If you die at age 90, you died prematurely relative to what we’d expect a month before you died, but (postmaturely? it should be a word) relative to what we’d expect and bet on 80 years before your death (i.e., at age 10).
Now, you may still think there’s a paradox in the following sense: let’s say the median lifespan expected at birth is 70. That means that the 50% of people who died before 70 died prematurely relative to all predictions made throughout their lives, while for the remaining 50% some of the predictions were too pessimistic (those made early in their lives) but some were optimistic. Isn’t there still a skew towards being surprised that people died early?
The imbalance disappears if we count not people, but people-seconds. I.e., if we predict how long everyone is going to live at every second of their lives, the average prediction will not be either pre- or post-mature. The people who live longer will accumulate more pessimistic early death predictions through the sheer fact that they live more seconds and so more predictions are made about them. A person who lives to 100 may accumulate 95 years of too-pessimistic predictions and only 5 years of too-optimistic ones.
Thanks for this. This certainly sounds plausible, though whether the premature and post-mature predictions would exactly cancel out isn’t obvious. (Not sure without trying the maths, and it may or may not be tricky—this is what actuaries are for.)
Also I’m not sure whether it requires the life expectancy predictions to be made on the same basis for everyone (e.g. life expectancy tables) or if it would still work for individually tailored predictions.
I can see this could dissolve most of the paradox, but (as I threw as many confusions as I could think of into the post!) I sense one may still remain about tailored predictions. At the extreme, in a deterministic world, God could calculate our individual time of death when we’re born. All his life expectancy predictions made at any time would be correct, and he wouldn’t be surprised when we die; but nonetheless dying age 20 would still be premature. (And not just because we can’t make perfect predictions.) Possibly ‘premature’ means slightly different things in different contexts.
If you die at age 90, you died prematurely relative to what we’d expect a month before you died, but (postmaturely? it should be a word) relative to what we’d expect and bet on 80 years before your death (i.e., at age 10).
Now, you may still think there’s a paradox in the following sense: let’s say the median lifespan expected at birth is 70. That means that the 50% of people who died before 70 died prematurely relative to all predictions made throughout their lives, while for the remaining 50% some of the predictions were too pessimistic (those made early in their lives) but some were optimistic. Isn’t there still a skew towards being surprised that people died early?
The imbalance disappears if we count not people, but people-seconds. I.e., if we predict how long everyone is going to live at every second of their lives, the average prediction will not be either pre- or post-mature. The people who live longer will accumulate more pessimistic early death predictions through the sheer fact that they live more seconds and so more predictions are made about them. A person who lives to 100 may accumulate 95 years of too-pessimistic predictions and only 5 years of too-optimistic ones.
Thanks for this. This certainly sounds plausible, though whether the premature and post-mature predictions would exactly cancel out isn’t obvious. (Not sure without trying the maths, and it may or may not be tricky—this is what actuaries are for.)
Also I’m not sure whether it requires the life expectancy predictions to be made on the same basis for everyone (e.g. life expectancy tables) or if it would still work for individually tailored predictions.
I can see this could dissolve most of the paradox, but (as I threw as many confusions as I could think of into the post!) I sense one may still remain about tailored predictions. At the extreme, in a deterministic world, God could calculate our individual time of death when we’re born. All his life expectancy predictions made at any time would be correct, and he wouldn’t be surprised when we die; but nonetheless dying age 20 would still be premature. (And not just because we can’t make perfect predictions.) Possibly ‘premature’ means slightly different things in different contexts.