Same with humans, to a degree. Actuarials place your chance of dying at 50% after the age of 80. So we 'stop aging' after 80!
Annual chance of dying is 5% at 80 and continues rising every year (9% by 85, 16% by 90, 25% by 95, 35% by 100).
Saying that your chance of dying is 50% after 80 != saying it's the same consistently after 80?
“The Gompertz–Makeham law states that the human death rate is the sum of an age-dependent component (the Gompertz function, named after Benjamin Gompertz), which increases exponentially with age and an age-independent component (the Makeham term, named after William Makeham). In a protected environment where external causes of death are rare (laboratory conditions, low mortality countries, etc.), the age-independent mortality component is often negligible. In this case the formula simplifies to a Gompertz law of mortality. In 1825, Benjamin Gompertz proposed an exponential increase in death rates with age.
The Gompertz–Makeham law of mortality describes the age dynamics of human mortality rather accurately in the age window from about 30 to 80 years of age.
You probably remembered the first part of the sentence following that:
“At more advanced ages, some studies have found that death rates increase more slowly – a phenomenon known as the late-life mortality deceleration – but more recent studies disagree.”
Even if that were true (something wikipedia contests. See also https://en.wikipedia.org/wiki/Late-life_mortality_decelerati...), that doesn’t mean rate of death decreases, just that it increases slower than this model predicts.
Sorry, couldn't miss a factorial joke.
I think the observation they're trying to convey is that your expected number of years remaining goes down by much less than one year per year at those ages. A 90-year-old can expect to live for another 4.5 years, but on their 91st birthday, the chart surprisingly predicts not 3.5 but 4.2 years remaining. The number of expected years left drops more than 0.95 years per year until age 20, 0.9 years per year until age 40, down to 0.8 at 60, 0.5 at 80, and 0.1 at 100.
To have an average of 4.5, you need people to die before and after the mark.
So a lot of people drop off between 91 and 92. But those who make it to 92 have about 4.2 years remaining.
If you have a population of 100 people and 50 of them will live less than 1 year, and 50 of them will live an average of 10 years, that's 5.5 years on average for the whole population. But if you check that same population one year later, you will have 50 people who all live 9 years on average. You've managed to increase the average by eliminating the bottom.
Same thing is happening here.
And it's probably similar to professional sports careers. The average NFL career is about 3 years. However, if you make to 3 years, your average career length is about 7 years.
We probably need more of a median or mode than a mean.
The set of people alive at age N has size Sn. Some of them die. Some survive and form a new set of people alive at age N+1 with size Sn+1. Sn+1 <= Sn.
If the expected number of remaining years at age N was Y, death removed all the people that actually lived only 1 year or less, so the expected number of remaining years for people of age N+1 must be greater than Y.
Life expectancy at birth is always lower than at any other age.
Check https://en.wikipedia.org/wiki/Demography_of_the_Roman_Empire
> When the high infant mortality rate is factored in (life expectancy at birth) inhabitants of the Roman Empire had a life expectancy at birth of about 22–33 years
> The 46-49% that survived to their mid-teens could, on average, expect to reach around 48–54
No, that is neither necessary nor true. It must be greater than Y-1, not Y. Your way would mean that the expected duration of a life was infinite.
But this is a necessary fact about everything. The alternative would be that the expected complete lifespan of an 81-year-old would be less than the expected complete lifespan of an 80-year-old, and that forms a logical contradiction with the fact that, in order to achieve that longer lifespan, the 80-year-old must become an 81-year-old.
It's calculating P(death|age = N), not P(death|age <= N). Now luckily you can calculate the second one, by adding all values up to that age together.
I would argue the value you're looking for, "when you die", is different still: P(death|age <= N, current_age=M), where M is your current age. You know, taking into account that you didn't die from sudden infant death syndrome or measles, or you wouldn't be here, but leaving everything in the future up to chance. To get that value, you should the odds of dying at all ages up to N, but only starting at your current age.
At a certain point, humans appear to stop aging. Just it is at 105, not 80 :)
(that is, chance of flipping tails 10 times in a row is 0.5¹⁰ - chance of any head is what's left)