Catenation Property of Information – the secrets of intelligence and language

Several decades after the concept of AI (Artificial Intelligence) being put forward, intelligence is still mysterious for our human beings. All kinds of theoretical systems try to solve the problem from different ways, but leave it unsolved till present. After ten years of observing and analyzing information, the author discovered CPI (the catenation property of information). The article made a scientific inquiry of the inherent interconnection between the CPI, intelligence and language and revealed the secrets of them.

Key words: cognitive linguistics, CPI, intelligence, language

Intelligence was taken as sacred, unsurpassed, and unique and owned by only human beings. It was regarded as the spiritual power with unlimited tremendous potentiality. Philosophy, Psychology, Cognitive Science, Noetic Science, Logic Science, Linguistics, Computing Science and so on, intelligence was explored in all these fields. After the 1956 Dartmouth Meeting with the concept Artificial Intelligence being put forward, more and more researchers devoted into the research of AI enthusiastically. Symbolicism, Connectionism and Behaviorism different academic schools probe into intelligence with different methods. Take NLU (Natural Language Understanding) as example, ever since 1950s, many NLU theoretical systems were developed, such as Transformational-generative Grammar, Dependency Grammar, Semantic Network, Montague Grammar, Systemic Grammar, Case Grammar, Conceptual Dependency, Situation Semantics and so on. In the recent years, corpus linguistics got well developed too.

However, in order to simulate the intelligence, all these method systems must take computing as the basement. It’s the essential condition to have the algorithm for computers to process any problem. With given algorithms, computers can only process problems that the algorithms enable computers to deal with. The amount of information was infinite and its change and development appear to be boundless. It’s impossible for us human beings to endow computer with the algorithms worked out from the interrelationships among all the information so that the computer can react reasonably to any received information. The human intelligence is infinite. The computer can only operate in accordance with the given algorithms. At present, none algorithm can realize the cognition of all the things’ relationships. It seems that as long as we human beings afford computers certain algorithm, they can not obtain real intelligence. But without algorithm, there will be no computing to speak of. Unless having a non-algorithmic algorithm or there will be no real intelligence. Everyone can see that it’s contradictory at the first sound.

However with the discovery of one property of information, the sounded self-contradictory problem was solved very well. That’s the discovery of CPI (the catenation property of information).

CPI Definition: CPI is one property of information. It reflects that all information can take advantage of each other and fulfill the incomplete self-replication. CPI is measured by CPID (CPI degree) which is a physical quantity for the measurement of interrelationship degrees of information.

About catenation property, in order to make it easy to understand, let’s have a more visual explanation through Fig.1.

Fig. 1. An iron ball falls on the ground, an indentation is left on the ground by the iron ball

At the same time, the dust is left on the iron ball by the ground. The indentation has part of the features of the ball. It’s an incomplete self-replication that the ball makes on the ground. The dust shows part of the features of the ground. It’s an incomplete self-replication that the ground makes on the ball. They make use of each other to fulfill the self-replication. Each of them make the other poses part of the features of their own. That’s to say they implement the incomplete self-replication (see Fig.1 A, A’). Definitely, for some cases it’s easy to aware but for other cases it’s not so easy to sense that. For example, in Fig.1 B’, it’s difficult for us to draw an instant conclusion about which ball causes the indentation, b1 or b2? However as long as the interaction exists between things, there will be the features of things left on each other. You aware it or not just ascribe to the current sense ability and technology capability.

CPI Corollary: The information of one thing in a certain hierarchy or aspect can always be embodied in a certain hierarchy or aspect of other things attribute to the CPI that all information can fulfill the incomplete self-replication by taking advantage of each other. So there are always certain direct or indirect similarities exist between informosome.

In order to verify whether the information of one thing in a certain hierarchy or aspect can always be embodied in a certain hierarchy or aspect of other things, we take two groups of random samples to have matching analysis based on five different fuzzy degrees. The parameters of the sample images are: 320x240 pixels, RGB, 16 bits with purely white background. The result data are as follows:

Table 1

F-L0 to F-L4 in Tab.1 represents the 5 fuzzy levels of the images from low to high

X represents that things in O-G1 and O-G2 do not satisfy CPI. Y represents that things in O-G1 and O-G2 satisfy CPI. Before fuzzy processing, we can see that all the items do not satisfy CPI. With the increasing of the fuzzy level, more and more images satisfy CPI. Till the end, all the results are Y. Here to dim the images is to unfold the information in different hierarchy or aspect of things. With the increasing of the fuzzy level, the subordination range increased too. For example, an image of an apple, with the increasing of its fuzzy level, may subordinate to apple, fruit, food, thing, objective existence. From the table we can see that the condition which satisfies CPI can always be found in certain hierarchy or aspect.

