Wednesday, November 14, 2012

On Aging

As you know, each passing year constitutes a gradually diminishing fraction of our age. For example, if you advance from age 4 to age 5, that year represented 1/4 of your life. When you advance from age 5 to 6, that year was 1/5 of your life, and so forth.

So our perceptual model of time can be modeled as

perceptual time(x) = 1/x

To find someone's perceptual age we take the integral (adding 1 since we're born at age 0)

perceptual age(x) = ∫ 1/x dx = log(x + 1)

To get an answer on the scale of years, we'll need to normalize by the expected age of a male, which is 75.5 years in the united states (of course, the expectation of my age will be different given that I have already made it to 30, but let's ignore that)

perceptual age(x) = log(x + 1) / log(75.5 + 1) * 75.5

.. which means that, even though I turned 30 today, I'm actually already 60 perceptual years old. Now we've all got a nice closed-form analytic method for calculating how depressed we should be on our birthdays!