## 1.1 The Information Theory on Change

In the development of information theory, Harry Nyquist and Ralph Vinton Lyon Hartley have seminal role in the information theory, in the light of which Shannon defines information with the mathematical equation and made continuous contributions. They lay foundation for quantitative calculation and rapid development of the information theory on change.

### 1.1.1 Information Communication

In an early stage, the information describes how the things vary because of the initial knowledge and low calculations. To mathematically clarify the nature of communication, Harry Nyquist made fundamental theoretical and practical contributions to telecommunications. He [1] analyzed the relationship between the speed of a telegraph system and the number of signal values used by the communication system. His principles of sampling continuous signals to convert them to digital signals [2], showed that the sampling rate must be at least twice the highest frequency present in the sample in order to reconstruct the original signal.

To establish a quantitative measure to compare the capacities of various communication-systems to transmit information, Ralph Vinton Lyon Hartley [3] distinguished between meaning and information. Information was defined as the number of possible messages, independent of whether they are meaningful. He further thought that messages are concrete and diverse symbols, and information is the abstract parameter in the messages. Under the umbrella of this definition of information, he gave a logarithmic law for the transmission of information in discrete messages. With the logarithm of the probability on a message occurrence to measure information, he took sample from a set of symbols to create a word. If the probability of each symbol is the same, and the selection is random, you can get different words. In 1955, he further presented the information theory of the Fourier analysis and wave mechanics.

Claude Elwood Shannon [4] acknowledged his debt to works by Nyquist and Hartley in the first paragraph of his paper “The Mathematical Theory of Communication”. He believed that the basic problem of communication was to accurately or approximately reproduce the message selected by another point at one point. Information is defined as a set of codes that encode the probability of occurrence of events, and the uncertainty of information is measured by using an entropy. A model of the communication system was given to solve the technical problems on accurately transmitting communication symbols, such as information capacity, statistical features of information sources, information source coding, channel coding, information measurement, and the relationship between channel capacity and noise.

As a result, for the first time in history, mankind clearly understood and grasped the essence of communication technology, which promoted the vigorous development of communication systems. Therefore, the information theory pays attention to the message transmission in information communication. The change of the symbol values transmits the message. The logarithm of the probability on a message occurrence models the information measurement.

### 1.1.2 Typical achievements of the information theory on change

Nowadays, there are many contributions to the information theory on change. The representative is Shannon information theory [4], including full information theory [5], general information theory [6, 7], representation information theory [8], unified information theory [9, 10], and information geometry theory [11]. These achievements strongly promoted human society from the industrial age to the information age.

#### 1.1.2.1 Shannon Information Theory

The idea is to extract the information from countless events. Information was described as “a group of codes with the probability of occurrence p1, p2, …, pn” with the entropy [4].

$$H(X)=H\left({p}_1,{p}_{2,}\cdots, {p}_n\right)=-k\sum \limits_{i=1}^n{p}_i\mathit{\log}{p}_i$$
(1.1)

It is a measure that reflects the uncertainty of information and lays the theoretical foundation of Shannon information theory. Sequentially, Wiener [12], Ashby [13], De Luca, and Termini [14] used their entropy equations to measure information. Shannon entropy was further expanded, i.e. cumulative residual entropy [15,16,17], joint entropy [18, 19], conditional entropy [20,21,22], exponential entropy [23], mutual information entropy [24, 25], cross entropy [26,27,28], maximum entropy principle [29, 30] and so on. These results have prompted the development of information entropy.

#### 1.1.2.2 Expansion from Shannon Information Theory

Zhong Yixin [5] proposed full information theory by taking “self-representation/self-revealing of the state of things and state changes” as the definition of information at the ontological level. He believes that full information includes the epistemological level information of the external form, internal meaning and utility value of the movement state of things and their changing modes. To truly master the epistemological information of the matter, you have to perceive its form, understand its meaning, and know its value. Simultaneously considering three factors, the formal is grammatical information, the meaning is semantic information, and the utility is pragmatic information.