For each item in Tab.1 we choose only some single informosome to perform the analysis. In reality, informosome usually exists in the form of large amount of informosome clusters. Although single informosome usually embodies only the information of shape and color, the informosome clusters can reflect all kinds of other characteristics. And the non-AV (not audio and video) information can be obtained indirectly from the video or audio informosome clusters. (Just like the electronic balance enables us to sense the weight with vision.) The larger the informosome clusters are the more characteristics and properties it can reflect. Let’s take dark cloud and rain as examples to give a more visual illustration about CPI of IC (informosome clusters). The correlative degree between dark cloud and rain in object shape is low. However IC can change the correlative degree that CPI brings among informosome. With IC formed under the effects of time similarity and spatial similarity the correlative degree is so enhanced that we think of rain at the sight of dark cloud and vice versa. The larger ICs are, the powerful the cognition and logic ability of the system will be.

The interrelationship among all things can be established and expressed by similarities in computing. In order to make it convenient for computer to operate and process, we divided the similarities of things into 3 varieties: appearance similarity, time similarity, spatial similarity. And each similarity was divided into direct and indirect similarity. The direct similarity and indirect similarity are relative to the perceptive mode and perceptive intensity. That’s to say; the direct similarity under one perceptive mode or perceptive intensity may be the indirect similarity under another perceptive mode or perceptive intensity and vice versa. So the indirect similarities can always be expressed through some other direct similarities.

What is the practical significance of CPI? The practical significance of CPI lies in that the interrelationship between things can be obtained from information by computing depending on CPI. By taking advantage of the different levels of similarity between information to express one thing with information of the related others, computing can realize the non-algorithmic algorithm and put intelligence into reality. About the so-called non-algorithmic algorithm, algorithm refers that using definite algorithm to process information, non-algorithm means that about the interrelationship among the infinite information of the world, we do not give a definitive algorithm but to extract it from information according to CPI. The original motive power of the infinite cognition ability of intelligence springs from the infinite information. Without the external environment, without receiving the external information, intelligence will never exist.

Certainly, for intelligence, there are still too many disputes until now. Some people insisted that we can not realize the real intelligence before we got a thorough understand of the human brain. It’s just like to say that it’s impossible to invent the spacecraft to land on the moon before we can find out a bird that can fly up into the moon. Obviously it’s not correspondent with practice.

The perspective of our surveying usually restricts our cognition about things radically. It’s just like how we look upon why apples fall on the ground. It ought to fall on the ground just like all the other things, no necessary to reconsider it, or there is certain gravitation which causes that? About AI, must we formalize the research questions and get the corresponding algorithm, just like what people have considered it for the long time, no necessary to reconsider it, or there is certain information property which causes that?

The amount of information is infinite. It’s impossible for the computer to store all the relationships between things to realize intelligence. CPI enables computer to extract relationships continually by receiving information. In fact, it is the property of information—CPI, which functions under certain constructions, so that the intelligent behavior recognition, association, creation and natural language come into reality.

About the function of CPI, let’s make a figurative illustration. If we take the brain as the engine of a car, then information is the gas and CPI is just like the characteristic of combustion. The combustion-characteristic put the power-output into reality under the construction of the motor. (If it’s not the motor-construction, maybe it will appear as explosion or other.) The running of the car is one of the representations. CPI put intelligence into reality under the construction of the brain. (If it’s not the brain-construction, maybe it will appear as stress response or other.)

What is the interconnection between CPI and intelligence? It seems that there are world of difference between the incomplete self-replication property of information and intelligence. And it seems that the simplicity of the incomplete self-replication property can never take rank with the complexity of intelligence. However, it’s just like that all colors can be obtained by the mixture of trichroism and the powerful and complex function of computer bases on the gate circuits. CPI is just like the general formula of relationship between things. It enables us to set up all the connection between things. It’s the fundamentality of all the complex phenomenon of intelligence.

According to the corollary of CPI, we know that there are always the direct or indirect similarities between informosome in a certain hierarchy or aspect. So we can always use several informosome with certain direct or indirect similarity to express one thing or to distinguish one thing from else. So CPI is just like the general formula that can be used to unfold the relationships of all things. It expresses all things with the similarities between them.

Then how to express things and relationships? The amount of information of the world is infinitive. Here we take only limited six points to represent things, and show their relationships.

