premise is that you can't open the insects to see its internal structure, and you can't know its procedure, then what you see is a full-scale bug that cannot be predicted. If the number of the inner state of the worm increases, then its behavior will be more unpredictable!
Ok, if you have completely understand how our bug is working, then you have understood the working principle of the map spirit! Because in essence, the last bug model is a map spirit!
2, how to understand the map of the map *
Just used a bug, the working principle of the map spirit, I believe that your first reflection is that such a model is too simple! He does not explain any of the problems in the real world! Below, I have to try to convince you, the model of the map spirit is great!
First of all, what I want to say is, in fact, each of us will decide, people think that people can be abstracted as a map foreground.
Top movement, keep eating
Paint, transfer
......
Top movement, keep eating
......
After moving, become hungry
......
Dark, keep hunger
......
......
Why can this abstraction? First we can consider extending the bug model just mentioned. Because the worm model is started with all the simplified premises, it is indeed simple. However, we can expand the input set of the bug, the output action set, and the internal status collection, this model is more practical. First, inwife can be in a three-dimensional space rather than a simple sheet of paper. And the vision of the bug is very good, it can read the information of 500 meters in the square, of course, inwomen can have other sensory organs, such as smell, auditory, etc., and these changes are only expanded. Dimension and range, there is no other more essential change. The same truth, the possible output collection of bugs is also abnormal, but it can not only move yourself, but also to transform it. Further, the internal state of the bug may be very much, and the program that controls its behavior may be abnormally complicated, then what is the lesson? This is hard to say, because with the increase of the number of states within the bug, we are gradually losing the predictive ability of the small insect behavior with the increase in the complexity of its environment. But all of these changes still do not escape the model of the map: enter the collection, output collection, internal status, and fixed programs! That is, these four things have grasp the fundamental of undeter information processing.
Can we also have this abstraction? Obviously, the input status collection is that you can see, hear, smell, feelings, all possible outputs is your row, and all expressions you can express. . The internal status collection is much more complicated. Because we can regard any of the status portfolios of neurocytes as an internal state, then all possible combinations of nerve cells will be astronomical numbers! It seems that you will say that this model is not right, and there are still many things in the nature of the thinking. For example, memory issues, people have memory, is the map spirit? In fact, as long as the map spirit has an internal state, it has the corresponding memory. For example, the bugs with hunger and eating two states will remember the world they have experienced: If you eat food, you will use it to "remember" eating food. What is memory? If you have experienced a thing and remember it, then as long as your next action is different from the action before and you remember this thing, it means that the matter has an impact on you, Explain that you really remember it.
Is the problem of learning reflected in the model? What is learning? It seems that there is not a study in the map forever model, because learning means changes to the program, while the Charter is not able to change its program during operation. However, we are not difficult to suppose, you can't actually open a person's head, so it's actual procedure rules you don't know. It is very likely that the rules of a map spirit have not changed, but it activates its internal state, so its behavior has changed in nature, although give it the same input, it gives a completely different output, thus In our view, it seems to learn! In fact, the programs of this Turing machine have not changed.
There are still many phenomena that seem to be included by the map, what is human emotions, emotions? You can think of it as an internal state, so you are in a good mood, your input and output is a set of rules, and it is completely another set when the mood is not good. This still does not escape the model range of the map foreground.
The next question is that the thinking of our people is not the fixed procedure like the Charter? This problem seems to be an impossible, because people's behavior is too unfair! You can't predict it! However, I will argue, no matter how neuron pass information, the law of change is fixed, can be programmed, then as a whole of neurons: the operation of the brain must also follow the fixed rules are also the procedure. So, if this is the case, it is astronomical, and the human brain will not exceed the model of the map spirit, so artificial intelligence is also possible! However, I think the answer to this question is likely to be so simple, we will discuss this problem in the final detail.
Anyway, I believe that you can experience it, the map foreground model is actually very powerful!
Third, calculate
1, what is calculation
Said so much, although maybe you have already learned the power of the map foreground, maybe I will be suspicious, however, you must still do not see what the chart and calculation is related. In fact, the map spirit is a theoretical computer model, its most master
It is still in calculation! So, let's take a look at what is calculation!
I can give a very modern understanding of the computing concept: a function change, if the change is changed into f (x) is a calculation! If we regard everything as information, then more accurate, calculation is the transformation of information! If you use this view, you will find that in fact, the nature is full of calculations! If we throw a small ball into the ground, the ball is playing again, so the earth has completed a calculation of the ball. Because you can completely abstract into information, it is nothing more than some, speed, shape, etc. can use information to describe the information, and the earth puts the little ball, nothing more than this information on the ball. In a certain change, the earth has completed a calculation! You can think of the whole land as a system, and the ball that throws down is the input to this system. So the ball that bounce back is the output of the system, and it can also be said that the calculation is a system completed once. Enter the transformation of the output! This is not tight, you will find that the real world is calculated! Because we can completely abstract the process of all nature into such an input and output system, all the variables of all nature are regarded as information, so calculation is not! It is also true that it is a view that there is a possibility of what DNA computer, bio computer, quantum computer, these fresh play in foreign countries! Because people put DNA chemical reactions, the wave function transformation of the quantum world is considered calculated, and naturally, it will combine these calculations to form a computer. However, it seems that our theorists are still trying to prove a certain theorem for the mapground, but it is not aware that the calculation is actually simple!