General information theory [6, 7] treated information as the ability to cause changes under the principles of noumenon and value. In a information logic system IF(R), a mathematical model of triples was 〈C, I, R〉, where C is information carrier, I is information, and R is the system that information belongs to. A series of operators between C, I, R and IF(R) are used to transmit, receive, and store information. Taking information, carrier, and belonging system as a complete system, general information theory opens a door to study the nature and operation of information by using mathematical methods. Moreover, three types of structural metrics are given to measure the degree of information change: internal, intermediate, and external. They are namely abstract, reality, and experiment, defined under different target and requirement.

Representation information theory [8] is the proportion of structural complexity changes caused by a group of objects removed from their categories, by understandings the principles of human concept communication and learning. Compared with Shannon information theory, there are some expansions. The first is to replace the symbol sequence with the conceptual structure. The second is to replace the probability with the category invariance. And the third is replaces simple events with a collection of group objects.

Unified information theory [9, 10] uses a consistent concept to contain many different information connotations. It describes information as the structure, state, or state of the system, considering information from grammatical to semantic and pragmatic state. Its analysis of the product of behavior change is like full information theory [5], while the theoretical depth and systematisms are far inferior to the latter.

#### 1.1.2.3 Information Geometry

In contrast with Shannon information entropy, information geometry theory is known as the second generation of information theory [31]. It contaminates probability statistics and geometric methods. Rao [32] used the geodesic distance to measure the difference between the probability distribution functions by defining the Riemann metric on the manifold with Fisher information matrix [33]. Efron [34] gave the curvature on the statistical manifold. Chentsov [35] presented a family of affine connections on the statistical manifold. Amari [36] proposed the concept of dual affine connections.

### 1.1.3 The Limitations of the Information Theory on Change

The information theory on change emphasizes the difference in size, amount, degree, or nature for telling an exact object from common objects. However, many researchers lack an outline and consistent consensus on the objects, purposes, and methods of information. People’s understanding of information is still divided, and the measurement on information is also inconsistent.

Regarding the object to study information, it is difficult to distinguish the relationship between objectively existing information and people’s subjective conscious activities. The information in people’s minds belongs to both objective and subjective categories, which is extremely complicated.

With regard to the purpose to study information, academic exploration and deduction are satisfied with. To a large extent, they ignore the numerous information systems in the objective world that have or will profoundly change human production and lifestyles. They also neglect the impact of acquisition, transmission, processing, storage and application in a information system, especially the actual guiding role of the research, design and development of large-scale integrated information systems.

For the method to study information, Shannon traditional probability and statistics methods for communication systems are inherited, which limits the proposal of more feasible and extensive method to comprehensively and systematically establish the theoretical foundation of information science. Furthermore, in the information theory represented by Shannon, the basic view is that only when the recipient of the information receives the information, the information can produce meaning.

## 1.2 Bottleneck Problems in Information Science

In an information system, information is integrated to reflect the static characteristics and dynamic changes of matter, which is a whole and difficult to separate in the real world. Nowadays, it is a trend to integrate, or make use of, different information systems to build a larger-scale system. However, there are various concepts on information with different connotations in information science. Lacking an outline on the objects, purposes, and methods, no consensus on the theory of information comes into being. The metrics is not systematic. It is difficult to guide the giant project.

### 1.2.1 Different Concept Descriptions

The pronouns of early information are with a certain meaning. The production, transmission and utilization of information is a human instinct. After the 1920s, with the large-scale production in the industrial age and the development of science and technology, the amount of information has increased rapidly. With the rapid increase in the amount of social information, people have to study how to obtain, process, transmit and use information in a timely and accurate manner. Some people go to explore information, and various definitions have been put forward for information.

• Information is a state that can be described in the form of numerical values, words, sounds, images, etc.;

• Information is an objective phenomenon described and represented by data as a carrier.