Fig. 2. Points A, B, C, D, E and F are used to represent things and the lines represent the similarities between them. Here we see that there are always some similarities between things. And the relationships among them present irregular three-dimensional reticulate structure

Different characteristics cause different similarity degrees between things. Usually things with certain similarity in different hierarchies or aspects are used to express each other. For example: fan-like ears, pillar-like legs, faucet-like nose, to guess an animal. Even the child knows that it’s elephant. That’s to express the elephant with fan, pillar and faucet. In Fig.2, if we take A as elephant, B as fan, C as pillar, D as faucet, then their relationship is A=Bpx+Cpx+Dpx. PX represents the characteristic of certain hierarchies or aspects of things. CPI can be used not only to express things but also to express logics. CPI enables the computer to unfold all series of intelligent phenomenon. It’s the fundament and spring of the complex intelligence.

What is the utilization of CPI? The above description may seem not so convenient for us to perceive the CPI utilization procedure. Now we’ll explain by example. In order to make it easier to understand, we take just the NLU (Natural Language Understanding) as example to explain the utilization of CPI.

For decades, in the field of NLU, people paid more attention to the imitation of the function of human brain and ignored the real origins of human intelligence—all the information of the real world. About the NLU study, ever since before, it was usually confined to the analysis of lexicon, syntax, semantics and pragmatics. From transformational generative grammar to HNC (hierarchical network of concepts), from syntactic analysis to large corpora, they all study about how information was transmitted by language. Why language can express information. It’s not because of information being transmitted by language, but language being the outcome of information interactions. So the breakthrough point of NLU does not lie in the analysis of the lexicon, syntax, semantics and pragmatics, but lies in the research of the regularity of information interaction. About the phenomenon of human obtaining information from language, it’s more reasonable to say that information transmits language than to say that language transmits information.

Now let’s just take video and audio information as example to explain how CPI was taken advantage of in the system of NLU.

Schematic Diagram of Relationship between Information and Language

Fig. 3. The following concepts were involved in the chart. 1. V-I: Video Information 2. A-I: Audio Information 3. Sy: Syncopate 4. G-C: Geminal Coupling 5. In & Ca: Integration & Catenation 6. C-S: Current State 7. S-I: Subjective Initiative 8. A-O: Audio Output

The video and audio information process self-definition syncopate desperately after information acquisition base on computing. Syncopate is to divide information into system-defined informosome so that to recalculate and establish the correlation degrees with more other informosome. After syncopation, different types of informosome process geminal coupling. Geminal coupling is used to express the different correlation degrees among different types of informosome caused by the time similarity and information intensity. The GC (Geminal Coupling) informosome and video, audio informosome involve in integration and catenation all together. Integration is used to express the different correlation degrees caused by the different time similarity and information intensity. Catenation is used to express the correlation degrees that are not limited by time similarity. The results of integration and catenation are conducted storage. The informosome in storage participate in integration and catenation at the same time. Storage is an accumulation process of information. Information attenuated during the course of storage in order to show the different hierarchies or aspects of informosome. It’s a progress of accelerating the catenation. The calculations between different types of information need to base on IE (information equivalent) which is the information-intensity conversion values about different types of information relative to specified intelligent system. The condition of the current maximum value of IE is called the current state. Subjective initiative is the result that current state reacts on the information receiving and processing. The audio output under subjective initiative is language.

With the concepts of integration and geminal coupling, all informosome are connected. With the concept of catenation, the connection was not limited by the time similarity and interval. The property of incomplete self-replication of information can be used to interpret the interrelationships between things. It puts the entire intelligent phenomenon such as thinking, imagination, creating, reasoning and language into reality.

For decades, there is no break-through in the field of AI. The crux of the matter is that people paid more attention to how to deal with information but ignored the researches of information property. CPI is the original power of intelligence and the infinite indispensable information is the real source of it. Information for intelligence just like oxygen for human body, it is undoubted that without external information without intelligence. In fact, it’s not the brain but the information that is the source of intelligence.

The discovery of CPI is the deepening of cognition about human self and the world. The cognition and utilization about CPI has great significance no matter in theory or in practice. It will motivate human beings’ non-biotic evolution and society improvement.

From the historical point of view, the discovery of CPI is not only the result of personal hard working, but also the result of science development. AI is the science fact that was born in the middle of the 20^th century. CPI is the stage symbol in the process of its development. It’s the wisdom crystallization of all human beings and the requirement and inevitable result of social development. It’s the crucial stage-symbol of human knowing about self. The utilization of CPI will lay a solid foundation for the liberation of mental work and initiate the approach to liberate human mental labor from the basement.

Surely, any new born thing needs a progress to develop. CPI is not an exception. However with the accumulation of all people’s hard working and devotion, intelligence will never be secrets.

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