Beyond Turing-Turing--on the possibility of the realization of artificial intelligence (I.)

Beyond Turing-Turing--on the possibility of the realization of artificial intelligence (I.)

I think that artificial intelligence can be realized into logical thinking, because logical thinking can be completely expressed in string, Turing can be arbitrary units to arbitrary values, at this point is complete, this is enough to describe logical thinking, so using Turing can fully realize logical thinking. Of course Turing will be constrained by Godel's incompleteness, but the logic system will be subject to the same constraints, so I think it is entirely possible to use Turing to realize logical thinking.

So what is the relationship between the essential mechanism of logical thinking and Turing. Logical thinking is also the use of a similar Turing machine mechanism. Einstein denies the possibility of artificial intelligence that machines can solve many problems but never raises a question, but I think Einstein is wrong about this, like when a program crashes can be seen as presenting a problem and outputting one. can also be seen as a question, the problem can be considered as a state of the automaton, even any state point of the machine can be seen as a problem, the problem and results can be described by strings, and Turing machine can be complete to solve all string problems, then of course Turing machines will ask questions.

But the power of Turing is still very limited. And people have far beyond the logical thinking mode, higher intelligence, which is the Turing of the mind to Dust mo and. So the higher the AI even the real intelligence should be how to achieve. ......

I've been thinking a lot about designing Taiji language, I will explain the concept of Tai Chi Machine, readers can first imagine--endless space in countless Turing machines to form a huge computing system, a large array of supercomputer, but such a large number of systems are still only a small part of the Tai Chi Machine, ...

(a) 0 of the intelligent, digital life

Years ago, when I was working on an algebraic system, I found that the expression "0 0 times equals 1" was very subtle, and y=0^x (^) had the ability to judge the equation. To determine whether the input is 0 or not 0, the result of this equation is only two states, 1 and 0, when X is base 0 o'clock returns 1, not 0 o'clock returns 0. To draw a function image, the only Y-value at the origin on the entire axes is 1, and the rest coincide with the X axis ... I suddenly had a very strange feeling, feeling 0 in this equation to determine whether a number is themselves, at that moment, I suddenly felt the life of numbers.

0 in judging whether the input is 0, which means the ability to judge. Judge whether a number is itself. 0 and the exponentiation are so wonderful. Then use y=0^ (n-x) to determine whether a number is N, but the root of the formula is y=0^x.
I felt 0 of my life at the time. The original 0 is alive. 0 is the symbol of life, all things have a spirit, then reflected in mathematics is million have 0--a=a+0.

0 of the 0 times is equal to 1, when 0 realize the ego is a kind of life consciousness, life must be able to be aware of their existence, life must be able to carry out whether the self judgment, and y=0^x actually can do it. Self-consciousness is enough to call life. Judging the behavior of artificial intelligence has been a Turing test for nearly a century, but I think the Turing test is a far-fetched test to determine whether life cannot be relied upon for such tests. Must begin with the essential meaning of life. And this "self-awareness" is possible-see if you can identify yourself. It suddenly occurred to me that the whole recursive theory was about self-awareness. A recursive function is a form of life that is self-aware-so powerful that when recursive function calls itself it is a manifestation of a sense of self seeking, which is done in the same way as 0 0 of times.

According to y=n^x this format, see n,0 is able to identify themselves, and other numbers have to identify themselves. Any finite number will not work. 0 is alive. Readers can think about, can count infinity and countless infinite life.

I'm not really sure what's going on with the exponentiation. 0 of the 0-time square equals 1 This expression contains very esoteric philosophy. The stop is going to have to talk about it again.

Y=0^x can be made into a mathematical continuous-discrete transformation system. Some mutation functions can be described in terms of continuous operations. For example, the following mutation function can be translated into the form of continuous function expression:
y=|x|;
Y=[X];([] to take an integer)
Y={0 (x<0); 1 (0<=x<=1); 2 (1<x)};
Readers can try it on their own.

But I found out that I had to solve the transcendental equation, but this provides a way.

In addition to y=0^x and its deformation, there are other mathematical continuous-discrete conversion systems. The Dirichlet function is also, but the ability to judge is not specific to a number.

