The other day I wrote in a post that no matter who you are, there are fewer people older than you every day. Juozas Baltusnikas commented, correctly, that this would not be true for the world’s oldest human.
This observation can, in fact, be generalized. There is a small group of people, all over the age of 100, for whom my statement is not true.
More formally, there is some age X such that if you are under that age, then at least one person older than you will die every day. Conversely, if you are above the age of X, then at least one day will go by when nobody older than you will die.
It is interesting to ask the question: “Approximately what is the size S of the set of people who are age X or greater?” I wonder what sorts of analysis tools you would use to approach such a question.
Other related questions are also interesting. For example, approximately what is the value of X? Do the values of S and X fluctuate significantly over time, or do they hold very steady?
Also, does it matter how many people are in the world? For example, if the world population varies from 2 billion people to 20 billion people, will the value of S change by a lot, or will it remain pretty much the same?
http://www.grg.org/calment.html suggests that the number of 109-year-olds is probably over 365, but not the number of 110-year-olds. So the cutoff is around 109 years, I think.
This is getting interesting. It could even lead someone to the scientific publication 🙂 For me also would be interesting to know the differences of X and S values between world regions, especially between regions where humans lifetime average is drastically different. It may be possible that S and/or X values are good indicators of public health.