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MARGINALIA

The Undiscovered Country

The statistics of death show leaps in modern life expectancy but fail to answer the question: Why do we die?

Robert L. Dorit

Death by the Numbers

Mortality%20(shown%20on%20a%20logarithmic%20scale)Click to Enlarge ImageGiven the many factors that enter into the calculation of life expectancy, however, this measure may not be the best way to understand death. Instead, we may want to look more closely at what demographers call age-specific measures, which quantify the probability of surviving a particular interval of life (usually a five-year span—ages zero to five, for example, or 40 to 45). We have known for a long time that surviving the first five years is a struggle, whereas the intervals between 5 and 30 are far less hazardous. We can also focus on the rate of mortality at a specific age, also known as the force of mortality.

Much of our understanding of the force of mortality is rooted in the work of a brilliant 19th-century English mathematician, Benjamin Gompertz. Unable to enter the English university system because he was Jewish, Gompertz taught himself mathematics and was eventually elected into the Royal Society in 1819. In 1825, he published in the Philosophical Transactions of the Royal Society of London "On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies." This 70-page paper with its sexy title was Gompertz's effort to help underwriters calculate life-insurance rates. In preparing the paper, Gompertz had examined death records from several English towns and noticed a clear pattern for age-specific death rates. This pattern, now known as the Gompertz curve, shows a well-behaved, exponential increase in the force of mortality with age. He argued that death, seemingly shaped by so many chance events, nonetheless follows a simple and predictable path. And so simple a path could only arise from an equally simple, age-dependent, underlying force that operates throughout our lifetimes.

It took almost 150 years for Gompertz's curve to be seriously questioned. In part because of increased life expectancy in certain parts of the world, more individuals were living longer, providing sufficient data to examine the force of mortality in later years—data that Gompertz didn't have. The result of adding the long-lived to the analysis was startling: The force of mortality, which grows exponentially throughout most of one's lifetime, actually moderates after age 75. Equally unexpected was the discovery that the dramatic differences in age-specific mortality around the world virtually disappear after age 75. In effect, if you are born in Bolivia, your chance of seeing 75 is significantly lower than if you had been born in Canada. But if you make it to 75 in either place, your chance of seeing 90 is virtually the same. Past a certain age, the imprints of birth and circumstance seem to give way to universal forces and constraints.

Keep in mind that we have been speaking of age-specific rates of death, and not the cumulative probability of death, which, like it or not, always sums to 100 percent. In the end, we all die. But in the meantime, we seem to be succeeding in delaying the inevitable. For optimists and narcissists, the trend of increasing lifespan extends over the horizon. Conversely, demographers, biologists and politicians have asserted over the past century that human beings cannot possibly live beyond 70, or 80, or 85, or the nice round number of 100. Yet as they speak, the maximum age at death continues to climb in many parts of the world. For what it's worth, Jeanne Calment lived to be 122 years old, died in 1997, and remembered meeting the abrasive and ill-smelling Vincent Van Gogh when he came to live in her hometown of Arles, France. Although this trend of ever-lengthening lifespans cannot continue indefinitely (even for optimists and narcissists), the actual limit—and even the demonstrable existence of a limit—is a subject of continuing controversy among demographers and gerontologists.

This controversy arises in part because convincing statistics about centenarians remain hard to come by, increasing the temptation to extrapolate from isolated cases. Until recently, the number of people aged 95-110 was so small that reliable age-specific mortality rates for that age bracket were hard to estimate. People living past 100, moreover, might represent a small, but unique, subsample of the human population. Their age-specific mortality rates, buried for the first 80 or so years in the mass of data from the shorter-lived, may well have been different throughout their entire lives, only coming to dominate the statistics as the rest of the population drops off.





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