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⭐ How Long Is Long in Longevity?
By Jesús-Adriá ⭐ How Long Is Long in Longevity?
By Jesús-Adrián Álvarez (Society of Actuaries Research Institute, 2023)
This research paper explores a fundamental question: When does a “long life” truly begin? Instead of using arbitrary ages like 60 or 70 to define old age, the author argues for a more scientific and population-based approach.
The paper reviews how societies have historically defined old age—often tied to fixed ages such as military service ending at 60, tax exemptions at 70, or retirement systems set at fixed ages. These traditional definitions, the author shows, are arbitrary and outdated, especially because modern people often reach their 70s or 80s in good health.
⭐ Main Purpose of the Study
To propose a formal, data-based definition of when longevity begins—not based on chronological age, but on how many people in a population are still alive at a given point.
The study introduces survivorship ages (s-ages), which answer the question:
➡️ At what age is a certain percentage (s) of the population still alive?
⭐ Key Idea: Longevity Begins at the s-Age Where Only 37% of the Population Is Alive
Using demographic reasoning and mathematical survival models, the author shows:
The cumulative hazard (total mortality exposure) reaches a value of 1 at the point where 37% of the population is still alive.
This means that at x(0.37)—the age when 37% survive—people have lived “long enough” to be considered longevous.
So instead of calling someone old at 60 or 70, the paper defines the onset of longevity as:
➡️ The age at which only 37% of people remain alive.
This threshold also matches findings from:
evolutionary biology (post-Darwinian longevity),
reliability theory, and
mortality mathematics,
making it a strong, interdisciplinary definition.
⭐ Why 37%?
Because mathematically, it is the survival level where the population has experienced enough mortality to eliminate the average lifespan.
This corresponds to important demographic markers such as:
>the modal age at death (most common age of death),
>the threshold age of the lifetable entropy, and
>the point where mortality shifts into “old-age deaths.”
>Across Denmark, France, and the U.S., the study shows that this threshold has steadily moved upward over decades—showing that longevity is increasing, not fixed.
⭐ Comparison With Other Longevity Indicators
The study compares:
>Life expectancy
>Modal age at death
>Entropy threshold age
>s-age x(0.37)
All of these indicators:
>occur well above age 70,
>have risen over time,
>behave similarly across countries.
>This proves that longevity is dynamic, not a fixed age.
⭐ Key Conclusions
Fixed ages like 60 or 70 are meaningless for defining old age. They do not reflect modern survival patterns.
>Longevity should be defined relative to population survival, not birthdays.
>The age where 37% of the population survives is a scientifically meaningful starting point for longevity.
>Longevity is comparative it only makes sense when comparing individuals within a population.
The threshold for longevity is increasing over time, reflecting rising life spans.
⭐ Overall Meaning
This study redefines longevity using demographic science. Instead of saying “old age begins at 65,” the paper shows that the true beginning of a long life happens when someone has lived to an age that less than 40% of their peers reach. This shifts the understanding of ageing away from tradition and toward empirical reality, offering a modern, flexible way to measure old age.... |