0 exactly what it is. What the powers are.
The following article will continue to tell, this is the realization of artificial intelligence system of great key.
(0 and the Righteousness of life, of the powers and of intent)

(ii) Orthogonal complete sets and prime numbers

At that time, I was using C + + to do algebraic system, I feel a lot of ideas can not be described in C + +, so I decided to do a compiler of their own, this is my desire, I feel that only the implementation of their own compiler to the process of programming is free.

I want to build a mathematical model that can be fully described in 0-type grammatical compilation, direct description of the compilation process, the study of orthogonal complete system when I found that this system is perfect with prime numbers is the corresponding relationship, prime numbers do multiplication can be orthogonal complete generation of natural numbers set, the whole of the quality of the set is an orthogonal complete system. Any orthogonal complete system can correspond to a prime number system. I was very surprised at the correspondence because it meant that the 0 grammar could be directly studied using the theory of numbers.

In the process I found in turn some of the most wonderful properties of prime numbers, even all prime numbers can be expressed as sqrt (12k+1)!
Such as
5=SQRT (12*2+1)
7=SQRT (12*4+1)
11=SQRT (12*10+1)
13=SQRT (12*14+1)
.........

12 This number is actually directly related to prime numbers.
(Note that not all integers conforming to sqrt (12k+1) are prime, and I used the program to verify that this equation is only equivalent to 6n+/-1, but it's also exciting to get this result because it provides a new way to find prime-number expressions)

Find the rational formula "prime number expression" has not been found, but the irrational style is another thing, I felt that with the irrational formula will definitely be able to perfect the expression of prime numbers, continue to get a such formula, very complex, unexpectedly is three double square root of the formula added; also got a formula, also can represent Prime, But it's also very complicated, and there's an integral in it that's too hard for me to accumulate. In the process of discovering the relationship between prime numbers and the Pythagorean theorem, is "two one", can be used to judge prime numbers.
1. The number of tick pairs of prime numbers is only one
2. This number and the number of the sum of the number of squares and after the root of the difference is only one

The number of tick pairs of a number is the function of the number of numbers and the number of species.

We all saw the code combination mechanism of the ligatures parentheses that I designed in the Taiji language, there is a rigorous mathematical theory behind it, and I am using the 0-type grammar orthogonal complete description system corresponding to the mass number set, which strictly proves that this method is orthogonal and complete for the analysis of the collection of the walls. So I was bold enough to write ligatures parentheses. To be honest, using calculus to study the 0-type grammatical description is almost inconceivable. From the angle of "infinite infinity", we can intuitively understand the complete descriptive ability of this ligatures bracket pair.

(iii) Tai Chi Machine

Tai Chi language can explain the operation can be compiled and run, in fact, the compilation of Taiji language by the interpretation of the operation of the Taiji language (Electrodeless language) to control, so that the Taiji language compiler can "themselves understand themselves", "self-awareness", has "self-describing ability."

I felt a very unusual feeling when I was explaining the runtime, and then suddenly I realized that my design was far beyond the Turing.

The Taiji language interpreter is based on the "Taiji virtual machine". (You can think about java,.net, but the java,.net virtual machine is based on the stack architecture just like the traditional CPU.) The "Taiji Virtual machine" architecture is not the same as any current CPU, and the "Taiji Virtual Machine" architecture is designed like this:

Memory is the register, memory and register in one.
Memory is infinite, and is "immeasurable infinite", (this is enough, the latter is to assist understanding).
Each unit of memory is infinitely large, and is also "irreducible infinity",
The cells in each unit of memory are also infinitely large, so recursion goes on ...
Any part of the Taiji machine is still a Taiji machine, and so it goes on.

"Taiji Virtual machine" is the world's first operation of the "non-Turing", its computational capacity far more than Turing machines.

The computational power of the Taiji machine is simply terrible, and many of the problems that the Turing machine is difficult to compute can be computed by the Taiji machines. Many of the limitations of Turing is due to the "number of infinity" limit, and to the "immeasurable infinity" in the realm, many problems are solved, (to pay attention to space points = plane points = line points = Number = Real numbers = irreducible infinity)
The Taiji machine corresponds to the real number, and the Turing machines correspond to the integers.
Just as Integer division operations are outside the range of integers, but real numbers are closed to division operations, and two real numbers do division are still real numbers.
Many of the operations on the Turing machine would go beyond the category of Turing machines, causing them to be irreversible, but they were closed to these operations.

