## Friday, 21 December 2012

### Life expectancy in Middle-Earth: elves and mortality tables

 If Uruk hai drove buses the war of the ring would have been short.
A scary thought: I have an a priori chance of one in a thousand of dropping dead within next time this year (qx) in New Zealand, which is far more likely than winning the kiwi lotto (on a lotto day, 1:4M). Life is unfair, eh?
Luckily, I am not doing anything dangerous nor have any underlying conditions hence the a priori —although, I have not bought a lotto ticket either.
If I were in my nineties the chances change to a one in three or four per year, so the above figure is really low really. The reason is obvious, namely deterioration due to old age.
80% of the probability for young folk to die is due to external causes, which means accidents, homicide, suicide or war. For the elder folk it is due to diseases such as cancer. Boys do much more stupid stuff than girls, therefore for a woman of my age, the chances drop to one in three thousand.
The life expectancy is around 67 years in developed countries, but what would it be if one did not age?

Agerasia is the mythical state where one does not grow old. It is different from immortality as it does not include invulnerability: the probability of external causes still applies. As this probability does not change with age, age of death would follow a geometric distribution (and not a Gompertz–Makeham curve —thanks, Wikipedia!—) and the mean will consequently be 1/p. This means that on average a kiwi male would live 1,300 years, whereas a female 5,500 years.

In fantasy and science fiction, long-lived or agerasic humans and humanoids often appear, but those figures do not match the above…

In The Lord of the Rings, the dwarves had a life expectancy of 250 years or so the web informs me because they age slower than men. The elves do not grow old and lived about 1,000 years —Galadriel (Kate Blanchett) was probably one of the oldest and was a bit over 5,000 years. Middle Earth would just slightly more dangerous than New Zealand, but not by much. (In (ir)reality, elves are hardier than men, so the comparison is slightly unfair.) Possibly unsurprisingly, the US, on the other hand, is slightly more dangerous than Middle Earth.

In Iain M. Banks's Culture novels the folk of the Culture are said to live on average 400 years. The figure is so low because they get utterly bored after a while and kick the bucket, however one chap lived for 10,000 years, but he was rather bonkers.

In the bible, the patriarchs before the great flood lives for a long time. Their age of death are given which is really handy, but there are only ten of them and one, Enoch, did not technically die. Despite the small sample size, they lived on average 912 years, but the numbers are curious as they all died between 900 and 1,000 which is statistically impossible both under a geometric and a Gompertz distribution. The explanation that they get a "millenium crisis" at 900 does not fit as it is written they die of super-old age (which hits all of a sudden). Given that only Abel dies of external causes (1 in 10), it could be deduced that antediluvian Israel was much safer than New Zealand, Middle Earth or the US, but whatever rabbi wrote down the numbers wasn't well versed with statistics, so the bias is too strong for any conclusions.

Sources: Wikipedia, NZ life tables, some bible website, Iain Bank's Hydrogen Sonata and several unutterably nerdy LotR sites…