Walter Birnbaum

Walter Birnbaum | ASCRS

1970 to 1971

In selecting a title for the address of your 64th president, whose predecessors in the past 72 years have always had intriguing captions, I have arrived at one which, I must confess, may have lured you here under false pretenses. "The Sigmoidal Curve" does not refer to the anatomic structure of that name, and my paper will reveal no new surgical information about the terminal gut. The curve referred to is a mathematical one--the "S"-shaped curve of logistic elegance which graphically illustrates so many inorganic and biologic phenomena (Fig. 1). It is the curve of saturation, of the process of crystallization, of atomic chain reactions, of biologic growth, of economic cycles, and of population increases, to cite but a few examples.


The exponential law is the mathematical consequence of having a quantity that increases so that, the bigger it is, the faster it grows. A colony of rabbits or fruit flies which breed among themselves grows rapidly until some natural upper Emit is reached. Then the curve begins to level off at the top to make it "S"-shaped, otherwise known as a logistic curve or sigmoid. I shall refer to it here as it might relate to the history and future of medical specialties, with especial application to proctology, in the hope that it may, however faintly, illuminate our path and allow us to take the right turnings.