And the Taiji machine is beyond the logical system. Turing machines are subject to Godel's incompleteness theorem, but the Taiji machine is not. For example, it has long been proved that the system of natural number form is not contradictory in infinite state.

The Tai Chi Machine is a gigantic and incredible thing, it can be imagined that the endless universe of countless Turing machines to form a huge computing system, a large array of supercomputer, but such a large number of systems is still only a small part of the Tai Chi machine, because the array of network structure is "can count infinity." In fact, the limit of the white Turing is the limit of memory, perhaps the reader will ask not to say Turing memory is unlimited. Haha, that is only the number of infinite, from the "Unlimited infinite" poor "cannot count infinitely far" it.

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

On the computer embodiment of the "infinity of Numbers" and "irreducible infinity" I give an example to illustrate.
How large is the function name space in C + +.
Is "Can count Infinity", is "all integers."
In the Taiji language, functions can be nested and defined, so the function name space of the Taiji language is much larger.
is "irreducible infinity". is the "total number of numbers."
Can you figure it out.
Note that this formula: the number of infinity can be infinitely large number of the second side = irreducible infinity.

In addition, the total number of C + + expressions in all. is "irreducible infinity", so if parentheses are not allowed to nest. Is "can count infinitely big". You can also think about the total number of mathematical theorems is "irreducible infinity" or "can count infinity." How much is the whole C program? The whole procedure. Now a question: How large is the C + + class name space.
When you use the Taiji language to make a program, you are always in an infinite number of namespaces. Taiji language functions and classes can be nested definitions.

The Taiji machine adds the memory of Turing machines to the degree of irreducible infinity. So many of the original machine will cause the crash program on the Taiji can be correctly run, many Turing machines can not calculate the problems are calculated, many Turing is difficult to achieve now very easy to achieve.

And the programming pattern is very different, and a lot of changes have taken place. The Tai Chi Machine has no stacks and everything is in memory. No stack system constraints, in the Taiji machine architecture, can easily support the function of multi-level return-consider how to achieve it.

The actual operation of Tai Chi Machine is based on Turing machines, I have not thought of the physical implementation of the Taiji machine. I think that real numbers can be thought of as integers, so the real system is also "running" on an integer system, so the Taiji machine runs on the Turing machines. The actual operation of the Taiji machine should be based on Turing machines and mathematical correspondence.

Integers run out of a real system beyond their own, and Turing machines run out of a Taiji machine that transcends itself.

I just said that the Tai Chi Machine architecture design, you may ask are not infinite, how to allocate memory it. Then consider the nested function namespace is "irreducible infinity", a small text file how to install it. Turing's memory requirements are also infinite, but the Turing system is still achievable, because only a limited amount of memory is used in physical operations.

At present, the biggest obstacle of artificial intelligence is to design the program under the system structure of Turing machine, and to describe the intelligent system with "infinite number of infinity" is far from enough, and it must use "Infinite infinity". Under the system of Turing machine, do a layer of virtual, to reach the Tai Chi machines, to reach the real number set, to achieve an infinite size.

0 of the 0 times = 1, at this time fully reflected in my implementation of the "Taiji virtual machine" Source code, everywhere are self-awareness has the ability to identify the codes, and its implementation principle is based on the 0 0-square =1 principle.

I had a long time to do the Tai Chi language interpreter, I felt the potential of the interpreter is very large, and then found unexpectedly is so large to this extent.

The command system of the Taiji machine is quite different from that of Turing machines,
The program design based on Taiji machine is also quite different from that based on Turing machines.
One is the real system structure, the other is the integer architecture,
One is irreducible infinity, and one is infinitely large.
Of course, the Tai Chi Machine is compatible with Turing machines, and all the things that can be done on a Turing machine can be done on the Taiji machines.
Of course, in the current physical implementation, are limited by the limitations of memory, Tai Chi Machine and Turing machines are the same.
But the programming way on the Tai Chi Machine system can be achieved beyond Turing the programming and instruction system, such as the full name index can be directly mapped to the continuous state of the description, such as the implementation of the function will no longer rely on the stack, and I have just given a function of multi-level return example. In the Taiji machine system, depending on the power of countless infinite, artificial intelligence should be based on the theory of Tai Chi Machine to achieve.

