The math of turning 40, Time Dilation and Back to the Future

First - Happy Canada Day!

Second, I'll be turning 40 pretty soon and it got me thinking about the phrase "middle age".  It's always been my observation that life is "speeding up".  When I was a kid, the time between Christmas from one year to another seemed to take an eternity.  Yet now, I struggle to remember that 1993 wasn't 9 years ago, but 19!  What's going on?

My theory is that we are terrible at tracking time.  Instead we can track "relative time".  When we are six years old, the time from one Christmas to the next is fully one sixth of our lifetime - in fact, given that, at age six, we may not have any memories earlier than age three, we could conclude that each year is fully a third of our existence.  However, once we reach age 40, each year is only a sliver of our total existence, and thus seems much smaller.  This seems to be the only reasonable explanation of where my 30s went in a blink of an eye.

So, I decided to model this behavior and see what I discovered.  I made the initial assumption that our memories start at age 5 and end, with death, at age 80.  I then figured out the relative length of each year, to determine how long each year feels to us.  The results are interesting:

Let's first look at the cumulative chart.  This example takes the relative age for each year.  By measuring the areas under the curve we can determine the age of equal "relative age", or the ranges of ages which should "feel" the same period of time, taking into account the apparent acceleration of the years.

This shows that the first quarter of our life is over by age 10, the second by age 20, the third by age 40, and the last quarter, by age 80 (which, if you think of the math, makes perfect sense).  If I think of my childhood, this also feels right as well.  My teenage years, which technically lasted as long as my 30s, were a lifetime!  My 30s, I believed, happened when I went out for lunch one day.

So, the horror that we can realize is that 40 is not middle age - 20 is!  By the time you reach 40, you've lived fully 75% of your apparent life timeline.  Even though you are halfway through your life, the remaining years will seem like the blink of an eye.

Another way to look at this is with this graph:

This lets us determine what age corresponds to the percentage of apparent life lived.  For example, as shown, the age at which you have lived 60% of your perceived life is actually 25.  On one hand, this is a clear call to enjoy your youth, on the other hand it shows that we've all been given the gift that our youth lasts a disproportionately long period of time - which is great if you had a good youth, not so great if you didn't.

Now, interestingly enough, these results are driven by the assumption that you have perfect memory of your life, and thus each minute seems progressively quicker than the minute before.  This leads to some interesting conclusions.  The first is that there is a real cost to memories - their cumulative effect serves to make your life appear to go quicker.  So, if at all possible, there's little point fixating and hanging on to bad memories.  Relieving them serves to slow down the perceived acceleration of time.  As well, there is possibly the saving grace that, as you age, your memory of earlier events starts to diminish.  This will put more relative weight in the later years and appear to slow time down.  Looking at the first graph, if you were able to forget the first 10 years of your life completely, then the effect is dramatic on shifting the relative weights of the later years.  Is it possible that there is some benefit to dementia and memory loss in your later years?  I doubt the benefits outweigh the dramatic costs, but it's an interesting thought.

This also leads to some conclusions about kids.  As I watch my kids grow up, I get to experience, vicariously, their experiences.  While overall life is zipping by for me, and they are growing up at an incredible rate (from my point of view), they also help to slow my life down by providing an external reference point to my life.  Time dilation may be part of Einstein's theory of relativity, but its also alive and well between two people at dramatically different points of their life.

So, as I round out the first 75% of my life, and I see that we are almost in 2015, the year at which Back to the Future will be as far from me as 1955 was for my Dad when the movie first came out in 1985 (and led him to say that he felt old!), I can really question the phrase that "life begins at 40".  If it does, then life sure felt like it took a long time getting started.  Enjoy every moment that you live, and savor every good memory you have.  Even if you live to 80, you're just not here very long.