Numbers: Fun and Facts by J. Newton Friend; Mathematical Puzzles and Pastimes by AaronBakstReview by: Philip RabinowitzThe Scientific Monthly, Vol. 80, No. 6 (Jun., 1955), p. 387Published by: American Association for the Advancement of ScienceStable URL: http://www.jstor.org/stable/21574 .

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apply the techniques to obtain results and, thus, more easily see the power and wide applicability of the techniques. A judicious selection of sequences of related problems could well meet many of these criticisms. The book should become popular as a textbook and reference for graduate physics courses in statistical mechanics.

JEROME ROTHSTEIN

Signal Corps Engineering Laboratories

Numbers: Fun and Facts. J. Newton Friend. Scribner's, New York, 1954. xi+ 208 pp. Illus. $2.75.

Mathematical Puzzles and Pastimes. Aaron Bakst. Van Nostrand, New York-Toronto; Macmillan, London, 1954. vi + 206 pp. Illus. $3.75.

T HESE two books overlap in several areas while maintaining their individual approach. The title

of the first, Numbers: Fun and Facts, gives an accurate description of its contents. Friend gives a historical sketch on the origin of numbers, together with many interesting traditions and superstitions associated with individual numbers ranging from 1 to 1 billion. Num- bers with interesting and curious mathematical proper- ties are discussed at some length. A large section of problems, some of a trivial nature and some of con- siderable difficulty, rounds out the book.

The second book, Mathematical Puzzles and Pas- times, also contains a rather large selection of problems as well as some discussion of mathematically interesting numbers. Number systems are discussed in some detail, but the sexadecimal system is barely mentioned. This is unfortunate, since numbers to the base 16 are in constant use in many digital computer installations. Bakst discusses general principles that are used in solving various mathematical problems, both numerical and geometric. A perpetual calendar and an Easter date calendar are a bonus feature of this book. Both books have much to interest anyone who delights in numbers, but unfortunately several false statements, in addition to the usual typographic errors, appear.

PHILIP RABINOWITZ National Bureau of Standards

Elements of Algebra. Howard Levi. Chelsea, New York, 1954. 160 pp. $3.25. T HIS textbook, which is for use in a course in gen-

eral studies, is quite a departure from the usual approach to algebra. Although the author asserts that no previous knowledge of algebra is presupposed, but only curiosity, it is important that the student have some mathematical maturity. The material, or at least a part of it, seems more of an introduction to what is usually called modern algebra.

Levi points out many of the pitfalls of the student who has only inadequate concepts and ideas of the use and manipulation of the symbols. The material is developed logically, starting first with sets and cardinal numbers, and followed by the laws of addition and

multiplication. By use of these laws, expressions such as monomials and polynomials, are introduced.

The development of integers is excellent, and also, in sequence, rationals and irrationals. Then the treat- ment of real numbers and the number system in general follow easily. The material on order is the type that is usually encountered and is important because it points out that usually accepted concepts can often be logi- cally developed.

There are two rather glaring weaknesses in this book. The treatment of equations leaves much to be desired, and the introduction of groups, rings, and fields should either be omitted or discussed in more detail. Other- wise the book is certainly suitable for the purposes set forth in the preface.

HERBERT L. LEE Department of Mathematics, University of Tennessee

Pygmies and Dream Giants. Kilton Stewart. Norton, New York, 1954. 295 pp. $3.75.

1.ERE is a rare book, recording modern psychic tests, dream interpretations, and personal ad-

ventures among the primitive peoples of the northern island of Luzon, the Philippines. Stewart has written an account of his understanding of, and wild experi- ences among, strange tribes of pygmies, including the Ifugao, Ilongots, Kalingas, Kankanai, and Bontocs.

His chief interest centers in the psychological under- standing and interpretation of his willing and spon- taneous "friends" who revealed their dreams, spirit possession, and mental ways to him. Stewart states that his purpose

. . . was to determine as best I could what kind of native intelligence the people of these nonliterate societies had in the beginning, and then to find out what kind of mind was built up on that basic in- telligence by the group processes in which they found themselves involved, especially as revealed by their dreams, visions and ceremonial procedures. (p. 25)

Armed only with necessary, useful medicines and a minimum of food and water, but with a battery of tests (the maze, draw a man, and emotional response) and a native guide and interpreter, Stewart set out to find scientific and romantic adventure. His account is filled with fascinating thrills.

Living with the native groups, he participated in their ceremonies and other phases of their daily lives and shared their food, their ways, and their thoughts. The resulting description of these people holds much of a solid ethnological nature. As the result of his labors, weird experiences, and capital luck, Stewart believes that he has an understanding of

. . .this universal man . . . who is the same as all other men in the sight of God and law . . . and to determine what the various (and different) cultures do to this universal individual. (p. 26) Although the separate chapters do bring the reader

the personal feelings of the author as he lived among these little-known and little-studied societies, I find

June 1955 387

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