• Information is the result of data processing and extraction, and is also useful knowledge for humans.

• Information is a message with a certain meaning implicit in a physical signal;

• The purpose of signal processing is to obtain useful information from the signal.

In general terms, information is an objective phenomenon that can be described, and it is also knowledge with a certain physical meaning.

As Shannon said, “The basic results of information theory (in the narrow sense) are all aimed at some very special problems. They may not be suitable for psychology, economics, and some other social science fields.” The limitations of the special information theory are mainly manifested in the three aspects:

• Firstly, the form of information is considered, neglecting the meaning and value of information. This problem cannot be avoided when processing and using information;

• Secondly, it is limited to the category of eliminating random uncertainty under probability theory by studying a random process with clear boundaries between right and wrong. Actually, it is more of the fuzzy phenomenon of “this and the other”. These universal ambiguities cannot be solved with the information theory in the narrow sense;

• Thirdly, statistical information is considered more than non-statistical information. The information transmission is involved, ignoring other information processes that are broader and more important.

### 1.2.2 Different Essential Connotation

There is a significant difference between objective information and subjective cognition. People can recognize, describe, and use information, but they cannot change information with their own subjective thoughts. Even if people have different interpretations of information under their respective subject areas and knowledge background, the objectivity of the source and content of information cannot be denied. As the material is not transferred by human will, the objectivity of information is also not shift with people’s thoughts. Facing the same objective information, there various subjective cognition.

• Objective information exists on the objects, while subjective cognition is in the brain. Objective information is in the form of written or spoken language on paper, sound waves in the air, electromagnetic signals in the tape recorder, and so on. But subjective cognition only exists in human brain.

• Objective information is easy to perceive, while subjective cognition is difficult to perceive. People can smoothly perceive the specific content of objective information through light and sound. But the cognitive process of participants can be reflected to a certain extent through the content of their retelling, and it is difficult to be strictly and accurately determined from the difference of information before and after measurement.

• The state of objective information is stable, while the one of subjective cognition is complicated. Objective information may be recorded on paper or audio, and its specific content could be maintained for a long period of time. However, the differences in various reported content showed obvious irregularities, which reflected subjective cognition on the complexity of change.

• Objective information is easy to repeat, while subjective cognition changes with time. It is easy to repetitively use the same objective information under various circumstances at different time. But the results of them may different from each other, reflecting the time-varying effect of subjective cognition due to changes in subjective information and objective conditions.

There are indeed fundamental differences between objective information and subjective cognition. People have to change the purpose, theories, methods and means of studying objective information and subjective cognition. Relatively, it is more intuitive, simpler and easier to study objective information than subjective cognition. So it is necessary to distinguish the objective and subjective attributes of information, and to define information in the category of objectivity.

### 1.2.3 Difficulty to Guide the Giant Project

It is difficult to adapt to the current needs of informatization when evaluating the effectiveness of complex systems such as operating status, fault discovery and handling. Good correspondence and quantification are the basis to build and evaluate a complex information system. A metric system with multiple indicators may lead to the improvement of overall construction effectiveness. The application effectiveness is the core to build a quality-efficiency indicator system, but there is still a lack of an indicator system to measure the quality and efficiency of complex system informatization. People have to pay attention to the operational quality and operational effectiveness of the complex system under the informatization. The traditional index system is often oriented to the quality of system equipment, such as resource allocation and failure occurrence. Nowadays, it imperative to develop the performance indicators for specific fields under the information metrics of information systems, so as to provide benchmark guidance for comprehensively analyzing, implementing and evaluating the complex system.

System-of-systems (SoS) is a system composed of a series of complex systems [37]. SoS engineering implementation combines many systems with independent operation, independent management, location distribution, emergent behavior and gradual development. The process not only maintains their respective independence, but also realizes more and stronger capabilities of the whole system. When various complex systems converge to form an SoS, it is necessary to further enrich and deepen related theories and methods to effectively solve main problems such as integration, sharing, coordination, evaluation and optimization.