Below back to the map spirit! Why is the map forever is a computing device? Very simple, the map spirit is also a system that transforms the input information to the output information. For example, the bugs mentioned earlier, a checkered color information on the paper tape is the input of the bug, and the actions taken by the bug are its output. But then you will find that it seems that the output of the beafwhewworm is too simple. Because it has only a few simple output actions. However, don't forget, the complexity comes from the combination! Although the output movement of each small worm is simple, it is possible to be very complicated when all of these output movements are combined. For example, we can regard the paper strip of the initial moment as input information, then after a long time, for 100 years, the insects have been output by the information whose last smeared paper strip is the output information. Then the buffer is completed, it is calculated. In fact, in the formal definition of the map foreground, there is a so-called downtime. When the map spirit is a stopped state, we think that it is calculated, so it is not necessary to wait for 100 years.
2. Computing combination
More interest in, we can combine several computing systems to make a larger computing system. For example, the little ball is, if you put a seesaw on the ground, this ball will fell to the other end of this seesaw, and the other side of the seesaw may still be a small ball, so this ball will be bounced again. Take another seesaw ...
We naturally can complete a larger calculation by combining several map foregrounds. If a map spirit is input to another map spirit, then enter another picture spirit ..., this is Combine the calculation! Maybe you still worry about the unlimited internal state of the earlier, so now, you don't really understand, in fact, we don't need to write an infinitely complex program list, but only these maps Combination can produce complex behavior.
With the combination of the map spirit, we can start construct complex Turing machine from the easiest way of illustration. So what is the easiest way of Junchair? We know that the simplest information is 0 and 1, and the simplest calculation is the Boolean calculation for 0 or 1. Boolean operations are inherently inherent: with, or, not. From the simplest logic operation, we can actually construct any map forever! This is not difficult to understand: Any diagram can perform input, output information 01 encoding, and any transformation can eventually decompose into transformation of 01 encoding, and all calculations encoded to 01 can be decomposed into the previous Three operations. Perhaps now you understand why people who study your computer have to study the basic Boolean circuit. The mystery is that the use of the Boolean circuit can be combined! 3, conquer unlimited ways!
Recalling how you learn how to learn to operate. When you start, you will only die hard. For example, you remember 1 1 = 2, remember 2 4 = 6, .... However, no matter how much fixed number is remembered, you don't call the addition. The reason is very simple, if you remember the N logarithd addition, then I will always take the N 1 log that you didn't remember, so you still don't calculate. In principle. The number of natural numbers is endless, so any two numbers can also be infinite, and if we use a hard-back hard to remember, how can we remember the calculation of endless numbers? But with the growth of age, you will finally learn the addition operation! It's strange, you must understand that in fact, the additional operation does not need to remember the results of all numbers, but only need to remember any two numbers within 10, and know that the carrying rules can be.
How did you do it? Suppose you want to calculate the results of 32 69, you will write 32 to a line, write 69 to the next line, and then align them. So you start calculating 2 9 = 11, enter one bit, then calculate 3 1 = 10, then calculate 9 1 = 10 and then enter one bit, and finally, the results of each of the calculations are quite The final answer 101. This simple example gives us inspiration: the process of doing the method is a mechanical calculation process, where input is 32 and 69, the output is 101. Your program rules are specific to the number of numbers within any two 10. This way, you can calculate the addition of two numbers based on the fixed addition computing program.
I don't know if you find it, this method of calculating the addition will let you find a way to use limited rules to deal with unlimited possible situation! What we just said, in fact, the natural number is unlimited, so all possible addition results are also unlimited. However, use the operation method just mentioned, whether the number of input numbers is, as long as you write the number to calculate, you must calculate the final result without having to die hard. All addition!
Therefore, it is possible to calculate this simple concept, which is a way to deal with unlimited ways! Let's take another example: if you give you a number of sets: 1, 2 3, 6 5, 10 18, 36, these 4 pairs, what is the number of 102 corresponding to you? Obviously, if only the knowledge you have known, it is impossible to know the answer, because there is no knowledge of the 102 corresponding to the number. However, if you have a program rule that generates this group, it is to see that if the first number is X, then the second number is 2X, you must know that 102 corresponds to 204. That is, you actually use 2X these two characters to remember all such numbers such as 1, 2 3, 6 102, 204.
This seems to be very strange. How can I use limited characters to deal with unlimited species? In fact, when no one is asking you, you haven't stored 2X, and when I ask you 102? I am equivalent to entering you information: 102, and you are just a series of processing transformations based on this input information 102 to get the output information 204. Therefore, the input information is like the raw material, and your procedure rules are processing methods, only in raw materials, you can output the final product.
This makes me can't help but think of the expert system method. In fact, an expert system is a large rule base. It is also equivalent to a lot of special rules such as 1, 2 3, 6 5, 10. And no matter how much it stores, the total will be limited, you just find a problem that it is not stored, it will be powerful. Therefore, the expert system will fail when you ask 102, and there is a failure! How to solve the problem? People have come up with many ways, such as the method of the rules, in fact, the email is equivalent to the procedures that have just been calculated, or 2X. Using meta rules can indeed respond to infinite cases. So, this is why you ask if there are any two numbers of computers, which can always give your correct answer, although it doesn't have to remember all these additional information.
However, is it just a meta-rule to solve all problems?
