Conditional Life Expectancy

I got a card on my last birthday that said

Birthdays are good for you. Statistics prove that the people who have the most live the longest

Larry Lorenzoni

I googled Larry and it turns-out he has a suspect background with children, but that aside it's a pretty good quote for a card. I then realised that this is actually an interpretation of conditional life expectancy that you get in life-tables. Most life-tables are life-expectancy from birth but as you get old by the simple fact that you've survived up to that point your life expectancy changes. You are more likely to live longer by having made it to another birthday. Its not just the birthday that you've just reached but your expected time of death will be nudged further off into the future too. The gap between now and the fateful day may get smaller but there'll always be a bit more life tagged-on to where you are today.

Looking at the quote another way, its a confusion with cause and effect. Its not that people who have the most birthdays live the longest but rather that people who live the longest have the most. A birthday is a consequence of ageing and not the other way around.

Then of course, you could just say that its a birthday card and stop sucking all the fun out of it. Unfortunately though, with age I think fun-sucking happens more and more.