To achieve a wider range and a higher level of sharing and collaboration, it is essential to optimize the overall performance of SoS under the basic requirements when integrating various systems. So it is necessary to effectively bridge the gap between the comprehensive integration of large-scale SoS and individual development of various systems. It may clearly expresses and maintains various information relationships among different systems without bogged down by tedious details, and reasonably balances the allocation of tasks. With the expansion of an SoS, it is important to reshape the original business model in an all-round way that the capacity and effectiveness of SoS as a whole can be improved from local to global, from short-term to lasting, and from relatively simple ideal settings to complex practical environments, through continuous quality-effectiveness analysis with key performance indicators and popularization, in order to achieve a good state of stability, universality, long-term operation, continuous evolution and continuous improvement.

According to the top-level design of the complex system, the system-level components of the complex system can be obtained, and each system-level component is an information system that manages objective information. The rapid development of information technologies such as cloud computing, Internet of Things, mobile Internet, big data, and artificial intelligence has increased the scale of information systems. Furthermore, the super-large-scale complex system needs to consider more factors, such as high-dimensional, multi-source, heterogeneous, nonlinear, uncertain, etc., making the information system more and more complex, and fewer and fewer problems can be solved correctly. Many problems need to be solved approximately by numerical calculation methods. The information system has encountered a major theoretical bottleneck of “difficult to model, difficult to measure, and difficult to calculate”.

The operation of a complex system is a typical complex giant system problem. The factors that affect the results of the operation include basic equipment factors, user behavior factors, etc., and there are many cross-influences between each other. When the information system transitions from big data to strong intelligence, the scale of the information system becomes larger and more complex. As the scale and complexity of informatization in various industries continue to expand, such as air traffic control systems, Smart Court, etc. Focusing on the equipment of the complex system and taking fault handling as the goal, it has been difficult to adapt to the current needs of informatization. How to ensure the high-quality, efficient operation, and great value of informatization has become the focus of attention in the complex system.

The information theory on change said that it is impossible to effectively evaluate and guide the efficiency and capabilities of complex information systems and intelligent computing, which severely restricts the depth and breadth of the construction and application of big data intelligent information systems, and it has been difficult to fully satisfy big data. The increasingly complex and huge needs of intelligent systems have made it difficult to support the sustainable development of the complex world. It is urgent to break through the original shackles of information theory.

## 1.3 The Information Theory on Reflection

Information is the constituent element of the world, and it also reflects the nature of things in the world and the laws of their movement. In a information space, the real world is the essence and true nature of the information space, and provides the source of all information. In turn, the information space reflects the real world and feedbacks the real world by simulating and deducing objects and movements that are costly to conduct physically.

### 1.3.1 The Objective World and the Subjective World

The world is divided into two categories: the subjective world and the objective world [38]. Generally, the subjective world refers to the world of consciousness and ideas, and is the sum of the spiritual and psychological activities of understanding and grasping the entire world. It includes both the process of consciousness activities and the results of consciousness activities. Human concepts, will, desires, emotions, beliefs, etc., are different forms and manifestations of the subjective world. It relies on mankind’s active thinking and awareness of the objective world, mainly cognition, understanding, control and utilization, and is the unity of knowledge, affection, and intention. The objective world refers to the material and perceivable world, which is the sum of all matter and its movement outside of conscious activities. It can be divided into two parts: natural existence and social existence. The former does not depend on anything but exists objectively, and the latter is formed in the process of human social practice but is not transferred by human will. The objective world does not depend on people’s subjective consciousness. It is mainly the connotative nature of the world and the law of extensional motion, rather than a collection of consciousness and concepts.