If you give you three groups, arrange a table:
1, 2 3, 6 4, 8 100,200
3, 9 2, 6 8, 24 100, 300
1, 4 2, 8 3, 12 100, 400
So ask you on Chain 6, 3 this figure corresponds to how much? We must first find out the law of the first line is 2x no doubt, the second line? Is 3X, the third line is 4X, then the 6th line should be 7X, thus on the 6th line 3
It should correspond to 21! Here is not queued as before, although we get the rules of each line, such as the first line of 2X, but with the increase of the number of rows, this rule itself has changed, so the second line is 3X, the third line is 4X, etc., so we have received a rule itself, that is, if the number of rows is n, then the rule of this line is (n 1) x. We obviously be calculated based on the input N and X. Put this in the expert system, this principle is the rules of the rules, the rules of the rules of the rules ... should be endless! However, the expert system itself does not automatically summarizes these rules, and people must write these royal rules to the program in advance, which is the largest drawback of the expert system. And we seem to always attribute rules in some individual events. Further, can machines can be summarized? This is equivalent to saying: Can you program a program for the summary method? This is also a very interesting question, which will be discussed in detail below! It is conceivable that if we find the truly summary method, then write such a program, it will learn from himself. We don't have to prepare procedures and rules again. This is the ultimate goal of artificial intelligence!
4, summary *
I remember Jin Daxia in his martial arts novel: "Ying Tian Dragon Slayer" has told such a story: Wulin Tailou Zhang Sanfeng is in anxious to teach his new martial arts "Taijiquan" to the new show Zhang Wuji. In addition to a superb "internal success", Zhang has a very high understanding of martial arts. Therefore, when Zhang Sanfeng gave him a Taijiquan, he remembered all the moves and re-hit the Taijiquan to Zhang Sanfeng on the spot. In the process of Zhang Wujian, Zhang Sanfeng asked him a question: "You have forgotten a few tricks?" His answer makes others unpractory, because he is there to try to figure out the mysteries of Taijiquan, more and more people who have forgotten. The people next to it do not understand, such a learning method is so fast, how can I learn martial arts? However, how long, Zhang Wu said that he has forgotten all the moves. Zhang Sanfeng said with a smile: "Yes, you finally learned the 'Taijiquan'." From this example, what have we seen? Zhang Wuji can learn to be Tai Chi, it is because he has been able to abstract a higher level of martial arts law from the specific one, and thus, when he has forgotten all the tangible martial arts tricks, It has already mastered the essence of Tai Chi. The Taiji martial arts pay attention to the power to fight, with Jouchi. To put it bluntly, I didn't have a fixed trick in advance, and I waited until the enemy attacked me again to generate cracking trisss.
In the map foreground model, we are not difficult to find that if specific martial arts recruits are metaphor, it should be the output of the tricks into the map spirit, so the Terrace is trying to fight, and the method of Jouchi is actually Similar to the 2X Turing program that is speaking on the previous section! Therefore, the process of Zhang Wuji Temple's Temperature is a process from a special input and output to a general algorithm. It can also be said that Zhang Wuji uses the summary learning method!
However, carefully observe the narrative of the previous section, we will find it. Although the Tri Machine can calculate the results of 2X, the abstract 2X itself is not automatically generated by the machine, but it is necessary for our external people to program. So, in the face of such a problem, can the Tri Machine can summon thinking like Zhang Wuji?
It can be envisioned that if the computer really has no one, we can save more people! We don't even need to make a computers, which will automatically summarize the general general rules from several specific examples. However, can the computer have real summation? Let us take a closer think about this problem.
We said that if the computer can be automatically summarized, we can write a program P for the induction method. This program can be understood as input is some special number, and the output is the program that can generate these number pairs. That is to say, the specifically "recruitment" is input, and the general rules of these "recruitions" are output. If the program P really can summarize itself, then P will inevitably pay out the law. We have discussed, in fact, any program can be seen as an input to the input. Then the program P is natural. Suppose these pairs of pairs (A, B), (C, D), (E, F), ... are all input and output of the program P, then we pick out 1000 (in turn is enough). Enter this 1000 special circumstances into the P, then P should be able to generate the commonality of these pairs, that is, Pershable! In other words, the program P produces itself, and P will give himself out! This seems to fall into the strange circle! In addition, our humanity is designed to p, if P can sum up all the laws, then p can also summarize "people"
Said to P "It is still a rule of itself! This problem seems to have a lot. In turn, if it is assumed to pay out the regular program P does not exist, then why do our human beings can always return the law? What is The specific problem is indexable, what is the problem is unreasonable? However, these seemingly important issues have no uniform answer yet! We will also see that many problems involve the logic of the strange circle, but due to calculation Theory has touched the root of logic and information, so the directive logic strange circle is not surprising.
Fourth, simulation
1, what is the simulation?
What is an simulation? Another basic problem, Einstein said, the more basic concepts, the more it is difficult to draw. Simulation This concept is a difficult problem.
If you stand in front of a friend, I have done some ghost faces. Then he will learn your move, then he has analog you to simulate you.
Obviously, there is a series of correspondence between you and your friends: Your hand corresponds to his hand, your eyes correspond to its eyes, your mouth corresponds to his mouth .... And your hand, your eyes, the movement of your mouth will also correspond to his hand, your eyes, and your mouth. Therefore, the key to the simulation is corresponding! If the elements in the collection A can completely correspond to the elements in B, then A can simulate B.
