OuYang

Several Comments on Modern Science and Systemic Modeling

Director's Comments: This note is devoted to an organized conversation with Professor Shoucheng OuYang on several important issues related to systemic thinking and modern science. These issues include the state of the modern science, the concept of time, usage of mathematics in the modern science, nonlinear mystery, chaos theory, etc.

During July 22 -- September 31, 2000, Professor Shoucheng OuYang, founder of blown-up theory, was invited by me and visited International Institute for General Systems Studies, Inc., at Grove City, PA, USA. During this time period, several scholars visited our institute and Professor OuYang. Many interesting and fruitful discussions took place during this period of time. As requested by various participants of the discussions and lectures, and due to the fact that his points of view on some problems of the modern science have been totally new to all his colleagues in the western world, I will in this note highlight several key points of these conversations with Professor OuYang. For a more detailed account of Professor OuYang, the reader is advised to consult with [1]. In the rest of this note, Q stands for comments and questions of some participants and OuYang for Shoucheng OuYang. All the statements herein are modified versions by me. If any statement is inappropriate or incorrect, I will be responsible for future corrections.

Briefly, Professor OuYang has been known among his colleagues as a strange characteristic, and has been seen by Professor Wu Xuemou, father of pansystems theory, as a figure with one foot in the Heaven and the other in the Nether World. Professor OuYang has had the spirit to challenge authorities and well-accepted theories from the angle of practical applications, where he discovered theories and developed theories. After 30 plus years of practical experiences and thinkings, he successfully established the known blown-up theory and tropos theory. Among his works, he discovered a practical application of the concept of yin-yang, which was introduced over 3000 years ago, through clockwise and counterclockwise rotations of materials. Especially, OuYang's explanation of "time" has astonished many colleagues.

The Dialog

Q: In your opinion, what kind of a science is the modern science?

OuYang: This problem should be seen from at least the following six angles.

1. In terms of physical states, there exist four known states: waves, mutual reactions of waves and eddies, eddies, and blown-ups of eddies. The so-called modern science is the study of the first state: waves. As for the other three states, the modern science has not yet dealt with, since neither mature theories nor methods exits to handle three situations.

2. In terms of the mathematical physics forms of motion, waves belong to the property of periods. Mutual reactions between waves and eddies are quasi-periodic. Eddies are irregular. And, blown-ups of eddies are relatively non-periodic.

3. In terms of forms of actions, waves take the linear form of the first push, mutual reactions between waves and eddies the nonlinear form of the combined effects of the first push and the second stir. The other two cases all belong to the nonlinear form of the second stir.

4. In terms of its position in the "knowledge river", the modern science is located at the end of the era characterized by regularization. That is because before the time of Lao Tzu of China and of Heraclitus and Democritus of Greece, both eastern and western civilizations had employed irregular structural analyses to understand and to shape the objective world. Roughly speaking, the period of human knowledge transformation is about 2,500 -- 3,000 years. From the time of Lao Tzu and Heraclitus, about 2,500 years has passed by. This time period has been characterized with the regularization of Confucius and Aristotle. So, an interesting question for now is: During the next time period of 2,500 -- 3,000 years, in which direction will the knowledge river flow to? Based on the current activities in science, there has appeared a group of scholars who have proposed various opinions different of well-accepted theories and methodologies of our era of regularization. I am lucky to be one of these scholars.

5. In terms of how to understand the concept of time, the modern science has not resolved this important question.

Q: We learned that you have established a very special explanation for this concept.

OuYang: My explanation is not special. It is an implementation of Lao Tzu's teaching. I think that "time is originated from the rotation of materials and does not occupy a physical dimension." That is, time is not a material. However, without materials, there would be no time. In other words, "time exists after materials and parasites on materials". This end is another realization of Lao Tzu's "have and have not appear at the same time with different names".

In this sense, the modern science can be seen as a science without time. The most the modern science has touched on is only a small part of what we experience and felt, since the revolutionary velocity of the Earth is within the range of human senses. As for the part of human senses about fluids, the modern science has shown its incapability. So, nothing outside our sensing abilities has been dealt with by the modern science at all.

Q: Your explanation of time is indeed very interesting. You can write a high quality paper on this concept alone.

OuYang: My sixth point about your very first question is seeing the modern science as a methodology. It consists of two parts. One is the automorphism of the initial values of integral or differential equation systems, developed on the basis of Newton's determinism, and the other statistical historical replay, developed on the basis of randomness and stochastics. Their essence is the same:

Past quantities = present quantities = future quantities

Which does not truly deal with evolutions at all.