The objective world and the subjective world are related and distinguished. The information in the objective world can act on the subjective world. We can treat the consciousness, concepts, thinking, and decision-making formed by humans and even other students from the information of the objective world as information. Owing to the objectivity of information, people can collect, transmit, process, aggregate, and apply information with various means. The rapid development of emerging technologies, such as artificial intelligence, brain-like systems, and brain–computer interfaces, is driven by advances that simulate the human mind and then transform humanity’s subjective processes into objective information that can be processed by information systems. At the same time, there are still many essential differences between information in the objective world and consciousness or concepts in the subjective world.

The subjective world consciousness and the objective world information are heterogeneous. The objective world exists outside of human conscious activities, has direct reality, and moves according to its own inherent laws. The information it reflects is objectively existing, but it is different for different subjects. The material basis of external natural existence lies, and the material basis of human social existence is the material production method. Consciousness exists in the human brain, which is extensive and stretchable, and is mainly reflected in the spirit and thinking activities. In this sense, the subjective world is the range and boundary of the intelligence, wisdom, and thinking ability of the subject's conscious activities, as well as the range of thinking capacity that it can accept, understand, and process information. This also directly leads to individual differences, and different subjects may have different understandings when dealing with the same objective information.

On the other hand, the subjective world and the objective world are opposed and unified. Generally speaking, the objective world determines the subjective world, and the objective world is the external space of the subjective world. However, the subjective world is a kind of conscious existence after all. People can assemble and construct objects at will within consciousness, so that the subjective world can not only be the expression and reflection of the objective world, but also deviate from the objective world in some aspects, or even transcend the objective world. The world makes predictions for the future based on existing information. This has led to the incomplete synchronization of the development of the subjective world and the objective world. The subjective world and the objective world have a complicated contradictory relationship. On the one hand, the subjective world affirms and reflects the objective world; on the other hand, it deviates, denies, and transcends the objective world. The two are always intertwined.

Popper [39] further proposed three worlds. The first world is the world of physical objects or physical states composed of all matter and various phenomena in the objective world; the second world is the world of consciousness or mental state, or the world of behavioral intentions about activities; and the third world is the world of the objective content of thoughts. Actually, the third world is the world of human spiritual products, especially the world of scientific thoughts, poetic thoughts, and works of art, and especially emphasized the objective reality and independence of the third world.

Knowledge is the previously unknown patterns in the objective sense or in the subjective recognition. When people produce objective knowledge through subjective spirit, the third world becomes an objective reality, and its existence separates from human beings and exists alone. It can be seen that Popper’s first world and third world are actually a further division of the objective world, that is, the first world contains a part of objective information, the second world is the subjective world in the usual sense, and the third world is completely composed of objective information. Composition, regardless of whether people are aware of the content of these thoughts, they all exist autonomously.

### 1.3.2 Trinity of the Objective World

In the objective world that does not depend on human subjective consciousness, matter, energy, information are its three major constituent elements, which is also called the ternary nature of the objective world. Wiener [12] pointed out that “information is information, not matter or energy.” Steucke [40] deepened this view and said that “information is the third thing alongside matter and energy”. Thus formed the world's material, energy, and information “trilogy”. In fact, the world here refers to the objective world, and does not include the subjective world, because matter and energy obviously only belong to the category of the objective world.

Information is the third thing juxtaposed with matter and energy. It reflects the existence and movement of matter. The world is material, matter is in motion, and motion is regular. The true unity of the world lies in its materiality. From the perspective of nature, things are formed and developed under their own inherent laws, have their own origin and development history, and are all components of a unified material world. Human society is also the long-term development of the material world. Heraclitus said that “one cannot step into the same river twice.” The whole world is the eternally moving material world. The movement in philosophy refers to the changes and processes of all things, which are the inherent attributes of matter and the form of matter existence. Everything is in motion. Some movement is obvious, and people can directly feel it, such as moving cars, flowing rivers, piercing meteors, etc. Some change slowly, and it is not easy to notice, for example, Mount Everest has risen 1600 m in 500,000 years. The laws of nature are mostly expressed as dynamic laws, revealing the one-to-one correspondence between certain things, and pointing out that the existence of one kind of thing must lead to the occurrence of another certain thing. The law of social development is mainly manifested as the law of statistics, which reveals not a simple one-to-one correspondence between things, but a regular relationship between a certain inevitability and a variety of random phenomena [41].