An example of being a ghost face in your friends, if this time you make the face and the actions are not immediately imitated but have been recorded by him with some symbolic language. For example: "X-month X day, madman XX rushed me to make a ghost face: he stretched out the left handicon finger to put the meat on the right eye, and spit out his long tongue!". After the day, after your friend took out the diary, follow the above description, I did this. Obviously he still simulates your movements at the time. So, is your friend's diary? Isn't the dialogue of your face action? It seems that the answer is because this text does not have a half similar image. However, your friends are in accordance with this description of the simulation of the face action. In other words, he translated the text into his movements, and his action is the simulation of you. The process of this translation is obviously a transformation of some kind of information, we can understand it as a calculated process, that is, the algorithm process that can be implemented by the map spirit. Therefore, we said that the instructions on the diary also constitute an simulation of your face action because this information is also corresponding to your polish face action. Specifically, we can use the following figure:
Here A is your face action, B is the face action made by your friend, and C is a description of the diary. Your friend's action B simulates your action a, and the action information of B is obtained by executing the description of C, that is, there is a transformation of information from C to B. This way we believe that C is also analog A.
2, simulation between the map spirit
The following is to consider the simulation between the map. According to the previous definition, a diagram spirit includes: input set I, output set O, internal status set S, and program rule table T four elements. Then, if the elements between the two charters have the corresponding relationships, they believe that the two maps can simulate each other. However, the function of the map spirit is to complete the calculation of the input information to obtain the output information. We care about the correspondence between the input and outputs. Thus, one map foreground A. If you want to simulate b, it is not necessarily to simulate all input, output, internal state, and program rules.
A
B
C
simulation
Transform
simulation
Table these elements, but as long as they are given input information, it is possible to simulate the output information of B.
Therefore, we can use the following graph to represent the simulation between the map spirit:
That is to say, when the same input information is given, as long as the output information O 'can analog information O, it is considered that B simulates A. The information o 'simulation of information o conforms to the definition of our superior collection between generalities. That is to say, if there is another diagram spirit that can calculate the information o 'and map into information O, it is considered to simulate O. To put it bluntly, O 'can be different from o, but as long as you can convert O' to the same O ', it is considered o' to simulate O. Thus, the map spirit is simulated in the map forever. Further, we can assume that the information entered by A and B is different, one i, the other is I ', then there is also analog correspondence between I and I', we still think that B can simulate A. That is, the following figure:
One thing to pay attention to, if the A Tunnel is simulated, then it is not necessarily a B figure spirit to simulate a map spirit. Because there is a possibility that the information is more than the information processed than the B T. That is, if the information processed by B can be 1, 2, 3, 4, and the information of the A process is outside the four numbers, and there are 5, 6, 7, 8, then obviously when the input 1234 is a Analog B, while B is not defined when entering 5678, can not complete any operation. At this time B obviously can't simulate A.
3, calculate equivalence
What is the use of so many knowledge about simulation? A key role of simulation is to clarify what is equivalent. For example, in order to complete the additional operation, you wrote a program, and I also wrote another program, although we may be completely different, but as long as the two programs can be mutually simulated, it is given Two numbers, we all calculate them correctly, then we are equivalent to the two programs!
Specifically, if A can simulate B, and B can also simulate A, then A and B are calculated equivalents. Calculating equivalents is very powerful because it reveals a very common law in our universe. We still use the addition algorithm just mentioned as an example. Although the method of calculating two numbers may have an endless, it is also possible to achieve a variety of computer languages, what C, Basic, Java, etc., it is more likely to run on different computers, however all of these The results of these calculations are the same. That is to say, all computer programs that calculate the equivalent calculation algorithm are all things, so the addition algorithm is a certain eternal and independent!
Look! We found some kind of eternal life in the universe, which reflects some essential in the law of the universe.
Enter information i
Figure foreground A
Figure foreground B
Output information O
Output information o '
simulation
simulation
simulation
simulation
Output information o '
Output information O
Figure foreground B
Figure foreground A
Enter information i
Enter information I '
simulation
nice! The calculation is equivalent to the law of conservation of energy, I even think that the calculation is more equivalent to the law of conservation of energy! Because the rule of energy conservation is still to portray a certain property of the physical system, calculating the equivalence of equivalence is a very extensive conservation and symmetry between the very extensive information system, and all systems can be abstract The system, even the material world, so calculation is equivalent to some advanced symmetrical, eternal, beautiful things across all systems.
In order to further understand the power of calculation and equivalence, we may wish to science. Suppose we can use a computer to simulate someone, such as Zhang San's thinking process (that is, hypotheses that true artificial intelligence can be achieved). That means that we can use a computer software x to complete the simulation of Zhang Sanzi. In this way, this software will implement the thinking process of Zhang San this person on everything that has calculated equivalence. For example, we are completely likely to collide a lot of molecules to realize X-this software, then complete the simulation of Zhang Sanzi in the process of this large pile of molecular collision, that is, Zhang San's will of this person. A large pile of molecular systems go! Further, we can also find enough people such as all people on this planet to simulate the collision of the large pile of molecules, thereby completing the calculation of software X. what does this mean? It means that Zhang San's thinking or consciousness is in the group of people! It is very likely that these people constituting software X don't realize the emergence of the awareness of their upper level. More interesting is that Zhang San is very likely to be in that group! I believe that you have been able to refer to the power of calculation, then I also believe that you can understand why any computer we use is just a Turn machine.
4, meaning *
Consider the following three sentences: "Please close the window!", "Please close the window!", "01001110111". These three sentences say three people in different rooms, respectively. The first sentence tells a Chinese, so he closed the window; the second sentence told an British, he also closed the window; the third sentence tells a robot, he also closed the window. These three sentences are obviously different from the surface, but when they let different people come to listen, they have reached the same final result: the window is closed. So, we will naturally think, what is the same? Obviously, the answer is their meaning. But what is it meaningful?
