A Novel Map of Knowledge for Science

by   Fan Shen, et al.
Queen's University Belfast

With the expansion of scientific research, the number of scientific research results is increasing. How to summarize these data has become an urgent problem. Therefore, knowledge mapping methods come into being, providing a lot of management and application functions. However, it is still a problem to fully understand the knowledge map, especially in the field of sociology. In this paper, a three-dimensional knowledge map is proposed with time, space and number based on category and numericity, which concludes all the scientific problems related to numericity interdisciplinary. Compared with the traditional way, this map is normative, and puts forward the general production criteria of labeling and digitization. It is also intuitive and readable, on which nature, society and formal science are expressed in the same picture. The scientific methodologies are summarized, so that the methods with similar logic between different disciplines can be used for reference in development. Some social subjects are expressed more vividly than traditional text-based expressions, and are compatible with the natural science system. Mathematics also show its importance on the map as formal Science, indicating that it is the key to the development of science. This is not only a preliminary model of a comprehensive scientific worldview, but also a preliminary framework for the connection and cooperation of various disciplines in the future.


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With the expansion of scientific research, the number of scientific research results is increasing. How to summarize these data has become an urgent problem[1] Therefore, knowledge mapping methods come into being, providing a lot of management and application functions[2, 3]. However, it is still a problem to fully understand the knowledge map, especially in the field of sociology[4, 5]. In this paper, a three-dimensional knowledge map is proposed with time, space and number based on category and numericity, which concludes all the scientific problems related to numericity interdisciplinary. Compared with the traditional way, this map is normative, and puts forward the general production criteria of labeling and digitization. It is also intuitive and readable, on which nature, society and formal science are expressed in the same picture. Some social subjects are expressed more vividly than traditional text-based expressions, and are compatible with the natural science system. Mathematics also show its importance on the map as formal Science, indicating that it is the key to the development of science. This is not only a preliminary model of a comprehensive scientific worldview, but also a preliminary framework for the connection and cooperation of various disciplines in the future.

Keywords Map of Knowledge, Categorization, Scientific method, Scientific disciplines, TSN-CS

1 Introduction

With the development of society, the accumulation of scientific and technological knowledge is increasing, and there are more and more interdisciplinary subjects[6, 7, 8]

. The cost of knowledge classification, learning, retrieval and application is also getting higher. Scientists have been trying to find a way to classify knowledge

[9, 10], but there is no systematic objective method at present.

A long time ago, under the simple category theory, Ionian philosophy consider there are 4 basic elements of matter, while ancient China divided them into 5 elements. After that, philosophy of science rose, Aristotle, Kant[11], Hegel[12] and more scientists made contribution in their own ways. In order to provide a reliable theoretical foundation for modern science, philosophers seek a comprehensive philosophy of science[13, 14]. At the same time, social sciences are moving towards quantification[15], religious philosophy is also seeking new deconstruction, integration and progress[16, 17, 18], although they are too complex to construct recognized frameworks.

With the advent of information explosion era, the task of scientific knowledge map has gradually changed from philosophical discussion to numerical summarization[19, 20]

. Knowledge map is becoming popular gradually, and its drawing is more completed by information science, knowledge engineering and informatics

[21, 22]. The focus of scientific attention began to fall on each specific discipline, and the cognitive differences between them became bigger[23], which reduced the level of overall thinking[24].

This paper will try to build a framework from the engineering perspective with the simplest mathematical and categorical thinking, so as to understand the nature and mission of science conveniently. At the same time, the numerical framework can be managed by computer, and can also be analyzed and mined by machine learning. In this way, scientific research can be carried out more clearly and effectively under the guidance of logic and philosophical methodology.

2 Definition of Coordinate System

In this paper, the three basic dimensions of time, space and number are adopted, and the logarithmic coordinate axis is used to construct the three-dimensional coordinate system considering the scale differences among various disciplines. Therefore, , , , where t is a time measure in seconds, s is a spatial measure in meters and n is the number, and the unit is constant . In this paper, this system is called as Time-Space-Number Coordinate System (TSN-CS).

