You’ve got your whole life ahead of you

There’s a nicely morbid Perry Bible Fellowship comic showing a kid on his birthday:

PBF032-Todays_My_Birthday

That’s what you get with strict determinism: the day we die is already decided on the day we are born; on the day the universe was born, in fact. But since we ordinary mortals do not have access to Death’s all powerful computing machine that lets him calculate the end of all tales (an abacus?!), we have to use statistics. Specifically, we like to use life expectancy, which is basically the average age of death of a certain population at a certain time.
Calculating it is rather easy for times far away in the past. What was the life expectancy for infants at 1900? Just look at all the people who were born in 1900, and take the average of their life spans. For modern times it’s a bit more complicated, since there are still so many yucky living people who spoil your statistics, but we get good results under reasonable assumptions.

Here’s a cool thing about life: if you haven’t died so far (and, as you are reading this, I assume you haven’t), you will statistically outlive the average baby born on the same year as you. In other words, the older you are, the older you die. This is pretty obvious, but it’s a nice pat on the back as it shows your accomplishments in the field of “not dying”. Are you 30? Congratulations! You should no longer be afraid of dying from chicken pox, drowning in a bucket, baby measles and child-malnutrition; and your chances of going to war are severely reduced. So you have to take out all those deaths out of the equation, and the net result is that your projected age goes up.

But there is a contrasting force in this whole ordeal: the older you are, the less time you have to live – because you’ve already lived some portion of your life. The life expectancy of an infant born in the United States in 2013 is about 78 years. She has 78 years ahead of her. The life expectancy of a 90 year old in the United States in 2013 is 94. She will die older (she has already passed the 78 year mark), but only has 4 years ahead of her.

This leads to the question: what is “the best age to be alive”, in the sense that “your whole life ahead of you” is the longest period of time? This depends crucially on the mortality statistics: we can imagine that in a world where most children don’t make it to age 10, people who are 30 will have more to look forward to than five year olds.

In fact, this is what happened in Massachusetts during the 1850’s (data found here):

life_1850_female

In orange, we see how many years a person has left to live as a function of age in Massachusetts in 1850. We see that a baby just born has roughly 40 years ahead of her, while a child who made it to age 10 has about 47 years ahead of her! In the 1850’s during childhood, every year you grow older actually increases your life expectancy! In view of the comic at the beginning of the post, for these children, every time they celebrate their birthday, Death should add a bead to their life total (statistically speaking, of course; deterministically we are all doomed anyway). Newborn babies and 20-year olds can expect to live the same amount of time.
The yellow line plots the function y = x. The place where it crosses the orange line is the “half-life” point – the age where you have put as much time behind you as you have in front of you.
Finally, in blue, we see the average age of death. It continuously rises as a function of the age of the person in question. Notice that it is always above the yellow line y = x: This just means that when you look at a specific living person, that person will die older than she is right now. Unfortunately the data I have only goes up to 80 years, but eventually the blue line and the yellow line should coincide, at the age of the oldest person who ever lived.

But that was way back a hundred and fifty years ago. With the advancement of modern medicine, food, and infrastructure, are things any different now? Indeed they are. Here is the United States data for 2013 (data found here):

life_2013_combined

First, life expectancy went up; that’s a no brainer. But what’s interesting is that now the orange line no longer has a peak in the beginning. Further, the blue curve stays almost flat for the first ~40 years or so of life: The difference in the expected age of someone who is 40 and someone who was just born is a mere 4 years; contrast this to the whopping 29 years in 1850.
We have so completely decimated child and youth mortality, that it no longer “pays off” to grow older, in terms of gains in life expectancy. Looking at the data shows that this phenomenon – the lack of orange peak – started in the 1920’s, at least in the United States.
So the Death and the Abacus comic is indeed relevant – but only for the modern era. In the past, getting to 10 would have warranted a real celebration – for that is the age where “you’ve got your whole life ahead of you” carries the most weight. But today? The countdown starts with your first gasping scream for air.

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3 comments

  1. “if you haven’t died so far (and, as you are reading this, I assume you haven’t), you will statistically outlive the average baby born on the same year as you.” – nope. Perhaps you meant “someone born the same year as you and dead this year”?

    • Oh, I see what you meant. It’s not very clear from the way you phrase it. Maybe “if you haven’t died so far, your life expectancy is now higher than it was on the day you were born”, or even “if you’re still alive, you’re life expectancy is higher than it was yesterday”?

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