The level of development of every natural science is determined by the depth to which the subject has been penetrated by measurement techniques and by the detail with which the relationships among the resulting quantitative expressions have been studied. This is just what is meant when it is said, for example, that genetics, psychology, or linguistics have become competent exact sciences. The center of gravity of these sciences has been moving ever more noticeably from general considerations, allowing a substantial nonuniqueness in the conclusions drawn, toward the discovery of controlling quantitative relationships. Of course, increasing the accuracy of the agreement between theory and experiment requires improvements not only in the measurement techniques used but, especially, in the theory. The aim of a theory is taken to be the analysis of relationships among the observed quantities, starting ultimately with some fundamental irrefutable statements, i.e., laws of nature. In physics (mathematics must be given special consideration from this standpoint), the most developed natural science, it is customary to first examine the simplest models, idealized schemes each of which only involves one or two of these laws. In real experiments an increase in accuracy is always associated with a departure from the initial idealization; however, in physics this has usually led to a gradual improvement in the approximation as the model of the phenomena becomes more complex, rather than to a rejection of the previous description.


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Literature Cited

  1. 1.
    L. A. Mandel’shtam, Complete Works [in Russian], Nauka, Moscow (1955), Vol. 4.Google Scholar
  2. 2.
    A. A. Andronov, A. A. Vitt, and S. É. Khaikin, The Theory of Oscillations [in Russian], Fizmatgiz, Moscow (1959).Google Scholar
  3. 3.
    G. Polya, Mathematics and Plausible Reasoning, Princeton University Press (1969).Google Scholar
  4. 4.
    I. Kepler, A New Stereometry of Wine Casks [Russian translation], GTTI, Moscow-Leningrad (1948).Google Scholar
  5. 5.
    R. Courant and H. Robbins, What Is Mathematics ? Oxford University Press (1941).Google Scholar
  6. 6.
    L. I. Gudzenko, Izv. Vyssh. Ucheb. Zaved., Radiofizika, 5: 572 (1962).Google Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • N. G. Basov
    • 1
  1. 1.P. N. Lebedev Physics InstituteAcademy of Sciences of the USSRMoscowUSSR

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