Q: The modern science is measured by the level of mathematics employed. What is your opinion on this end?

OuYang: Since the time when Newton published his <<Mathematical Principles of Natural Philosophy>>, not only natural sciences and social sciences, but also philosophy -- the ultimate level of human thinking -- have seemed to treat mathematics as their highest level of standard or quality. However, mathematics is not equal to theories of numbers. Unfortunately, the modern science has been characterized by quantitative analysis and developed to such a degree that results of quantitative analysis are seen and treated as physical realities or laws of the physical world. As for whether or not quantities can be used to substitute materials or seen as materials, there exist at least the following problems:

1. Quantities are uncertain

Well-known irrational numbers, such as square root of 2, e, …, are uncertain in practical applications. However, these numbers can't be seen as uncertain. Next, the situation of large quantities with small increments is uncertain, since it can't be measured or calculated accurately. The third is the mutual reaction of many variables. Here, no matter whether it is the quantitative precision or acting effects, no levels of quantitative magnitudes can be adequate to represent the situation.

2. The artificiality of 0 and ¥

The important number 0 is a human invention and not an objective existence. Evidently, without the number 0, the entire mathematics would paralyze, since this number 0 helps the establishment of base systems of all numbers. Secondly, the reciprocal of 0 is ¥ . Up to now, we all know that the product of 0 and any number is 0 and that the division of a non-zero number by 0 is ¥ . That is, the operations of multiplication and division with 0 have become orderless. Mathematics has always been characterized by its logic rigor. However, the multiplication and division of 0 have led to a paradox. What's important in applications is that 0 can neither make a piece of sand disappear nor make a piece of sand infinitely large. Therefore, quantities can't be used to substitute materials.

3. Current quantitative analysis is about regularization and large probabilization

Evidently, it has been known that calculus is valid on the basis of continuity and that statistical methods are powerful within the range of stable series. However, what's truly important is irregularities and small probability objective existences. So, the current mathematical methods are still not powerful enough to represent the physical world accurately.

4. Equal-quantitative non-isomorphisms

Quantities are a way of abstraction for counting, which is not the same as any other physical properties. So, they are not powerful enough to deal with the problem of materials' structures.

5. Non-dimensionalization

Non-dimensionalization is one key method used to deal with partial differential equations. However, after non-dimensionalization is carried out successfully, even if the resultant equations are solvable analytically, the solution does not really tell anything useful.

6. Quantitative continuity and continuous particles

The continuity of quantities cannot be applied to mean the existence of continuous particles. In fact, no one has seen a mathematical point and there does not exist any continuous media in real-life, since no matter how small particles can be, their ball-shape guarantees that they can't fill up a space completely to form a so-called continuous media. Conversely, due to the property of non-separability of irrational numbers, no continuous particles can be separated out of a continuous media. Therefore, the particle mechanics is neither an epistemology nor a part of philosophy. As a theory, it is not logically rigorous. As a method, it is only an approximation under special conditions with vibrations of solids and wave motions of fluids as its range of valid applications.

What is left behind by the modern science, developed in the past 300 plus years, is only the chimes of a midnight church bell (waves).

Q: According to what you just said, the theoretical physics, derived largely on quantitative analysis, wouold naturally contain many problems of principle?

OuYang: It can be said that the mechanics, developed since the time of Newton, in essence, has not really resolved the problem of what forces are. In other words, all the studies from Newton to Einstein have continuously stayed in the Aristotle's logic system, where forces exist independently outside materials, including Einstein's mutual reactions of energy propagation. However, mutual reactions can't be linear manifolds. Up to now, studies of dynamic systems have been limited to the analysis of forms of motion of the object being acted upon; and these so-called forms are all quantities. That is why the science still can't answer the following question: Even though there does not exist any "God" in natural sciences, how can the natural sciences still be "first push"? Here, Newton's second law of mechanics is a realization of the first push by "God". Quantities are abstract counting intuitively seen out of materials. So, they are not the same as any physical materials. However, the modern science has accidentally been supported solely on quantitative analysis, and has been developed to such a state that without quantitative analysis, no theory will be seen as scientific. Now, an apple plus a pear equals two fruits. What do these "two fruits" tell us?

What Newton's third law tells us is nothing more than the equal quantitative acting and reacting. However, the law does not spell out the most important information on how the acting and reacting objects would move or whether or not their motions would follow the second law. Currently, there is no explanation on what the "universality" (or the choicelessness of falling objects) and "gravitation" in Newton's law of universal gravitation are.

