Mathematization of natural sciences

Exact science in its generally accepted sense can be referred to as a family of specialized natural sciences, each of them providing evidence and information about the different aspects of nature by somewhat different working methods. It follows that mathematics in its pure sense does not enter into this frame, its object of study being not nature itself. Being independent of all observations of the outside world, it attempts to build logical systems based on axioms. In other words, it concentrates on formulating the language of mathematical symbols and equations which may be applied to the functional relations found in nature.

This “mathematization”, in the opinion of most specialists, is witnessed first in physics which deals with general laws of matter and energy on subatomic, atomic and molecular levels. Further application of these mathematical laws and studies is made by chemistry and results in structural bonds between the elements of matter being established.

 

2) Check up for comprehension:

1. What is generally understood by exact science? 2. How does the author describe “specialized” natural sciences? 3. Why does mathematics not belong to this family? 4. What is the objective of mathematics? 5. Is there only one definition of the objective? 6. What does the application of mathematical laws in chemistry result in?

 

 

Text 3. A. Read the introduction to yourself and state its topic (follow the guide words to the author's thought equivalent to однако, скорее, noэтому ). Answer the questions: What is the main characteristic of the problems discussed in the four units of this book? Are the problems discussed in detail and covered in full?

INTRODUCTION

In the four units, forming this book an attempt is made to keep the discussion within the range of problems of common interest for most scientists whatever their particular fields. However, it is by no means claimed that the items grouped under the same topic deal with the problem discussed in sufficient detail, let alone cover it in full. Rather, it should be emphasized that the items include but fragments of opinions concerning the subject under discussion expressed by outstanding scientists on different occasions. Therefore, what is presented here is, of necessity, only part of what was said
elsewhere.

The first discussion is focused on the relations between pure and applied research, theory and experiment, science and technology, scientist and layman. The discussion is opened by the Soviet physicist academician Lev Artsimovitch and concluded by the American physicist prof. K. K. Darrow. It covers the following items: A. Science and Technology. B. What Science Is. G. Research: Fundamental and Applied, and the Public. D. Scientific Innovation: Its Impact on Technology.

B. Give Russian equivalents of: an attempt is made; what is presented here is... only part of what was said elsewhere.

Text 4. A. Look through the text concentrating on the beginning of each paragraph and write down a plan, either in English or in Russian (time limit — 10 min.):

SCIENCE AND TECHNOLOGY

1. Science problems can be roughly classified as analytic and synthetic. In analytic problems we seek the principles of the most profound natural processes, the scientist working always at the edge of the unknown. This is the situation today, for instance, within the two extremes of research in physics — elementary particle Physics and astrophysics — both concerned with the properties of matter, one on the smallest, the other on the grandest scale. Research objectives in these fields are determined by the internal logic of the development of the field itself. Revolutionary shocks to the foundations of scientific ideas can be anticipated from these very areas.

2. As to synthetic problems, they are more often studied because of the possibilities which they hold for practical applications, immediate and distant, than because their solution is called for by the logic of science. This kind of motivation strongly influences the nature of scientific thinking and the methods employed in solving problems. Instead of the traditional scientific question: “How is this to be explained” the question behind the research becomes “How is this to be done?” The doing involves the production of a new substance or a new process with certain predetermined characteristics. In many areas of science, the division between science and technology is being erased and the chain of research gradually becomes the sequence of technological and engineering stages involved in working out a problem.

3. In this sense, science is a Janus-headed figure. On the one hand, it is pure science, striving to reach the essence of the laws of the material world. On the other hand, it is the basis of a new technology, the workshop of bold technical ideas, and the driving force behind continuous technical progress.

4. In popular books and journals we often read that science is making greater strides every year, that in various fields of science discovery is followed by discovery in at steady stream of increasing significance and that one daring theory opens the way to the next. Such may be the impression with research becoming a collective doing and scientific data exchange a much faster process. Every new idea should immediately be taken up and developed further, forming the initial point of an avanlanche-like process.

5. Things are, in fact, much more complex than that. Even year scientists are faced with the problems of working through thicker and tougher material, phenomena at or near the surface having long been explored, researched, and understood. The new relations that we study, say, in the world of elementary particles at dimensions of the order of 10^-13 cm or in the world of superstellar objects at distances of billions of light years from us, demand extremely intense efforts on the part of physicists and astrophysicists, the continuous modernization of laboratories with experimental facilities becoming more and more grandiose and costing enormous sums. Moreover, it should be stressed that scientific equipment rapidly becomes obsolete. Consequently, the pace of scientific development in the areas of greatest theoretical significance is drastically limited by the rate of building new research facilities, the latter depending on a number of economic and technological factors not directly linked to the aims of the research. It may take, for example, more than 10 years from the initial decision to build a 100—200 billion electron volt accelerator to its completion. It should be borne in mind, too, that few measurements and readings given by these great facilities push science forward, results of any great significance being very rare. For instance, tens of thousands of pictures taken during the operation of an accelerator will have to be scrutinized in the hope of finding, among typically trite processes, signs of a new interaction or of a new event whose presence or absence may confirm a theoretical idea.

 

B. Paragraph Study.

Read paragraph 1.

1. Identify the topic sentence and the illustrating sentences. Find the sentence containing the author's prognosis and the word indicating that it is a prognosis.

2. What is meant by the situation and these very areas?

Read paragraph 2.

1. Identify the topic sentence. Answer the questions: What are the two motive forces behind synthetic and analytic research? What are the consequences arising from the change in motivation for research? What is the present-day relation between science and technology? What is meant by the doing?

2. Identify two sentences similar in meaning in paragraphs 1 and 2.

3. Identify the words which reveal a comparison in the first sentence of paragraph 2.

4. Translate the last sentence of the paragraph into Russian.

Read paragraph 3.

1. Identify the topic sentence and the sentences developing its idea.

2. Give Russian equivalents of striving to reach the essence … and the workshop of bold technical ideas.