Each discipline is located to the coordinate axis with the numerical attribute of its research object. For example, the time quantity can be selected as the overall life or cycle period, and the space quantity can be selected as its own diameter, orbit diameter, movement distance, etc. In particular, in order to distinguish the composition of each other, taking the human individual as the benchmark, the number of groups composed of human individuals is recorded as , while the number of cells and molecules constituting the human body is recorded as . Due to the limitations of the author’s knowledge scope and working time, this paper only selects some typical disciplines and puts them into the coordinate system as examples, as shown in table 1. The final form of knowledge map is shown in the figure 1.

Discipline Sample Reference
Classical mechanics Human observer 1.0E+00 1.0E+00 1.0E+00 Human as observer
Galactic astronomy Galaxy 7.1E+15 1.0E+21 2.0E+12 Galactic year from wiki
Planetary science Planet earth 8.6E+04 1.3E+07 1.0E+00 Earth’s rotation
Stellar astronomy Star sun 2.1E+06 1.4E+09 1.0E+00 Solar rotation
Biology Macro molecular 1.2E+01 1.0E-09 1.0E-27

Same as molecular (estimated)

Chemistry Atom 4.0E-07 1.1E-10 1.0E-28 Bohr radius
Chemistry Molecular 1.2E+01 7.4E-11 1.0E-27 From atom/3 (est.)
Engineering Machinery big 3.2E+08 3.0E+02 1.0E+02 10 years (estimated)
Engineering Machinery small 1.6E+07 1.0E-03 1.0E+00 0.5 year (estimated)
Medicine Organ/Cell 2.6E+05 2.0E-05 1.0E-14 Villi of small intestine renew in 3 days
Optics Moving light A 1.0E+13 3.0E+21 1.0E+00
Optics Moving light B 1.0E-10 3.0E-02 1.0E+00
Optics Photon 1.3E-15 2.8E-15 1.0E-28 Violet light
Quantum mechanics Electron 4.5E-07 2.8E-15 1.0E-30 From wiki and calculation
Quantum mechanics Virtual quantum 1.8E-02 1.1E-10 1.0E-30 Scaled from orbit of Electron
Macroeconomics A country (UK) 3.2E+07 5.6E+05 6.8E+07 1 country
Microeconomics A people 3.2E+07 1.5E+01 1.0E+00 1 people
Politics Capitalism 2.6E+06 1.0E+02 2.0E+02 1 middle company
Politics Libertarianism 2.6E+06 5.0E+00 1.0E+00 1 people
Politics Socialism 2.6E+06 5.6E+05 6.8E+07 3 month
philosophy of religion Buddhism sentence A 1.0E+00 1.0E+00 2.1E-05 From Buddhism x60n1115
philosophy of religion Taoism sentence A 2.2E+09 1.0E+00 1.0E+00 From Tao Te Ching
Sociology (Marxism) A company 8.6E+04 1.0E+02 2.0E+02 1 company
Sociology (Marxism) A country (UK) 8.6E+04 5.6E+05 6.8E+07 1 country (UK)
Sociology (Marxism) A people 8.6E+04 5.0E+00 1.0E+00 1 people
Table 1: Coordinate values of disciplines/objects on TSN-CS
Figure 1: Natural, Formal and Social Sciences on TSN-CS

As shown in the figure 1, it can be seen that the coordinate system represents a number of disciplines of natural science, including basic sciences such as physics and biology, as well as applied sciences such as engineering and medicine. Most of them are located on or below the plane of . At the same time, due to the establishment of innovative quantitative axis, social sciences also get objective expression in numerical level, most of them are located in the position of . Statistics in formal science is represented by arrows. As a typical mathematical operation, it exists in various disciplines of quantum mechanics and sociology in physics. Obviously, the coordinate system provides a new possibility for scientific induction.

3 Natural Science on TSN-CS

Most disciplines of natural science can be positioned on TSN-CS as figure 1.

Engineering machinery is the most mature theory and the most successful application subject. Compared with other disciplines, it is closest to the plane and is not far away from the observer in scale. Therefore, a preliminary conjecture can be made, that the closer to the plane, and the smaller the distance to the observer’s origin, the simpler the subject will be.

