A third of my life

I’m 28 years old. A perfect age! (Don’t wish me a happy birthday, I’ve been 28 for a few months.)

Recently it occurred to me that I’ve lived a third of my life, at least if you believe the classic biography of Diophantus:

‘Here lies Diophantus,’ the wonder behold.
Through art algebraic, the stone tells how old:
‘God gave him his boyhood one-sixth of his life,
One twelfth more as youth while whiskers grew rife;
And then yet one-seventh ere marriage begun;
In five years there came a bouncing new son.
Alas, the dear child of master and sage
After attaining half the measure of his father’s life chill fate took him. After consoling his fate by the science of numbers for four years, he ended his life.’

(translation from Wikipedia)

I’m pretentious enough to quote this in Latin, except that I don’t know Latin. If you are pretentious enough to know Latin (and I think I have at least one reader who is), go to the Wikipedia article for the original.

But there are other classical amounts of time that are cited as the typical lifespan: “three score years and ten” Psalm 90:10 is the most frequently mentioned. Genesis 6:3 suggests that the maximum human liefspan is 120 years. My father says he’ll live until 100 (I think he started saying this in his forties, so he could convince himself that he wasn’t middle-aged yet).

So what proportion of my life have I lived? Or, because you don’t care about me, what proportion of one’s life has one lived at age X? We can’t just divide by the life expectancy. Let’s say life expectancy is 70; then I’d have lived two-fifths of my life by now. But that means that when I am 70, I will have lived my entire life. And when I’m 77, I will have lived 110% of my life! Clearly the proportion of my life that I’ve lived, at 28, is 28 divided by the expected age at which a 28-year-old dies.  A quick look at a life table says that the “expectation of life at age [28]” is 50.8 — so a typical 28-year-old should expect to live to 28 + 50.8 = 77.8. Therefore I have lived 28/78.8 of my life, or about 35.5 percent. The life expectancy at birth, according to the same table, is 77.4, and 28/77.4 is about 36.2 percent. I just got 0.7 percent of my life back by doing this calculation! But I’ve probably spent more than 0.7 percent of my life learning how to do such calculations.