MATHEMATICAL BIOPHYSICS

There has recently been another approach to the problem: How does a brain think? A group of men, many of them in and near Chicago, have been saying: “We know the properties of nerves, nerve impulses, and simple nerve networks. We know the activity of the brain. What mathematical model of nerve networks is necessary to account for the activity of the brain?” These men have used mathematics, statistics, and mathematical logic in the effort to attack this problem, and they support a Bulletin of Mathematical Biophysics.

Householder, Alston S., A Neural Mechanism for Discrimination, Psychometrika, vol. 4, no. 1, Dec. 1939, pp. 45-58.

Householder, Alston S., and Herbert D. Landahl, Mathematical Biophysics of the Central Nervous System, Bloomington, Ind.: Principia Press, 1945.

Landahl, Herbert D., Contributions to the Mathematical Biophysics of the Central Nervous System, Bulletin of Mathematical Biophysics, vol. 1, no. 2, June 1939, pp. 95-118.

Landahl, Herbert D., Warren S. McCulloch, and Walter Pitts, A Statistical Consequence of the Logical Calculus of Nervous Nets, Bulletin of Mathematical Biophysics, vol. 5, no. 4, Dec. 1943, pp. 135-137.

Landahl, Herbert D., A Note on the Mathematical Biophysics of Central Excitation and Inhibition, Bulletin of Mathematical Biophysics, vol. 7, no. 4, Dec. 1945, pp. 219-221.

Lettvin, Jerome Y., and Walter Pitts, A Mathematical Theory of the Affective Psychoses, Bulletin of Mathematical Biophysics, vol. 5, no. 4, Dec. 1943, pp. 139-148.

McCulloch, Warren S., and Walter Pitts, A Logical Calculus of the Ideas Immanent in Nervous Activity, Bulletin of Mathematical Biophysics, vol. 5, no. 4, Dec. 1943, pp. 115-133.

Rashevsky, N., Mathematical Biophysics, Chicago: University of Chicago Press. Revised edition, 1948, 669 pp.

Rashevsky, N., Mathematical Biophysics of Abstraction and Logical Thinking, Bulletin of Mathematical Biophysics, vol. 7, no. 3, Sept. 1945, pp. 133-148.

Rashevsky, N., Some Remarks on the Boolean Algebra of Nervous Nets in Mathematical Biophysics, Bulletin of Mathematical Biophysics, vol. 7, no. 4, Dec. 1945, pp. 203-211.

Rashevsky, N., A Suggestion for Another Statistical Interpretation of the Fundamental Equations of the Mathematical Biophysics of the Central Nervous System, Bulletin of Mathematical Biophysics, vol. 7, no. 4, Dec. 1945, pp. 223-226.

Rashevsky, N., The Neural Mechanism of Logical Thinking, Bulletin of Mathematical Biophysics, vol. 8, no. 1, Mar. 1946, pp. 29-40.

LANGUAGES: WORDS AND SYMBOLS
FOR THINKING

Hardly any field of techniques for thinking is more fascinating than language. The following list of references, of course, is short; it is meant chiefly as an introduction pointing out a number of different paths into the field of language and languages. Such topics as the following are introduced by the references in this list:

Bloomfield, Leonard, Language, New York: Henry Holt & Co., 1933, 564 pp.

Bodmer, Frederick, and Launcelot Hogben, The Loom of Language, New York: W. W. Norton & Co., 1944, 692 pp.

Flesch, Rudolf, The Art of Plain Talk, New York: Harper & Brothers, 1946, 210 pp.

Graff, Willem L., Language and Languages: An Introduction to Linguistics, New York: D. Appleton & Co., 1932, 487 pp.

Hayakawa, S. I., Language in Action, New York: Harcourt, Brace & Co., 1941, 345 pp.

Jespersen, Otto, The Philosophy of Grammar, New York: Henry Holt & Co., 1929 (third printing), 359 pp.

Jespersen, Otto, Analytic Syntax,

In this book, by means of a well-contrived system of letters and signs, the great linguistic scholar Jespersen depicts all the important inter-relations of English words and parts of words in connected speech.

Ogden, C. K., The System of Basic English, New York: Harcourt, Brace & Co., 1934, 320 pp.

Schlauch, Margaret, The Gift of Tongues, New York: Modern Age Books, 1942, 342 pp.

Walpole, Hugh R., Semantics: The Nature of Words and Their Meanings, New York: W. W. Norton & Co., 1941, 264 pp.

LANGUAGES:
MACHINES FOR THINKING

For many years, nearly all references about machines as a language for thinking have been specialized and limited. Colleges with scholars who write textbooks usually have not had a variety of expensive and versatile computing machinery. As a result, the main environment for stimulating possible authors has until recently been missing. The list of references is accordingly brief.

Aiken, Howard H., and others, Proceedings of a Symposium on Large-Scale Digital Calculating Machinery, Cambridge, Mass.: Harvard University Press, 1948, 302 pp.

Comrie, John Leslie, The Application of Commercial Calculating Machines to Scientific Computing, Mathematical Tables and Other Aids to Computation, vol. 2, no. 16, Oct. 1946, pp. 149-159.

Crew, E. W., Calculating Machines, The Engineer, vol. 172, Dec. 1941, pp. 438-441.

Fry, Macon, Designing Computing Mechanisms, Cleveland, Ohio: Penton Publishing Co., 1946, 48 pp. (Reprinted from Machine Design, Aug. 1945 through Feb. 1946.)

Hartree, D. R., Calculating Machines: Recent and Prospective Developments and Their Impact on Mathematical Physics, Cambridge, England: The University Press, 1947, 40 pp.

Horsburgh, E. H., Modern Instruments and Methods of Calculation, London: G. Bell and Sons, Ltd., 1914, 343 pp.

Lilley, S., Mathematical Machines, Nature, vol. 149, Apr. 25, 1942, pp. 462-465.

Murray, Francis J., The Theory of Mathematical Machines, New York: King’s Crown Press, 1947, 116 pp.

The author states that a mathematical machine is a mechanism that provides information concerning the relationships among a specified set of mathematical concepts.

Turck, J. A. V., The Origin of Modern Calculating Machines, Chicago: Western Society of Engineers, 1921.

Recently, however, some magazine and newspaper publishers have seen news value in machines that think, and some good general articles with appeal to a wide audience have appeared. For the references to these articles, see the section of this supplement entitled “Digital Machines—Miscellaneous.”