4. Find a relation between the doubling period Tп, life time τπ and the coefficient of problem reproduction g.

Solution. By the definition K(t) = gK(t₀), then similarly to the expression (5) one gets:

T_g = lng/а (15)

According to the definition (8):

T_g = τп(t) (16)

Then, solving the equations (6), (15) and (16) jointly, one gets:

T_п(t) = ln2 * _π(t)/lng, (17)

what is required to prove.

In the general case the equation (1) will be rewritten in the form:

dK(t)/dt = gK(t) (18)

Then similarly to (3) a solution of the equation (18) will have the form:

Obviously from the expression (19) for the chain reaction of the process of knowledge the coefficient of reproduction of the urgent scientific problems g have a value:

g > 1 (20)

This leads to the fundamental conclusion:

The general number of the urgent problems as the civilization is developing gradually increases. For timely immediate solution of new problems it is required to involve more and more number of scientific employers. Hence, it is necessary to create new research institutes systematically.

5. Coefficient of problem reproduction “g” and main conclusions connected with it.

A coefficient of problem reproduction g – is a number equal to a ratio of newly arising problems to the number of the old scientific problems in this developing society.

At g = 1 the mankind or a society begin to solve infinitely qualitatively the same problems of practical character and the society does not develop intellectually.

At g < 1 the society for the finite time period completely solves all problems, worked by the previous generations, completely loses the intellectual interest to existence. As a result of the intellectual degeneration the society as a civilization dies.

Thus it is seen that the science is not only the significant factor in the society, but substantially is the main determinative condition for life of the human society. By this reason the strict consideration of the basis of planning of the scientific research is quite actual.

Conclusions:

1. The science is the main determinative condition for the life of the human society;

2. The large scientific potential causes the large economic potential, but not vice versa;

3. For the creation of the large scientific (and hence economic) potential it is necessary the large country (or group of countries) with large population.

6. Goals and objective regularities of science development.

A classification of the practical direction of the science is usually reduced to division of the scientific research for fundamental, applied and industrial. The last two types of the scientific research do not require any comments, the basis of their planning, methods of carrying out and order of accounting are obvious – they are subordinated to the Objective and Schedule plan of the Requester (“who pays that orders the music”).

The social-psychological problem is a conception of “fundamental research”, that is that process of knowledge, which obeys the relations (1) - (21). What is the “fundamental research” and what they are necessary for (“fundamental” – strong, hard, large, basic, deep, substantial). In the Large Soviet Encyclopedia the conception of the fundamental scientific research is defined the following way: «Scientific research – is a process of production of knowledge, one of types of cognitive activity.

Scientific research is characterized by objectivity, reproducibility, conclusiveness, accuracy (what is understood differently in different field of science). There are two levels interrelated with each other: empirical and theoretical. There are established new facts of science and on the base of their generalization the regularities, general for this subject field, are formulated, which allow explaining the earlier discovered facts and empirical regularities, and also prognosticating the future events and facts.

The basic components of the scientific research are the problem formulation; preliminary analysis of the information available, conditions and methods of problems solution; formulation of the initial hypothesis; planning and organization of the experiment; carrying out of experiment; analysis and generalization of the results obtained; final formulation of new facts and laws; obtaining of explanations or scientific prognostications. For the applied scientific research the additional stage: implementation of the obtained results into the industry.