The essence of truly answering significance is a very difficult problem, and now people are trying to understand what semantics. Although we still have not fully answered this problem, it may wish to consider this problem from the views of the map spirit, calculations, and calculate equivalents. If Chinese people, British, robots are viewed as a map spirit, and the three sentences are regarded as the input information for them, then the final result is the output of the Chart Ling Machine. At this time, we saw three results were the same. That is, it is possible to simulate each other.
Considering these three sentences, it is clear that they all have the same meaning. According to the previous description, the map of the mutual simulation is equivalent to equivalence. Thus, after listening to the closed window instruction, the map spirit acts in accordance with the instructions has the same calculation equivalence. And this calculation is equivalent to the first-mentioned addition rule, which is independent of the computing system, executing agency. Thus, we can get the following picture:
Through this comparative map, we don't have to conclusion: the meaning of the so-called language is to implement the calculation of this language system!
How do we know that different languages express the same meaning? Obviously, we can understand that "Please close the window" and "please close the window" is the same, and the work made by the translation is nothing more than entering Chinese information to output English information such as information conversion work, thus A calculation process!
However, when there is no translation from a language to another language, we can't determine whether a symbol sequence is meaningful for a fixed map spirit. That is to say, although we can't understand what the bird is what mean, but does not deny that their call may make sense, because only birdself can understand the meaning of the sound.
Five, universal figure
1, encoding
In fact, this "universal figure spirit" I said is the "General Trimplate" in computer terms, and English is Universal Turing Machine. And I said it is "universal figure spirit" is complete because this name seems to be more intuitive. The concept of simulation has been described earlier, then it will naturally produce such a problem: there is no map spirit that can simulate all other map foresses? The answer is present. This map spirit that can simulate all other maps is called a general map spirit, which is what we said "Universal Turing Machine". This type of machine is in this area, it is universal!
How will "universal figure spirit" work? If I entered the information x into the map forever M, m can calculate a result O. So if I entered X and M information to the universal map forever, then the multi-player will also output O, which is that the universal map of the chart can simulate any special map forever. In this way, we can "change the" universal charting machine "rules only by changing the values of input X and M. Therefore, it can also be considered that the universal charter can be programmed. The two words here are quoted, because any Turing machine can't change after the rules after birth, so we can change the rules of "universal map forever", just because it seems like this, in fact No change.
To explain why "Universal Chart Ling Machine" exists, and how it simulates any other map of the opportunity, we must first understand how to enter any of the map spirit into the "Universal Chartling Machine", this needs Understanding the concept of the encoding. What is encoding? You can understand that the number is encoded for a number of things.
In fact, each of us is dealing with the code every day. Everyone has an ID card, and this identity card has one
Language
Executor
Please close the window!
Chinese people
Please close the window!
British
01001110111
robot
Consent
Consent
Equivalence
Equivalence
The same part:
significance
Calculate equivalence
Input instruction
Input instruction
Input instruction
A ID number? Then this number is your number. When I was in school, I assigned a student number to each of us.
26 letters can be encoded, such as A correspondence 1, b corresponds to 2, ..., this is obvious. However, any English word can be encoded, it is not so easy to see. In fact, we can list all words in order to dictionary. That is to say, the shorter the words of the letter, the shorter the character length, and the word is long, and the letter is ranked behind. For example, a possible dictionary order:
A, About, An ..., Bad, Be, Behave ... ..
As long as there is such a row, we can give each word to a number, the simplest method is to assign 1, the second assignment 2, ..., so we give all the words. .
The discussion below will not be encoded. We assume that all the inputs of all the maps of the discussion are only 0,1, and its output is only 0, 1, 2, 3 four movements represent forward movement, post-shift, painting 0, and write 1 . The number of internal states is up to 10,000 (there are more enough). The program is considered below.
Suppose the charter table of the map is:
Current internal state S input value i output action o Next time internal state S '
2 1 0 3
1 0 3 2
3 0 1 1
... ...
Then we can write it to a row, this is 2, 1, 0, 3; 1, 0, 4, 2; 3, 0, 1, 1, pay attention to "," separately, input values, output The state of the action and next time, and ";" separates a row of specific procedures. This way, no matter how big this table, we can write it into such a string. This string is equivalent to an English word, which is a description of the Turai program. Similarly, other map foregrounds can also get such a word description, then we re-encode these descriptions with a word, which is also encoded for all maps. If the encoding of a map is M, the information it read is X, which simply uses "." Separated by ".", The method is separated from the method into the "universal map spirit", and the special algorithm is applied. This universal machine can derive the simulation result for M calculation X. In fact, it can be proved by the agencies that the universal charter is exist for any coding. Here we do not describe the proof process.
2, self-suite
Since the "Universal Chart Ling Machine" can simulate any of the action of a map spirit, can it simulate its own actions? The answer is yes. We first saw the "universal chart forever" is also a map spirit, and there is a set of fixed input, output, state, and fixed procedures, so it can also be encoded. So we can input it your own encoded information to it yourself. This is like a snake bites his tail. What happens? It will produce a strange circle, although we haven't seen any bad signs now, but in the next section, we will see what conclusions will be born in this strange circle. And we will also see that this strange circle is related to the Canton diagonal rule, the Gö der theorem.
