Max Borst and Bortkiewicz's Law

BORST, Max, a distinguished pathologist. Born in 1869, he graduated from the medical faculty of the University of Würzburg in 1892. From 1893 to 1904, he served as an assistant at the Pathological Institute of the University of Würzburg, where he worked under the guidance of Rindfleisch, one of the greatest pathologists of that time. In 1904, he was elected professor of pathological anatomy in Cologne, from where he moved in 1905 to the same chair in Göttingen, and in 1907 to Würzburg. In 1910, he was elected professor and director of the Pathological Institute in Munich; he holds this latter position at the present time. Borst's scientific works concern, mainly, the pathology of inflammation, regeneration, transplantation, and tumors. Regarding inflammation, Borst succeeded in bringing significant clarity to the complex question of the significance of irritation in the origin of the inflammatory reaction of tissues. In the chapter on regeneration, he clarified the course of the process of regeneration of tendons, cartilage, serous membranes, and many details of wound healing in general; a series of Borst's experimental works concerns the transplantation

of blood vessels, joints, and certain organs. But Borst's research on tumors is of the greatest importance; in this field, he is a leading specialist. In addition to individual works concerning various questions of tumor growth, in 1902 Borst released a major two-volume work on tumors, "The Theory of Tumors" ("Die Lehre von den Geschwülsten"), which became a classic textbook on this branch of pathology; for this work, Borst was elected an honorary professor of the University of Bonn. Borst summarized the latest data concerning tumors in the book "Die allgemeine Pathologie der malignen Geschwülste," published in 1924. Borst's textbook on pathological histology ("Lehrbuch der pathologischen Histologie," 2nd edition, 1926) is also well known. BORTKIEWICZ'S LAW, otherwise known as the "law of small numbers," consists in the fact that certain phenomena reveal a high degree of correspondence between actual, observed fluctuations, expressed in statistical numbers, and theoretical fluctuations, calculated in accordance with the law of normal errors ("stability" in the sense of Lexis), not in large, but in small masses. This "stability" is inherent in phenomena with a small number of occurrences, their onset at long intervals of time and space, or, expressed in terms of probability theory, phenomena with a small number of chances for the appearance of each individual event. Logically, this position is explained by the fact that such rare phenomena, being interspersed in masses of phenomena that occur frequently (e.g., suicide as one of the causes of death), retain the "stability" inherent in these masses, which yield large numbers. The "law of small numbers" is also historically connected with the latter, as it was noted by Bortkiewicz as a result of studying the question of the "stability" of large numbers (see Lexis).