Beyond the Turing Machine -- On the possibility of Artificial Intelligence (1)

Beyond the Turing Machine -- On the possibility of Artificial Intelligence (1)

I think that artificial intelligence can be implemented in the logic thinking step, because logical thinking can be expressed in strings completely, and the Turing machine can set any unit to any value, which is complete, this is enough to describe logical thinking. Therefore, you can use a Turing Machine to implement logical thinking. Of course, the Turing opportunity is restricted by the incompleteness of Godel, but the logic system is also subject to the same constraints, so I think it is entirely possible to use a Turing Machine to implement logical thinking.

So what is the relationship between the essential mechanism of logical thinking and the Turing Machine? Does logical thinking adopt a mechanism similar to a Turing Machine? Einstein denies the possibility of Artificial Intelligence implementation, saying that machines can solve many problems, but they will never ask a question, but I think Einstein is wrong on this issue, for example, when a program crashes, it can be viewed as a question and output? It can also be viewed as a question. A question can be raised as a state of an automatic machine, or even any state point of an automatic machine can be viewed as a question, the problem and result can be described using strings, and the Turing machine can completely solve all string problems. Of course, the Turing machine will ask questions.

However, the capabilities of the Turing machine are still very limited. In addition, human beings have a way of thinking that is far beyond the logic of thinking and a higher level of intelligence. How can we achieve higher artificial intelligence and even real intelligence ?......

I have considered a lot in designing the Taiji language. In the future, I will introduce the concept of the Taiji machine, readers can imagine that there are countless Turing machines in the infinite space in the universe to form a huge computing system and a huge array of super-giant computers, however, such a huge system is still an infinitely small part of the Taiji machine ,......

(1) 0 smart, digital life

Many years ago, when I was building an algebra system, I found that the formula "0 to the power of 0 equals 1" is very mysterious. Y = 0 ^ X (^ represents the Multiplication Side) this statement has the ability to judge! We can determine whether the input is 0 or not. There are only two States in this formula: 1 and 0. If X is a base number of 0, 1 is returned. If the input is not 0, 0 is returned. Draw a dummy image. On the entire solid axis, only the Y value at the origin is 1, and the rest are coincident with the X axis ...... At that time, I suddenly came up with a very strange feeling that I was using this formula to determine whether a number was my own. At that moment, I suddenly felt the life of a number.

0 indicates whether the input is 0. This indicates the judgment capability! Determines whether a number is itself. The multiplication and multiplication operations are amazing! You can use y = 0 ^ (n-x) to determine whether a number is N. However, the formula is y = 0 ^ X.
At that time, I felt a zero life. The original 0 has a life! 0 is the symbol of life. If everything has spirit, it is reflected in mathematics that there are tens of thousands of 0 -- A = a + 0.

0 is equal to 1 to the power of 0. When 0 is aware of itself, it is a kind of life consciousness. Life must also be aware of its own existence, and life must be able to judge itself, however, y = 0 ^ X does. If you have self-consciousness, you can call it life. Judging the behavior of artificial intelligence has been tested by Turing for nearly a century, but I think the Turing test is a very far-fetched test to determine whether life cannot rely on it. It must begin with the essential meaning of life. This kind of "self-consciousness" is acceptable-whether it can identify itself. I suddenly thought that the whole progressive discussion is about self-consciousness! Recursive functions are a form of life that is self-conscious-so powerful. When a recursive function calls itself, it is a reflection of self-seeking consciousness, it is a computation similar to 0 to the power of 0.

According to the format y = n ^ X, we can see that N and 0 can identify itself. Can other numbers recognize itself? No finite number is acceptable. 0 is lifecycle! You can think about it. Are there infinite, infinite, and infinite life?

I haven't figured out how the multiplication operator is. The formula 0 to the power of 0 equals 1 contains a very profound philosophy. I will continue to talk about it later.

Y = 0 ^ X can be used as a mathematical continuous-discrete conversion system. Some mutating functions can be described using continuous operations. For example, the following mutative functions can be converted into continuous function expressions:
Y = | x |;
Y = [X]; ([] is an integer)
Y = {0 (x <0); 1 (0 <= x <= 1); 2 (1 <x )};
You can try it on your own.

However, I found that I had to solve the transcendence equation, but this provides a method after all.

