Life expectancy may not be what you expect

Odd Nectar makes some good points against ID.

Along the way, he says the following (LE is "life expectancy"):
"If we look back at the Greco-Roman days, LE was about 25 years. Now that's design at its best, don't you think? I suppose if I were an illiterate desert farmer circa 100 b.c.e. having a staring contest with death at 20 years of age..."

The implication being that if your life expectancy is 25 (actually, 25 is could even be a little high), and you're 20, you expect to live only a few more years ("a staring contest with death"). In fact, most people would assume you expect to live five more years.

Here's a simple two part experiment that may help with the ideas. (You can actually do this experiment if you like, but it will take a while. Or you can simulate it on a computer if you know how). Or, if you're in a hurry, I'll just tell you the answers (for a fair die) in a little while.


I) roll a six-sided die, counting the number of rolls until you get a '1' (including the roll on which you do get a 1). Repeat this many times (say, until you get 90 ones - it should be about 540 rolls, give or take). Average the counts for each set of rolls until a '1' appeared

II) roll a die 4 times. If you didn't get a '1' in those rolls, start counting how many additional rolls you need until you get a 1 (if you did get a '1' in those initial 4 rolls, forget that one and start over). Repeat this many times. [Actually, you can use the information from the experiment in part (I): if the count of rolls was 4 or less, throw it away, and if it was greater than 4, subtract 4 from the count.] Average the counts you keep.

The question we're interested in is "How much larger is the average in experiment I than in experiment II?"

What you you guess?

A lot of people would guess 4. (It's the same as the reasoning in the life expectancy example I quoted above.)

Well, actually, the averages are much closer. If you roll a great many times, and your die is fair, you should get 6 for both!

(I just did this experiment using Excel to simulate the die roll - 540 times for experiment I and reused the 272 of them that exceeded 4 for experiment II - the results were about 5.8 and 5.4, which is not quite as close to six as it should be, but at least we can clearly see that the two numbers don't differ by anything like 4.

[Why is this related to life expectancy? Well, assume we have some creature that has a 1/6 chance of death each year (it dies when it rolls a '1') - so its life expectancy is six years. When it reaches 4 years of age, what's its remaining life expectancy? ... in this case, the answer still six!]

Human life expectancy is not that much like the die roll experiment (even if we put a lot more sides on the die), because the probability of death isn't constant at all ages. However, the basic ideas carry over.

Actually, in ancient times, at age 20, your remaining life expectancy then may even have been more than an addtional 25 years!

At birth, the average life span may have been 25, but the average adult was far older than 25.

What made life expectancy so low? Well, higher death rates, obviously, but the higher death rates didn't impact all ages equally. Most of the increase in death rates was for the youngest ages - especially for newborns. If you could survive past about 5 years of age, death rates were much lower - your chances of making it to adulthood were pretty good, and once you were an adult, your life expectancy was reasonable (not great by today's standards, but it was a lot more than a handful of years).

To simplify things dramatically, imagine there's a 50% chance of dying in your first month, and a life expectancy at birth of 25. What's your life expectancy if you survive that first month?

Well, it's 50 (less maybe a few weeks). The overall average in this case will be the average of the lifespan of those who die in the first month - almost 0 - and those who don't. If those who don't die near birth average 50 years, that makes the overall average lifespan (0 + 50)/2 = 25.

Infant mortality rates were extremely high. I don't know the figures for ancient times, but 50% within the first few years is probably reasonably close.

So your expected lifespan at birth was 25, but your expected lifespan conditional on getting past the most dangerous early part was much higher.

Most of the increase in our lifespan during the 19th and 20th centuries was caused by dramatically reduced infant mortality. A large number of dead infants has a huge impact on the average lifespan, so when you improve infant survival, you greatly increase average lifespan. Of course, survival at all ages improved a lot, but it was the infant mortality where the greatest improvements were realised (and these are also the ages where that survival has the greatest impact on average lifespan).

And what was the dramatic increase in lifespan caused by? Mostly better sanitation, clean drinking water, fewer foodborne diseases (with improvements in handling, storage and so on) and other basic disease prevention measures. Inventions like antibiotics in the mid-20th century were amazing, saving/prolonging millions of lives - but basic sanitation and clean water was even more dramatic, particularly among the young - the biggest improvements in expected lifespan happened before the advent of antibiotics.

So our 20 year old Roman-era desert farmer was not staring death in the face, waiting out his last handful of years ... a 20 year old faced many dangers, but their life was much less risky than the at-birth expectancy figure might make you think, unless you're also thinking about the fact that surviving the first few years was the really hard part.