In the ternary nature of the objective world, matter is an objective existence that does not depend on human subjective consciousness but can be reflected by human consciousness. From the new perspective of the trinity of matter, energy, and information in the real world, energy is the material movement ability that does not depend on human subjective consciousness, and information uses matter or energy as a medium. Information reflects the material nature, internal connections and movement patterns of natural and human things in the objective and subjective worlds. In short, matter is the existence of origin, energy is the existence of movement ability, and information is the existence of the connection of things. All kinds of physical information systems can and can only acquire, transmit, process and apply various objectively existing information. Dynamics are essentially the mathematical expression of the regularities and mechanics of motion and change in space and time [42,43,44,45]. It is crucial to comprehensively study the principles of information movement and utilization from the overall perspective of the real world, society, and information systems. Therefore, the cognition of ternary nature satisfies the objective requirements of the operating objects of the information system. These views are completely based on the objective reality of information, which helps the birth of objective information theory [42].

### 1.3.3 Contributions from Objective Information Theory

Objective information theory (OIT) gives a philosophical view that information is the objective reflection of things and their motion states in the objective and subjective world. It presents the concept of information, mathematical definition, sextuple model, primary properties, and metric systems (see Fig. 1.1) for conducting profound and quantitative investigations.

The first is to clearly define the essence of information in the objective category. In response to the diverse conceptual connotations and lack of a comprehensive metric system of information, OIT studies the methods of information reflecting the nature of things in the world and the laws of their movements. It not only conforms to the fundamental positioning of information as one of the three major components of the objective world, but also adapts to the operational requirements that information systems can and can only process objective and real information. Since the information in people’s minds belongs to both objective and subjective categories, many studies do not distinguish the relationship between objective information and subjective conscious activities, which makes the problem extremely complicated. OIT focuses on simplifying the complex, decoupling the objective and subjective attributes of information to a certain extent, and combining the operational requirements of the information system.

The second is to put forward the mathematical expression of information and the sextuple model, which provide a unified, clear, convenient and feasible mathematical theory basis for all subsequent studies. Based on the objective reality of information, the definition of information is proposed. Information is an objective reflection of things and their movement in the objective world and subjective world. In the light of the definition, the sextuple model of information includes noumenon, state occurrence time, state function carrier, reflection time, and reflection function. This model deconstructs the concept of information in three important ways: the dual deconstruction of information subjects, the temporal deconstruction of information duration, and the form deconstruction of information contents. Through these three important deconstructions, we can not only measure the capacity of information, but also other aspects of the information more profoundly, comprehensively and quantitatively.

The third is the information sextuple model combines the internal characteristics and external needs of information. It embodies the rationality of information and its model definition. Through the proof of the basic nature of the information, the model is further improved. It defines information as the reflection from a state set to a reflection set. Objectivity is the constraint of information perception. restorability refers to the fundamental premise of information application. Transitivity is the basic mode of information transmission. Relevance is the important meaning of information existence. Combinability proves that information has a combinatorial nature.

The fourth is that an information metric system is inferred from the sextuple model and the basic properties of information. The metric system of objective information mainly includes 11 indicators: volume, delay, scope, granularity, variety, duration, sampling rate, aggregation, coverage, distortion, and mismatch. The entire system is more comprehensive, and there is independence between measurements. Each metric is expressed in quantitative forms such as the measurement, potential and distance of a specific element. Each element is in several metrics. It provides a basis for quantitative research and analysis of information operation and application of information systems. The significance of such metric system is that it provides important measurement guidance for the evaluation of information systems, apart from providing the ground for information measurement. As the main efficacies of information systems depend on the input and output information, the benchmark for judging information systems should be based on the evaluation indicators of these input and output information.