Q: Nonlinearity has been a hot topic in the modern science. Could you talk about your opinion on this subject matter?

OuYang: What needs to be clear first is that the concept of nonlinearity currently, widely discussed is the nonlinearity of dynamic systems. What is strange and interesting to observe is that even though such nonlinearity has been known to be the mutual reactions of dynamic forces, the dynamic term has been mostly linearized. Studies on mutual reactions belong to the category of problems of Newton's third law. They are studies about face-to-face fightings, which are different of Newton' second law, which is about being beaten. So, problems of Newton's third law should not be treated as those of the second law. Since it is difficult for face-to-face fightings to hit opponents' centers of masses exactly at the same time, the consequences of these fightings are spinning motions. That is, the central difference between nonlinear and linear dynamics is that of forms of movements, where nonlinear dynamics implies rotations and linear dynamics rectilinear movementes. In other words, nonlinearity should not be and can't be linearized or semi-linearized.

Q: I learned that you have a different point of view on chaos from those researchers specialized in chaos theory. Could you please spend some time on this matter?

OuYang: What I need to declare is that I am not against chaos. Instead, I do not agree with many claims of the so-called chaos theory. As effects of mutual reactions between quasi-equal quantities, it does not need to be termed to as chaos, what a misleading word. Of course, there is no need to change the term now especially since it has been so widely employed (in several different ways).

In terms of the chaos theory, it does not itself know what is meant by "chaos". The purpose of the theory is to describe the non-periodic phenomena, which in fact is the problem of computational inaccuracy experienced by large quantities with infinitesimal differences. The so-called "chaos" can be obtained out of both linear and nonlinear models. Therefore, the concept of chaos cannot be employed as a characteristic of nonlinearity. And, if the characteristics of nonlinearity are called chaos, then the study of the chaos theory should be ended.

Next, the chaos of the chaos theory is not really about non-periodic flows. Instead, it is the graph in relevant phase spaces resulted from the quasi-equilibrium solutions out of error-value calculations. These error-value calculations appear when either the evolution values and the initial values or evolution values themselves are quasi-equal, or say, approximately equal. Also, the chaos of the chaos theory may appear when the time step is small. In this case, the graphs, approximating the phase space of the initial values and consisting of error-value evolutions caused by the small time step, will be the so-called chaos.

What needs to be pointed out is that the chaos of the chaos theory is sensitive not only to the initial values, but also to all parameters and variables involved in the calculations. Especially, it has been almost 40 years since the time when the concept of chaos was first introduced. The main activities of chaos are still pretty much staying at the "sensitivity to initial values". This end at least indicates the fact that no much progress has been made in the chaos theory itself in the past 40 years. At the same time, since it has been seen as a scientific truth, there is no need for any one to protect it from different opinions and objections.

2. Related Publications and Readings

All points of view presented here, are either new or can be read in the following references with detailed theoretical analysis and numerical computations. At this junction, I would like to express my sincere thanks to many colleagues who had more or less involved in our discussions or debates during July 22 -- September 31, 2000. Specifically, I feel in debt to Professors Hector Sabelli, George Highland, Richard Port, Zhenqiu Ren, and retired IBM computer expert Don McNeil.

[1] Y. Lin (1998). Mystery of nonlinearity and Lorenz's chaos. Kybernetes: The International Journal for Systems and Cybernetics, vol 27, nos. 6 & 7.

[2] S. C. OuYang, J. H. Miao, Y. Wu, Y. Lin, T. Y. Peng and T. G. Xiao (2000). Second stir and incompleteness of quantitative analysis. Kybernetes: The International Journal for Systems and Cybernetics, vol. 29, pp. 53 -- 70.

[3] Y. Lin (2000). Some impacts of the second dimension. Proceedings of the 15^th European Meeting on Cybernetics and Systems Research, Vienna, April 25 - 28, 2000. Pp. 3 - 8.

[4] Y. Lin, C. Li, S. C. OuYang and Y. Wu (1998). The mathematical structure of population and Lorenz's models and the problem of 'chaos'. Systems Analysis Modelling Simulation, vol. 30, pp. 93 - 108.

[5] Y. Lin and Y. Wu (1998). Blown-ups and the concept of whole evolution in systems science. Problems of Nonlinear Analysis in Engineering Systems, vol. 4, np. 7, pp. 16 - 31.

[6] S. C. OuYang (1998). Structural analysis and weather forecasting (in Chinese). Press of Meteorology, Beijing.