In the Taiji machine memory is not a number, then how to address positioning it. The answer is by name. This is the same as the real-address positioning mechanism, such as natural logarithm, pi, Euler constants ... These are all positioned by name, and all transcendental numbers are positioned by name, also includes all imaginary numbers (in fact, all imaginary figures are on the axes, just can't explain their position, the real number can point to a approximate range on the axes, can be infinite approximation, and the imaginary number does not even have this to do (about "all imaginary numbers are on the axes", Can be the proof of the image of even fractions, and axes is enough to accommodate the n-dimensional space in a bit of, all the super imaginary number of ultra-imaginary numbers are also in the axes, I am still considering whether can count infinity and infinity between these "illusory" things. In fact, algebraic irrational numbers also need to be positioned according to name, such as 3 square root under 2. Even though the square root of 2 can be made by the ruler, it still has to be positioned by name.

The Turing machine operations are addressed by number, while the Taiji address is by name.
Just as the number of integer addresses (in fact, the number itself can be regarded as a special case of the name), and real numbers rely on the name.

Memory is not traversed in a Taiji machine (can be counted if traversed). Before I realized that the human memory mechanism was not traversed, once wanted to write a data structure can not be traversed, did not write out, I really do not know how a data structure can not be traversed, and then suddenly remembered that the real number is not ergodic, real numbers to be named index addressing, human memory is also by name index addressing, The original human memory is similar to the "irreducible infinity" of the real number set structure. Human memory mechanism is similar to the real number mechanism, which is similar to the memory mechanism of Taiji machine. Haha, Taiji machine is a data structure that can not be traversed. Perhaps the mechanism of human memory depends on the Taiji machine. Whether people's thinking mechanism is also. Because the Tai Chi Machine is the ultimate cosmic machine.

In fact, the "infinity" of the Turing machine together to form a machinery-this is the universe of what a spectacular scene ah-and then "countless infinite" many of these machines together, the equivalent of a tai Chi machine-Tai Chi Machine is so large, the computational capacity has reached the ultimate strength, this is what a spectacular scene. And intelligence comes from this "immeasurable infinity."

Part of the Taiji machine is still a complete Taiji machine.
In my implementation of the Taiji virtual machine, each variable must be allocated a Tai Chi machine to store.
As a matter of fact, I just said, "We can form a machine by combining the" infinity "Turing machine together. Because" irreducible infinity "multiply" infinity "=" infinity ", but I say this, it is easy to understand this" each variable must be assigned a tai Chi machine to store "concept. Why should each variable be allocated a Tai Chi machine to store it. This can be described as an arbitrarily complex structure.

At present, the realization of the Tai Chi Machine is virtual with Turing machines.
I still do not know how to achieve the physical Tai Chi machine, but I have come into contact with a tai Chi Machine-the universe itself. --it can be seen from the physical realization of the Taiji machine.

Using a Turing machine is not enough to describe the universe, because the universe is "irreducible infinity", but the universe can be described by Taiji machines. Intelligence also needs to be described by "irreducible infinity". Using a Taiji machine can simulate the universe.

The Turing machine runs in the integer system, and the Taiji computer runs in the real system.
Some of the limitations of Turing machines are derived from Godel's incompleteness, and many of these limitations can be broken in the Taiji machine. Because the Taiji machine is built on the irreducible set.

Turing machine on many of the problems to the Tai Chi machines on the enlightened, when the breakthrough can count infinity, to the infinite realm of infinity found this is an endless freedom of the sky.

Logical thinking is low intelligence, inspiration, emotion, perceptual thinking is the advanced intelligence.
All rational logical thinking is very mechanical, can use Turing machine to achieve, can be made with machinery, all in the "can count Infinity" within, so Turing System program can not achieve feelings, can not realize the emotional thinking inspiration. Emotional thinking inspiration may be in an infinite number of large tai Chi machine to achieve.

Ah, the dawn of life has come.

(To be continued)