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Implications of the Rectangular Curve

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The rectangular curve is a critical concept, and its implications affect each of our lives. The rectangular curve is not a rectangle in the absolute sense, nor will it ever be. The changing shape of the curve results from both biological and environmental factors. Many biological phenomena describe what is often called a normal distribution. This is the familiar bell-shaped or Gaussian curve. If one studies the ages at death in a well-cared-for and relatively disease-free animal population, one finds that their ages at death are distributed on both sides of the average age of death, with the number of individuals becoming less frequent in both directions as one moves farther from the average age at death. A theoretical distribution of ages at death taking the shape of such a curve in humans is shown in Figure 4. This simple bell-shaped curve, with a mean of 85 years and a standard deviation of 4 years, might exemplify the age at death of an ideal disease-free, violence-free human society. The sharp downslope of the bell-shaped survival curve is analogous to the sharp downslope of the rectangular curve. In Figure 5, the first part of the curve becomes ever flatter, reflecting lower rates of infant mortality. Several factors prevent the total elimination of infant mortality and thus prevent the curve from becoming perfectly horizontal. These premature deaths are the result of birth of defective babies, premature disease, and violent death. Improvements in medicine can lower but never eliminate the birth of defective babies and premature disease. It seems likely that the ever dominant proportion of violent deaths during early life will prove recalcitrant to change and will form an ever larger fraction of total premature deaths.

So, the rectangular curve has an initial brief, steep downturn because of deaths shortly after birth, a very slow rate of decline through the middle years, a relatively abrupt turn to a very steep downslope as one nears the age of death of the ideal Gaussian curve, and a final flattening of the curve as the normal biological distribution of deaths results in a tail after the age of 90….

Thus, two profound characteristics of the mortality of man, the elimination of premature disease and the development of the sharp downslope representing natural death, have remained far from the public consciousness. These data have been available for many years. The first solid comments about rectangularization of the human survival curve can be found in prophetic statements in the 1920s. Many statisticians and actuaries working with national health data since that time have noted the increasingly rectangular shape of the curve, and many have speculated that it represents a natural species life limit. Entire theories of the aging process … have been built around the observed fact of a natural life span in man and animals. Yet, the public has remained largely ignorant of these developments.

A society in which life expectancy is believed to increase at every age and in which one becomes increasingly feeble as one grows older is a society heading for trouble. A society moving according to the curves of Figure 5, as our society is, is a society moving toward a world in which there is little or no disease, and individuals live out their natural life span fully and vigorously, with a brief terminal period of infirmity…. Dramatic changes in mortality patterns result in equally dramatic social changes.

Description

Figure 4 Sequential Survival Curves in the United States

Source: U.S. Bureau of Health Statistics.

Description

Figure 5 Ideal Mortality Curve in the Absence of Premature Death

Source: U.S. Bureau of Health Statistics.

Aging

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