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Science and the Imagination

ISSUE:  Autumn 1940

The Birth and Death of the Sun, By George Gamow. New York: The Viking Press. $3.00. Mathematics and the Imagination. By Edward Kasner and James Newman. New York: Simon and Schuster. $2.75.

Two excellent books, representing popular science at its highest level, may be reviewed together under this title.

George Gamow’s “The Birth and Death of the Sun” might impress a reader who was not familiar with the recent extraordinary progress of astrophysics as being imaginative to the point of fantasy; but it is a serious presentation, by an expert, of the present state of knowledge and reasonable hypothesis. After a brief introductory discussion of the difficulty of accounting for the enormous amount of energy which the sun has radiated during geological time, Dr. Gamow plunges boldly into his specialty of nuclear physics. His apology—”The author regrets the pain that this excursion into the domain of pure physics may cause some readers —but except for poets, no one should speak about stars without knowing the properties of matter of which they are constructed”—is quite unnecessary. The account of the “anatomy of atoms” and the transmutation of elements is of admirable lucidity and simplicity, and freed from any risk of heaviness by illustration, both verbal and pictorial, which are always accurate and illuminating, and often very entertaining—as when Rutherford’s experiments on the deflection of alpha-particles, which have penetrated an atom and been deviated by the nucleus, are compared with an imaginary South American customs officer who tested cotton bales for concealed munitions by firing bullets into them and finding that some ricocheted from the hidden metal.

The chapter on “The Alchemy of the Sun” then sets forth lucidly Bethe’s brilliant theory of the energy-liberating transformation of hydrogen into helium by a cycle of reactions in which atoms of carbon and nitrogen are transformed, but reconstructed at the end, so that the process can go on almost indefinitely. Bethe’s most recent experiments, which verify in the laboratory the last reactions of this chain, came too late to be included.

Astrophysicists in general will agree with the conclusion that the energy source of the main sequence of stars has thus been found, and also with the further deduction that the sun should continue shining for some ten billions of years, gradually growing a little smaller, but considerably brighter, until, at long last, it will contract rapidly and become a faint white dwarf.

The subsequent discussion of the energy-sources of the giant stars—which, though massive and luminous, are probably not hot enough inside to “turn on” Bethe’s process— presents the author’s theory of transmutation of the light elements—lithium, beryllium, and boron—in stars near the beginning of their evolution. Dr. Gamow states fairly the difficulty that these processes cannot furnish energy enough to keep these stars shining for more than a fraction of the two billions of years which several converging lines of evidence indicate as the approximate age of the Galaxy. The difficulties of the hypothesis that these stars were for most of this time in some unobserved diffuse and little luminous pre-stellar stage appear more serious to the reviewer than to the author; but we are here too near the frontier of advance to be dogmatic.

The white dwarfs, which, because of their enormous densities, are by common consent regarded as representing the latest observable stage of stellar life, are next discussed. The fact that most astronomers (unlike the author) conclude that there is a good deal of hydrogen in the interior of these stars is frankly stated, but their reasons are inadequately presented.

The final chapters, which deal with the origin of novae, planets, and nebula), include more speculative material. No mention is made of the very great difficulties which Spitzer has shown—doubtless too recently to be included—to beset the theory of the origin of planetary systems by collisions or other encounters.

In the astronomical part of the book there are a considerable number of factual errors—practically all in obiter dicta not affecting the general argument. For example, it was Nova Aquilae 1918 and not Nova Herculis 1934 whose spectrum was photographed before the outburst. These slips come in a field very full of detail and quite outside the range of the author’s main work in nuclear physics. They do not detract from the value of an unusually well written and interesting book.

Edward Kasner and James Newman have also written an admirable book—clear, accurate, covering a wide range, and withal witty and eminently readable. The average “gentle reader” has no conception of how picturesque—indeed, almost fantastic—are some of the results which mathematicians have reached, not by elaborate and laborious analysis, but by precise thinking which can be followed and understood by anyone who takes the trouble to exercise his mind for an hour or less.

In many places in this book, notably in the chapters on infinite and transcendental numbers, these results are presented with exceptional lucidity and simplicity; the reader who does not mind a moderate mental “work-out” can satisfy himself, without having to take anybody’s word for it, that an infinite number may be equal to a million times itself, or even to its own square, and that there may nevertheless be a greater infinite number which cannot in any sense be said to be equal to the first.

Other results, though proved by reasoning too intricate or severe to be appropriate in a book of the present type, can be stated so as to be fully comprehensible to the ordinary intelligent reader. A wealth of such examples may be found in the text, ranging from the transcendental numbers which cannot be expressed as roots of any algebraic equation of finite degree, to the bizarre space-filling curves and other “pathological” vagaries. Those who become lost in this wilderness of exuberant but rigidly logical products of the imagination may return to the simple and practically realizable surface, which may be made by pasting together the ends of a long paper ribbon after giving it a half twist— and on which a bookworm, boring through the paper, might meet another which had crawled along the surface, keeping always on the same side.

The less adventurous will find satisfaction in a chapter on mathematical pastimes, including a number of puzzles fit to try the mettle of experienced solvers, and in parts of those on probability and “Paradox Lost and Paradox Regained.” The latter begins with elementary fallacies, in which the error needs only to be pointed out, and ends at the very frontiers of reasoning, where the leading authorities upon mathematics and logic have not yet been able to reach agreement.

The book is heartily to be recommended to the general reader, and even more to the student interested in elementary mathematics, as an encouragement to go farther. There is a good index and also a long table of contents, so witty in its summary of each chapter that the reader is justly tempted to read the whole book afresh.


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