## 1.4 Discrimination of Two Information Views

Information is the blood, food, and vitality of the world [46]. The achievements of information have promoted human society from the industrial age to the information age [47]. But people’s understanding of information is various, and measuring information is also inconsistent consensus [38]. There is a lack of the widely adopted mathematical expressions to describe the concept of information.

The information theory on change believes that information can only produce meaning when the recipient of the information receives the information. The representative is Shannon information theory. It reveals that the capacity of information in communication systems can be defined as entropy, which has led many people to mathematically regard information as negative entropy. Probability theory and stochastic processes are taken as basic research tools to study the entire process of the generalized communication system, rather than the entire link. At present, there are still research directions such as the deepening of information concepts, the development of information distortion theory and its application in data compression, and the basic theories of computer-centric information processing systems. However, the concept of information is far beyond that in communication systems. Information entropy, as an information expression, cannot meet the general requirements of information science and technology. Shannon information theory cannot effectively evaluate and guide the efficiency and capabilities of information systems and intelligent computing increasing complexity. Scholars are far from reaching a consensus on the nature of information, which is considered as the key obstruction in developing a unified, convenient, and feasible mathematical information foundation. This severely restricts the depth and breadth of the construction and application of intelligent information systems in the era of big data.

The information theory on reflection think that information reflects the nature of things and the laws of their movement, regardless of whether things change or not. The representative is objective information theory. It defines the sextuple model and 11 metric indicators of information to depict the elements and characteristics in the complex information system. Its mathematical foundations are set theory, measurement theory, and topology. Although these theories are relatively abstract, they have a direct and clear correspondence with the statistics and calculation methods widely used by people every day. It is fully applicable to various specific tasks that are generally required in the process of informatization, such as big data, information stream, and information system design and evaluation.

The appearance of the two views of information theory has specific background. Before Shannon information theory, digital communication has made certain developments. With the mathematical principles of communication to create information theory, Shannon brought mankind into the information age and promoted the rapid development of information technology. In the twenty first century, with the development of communication hardware, the birth of big data has brought huge innovations to information systems. Big data has massive volume, a wide variety of categories, a relatively low value density, and a rapid growth rate. The infrastructures for big data have put forward new technical requirements. Shannon information theory on change cannot provide an ideal theoretical description of the complex information system on big data products. To sum up the previous theoretical results and current information changes, Xu Jianfeng et al. proposes objective information theory to revolve around the operating quality and results of complex information systems in the era of big data. From the new perspective of the trinity of matter, energy and information in the real world, it studies the methods of information reflecting the nature of things in the world and the laws of movement. It tries to solve the fundamental theoretical issues such as the nature of information, measurement methods, model algorithms, and computational controllability for the precise control of the applicable evolution, the quantitative calculation, and the inference of information patterns in information systems. Its completeness and practicality will also be tested and revised in many subsequent applications, because any kind of theories can reflect their value and be perfected only in practice.

## 1.5 Chapter Summary

Everything in the world can express existence and movement through its objective reflection, that is, information. Information helps things interact with each other. So information can be viewed at the same value as matter and energy, and it is one-third of the world. People have understood the importance of information, and achieved fruitful results on research and applications. In particular, Shannon revealed the fundamentals of information transmission, and made outstanding contributions to human beings’ progress towards an information society; Zhong Yixin proposed the theory of total information, opening a door for the in-depth interaction of information with human cognition and intelligence. Under the axiomatization, Burgin established the model and operator system of general information theory, providing a demonstration for the use of mathematical tools to study the nature and operation of information. Based on previous results, this chapter explores the information connotation from the information theory on change to the information theory on reflection. There is no consensus on the conceptual description, essential connotation, and theoretical level, especially if the measurement system is not a system, it is difficult to guide the implementation of information system engineering. In complex information systems, information integration reflects the static characteristics and dynamic changes of things, and it is necessary to solve fundamental theoretical problems in information science, such as information essence, measurement methods, model algorithms, and controllability of calculations.