Once the Tu Line can read the program as data to write, there will be a lot of interesting situations. First of all, there is a diagram spirit that can complete self-replication! In fact, the computer virus is doing this! We will express how this special map spirit is constructed. We assume that if a map spirit is X, then its encoding is recorded as
Then the "universal chart forever" can output Print to the paper strip, and x and The content will be exchanged before and after, and the agencies ensure that such a chart is present. Thus when B is read to the information on the paper strip, it will print out the encoding of the map spirit that can print is , and then the and positions are constituted. , so P puts itself a copy. It seems that this self-replication program is impossible, because this contains an endless strange circle. P To generate itself means that at least P> contains at least one , and this contains at least one ..., the last P is inevitably an infinite program, however We can prove that P is possible. With a lot of interesting conclusions, it is possible to have a large group of map spirit, let them collide with each other. When you encounter a piece, a map spirit can read another map forever. Code and modify the encoding of this map. So what will this be like this to "soup"? Fang Dana, the San Tami Institute, has studied this experiment and has got an amazing conclusion: in such a system, it will be born, self-maintained, self-maintenance, and the complex tissue of life, and these organizations can further unite. Composition of larger organization! Six, shutdown issues 1, dead cycle Let's take a look at a very simple guessing game before going on formally discussed. If I have a coin in my two fists, the other is not, then let you guess which one? So you told me there in your left hand. At this time, I won't open your hand, but let's take a hands and feet, then reach the fist, open your hand! Ha, you are wrong, the coins are in the right hand! Probably fool can see my trick! Needless to say, I adopt this method I guarantee a hundred wins. Because I am always waiting for you to change my strategy after which one has a coin. Therefore, the state after this change is no longer guess. Probably you will feel incredible: In fact, the problematic shutdown problem is a principle similar to the game! Let's take a look at what is going on. Let us consider such a problem: there is no program, such as P, can determine whether any program X will fall into a dead cycle in the case of input Y? We may wish to set P (x, y) to indicate that the P judgaration is X. The data is Y. If there is a dead cycle, then P (x, y) outputs a YES. If there is no dead cycle, then p (x, y) outputs a NO. Our question is this P (X, Y) existence? This is a shutdown issue. The so-called a program x is stopping Y, it is said that X does not have a dead cycle. In turn, if it doesn't stop, there is a dead cycle, so it is a matter of stopping and death. So, is this program P existing in this judgment problem? The answer does not exist. Below I can prove my conclusion. We may wish to assume that the program P exists. Then we can design a new program Q in P, as follows: X is any program code: Program Q (x) { M = P (x, x) Do while (m = no) ... ... End DO IF m = YES TEN RETURN } In this program, it is: Enter any program x, call function p (x, x) and get the return value M, if m = NO, that is, according to the definition of P, P determined that the program X acts to itself There is no dead cycle on the XX. Then q will not stop the statement between do while and end do. If M = YES, we know that this means that P is determined that the program X is dead cycle on X. Return, end the function. We can see that the function q (x) of this definition is no problem. Let's go to the key moment: We ask Q (q) whether Q (Q) will die on the Q (Q) will not die. Of course, we can use strong function P (q, q) to calculate this problem. Suppose Q (Q) will die, then p (q, q) will return yes. However, according to the definition of the Q function, the x = Q will then find Yes that will be returned due to P (Q, Q), that is, M = YES, so the Q function will end immediately, that is, the program Q (Q) did not have death. cycle. However, if Q (Q) does not have a dead cycle, P (q, q) should return NO, so according to the definition of Q function, the x = Q will be entered in Q (Q), so that the program is Will go to the Do While cycle, and this cycle is clearly a dead cycle. Therefore, Q (Q) has a dead cycle! This also leads to contradictions. Whether q (q) will not have a dead cycle, there will be contradictions, but where is wrong? The answer can only be the first premise, that is to say that our most started hypothesis P (x, y) can determine whether any program X is incorrect when entering Y, is wrong! That is to say such a program P (x, y) does not exist! 2, how to understand Maybe you will feel a little weird, why doesn't there be such a P (X, Y) program? Only P (X, Y) in the above argumentation will cause contradictions when they act to P (Q, Q). It doesn't seem to explain whether the P acts cannot be judged in other programs. For example, you can consider writing such a program, when a program do while (t) is discovered, here T is always true, this sentence is when it appears, it is judged that this program has a dead cycle. This is obviously possible. But the key to the problem is that you assume that P (x, y) can determine whether any one of the programs is dead! The most critical is this "any program". Because if you have written a program P to determine if a program P is written in accordance with the judgment of the DO While (T) statement, then I will build a program Q according to your program P, That is to use the argument method mentioned above, we may wish to write to qp (the meaning of the subscript P "means the Q) constructed according to your program P). So your P is in a strange thing in P (Q, Q)! Maybe you still don't have to pass, so you improve your program to become P ', this time P' can determine all the procedures that contain qp. Then I will build an updated QP 'according to your new program P', your program P 'still can't judge, of course, you can also construct p' ', p' '', ..., I will follow. Construct qp '', qp '', ..., in turn, this process is endless! Because I always construct the program, so you are water, I am a boat, the water is boat, I can always be higher than you! This is like the game that guess the coin that I just started. You want to guess my coins, you must tell me that an answer is the left hand or the right hand, but the key issue is that I can always adjust dynamic adjustment according to your answer, so that you will never guess! The same is true for shutdown, I can always construct your question in your program P Q, I will always win! Very simple, because you should always construct a good P, it is equivalent to saying that the coin is in the hand! 3, diagonal deletion method I mentioned the Tuling shutdown when I started, Gotel, etc., from Canto's diagonal deletion. So let's take a look, how can I prove the Magine shutdown if I use the diagonal deletion? With this new proof idea, maybe you will be more clearly recognized that the nature of the shutdown issue is. The problem has not changed, whether there is a program P (x, y) to determine whether any program X is dead cycle when entering Y, or whether it is stopped. We still use anti-confidence, assuming that such p (x, y) is present. And we know that the program x itself can be edited Codes. That is, you can numbered all the programs: 1, 2, 3, ..., and the data Y itself is also such numbers 1, 2, 3, ..., so we can arrange each pair of X and Y In a table. For example, the columns are indicated by the data Y, and the line indicates that the programs x, such that the value of p (x, y) is also YES or NO, which can be written on the corresponding position of the first line Y column, indicating P (X, Y) The result of determining the X acts in the input Y will die on the cycle. For example, the table below is an example: 1 2 3 4 5 6 ... Y ... 