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This paper explores a deceptively simple question: This paper explores a deceptively simple question: When does longevity actually begin?
Historically, societies have defined “old age” using fixed ages such as 60, 65, or 70, but this study shows that such ages are arbitrary, outdated, and demographically meaningless. Instead, the author proposes a scientific, population-based approach to define the true onset of longevity.
🧠 1. Main Argument
Traditional age thresholds (60–70 years) are not reliable indicators of longevity because:
They were created for social or economic reasons (military service, taxes, pensions).
They ignore how populations change over time.
They do not reflect biological, demographic, or evolutionary realities.
How Long is Long in Longevity
The study’s central idea:
Longevity should not be defined by chronological age—but by how many people remain alive at a given age.
How Long is Long in Longevity
The paper therefore redefines longevity in terms of survivorship, not age.
🔍 2. Why Chronological Age Is Misleading
The author reviews commonly used demographic indicators:
A. Life expectancy
Measures the average lifespan.
Useful, but only shows the mean and not the distribution.
How Long is Long in Longevity
B. Modal age at death (M)
The most common age at death.
Meaningful, but problematic in populations with high infant mortality.
How Long is Long in Longevity
C. Lifetable entropy threshold
Measures lifespan variability and identifies where mortality improvements matter most.
How Long is Long in Longevity
Each indicator gives partial insight, but none fully captures when a life becomes “long.”
🌱 3. A New Concept: Survivorship Ages (s-ages)
The author introduces s-ages, defined as:
x(s) = the age at which a proportion s of the population remains alive.
How Long is Long in Longevity
This is the inverse of the survival function:
s = 1 → birth
s = 0.5 → median lifespan
s = 0.37 → the proposed longevity threshold
S-ages reflect how survival shifts across generations and are mathematically tied to mortality, failure rates, and evolutionary pressures.
⚡ 4. The Key Scientific Breakthrough: Longevity Begins at x(0.37)
Why 37%?
Using the cumulative hazard concept from reliability theory, the author shows:
When cumulative hazard H(x) = 1, the population has experienced enough mortality to kill the average individual.
Mathematically, H(x) = −ln(s).
Setting H(x) = 1 gives s = e⁻¹ ≈ 0.37.
How Long is Long in Longevity
Interpretation:
Longevity begins at the age when only 37% of the population remains alive—x(0.37).
This is a scientifically grounded threshold based on:
Demography
Reliability theory
Evolutionary biology
Not arbitrary retirement-age traditions.
🧬 5. Biological Meaning (Evolutionary View)
Evolutionary biologists argue:
Natural selection weakens after reproductive ages.
Early-life forces determine vitality; later life is governed by “force of failure.”
How Long is Long in Longevity
By linking these views:
The onset of longevity is the point where natural selection stops dominating and accumulated damage becomes the main driver of survival.
This aligns perfectly with the hazard threshold H(x) = 1 → s = 0.37.
📊 6. Empirical Evidence (USA, Denmark, France, 1950–2020)
The paper shows survival curves and s-ages shifting toward older ages across decades.
Key patterns:
The longevity threshold x(0.37) consistently lies well above age 70.
It increases over time along with life expectancy, the entropy threshold, and modal age at death.
All indicators move upward together—showing that longevity is dynamic, not fixed.
How Long is Long in Longevity
In all countries studied:
People in the 1950s reached the x(0.37) longevity threshold much earlier than people today.
Meaning: survival to advanced ages is improving steadily.
🔑 7. Major Conclusions
✔ Longevity cannot be defined by a fixed age like 60 or 65.
✔ Longevity is a population-relative concept—based on survival, not age.
✔ The scientifically justified threshold is:
The age at which only 37% of the population remains alive — x(0.37).
✔ All longevity indicators point to a continuously increasing threshold over time.
✔ Old age today begins much later than traditional retirement ages.
🌟 Perfect One-Sentence Summary
Longevity should be defined not by chronological age but by the survival threshold x(0.37), where only 37% of the population is still alive—marking the scientifically grounded onset of a long life.
If you want, I can also create:
📌 A diagram of the 37% longevity threshold
📌 A mind map
📌 A short summary
📌 A comparison with your other longevity PDFs
📌 A PowerPoint presentation
Just tell me!... |