The manager as a teacher: selected aspects of stimulation of scientific thinking
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thing with certain degree (e.g. 80%) of probability. Statistical models apply when we do not know all elements of the system and laws of their interaction. Then we hunt for words systems on the basis of significant features, we somewise measure the results of action of all these systems operating in words conditions (clinical tests) and calculate mean value of the result of action. Having assumed that the given subject closely approximates the others, because otherwise he/she would not be words to them, we say: “Once these (people) have such-and-such parameters of the given system in such-and-such conditions and they live without any problems, then he/she should have these same parameters if he/she is in the same conditions”. However, a subjects living conditions do always vary. Change or failure to account even one significant parameter can change considerably the results of statistical researches, and this is a serious drawback of statistical mathematical models. Moreover, statistical models often do not reveal the essence of pathological process at all. The functional residual capacity (FRC) of lungs shows volume of lungs in the end of normal exhalation and is a certain indicator of the number of functional units of ventilation (FUV). Hence, the increase in FRC indicates the increase in the number FUV? But in patients with pulmonary emphysema FRC is considerably oversized. All right then, does this mean that the number of FUV in such patients is increased? It is nonsense, as we know that due to emphysema destruction of FUV occurs! And in patients with insufficiency of pumping function of left ventricle reduction of FRC is observed. Does this mean that the number of FUV is reduced in such patients? It is impossible to give definite answer to these questions without the knowledge of the dynamics of external respiration system function and pulmonary blood circulation. Hence, the major drawback of statistical models consists in that sufficiently reliable results of researches can be obtained only in the event that all significant conditions defining the given group of subjects are strictly observed. Alteration or addition of one or several significant conditions of research, for example, stature/height, sex, weight, the colour of eyes, open window during sleep, place of residence, etc., may alter very much the final result by adding a new group of subjects. As a result, if we wish to know, e.g. vital capacity of lungs in the inhabitants of New York we must conduct research among the inhabitants of New York rather than the inhabitants of Moscow, Paris or Beijing, and these data may not apply, for example, to the inhabitants of Rio de Janeiro. Moreover, standards/norms may differ in the inhabitants of different areas of New York depending on national/ethnic/ identity, environmental pollution in these areas, social level and etc. Surely, one may investigate all conceivable variety of groups of subjects and develop specifications/standards, for example, for males aged from... to..., smokers or non-smokers of cigars (tobacco pipes, cigarettes or cigarettes with cardboard holder) with high (low) concentration of nicotine, aboriginals (emigrants), white, dark- or yellow-skinned, etc. It would require enormous efforts and still would not be justified, since the world is continually changing and one would have to do this work every time again. Its all the more so impossible to develop statistical specifications/standards for infinite number of groups of subjects in the course of dynamic processes, for example, physical activities and at different phases of pathological processes, etc., when the number of values of each separate parameter is quite large. When the systems details are completely uncertain, although the variants of the systems reaction and their probabilistic weighting factors are known, statistical mathematical model of system arises. Inaccuracy of these models is of fundamental character and is stipulated by probabilistic character of functions. In process of studying of the system details of its structure become apparent. As a result an empirical model emerges in the form of a formula. The degree of accuracy of this model is higher than that of statistical, but it is still of probabilistic character. When all details of the system are known and the mechanism of its operation is entirely exposed the deterministic mathematical model appears in the form of the formula. Its accuracy is only stipulated by the accuracy of measurement methods. Application of statistical mathematical models is justified at the first stages of any cognition process when details of phenomenon in question are unknown. At this stage of cognition a “black box” concept is introduced when we know nothing about the structure of this “box”, but we do know its reaction to certain influences. Types of its reactions are revealed by means of statistical models and thereafter, with the help of logic, details of its systems and their interaction are becoming exposed. When all that is revealed, deterministic models come into play and the evaluation of the systems functions is made not on the basis of tabular data, but on the basis of due curve of the system function. Due curve of a systems function is a due range of values of function of the given concrete system in the given concrete subject, with its load varying from minimum to maximum. Nowadays due curves are scarcely used, instead extreme minimum and maximum due values are applied. For example, due ventilation of lungs in quiescence state and in the state of peak load. For this purpose maximum load is given to individuals in homotypic groups and pulmonary ventilation in quiescence state and in the state of peak load is measured. Following statistical processing due values of pulmonary ventilation for the conditions of rest and peak load are obtained. The drawback of extreme due values consists in that this method is of little use for the patients. Not all patients are able to normally perform a stress test and discontinue it long before due maximum value is achieved. The patient, for example, could have shown due pulmonary ventilation, but he/she just stopped the load test too early. How can the function be estimated then? It can be only done by means of due curve. If the actual curve coincides with the due curve, the function is normal at the site where coincidence occurred. If actual curve is lower than the due one, it is a lagging curve. Inclined straight line consisting of vertical pieces of line is the due curve. Vertical dotted straight line is the boundary of transition of normal or lagging function into the inadequate line (a plateau). The drawback of due curves is that in order to build them it is necessary to use deterministic mathematical models of systems which number is currently very low. They are built on the basis of knowledge of cause-and-effect relationship between the system elements. These models are the most complex, labor-consuming and for the time being are in many cases impracticable. Therefore, these models are scarcely used in the sphere of applied medicine and this is the reason for the absence of analytical medicine. But they are the most accurate and show what parameters should be present in the given concrete subject at any point of time. Only the use of due curve functions allows for evaluating actual curves properly. The difference of the deterministic mathematical models from statistical tables consists in that in the first case due values for the concrete given subject (the individuals due values) are obtained, while in the second case due values for the group of persons alike the given subject are developed. The possibility of building deterministic models depends only on the extent of our knowledge of executive elements of the system and laws of their interaction. Calculation of probability of a thrown stone hitting a designated target can be drawn as an example of statistical standard scale in the mechanic. After a series of throws, having made certain statistical calculations it is possible to predict that the next throw with such degree of probability will hit the mark. If deterministic mathematical model (ballistics) is used for this purpose, then knowing the stone weight, the force and the angle of throw, viscosity of air, speed and direction of wind, etc., it is possible to calculate and predict precisely the place where a stone will fall. “Give me a spot of support and I will up-end the globe”, said Archimedes, having in view that he had deterministic mathematical model of mechanics of movements. Any living organism is a very complex and multi-component system. Its impossible to account all parameters and their interrelations, therefore statistical mathematical models cannot describe adequately the condition of systems of organism. However, joint use of statistical and deterministic models allows, with sufficient degree of accuracy, to evaluate parameters of living system. In the lapse of time in process of accumulation of knowledge statistical models are replaced by deterministic. Engineering/technology is much simpler than biology and medicine because the objects of its knowledge are rather simple systems (machinery/vehicles) constructed by a man. Therefore, its development and process of replacement of statistical mathematical models for deterministic ones has made great strides as compared with medicine. Nevertheless, on the front line of any science including technical, where there is still no clarity about many things and still a lot has to be learnt, statistics stands its ground as it helps to reveal elements of systems and laws of their interaction. What do we examine the subject and conduct estimation of functions of the systems of his organism for? Do we do it in order to know to which extent he/she differs from the homothetic subject? Probably, yes. But, perhaps, the main objective of examination of