Compared with engineering science, the development of medicine, biology and chemistry to the micro part is more difficult. To a certain extent, medicine can be regarded as an applied discipline of biology[25], both of which are extremely difficult due to the large number of irregular cells in research and application. Compared with the two, chemistry is more tiny. This undoubtedly proves the importance of N-axis in the graph, that is, the number of research objects is an important indicator for the classification of disciplines.

The scales of modern physics from quantum mechanics to astronomy can be expressed on TSN-CS. With the invention of tools, the scope of physics is expanding both in micro and macro[26, 27].

The current quantum formula is given in the form of statistical probability

[28], which is different from most engineering and astronomical formulas. According to the thought of TSN-CS, this paper can double-locate quantum mechanics, one of which is located in the real quantum space-time scale that can not be observed accurately by human beings, and the other is located in the statistical space-time scale that can be observed accurately by human beings, which is a virtual point. Therefore, it can be assumed that the current quantum mechanics observation does not reach the real scale of quantum time and space, but only to reach the scale that can be studied by human beings, so it is a statistical formula. Therefore, Schrodinger’s cat paradox can be explained intuitively, that is, the half dead cat only sits on the virtual point, and the dead or alive of the cat in the real point can be obtained from the observation of an exact time.

4 Formal Science on TSN-CS

TSN-CS can also calibrate formal science. As can be seen from the figure 2, changes in time, space and quantity are involved in natural science research or engineering applications. This change is reflected in the movement of each coordinate axis direction, and the moving tool is mathematics. In the view of this paper, formal science themselves do not have real research object in the world, but are essential tools of science, which run through all aspects. They reorganize the information of the research object and transmit it to the observer, such as statistics, which reorganizes the economic data of the group into a single economic data for the observer.

In particular, on the number N-axis, due to the discrete characteristics of the research object, the downward differential operation can not be carried out, so it can only be counted upward. This may be one of the reasons why the social science had not created close connection with natural sciences, because it is unable to do reliable transform from high-level to lower. At present, there is no specific solution to this problem in mathematics. The hot machine learning optimization nowadays may be one of the solution for it.

5 Social Science on TSN-CS

Social sciences include sociology, economics, politics and so on. They are often difficult to be compatible with the natural science, because most of their research objects are groups rather than individuals. The N-axis of TSN-CS in this paper can express the number of individuals[29, 30]. For the convenience of observation on TSN-CS, this paper defines its T-value artificially, i.e. 1 year in economics, 1 month in politics and 1 day in sociology.

Economics is a subject that is relatively close to data in social science, so that several typical branches can be demarcated according to the attributes of their research objects. As the research object of macroeconomics is a country and society, and the research object of microeconomics is individuals and companies, the calibration of these 2 disciplines could be shown in the enlarged part of figure 1

. Obviously, there is no distinction between primary and secondary, and statistical methods can become a tool for connecting. This idea of local and global research is very similar to physics and industry, which is in line with the current general scientific logic, such as finite element method. However, there is no mature industrial method from macro to micro at present,, only through probability theory and optimization ideas such as game theory and dynamic programming to solve the ideal value, which needs further development of mathematics mentioned in the last section.

For politics, the ideology of comparative politics is selected to discuss in this paper. liberalism, capitalism and socialism are most typical ideologies, which respectively attach importance to the individual, capital and the whole society, and each has its own advantages. As shown in the figure 1, these respective focuses of ideologies can be clearly demarcated, and the differences are the focuses of some conflicts and wars in the world. Scientists may be able to help find a balanced and stable solution from the perspective of optimization theory, so as to avoid the political form itself becoming the fuse of interest disputes, even make the national policy more reasonable and effective.

The research field of sociology is broader than economics and politics. Many theoretical researches are difficult to be described by numerical value, but the development of sociology is gradually approaching numerical value. In the early period of sociology, Comte’s positivism advocated the observation and classification of objects. Later, Marxism introduced the mathematical formula of economics into the study of sociology[31], Émile Durkheim pioneered the introduction of statistics into sociology[32]. Nowadays, big data has become one of the indispensable sociological research methods. The more suitable typical example here is Marxist theory. As can be seen from the picture, in the early society, the means of production was in line with the positioning of individuals. With the development of capitalism, the means of production moved towards companies, and even large projects reached the national level. This is an intuitive expression of Marxist theory.

