Mathematical Thinking in Behavioral Sciences by David M. MessickReview by: Alex C. MichalosBiometrics, Vol. 25, No. 4 (Dec., 1969), pp. 782-783Published by: International Biometric SocietyStable URL: http://www.jstor.org/stable/2528585 .

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782 BIOMETRICS, DECEMBER 1969

This is one such booklet intended for ninth grade students which may be useful to a biometri- cian interested in deterministic models. A number of interesting problems are included. Many simple functions and their graphs are included. A second booklet on more complicated and refined aspects of functions and their graphs is planned for publication and translation.

W. T. F.

LAZARFELD, PAUL F. and HENRY, NEIL W. (Eds.) Readings in Mathematical Social Science. The M. I. T. Press, Cambridge, Massachusetts, and London, England,

182 1968. 371 pp. ($3.45 25/- (paperback). Alex C. Michalos, University of Gzuelph, G'uelph, Ontario, Canada and University of Pittsburgh, Pittsburgh, Pennsylvania.

This broadly representative collection of 18 essays (17 previously published) dealing with various applications of mathematics and mathematical models to problems in the social sciences should prove to be a very useful handbook for students and teachers alike. The pre- requisites seem to be introductory courses in statistics and probability, linear algebra, and calculus. While the editors have thoughtfully included some additional comments to aid the uninitiated through the more sophisticated mathematics, it is likely that most students will not be able to handle some of the material presented. Nevertheless, virtually everyone in- terested in mathematical approaches to social science should find something worthwhile in this collection. The annotated bibliographies alone are valuable sources of quick reviews of some of the relevant fairly recent literature.

After the brief introductory essay written by the editors, the book is divided into four sections. The first section contains four papers related to measurement problems. F. M. Lord considers relations between test scores and ability; W. A. Gibson compares factor, latent structure, and latent profile analysis; P. F. Lazarsfeld explains latent structure analysis and its relation to test scores; and G. Rasch considers the preservation and loss of data in item analysis.

The second section deals with small groups and begins with a study by R. D. Luce and A. D. Perry on the determination and elucidation of social relationships through matrix analysis. This is followed by a formalization of some of Leon Festinger's hypotheses by H. A. Simon and H. Guetzkow, including a review of some experimental results. J. G. Kemeny and J. L. Snell apply the model of Markov chains to experiments in conformity. J. S. Coleman presents a probabilistic model of reward and punishment in relation to the goals of different group members. Finally, G. Kreweras applies spectral analysis to the problem of predicting opinion changes in repeated elections, e. g., nominating elections in national conventions.

The third section is devoted to larger groups. H. C. White introduces some symbolic models of kinship systems, and this is followed by a consideration of optimal decision rules for organizations by J. Marschak. An excellent analysis of the (electoral) 'cube law' is presented by J. G. March with some corroborating evidence of its reliability. M. Shubik's essay on game theory and organizational decision making is a good introduction to the field. The remaining paper on the aggregation of group preferences by G. Th. Guilbaud would have been a nearly sufficient reason for me to recommend the purchase of the book. It is a model of lucidity which establishes a positive form of Arrow's General Possibility Theorem.

The final section has four papers, beginning with L. A. Goodman's analysis of birth control in relation to the distribution of children born. This is followed by a review of probabilistic mobility models by I. Blumen, M\i. Kogan, and P. J. McCarthy. R. R. Bush and F. Mosteller compare eight learning theory models on the same data, and the book ends with a study of B. Mandelbrot on his theory of word frequencies.

MESSICK, DAVID M. Mathematical Thinking in Behavioral Sciences. W. H. Freeman 183 and Company, San Francisco, California, 1968. 231 pp., $4.95.

Alex C. Michalos, Department of Philosophy, University of Pittsburgh, Pittsburgh, Pennsylvania.

