Recent Contributions to The Mathematical Theory of Communication

This paper is written in three main sections. In the first and third, W. W. is responsible both for the ideas and the form. The middle section, namely “2), Communication Problems of Level A” is an interpretation of mathematical papers by Dr. Claude E. Shannon of the Bell Telephone Laboratories. Dr. Shannon’s work roots back, as von Neumann has pointed out, to Boltzmann’s observation, in some of his work on statistical physics (1894), that entropy is related to “missing information,” inasmuch as it is related to the number of alternatives which remain possible to a physical system after all the macroscopically observable information concerning it has been recorded. L. Szilard (Zsch. f. Phys. Vol. 53, 1925) extended this idea to a general discussion of information in physics, and von Neumann (Math. Foundation of Quantum Mechanics, Berlin, 1932, Chap. V) treated information in quantum mechanics and particle physics. Dr. Shannon’s work connects more directly with certain ideas developed some twenty years ago by H. Nyquist and R. V. L. Hartley, both of the Bell Laboratories; and Dr. Shannon has himself emphasized that communication theory owes a great debt to Professor Norbert Wiener for much of its basic philosophy. Professor Wiener, on the other hand, points out that Shannon’s early work on switching and mathematical logic antedated his own interest in this field; and generously adds that Shannon certainly deserves credit for independent development of such fundamental aspects of the theory as the introduction of entropic ideas. Shannon has naturally been specially concerned to push the applications to engineering communication, while Wiener has been more concerned with biological application (central nervous system phenomena, etc.). 1 Introductory Note on the General Setting of the Analytical Communication Studies