For religious philosophy, the author does not know much except some popular statements from Buddhism and Taoism. Referring to the philosophy of hermeneutics paradigms[33], these statements can also be calibrated on TSN-CS as a draft. For example, the Buddhist Scripture consider that there are tens of thousands lives in a bowl of water (Philosophy of Buddhism: sencence A, see on figure 1). Taoism believes that life should be cherished and valued (Philosophy of Taoist sencence A). These philosophical thoughts can be calibrated to enrich these scriptures on TSN-CS, and the scientific orientation of religious philosophy can be obtained with certain extent.

In a word, only by establishing a reliable mathematical model between groups and individuals can some sociological problems be solved optimally. For example, Matthew effect in economics, corruption in politics and administration, aggregation and division of countries and groups. Relying on TSN-CS, scientists can identify some key needs like mathematical methods in sociology, and then focus on investment.

6 Novel Understandings from TSN-CS

Figure 2: Understanding from TSN-CS

In order to make the current science more clear, an observed zone can be created on TSN-CS, as shown in figure 2. The boundary of this zone is not accurate proved, but it can be determined that , when , where X could be T, S or N. It can be used to represent the observation range of current science, in which the research objects are observed and used. The string theory, which is expected to unify physics, is still much far away. In addition, taking light speed as the research object, a group of points can be defined, and a wall of light speed from can be obtained. At present, all known disciplines are located on the same side of the wall of light speed, while the other side belongs to the unidentified superluminal range. For the scientific problems close to the plane, it needs to be corrected by the special theory of relativity.

According to the figure 2, the goal of scientific research can be simply summarized into three parts:

  1. Discovery is to broaden the observed zone.

  2. Research is to acquire laws within observed zonee.

  3. Application is to apply acquired laws to human life.

According to TSN-CS, it can be predicted that the ultimate scientific theory of human expectation should not only be applicable to all scales of time and space, but also be able to adapt to the influence of number dimension.

7 Advantage and Limitation

This paper raised a new method for knowledge map in science, and obtained the TSN-CS, which enables to locate disciplines and research targets with numerical properties. This TSN-CS has the following advantages:

  1. Categorization: according to the traditional way, the knowledge map is demarcated in the form of three labels, which makes the categorization more standardized and intuitive.

  2. Numerization: according to the modern way, the disciplines is demarcated in an objective form, which makes the knowledge map objective and unified instead of subjective and arbitrary.

  3. Arrow of formal science: bring the formal science into the numerical knowledge map, find their position in scientific research, and better serve the natural science.

  4. Quantity axis: it enables social sciences to be incorporated into knowledge map, interact with natural sciences, and provide opportunities for formal sciences to be applied.

  5. Worldview: a more comprehensive understanding of scientific system can be obtained from this, which is conducive to the understanding of science itself and the development of philosophy of science.

  6. Foresight: current distribution of scientific knowledge could be found, so as to understand the current situation of human research. According to the vacancies and boundaries, future direction of research can be concluded, providing some references for the optimal allocation of research funds.

There are also some limitations in TSN-CS.

  1. Number of tags: Although this framework can calibrate many disciplines, it can only be used at relatively high level. For specific scientific problems, there may be a lot of overlap on the coordinate axis, and can not be accurately described. In addition, the number of dimensions can not be more than three according to human spatial cognition.

  2. Numerical difficulty: this method adopts the basic principle of numerization, many disciplines are not applicable as they can not be numerized. For example, many traditional sub disciplines of sociology, the structure of graphene, the morphology of animals and plants and other issues, it is difficult to find labels that can be used for numerization.

In a word, the purpose of this method is to provide some references for the application of philosophy of science and knowledge management in engineering and application view, so as to make the scientific research more comprehensive in vision, clearer in direction and closer in connection.


The author is very grateful to Queen’s University Belfast for the balance between work and life, which enables the author to think and write this paper freely after work.


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