This is an interesting collection of 27 generally nontechnical essays reprinted from Sci- entific American. Its aim is to present 'interesting (and often sophisticated) mathematical

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BOOK REVIEWS 783

ideas in such a way as to make them comprehensible [to freshmen and sophomores] and to encourage them to acquire the mathematical skill necessary to use and apply the ideas pro- ficiently.' It should accomplish its aim admirably. Moreover, it strikes me as a perfect gift for a high school graduate with some inclination toward mathematics, behavioral science, or both. For that matter, it could also be enjoyed by any layman or student with similar interests.

The papers range from 1948 to 1968 and are divided into five groups. The first group con- tains five papers on probability. Those of A. Ayer, R. Carnap, and M. Kac are philosophical. J. Cohen reports experiments with 'personal' probabilities and D. D. McCracken explains Monte Carlo simulation.

The second group has six papers on communication and control theory. N. Wiener describes the elements and potential of cybernetics, W. Weaver explains the basics of information theory, W. W. Peterson and W. H. Pierce discuss problems of the reliable transmission of information, and R. Bellman and A. Tustin review the principles of feedback and control.

Part three has four essays on game and decision theory. 0. Morgenstern outlines the elements of game theory, L. Hurwicz and A. Rapoport consider its philosophical and practical implications, and W. W. Cooper and A. Charnes review types of problems that are solvable by linear programming.

The fourth group of six papers pertains to computers and artificial intelligence. J. G. Kemeny considers techniques for obtaining complex processes from simple ones, L. S. Penrose explains how machines can 'reproduce,' W. Grey Walter describes his learning machine, A. Bernstein and M. de V. Roberts review their efforts to develop a program allowing a computer to play chess, M. L. Minsky considers recent (1966) attempts to design computers capable of analogical reasoning, and 0. G. Selfridge and U. Neisser discuss the problems of providing useful 'sensory' systems for computers.

The final set of six papers reviews recent computer applications. S. Ulam explains its use in mathematical physics, R. S. Sokal explains its use in biology, B. Julesz discusses its applica- tion to experiments with perception, M. A. B. Brazier considers the role of computers in extracting biological signals from the nervous system, R. S. Ledley and F. H. Ruddle explain computer analysis of chromosomes, and P. Suppes reviews some of the problems of student- machine interaction in education.

Reader's Note: In connection with review 170 of the book by K. C. Peng, The Design and Anal- ysis of Scientific Experiments, which appeared on page 438 of the June 1969 issue, a reader has called to the attention of the Book Review Editor an earlier review by S. K. Katti. The ref- erence for this is J. Amer. Statist. Ass. 62, 1508-9, 1967.

The following books have been received for review in Biometrics during the period March 28 to September 3, 1969:

ALEKSANDROV, A. D., KOLMOGOROV, A. N., and LAVRENT'EV, M. A. Mathematics: Its Content, Methods, and Meaning, 2nd Edn., Vols. 1, 2, and 3. Translated by S. H. Gould, K. A. Hirsch, and T. Bartha and translation edited by S. H. Gould. The M. I. T. Press, Cambridge, Massachusetts, 1969, first paperback edition. Vol. 1: xi + 376 pp.; Vol. 2: xi + 394 pp.; Vol. 3: xi + 372 pp., three-volume boxed set $10.00; per volume $3.95. (The three-volume boxed set remains available in hardcover at $30.00.)

AMERICAN STATISTICAL ASSOCIATION. Acceptance Sampling. (A Symposium.) The American Statistical Association, Washington, D. C., 1950. iv + 155 pp.

ATOMIC BOMB CASUALITY COMMISSION, Technical Reports, Hiroshima and Naga- saki: (i) ABCC Technical Reports 1959-69. 123 pp. (ii) BEEBE, G. W. and JOHNSON, K. G. Progress of the ABCC-JNIH Adult Health

Study of Atomic Bomb Survivors, Hiroshima and Nagasaki. Technical Report 16-67, 1967. 24 pp.

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