MATHEMATICS IN MEDICINE AND THE LIFE SCIENCES.
By Prof. GeorgeR. Stibitz (Physiology). Chicago: YearBook Medical Publishers, Inc., 1966. 391pp. $12.50.
Describing and defending the usefulness of mathematical models is the pervading theme of Professor George R. Stibitz' book, Mathematics in Medicine and the Life Sciences. The author writes, "The ability to recognize the behavior of parts of a phenomenon as similar to the behavior of parts of other phenomena is, I think, an important factor in what we refer to as 'understanding'." Suggestion of hypotheses by similarities of behavior is one of the functions of analogy. The underlying law generating the similarities is approximated by a mathematical model.
Analogy has generally been considered unimportant as a reasoning process during the last half century but has recently assumed new significance both as a logical tool and in the production of training devices such as the Link trainers of aeronautics. Developments in computer technology have contributed to the enhancement of analogy by providing convenient solutions and descriptions of mathematical models.
By participating as a pioneer, Professor Stibitz is well qualified to describe developments in applied mathematics over the last three decades. In 1938-39, he designed a computer to be used for performing complex arithmetic operations. It was composed of electrical relays and used fixed point arithmetic. In 1940, this computer was demonstrated before a regional meeting of the American Mathematical Society at Dartmouth College through a teletype communication link from Hanover to the location site of the computer in a Bell Telephone Laboratory in New York City. This demonstration was the first remote use of a computer.
In another pioneering task the author has reviewed the mathematical foundations necessary to fully utilize the key model, differential equations. Real and complex numbers, vectors, matrices, Boolean numbers and the like are termed "off the shelf model parts" since they tend to appear repeatedly in the. models as components, as do machine parts in shop bins.
By emphasizing mathematical concepts at the expense of classical anatomical and biochemical ones, Professor Stibitz risks running a collision course with some of the formulators of policy in medical research. Pappenheimer (Physiologist, 8:341-347,1965) suggests that mammalian physiologists travel light and perfect a sort of functional gross anatomy with emphasis on classical knowledge; on the other hand, Carlson (Physiologist, 9:61-62, 1966) feels that data collection is uninspiring unless done with the end view of supporting a concept or illustrating an analogue. Important discoveries have lately tended to stem from non-mathematical intellects. Antibiotics, steroids and tranquilizing drugs have been the products of chemical processes. Being new, the full utilization of computers has not yet been achieved. When applied, advances in computer technology will soon be considered to be of equal importance to chemical discoveries.
Professor Stibitz' complete, lucid, erudite book written with an anecdotal, historical technique will be an important factor in the realization of this advance.
Assistant Professor of Physiology