1 Yes No No Yes Yes NO ... YES ...... 2 no no yes yes no yes ...... NO ... ........................................................ X no yes no yes yes no ... yes ...... ........................................................ What is wrong here? We know that each of the tops of the above represents a determined program to achieve the results obtained by different data. For example, the result is the result given in 1, 2, 3, 4, ..., y, ..., is a sequence: NO, Yes, NO, Yes, Yes, NO, ..., Yes, ... Below we picked out the elements on the table diagonal. That is to find those 1st column 1, second lines, second columns, ... This can get a sequence: Yes, NO, NO, YES, ... And according to this sequence we can fully construct such a counter sequence: NO, Yes, Yes, NO, ... That is to say, this sequence is different from the previous diagonal sequence on each bit! This sequence is called a diagonal deletion sequence. So I asked, this diagonal delete sequence is on a certain line in our table? the answer is negative! This sequence must not be in the table. Because its first element is different from 1, 1, the second element is different from 2, 2, .... In order to explain: Assume that the diagonal deletion sequence is indeed listed on the table, then this sequence necessarily in a fixed line, such as the 1001th line. Then we will consider this elements of this 1001th line, 1001 column, we know that the element in the corresponding table according to the sequence is different from the elements in the sequence! Thus, there is a contradiction, that is, this constructed diagonal deletion sequence is not in the table! We can fully design a program Q makes q acts at 1, 2, ..., x, ..., the sequence generated on the diagonal deletion sequence, and the diagonal deletion sequence does not mean that the program P does not It is judged whether or not the program Q acts on any input. In fact, the program q here is the program Q for the previous session of the card. What is wrong with the proof method of deleting a diagonal? Error is that there is a complete table that can get such a full table, this table calculates all the programs to the answer. 4, what mean? We have seen it, there is indeed a type of problem we can construct it, and the map spirit is not solved. We know that the problem that the map spirit can't solve is the problem that all computers cannot solve, so such problems are also called uncapable. Therefore, there is inevitable to have the limit of the computer. In fact, use the price-equivalent principle of the calculation of our previous narrative, there are many problems that can be summed up as the Tulex stop problem, that is, the Tulex shutdown reveals something in the universe, all those computers cannot solve. Question From Essentially and Tulex Purchase Problem is calculated. For example, the 10th question 10 of Hilbert, which we mentioned at the beginning, it is a typical non-calculated problem! There are many problems that are uncapable, especially those involving all programs. For example, if there is a program to check if all the computer programs will be wrong? This is a very practical problem. We all know that the computer program is particularly prone to mistakes. In order to check the error of a computer program, our human beings must perform artificial inspections. Then I can invent a smart computer software, enter any computer program, this software will automatically help you check if the entered program is wrong? The answer remains do not exist. In fact, this problem can be proven to be substantially the same as the Tulex's shutdown! So our dreams are shattered! Tulex shutdown issues are also related to the unpredictability of complex systems. We always hope to predict the results of the complex system. Then I can invent a smart program, enter the rules of a complex system, and output the results of these rules? In principle, this kind of thing is impossible. It is also equivalent to the problem of Tulex shutdown. Therefore, the conclusion we have learned is: To figure out the results of a complex system, the only way is to actually operate such system, without any computer algorithm, can give the operation results of this system in advance. You may not agree with my point of view, because after all, we can invent a lot of ways to predict complex systems, without having to make complex systems to real operation. However, you still have not understood the questions here. We emphasize that there is no universal program to predict the operation results of all complex systems, but it does not say that there is no specific program to predict the results of a certain type of complex system. So how do this specific program get? Obviously we need to be programmed! That is to say, there is something that can't do some machines, and people can do it. This seems to have a heavy blow to artificially intelligent worship! Is artificial intelligence really impossible? Pengros once wrote a science: "Emperor New Brain" to demonstrate the impunity of artificial intelligence. The method it use is the logic we have. Because there is always a problem that can't be solved for any artificial intelligence program! But it seems that our human beings are not subject to this limit. We can always find if a program has a dead cycle, always finds a method of predicting a class of complex system, and we can also construct a problem such as Tulex shutdown. However, the facts are not as simple, and the opponents will argue immediately. In fact, for a specific person, such as Pengros, we can also use the front method to construct a problem that Pen Rose cannot solve! However, in fact, it is too much trouble to construct Pengros, and we just say that this problem is presented! Therefore, the computer is too unpopular, and people themselves are not superficial, so artificial intelligence is possible! Take a look at the arguments mentioned above seem to be very reasonable. Which one is correct? Do you really have a problem that someone does not solve the similar map spirit? In fact, if you want to completely answer this question, it is equivalent to ask if the limit of the graphic calculation is possible? How to transcend the charting machine shutdown problem? Below we will discuss this issue in detail. 