The inexorable rise in human life expectancy

That’s Maths: The growth of lifespan has remained linear, and there is little reason to suppose it will level off any time soon

There has been a four-decade increase in average length of life over the period since 1850. Photograph: Thinkstock

There has been a four-decade increase in average length of life over the period since 1850. Photograph: Thinkstock

 

Life expectancy has increased in a spectacular fashion over the past 150 years. There has been a four-decade increase in average length of life over the period since 1850. Globally, life expectancy has more than doubled, from about 25 years to about 65 for men and 70 for women.

Until recently, most experts, while recognising improvements in survival rates, have assumed that there is a hard upper bound on the length of life. Many projections have been made on the value of this ceiling, and many proposed limits have been broken shortly afterwards. It has been difficult even for experts in the field to imagine the substantial rises, which continue inexorably.

The growth of lifespan has remained extraordinarily linear, with an almost constant rate of increase over a long period of about three months with the passage of each calendar year. There is little justification to suppose that the average length of life must soon level off, or that there is some fundamental biological barrier to further increases. But many nonbiological factors influence length of life. Are we reaching a limit on lifespan?

The importance of forecasts

Forecasts of life expectancy are essential in planning for future pensions, healthcare and social services. These needs increase sharply as the number of elderly people grows. In changing circumstances, individuals must decide when to retire and estimate how much savings they will need.

Mathematical models used to forecast changes in lifespan and population age distributions may include numerous factors. In the simplest models, the historical growth is extrapolated into the future. But extensions of life expectancy are linked to advances in nutrition, education, income, medicine and sanitation, and more sophisticated and realistic forecasting models may allow for these, employing a range of statistical and analytical techniques.

Since time immemorial, people have dreamed of cheating death. The observed linear increase in lifespan will never lead to immortality. However, the number of centenarians is growing by more than 5 per cent per year in developed countries and, if current trends continue, many of Ireland’s younger citizens have reasonable prospects of living to 100.

What if life expectancy were to increase faster than time is passing? If more than one year were added to life expectancy for each calendar year elapsing, the average duration of life remaining would actually increase as people grew older. With nonlinear growth, life expectancy could break all bounds within a finite time. This hypothetical scenario is known as the actuarial escape velocity, by analogy with the velocity required for a projectile to break free from the Earth’s gravitational pull and escape to space. Theoretically, ageing could be prevented and lifespan would become biologically unlimited. In reality, accidents, disease, suicide, famine and war would still be with us, banishing hopes of immortality.

Since quality of life is of concern in addition to duration, various health expectancy indicators have been developed. Generally, they demonstrate that the number of years of good health is on the increase. Lifestyle changes involving smoking, alcohol, diet and exercise give individuals the power to enhance their health and lifespan prospects substantially.

There is no escaping death, but the arithmetic of life expectancy is subtle: in a world with ever-increasing longevity, our expected total lifespan increases with the passage of each calendar year.

  • Peter Lynch is emeritus professor at the school of mathematics and statistics, University College Dublin. He blogs at thatsmaths.com
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