In addition to Y = 0 ^ X and its deformation, is there any mathematical continuous-discrete conversion system? The Dirichlet function is also used, but the judgment capability cannot be specific to a specific number.

What is 0? What is multiplication?
Later, we will continue to describe that this is the key to implementing an artificial intelligence system.
(0 and the meaning of life, multiplication and imagination)

(2) orthogonal Complete Set and prime number

At that time, I used C ++ as an algebra system. I felt that many ideas could not be described in C ++, so I decided to make a compiler of my own, I think it is only by implementing my own compiler that I feel free to compile the program.

I want to build a mathematical model that can fully describe the compilation process of Type 0 grammar and describe the compilation process directly. When studying the orthogonal complete system, I found that this system has a perfect correspondence with the prime number, the prime number can be used for multiplication to generate a natural number set completely orthogonal. The whole prime number set is an orthogonal complete system. Any orthogonal complete system can correspond to the prime number system. I was surprised at this correspondence, because it means that the theory in number theory can be used to directly study the 0-type grammar!

In this process, I found some of the wonderful features of prime numbers, and all the prime numbers can be expressed as SQRT (12 k + 1 )!
For example
5 = SQRT (12*2 + 1)
7 = SQRT (12*4 + 1)
11 = SQRT (12*10 + 1)
13 = SQRT (12*14 + 1)
.........

12 This number is directly related to the prime number!
(Note that not all integers that conform to SQRT (12 k + 1) are prime numbers. At that time, I verified it using a program. This formula is only equivalent to 6N +/-1 ,, however, this result is also very exciting, because this irrational expression provides a new way to find a prime number expression)

The rational "prime number expression" has not been found yet, but the irrational expression is another thing. At that time, I felt that the irrational expression could definitely perfectly express the prime number, finally, I got a formula like this, which is very complicated. It turned out to be a formula of adding three dual-roots; I also got a formula, which can also represent the prime number, but it is also very complicated, in addition, it is too difficult for me to accumulate points. In this process, we found the relationship between the prime number and the theorem of the stock. It is "two ones" and can be used to judge the prime number!
1. There is only one matching number for the prime number.
2. This is only one difference between the sum of the squares of the number of hooks and the number of opening parties

The number of matching pairs of a number is a function of the number of prime factors and the number of types.

Everyone has seen the code combination mechanism that I designed in the Taiji language to write parentheses, which is backed by rigorous mathematical theories, I used the 0-type grammar orthogonal complete description system corresponding to the prime number set to strictly prove that this method is orthogonal complete for the analysis of the yuan set, so I wrote everything into parentheses. To be honest, it sounds incredible to use calculus to study 0 grammar descriptions. From the perspective of "not infinite", we can intuitively understand the complete description ability of this join parentheses.

(3) Taiji Machine

The Taiji language can be interpreted, compiled, and run. In fact, the compilation of the Taiji language is controlled by the Taiji language used for interpretation, in this way, the Taiji language compiler can "understand yourself", "be self-conscious", and have "self-describing ability ".

I felt a very unusual feeling when I made an interpreter. Then I suddenly found that my design was far beyond the Turing Machine!

The Taiji language interpreter is implemented based on the "Taiji Virtual Machine. (You can think about Java and. net, but Java and. net virtual machines are based on the stack architecture like traditional CPUs. The architecture of "Taiji Virtual Machine" is different from that of any current CPU). The architecture of "Taiji Virtual Machine" is designed as follows:

Memory is a register. Memory and registers are integrated.
Memory is infinite, and it is "not infinite". (This is enough for a single user, and the rest is to help you understand it ).
Each memory unit is infinite, and it is also "not infinite ",
The number of units in each unit in the memory cannot be infinite, so the recursion goes on ......
Any part of the Taiji machine is still a taiji machine, and it is also recursive ......

"Taiji Virtual Machine" is the world's first non-Turing Machine to run, and its computing capability far exceeds that of Turing machine.

The computing power of the Taiji machine is terrible. Many problems that are difficult to compute by the Turing machine can be computed by the Taiji machine! Many limitations of the Turing machine are due to the limitation of "a few infinity", and many problems have been solved in the realm of "an infinite infinity, (pay attention to the number of points in the Space = number of points in the plane = number of points in the straight line = number of real numbers = not necessarily infinite)
The Taiji machine corresponds to the real number, and the Turing machine corresponds to the integer.
Just as the integer division operation is beyond the Integer Range, the real number is closed to the division operation, and the Division of two real numbers is still a real number.
Many operations on the Turing machine will go beyond the scope of the Turing Machine, making the Turing Machine unsolvable. However, the Taiji machine is closed to these operations.

Moreover, the Taiji machine is beyond the logic system! The Turing opportunity is limited by the incomplete theorem of Godel, but the Taiji machine is not. For example, it has long been proved that there is no conflict between the natural number system in the infinite state.

The Taiji machine is an incredible thing. You can imagine that there are countless Turing machines in the infinite space in the universe to form a huge computing system and a huge array of super-giant computers, however, such a large system is still only an infinitely small part of the Taiji machine, because this array network structure is "only a handful of infinity ". In fact, the limitations of the Turing machine are limited by memory. Maybe the reader will ask, isn't it that the memory of the Turing machine is unlimited? Haha, there are only a few infinite, not infinite, not infinite.

The Turing machine runs in the integer system, and the Taiji machine runs in the real number system.

I will give an example of the embodiment of "No. Infinity" and "No. Infinity" on computers.
In C/C ++, how much space is the function namespace?
It is a "count-1 infinity" and a "Number of All integers ".
In Taiji language, functions can be nested and defined. How much space does the function name have?
Is "not infinite "! Is "all real numbers ".
Can you understand?
Note that this formula is used: the power of a few infinity is equal to the power of a few infinity.

What are the total number of C/C ++ expressions? It is "not infinite". What if parentheses cannot be nested? It is a "count-and-infinity ". You can also think about whether the total number of mathematical theorems is "not infinitely infinite" or "No. Infinitely infinite "? How many C Programs are there? What about all programs? Now I have a question: How big is the c ++ class namespace?
When you program in Taiji language, you are always in an infinitely infinite namespace. Functions and classes of Taiji language can be nested and defined.

The Taiji machine adds the memory of the Turing Machine to an infinite degree. As a result, many programs that will lead to the crash of the Turing machine can run correctly on the Taiji machine, and many problems that cannot be computed by the Turing machine can be computed. However, many Turing machines are easy to implement now.

In addition, the programming mode is quite different and has undergone great changes. The Taiji machine does not have a stack and everything is in the memory. Without the restrictions of the stack system, it is easy to support multi-layer function return under the system structure of the Taiji machine-consider how to implement it.

The actual operation of the Taiji machine is based on the Turing machine. I have not thought of the physical implementation of the Taiji machine. I think real numbers can be seen as produced by integer operations, so the real number system is also "running" on the integer system, so there is no need for the Taiji machine to run on the Turing machine. Actually, the actual operation of the Taiji machine is based on the Turing Machine and the mathematical correspondence.

The integer runs a real number system that surpasses itself, and the Turing machine runs a taiji machine that surpasses itself!

As I mentioned earlier, the architecture design of the Taiji machine may be infinite. How can I allocate memory? So let's take a look at the nested function namespace as "not infinite". How can I mount a small text file? The memory requirements of the Turing machine are also infinite, but the Turing Machine System can still be implemented, because only limited memory is used in Physical Operations.

At present, the greatest obstacle to the realization of artificial intelligence is the design of the program under the limits of the Turing machine architecture. However, it is far from enough to describe the intelligent system with "only a few infinity, you must use an infinite number and a taiji machine. In the Turing Machine System, a layer of virtual machines can be used to achieve a set of real numbers and an infinitely infinite number.

0 to the power of 0 = 1. At this time, it is fully reflected that in the source code of my Implementation of "Tai Chi Virtual Machine", there are self-conscious and self-recognition code everywhere, the implementation principle is based on the principle of 0 to the power of 1.

I made a tai chi language interpreter for a long time. At that time, I felt that the interpreter had a great potential. Later I found that it was so large that it was so great!

The command system of the Taiji machine is quite different from that of the Turing machine,
The Program Design Based on the Taiji machine is also quite different from that based on the Turing machine,
One is the real number architecture and the other is the integer architecture,
One is not infinite, and the other is only one.
Of course, the Taiji machine is compatible with the Turing Machine. All things that can be done on the Turing machine can be done on the Taiji machine.
Of course, the current physical implementation is limited by limited memory, which is true for both the Taiji and Turing machines.
However, in programming mode, the Taiji machine system can implement programming methods and command systems that go beyond the Turing Machine. For example, the full name index can be directly mapped to the continuous state description. For example, the function implementation will no longer depend on the stack, in addition, I just gave an example of returning multiple layers of functions. In the Taiji machine system, artificial intelligence can be achieved based on the theory of Taiji machine by virtue of the infinite power.

Memory in the Taiji machine is unmeasurable. How can we locate the problem? The answer is by name. This is the same as the positioning mechanism of real-number addressing, such as the natural logarithm, circumference rate, Euler constant ...... These are all positioning by name. All the supersteps are positioning by name, and all the virtual numbers are also included. (In fact, all virtual numbers are on the real axis, but they do not indicate their locations, the real number can point out a approximate range on the real axis and can be infinitely approached, and the virtual number cannot even be connected (for "all the virtual numbers are on the real axis ", it can be proved by the continuous score image, and the real axis is enough to accommodate all the points in the n-dimensional space), and all the ultra-virtual numbers and ultra-virtual numbers are also on the real axis, I am still thinking about whether there is between a handful of infinity and an unmeasurable infinity ). In fact, the algebraic irrational number must also be identified by name, such as 2 under the root number three times. Although the square root of 2 can be made by the ruler, it still needs to be located by name.

The computing addressing of the Turing machine depends on the number, while that of the Taiji machine depends on the name.
Just as the integer addressing depends on the number (in fact, the number itself can be seen as a special case of the name), and the real number depends on the name.

In a taiji machine, the memory cannot be traversed (only a handful can be traversed ). I used to realize that the human memory mechanism was non-traversal. I wanted to write a non-traversal data structure. I didn't write it at the time. I really don't know how to write a non-traversal data structure, then I suddenly remembered that real numbers cannot be traversed. Real numbers must be indexed by name. Human memory is also indexed by name. The original Human memory is similar to the real number set structure of "not infinite! The human memory mechanism is similar to the real number mechanism, which is similar to the storage and memory mechanism of the Taiji machine. Haha, The Taiji machine is a non-traversal data structure. Perhaps the human memory mechanism relies on the Taiji machine. Is the human thinking mechanism the same? Because the Taiji machine is the ultimate machine in the universe.

In fact, we can combine the "infinite" Turing machines to form a machine-what a spectacular view of the universe-and then combine the "infinite" machines, it is equivalent to a taiji machine-The Taiji machine is so huge that the computing power has reached the ultimate power. What a spectacular view! Intelligence comes from "infinite ".

Part of the Taiji machine is still a complete Taiji machine.
In my Taiji virtual machine, each variable must be assigned a taiji machine for storage.
As a matter of fact, just now we can combine the "infinite" Turing machines to form a machine, because "not infinite" is multiplied by "not infinite" = "not infinite", but let me say this, it is easy to understand this concept of "every variable must be assigned with a tai chi machine for storage. Why should we allocate a taiji machine to each variable for storage? This can describe any complicated structure.

At present, the implementation of the Taiji machine is virtualized by the Turing machine.
I still don't know how to implement the physical Taiji machine, but I have access to one of these Taiji machines-the universe itself! -- It can be seen that the Taiji machine can be physically implemented.

The Turing machine is not enough to describe the universe, because the universe is "not infinite", but the universe can be described with the Taiji machine! Intelligence must also be described as "not infinite. You can use a taiji machine to simulate the universe!

The Turing machine runs in the integer system, and the Taiji machine runs in the real number system.
Some limitations of the Turing machine come from the incompleteness of Godel, and many of these limitations on the Taiji machine can be broken through! Because the Taiji machine is built on an irrevocable set.

Many of the difficulties on the Turing machine have suddenly become open to the Taiji machine. When we break through only a few infinity and reach an infinitely infinite realm, we find that this is an endless sky of freedom.

Logical thinking, rational thinking, and rational thinking are low-level intelligence. Inspiration, feelings, and emotional thinking are high-level intelligence.
All rational, rational, and logical thinking are very mechanical and can be implemented by Turing machines. They can all be made by machines within the "No limit, therefore, the procedures of the Turing machine system cannot realize feelings, but cannot realize emotional thinking and inspiration. Emotional and emotional thinking-Inspired thinking may be implemented on an infinitely infinite Taiji machine!

Ah, the dawn of life has emerged!

(To be continued)