5, surpassing the graphic calculation * We still use the game that guess the coin as an example. After a few rounds of guessing the game, you are already annoyed and think that this game is unfair. So you think of a coup to deal with me: Whenever I let you say that the coin is in the hand, you will talk about an answer, such as the left hand. At this time, I will move the coin in the right hand according to your answer. At this time, you hurry to say, wrong, I guess your coins in the right hand! I can't adjust the strategy again to the left hand again. You hurry again: Yes on your left hand! ....... That's it, you have learned my way, according to my strategy, constantly adjust your strategy, so I can't win you. Can you use this method to be more than a transcendeum shutdown? We have seen a process similar to this. If you write a program P to determine if all programs are downtime, then I can construct a program Q is your program can't be judged. At this time, I haven't ended yet. You construct a new program P 'according to my Q, but I can construct a program Q' still let your program P 'can't solve. But you didn't end, and it constructed a new program P '', I was constructed Q '' .... At first glance, it seems that this process does not explain any problem. The reason is very simple, I ask for constructing a fixed program P to determine if all programs are downtime. And you are not a specific real program, but a changing programs that are unfunctive and unfunctive! And your total changing program sequence always wants to change according to the program I constructed! First of all, it is worthy of that this method is to use this method. We can indeed surpass the map spirit. As long as you repeatedly convert our programs, it is impossible to find out what it cannot solve. However, on the other hand, we will be very disappointed: such a transformation process does not give a real program! We have only a changing program sequence, but Not a actual existing program! This is the key to the problem: To completely surpass the limitations of the map, we must abandon the realism of the program. In other words, the program has changed to itself every moment. So this kind of constantly changed is it its own strange? Human science for thousands of years has been studying. Whether it is atomic, molecular or computer program, they must be an individual in existence, in this premise, science can study it! If we study it, it has become not it itself, then science is powerful. However, I can't help but ask such a question: I really don't have a fixed existence. Is there anything in every moment? This problem seems to be an ancient philosophy. I remember that Hercuite has mentioned that one person can't step into the same river twice. I think he said that this is the problem: because the river is no longer itself every moment. The river is a whole group of flowing water droplets. At the time, these water drops are not moving, and there is a passage, and when you step into this river, all the water droplets may be different, then How can we say that the whole of these water drops is the same as the same river? Consider our people again. You are likely to take a photo of you at the age of 3 and said to your friends: "Look, I am 3 years old!". However, what does this sentence mean? It means that you are 3 years old when the photo is reflected, you are the same individual! However, how different you are 3 years old and now! We know that you are undoubtedly a whole of a large pile of cells. Basic physiological knowledge tells us that all cells in the human body will be updated every approximately four years. In other words, your cells are all filled, let alone how many four years are you worse than now in 3 years old? Why do you say that you are now you are now? This problem seems to be metaphysics, but I do now we should really treat this problem seriously. Despite the perspective of the analysis, you are indeed an individual, but the common sense tells us that these two are indeed the same person! That means that your individual is not a constant fixed cell, but a constitutive composite of a large pile of cells at an updated one. This configuration uses a largest pile of cells to maintain their existence every moment! What did we get? Combining the discussion of the surpassing machine, the discussion of the survey of the survey, it was found that the original people also had this kind of thing in the river of Heracitt just satisfied the requirements of the transcendence. That is to say, there is also the river of Heracitt, there is no other yourself at all times. It is so possible that a change law of a similar change is a similar change is not going to surpass its own Tuling shutdown, such illusory individuals can really surpass the map spirit! Summarize the previous discussion, we are not difficult to give conclusions, and a solid death can not be changed, it is impossible to transcend the limitations of the map, but if a program has changed every moment, it is not its own This program is able to surpass the map spirit. Contacting people, we can get: Because people at all times have become the changes in the changes in the time, people are surpassed! Remember one of the problems I mentioned in front: "Can the human brain information processing process can be expressed as a fixed program?" My answer here is negative! That is to say, the process of human brain information processing is not a fixed program! How to make true artificial intelligence? Obviously, we can't construct a simple program, but must use other methods, what is this method? I haven't conclusions yet! Seven, the unreasonable At this point, I have already introduced some important concepts about the map spirit, calculated theory, and shutdown. However, there are many important issues in the field of calculation theory that have not been introduced. But I have to pay according to my interest. In the process of introducing the entire introduction, I introduced the conclusions that people have already gotten. On the other hand, I tried to show some problems in solving to everyone. Recalling, these hanging problems include the following: 1. Is there a fixed program? Is the human brain have a fixed procedure? 2, how to use a computer program to summarize? Is there any life-saving algorithm for all things? 3, what is meaning, more exact, what is semantic? 4. Is the Tuling shutdown question not exceed? 5, is it possible to intelligence? There are still many problems not commented in this article, but I think it is also quite important. For example, how do we use the map foreground model to represent a general learning process? A number of small map foregrounds are how to automatically construct a larger map foreground (this is the process of all-in-one self-organizational)? How to use the drawing machine model with the drawing machine model? In addition, the recent computationalism has set up all the processes in the universe to the calculation process, that is, the map spirit is doing operations. So can we explore the essence of time and space from the perspective of the map spirit? We know that the other class of calculation theory is to explore the calculated time and spatial complexity, then what is the relationship between this calculation time and the time and space of this universe? I hope that in the new century, people will eventually answer these questions! There are many errors and missions in writing, and there may be many logical vulnerabilities. If you find it, please tell me, I can't help but thank you! July 2004 Ji Zhi Club:
