The Inspection Paradox

Amir Aczel has a very nice post on the inspection paradox, which deals with phenomena of the sort we usually file under watched-pot-never-boils -- things like the fact that if you have to wait at a bus stop you usually have to wait a long time. If you waited the entire time, you would find that the average wait time for the entire day (for instance) is a certain amount of time, but if you're coming in during the day you'll probably have a wait time longer than that overall average, because you're more likely to come to the bus stop during a long wait period than a short one. I very much like the immigration example: immigration can, in and of itself, increase a nation's average life expectancy. The reason is that people can't age backwards. If you move to a country at the age of 30, you have increased by one the number of people in the country who will live to be older than 30. If you move to a country at the age of 50, then there is one more person in the country who cannot possibly die before 50, another person who is at least 50 and therefore did not die before that age. So Israel, with a very large number of immigrants, gets a boost in its life expectancy because it has lots and lots of people constantly coming in who cannot possibly die at a very early age, because they are already older.