When I was younger than about ten years old, there was nothing more terrible than being made to wait for a long period of time.  Waiting for an hour in an airport or in line for a rollercoaster was positively torturous.  Time just dragged on so slowly.  I couldn’t understand how adults could do it all the time; for my parents, having to stand in line or sit still in an airport for one hour was no big deal.

When I asked my mom why waiting was so much easier for adults than for kids, she said that people measure time relative to how long they have lived.  So waiting one hour for her (at age 32) was like waiting fifteen minutes for me (at age 8).  I’ve been thinking about this statement more and more lately, and it seems to hold up remarkably well.  As an adult now, an hour really is a lot shorter than it used to be.  But if my perception of time is slowing down, then how much of my apparent life have I already lived?

Let’s suppose that every time your age doubles, you live one “lifetime” which feels just as long as all the previous ones.  This would mean, for example, that the years between ages 10 and 20 feel just as long as the years between ages 20 and 40.  It makes sense to me — a 20-yeard-old probably feels as different from his 10-year-old self as a 40-year-old does looking back to age 20.  So we can divide a person’s life into all of its equally-weighted “lifetimes”.  We just need to decide how long the “first” lifetime is.  This is a pretty arbitrary choice, and you could argue for anything between a few months and a couple years.  I’m going to pick the only well-defined time scale there is for a newborn baby: 9 months.  I can only hypothesize that a newborn baby measures time relative to the time it spent in the womb.

Anyway, with this hypothesis we can map out all the “lifetimes” that will comprise my life, assuming I get to live to a ripe old age of 96:

1. Age 0 – 9 months.  During the first 9 months of my existence (outside the womb) I learned how to use the muscles of my body, developed a sense of “myself” as separate from other people, and came to understand that different people communicate with each other.  This is huge in ways I can’t wrap my brain around, but this chart sure is fascinating.
2. Age 9 – 18 months.  During the second 9 months of my life I learned to walk and play, began to speak, and learned who my family was.
3. Age 18 months – 3 years.  At age 3 I was in full-blown adventuring mode.  I ran, I played, I made friends, I started learning logic through simple games.  My personal favorite game at age 3, by the way, was throwing rocks into water and enjoying the ripple/splooshing sound they made.  It’s still pretty fun.
4. Age 3  – 6 years.  By age 6 I was in school and was learning about the complex nature of social interactions.  I could read and write and I was starting to develop a sense of the ways in which I was different from other 6 year olds.
5. Age 6 – 12 years.  My mom describes this as the “filling the computer” stage.  Of all my eight “lifetimes,” this is probably the one where learning happens the most quickly and fluidly.
6. Age 12 – 24 years.  This one is described by my mom as the “forming opinions” stage.  I developed a sense of ethics and morals that were different from my parents’, and decided (effectively) what kind of person I wanted to be.
7. Age 24 -48 years.  This one isn’t done yet, so I can only speculate on the transition from a young and energetic man to an older, more thoughtful man whose opinions have slowly transitioned to understandings.
8. Age 48 – 96 years. Again, I can only guess.

So I get to live 8 lifetimes (maybe 7 and a half is more realistic).  It’s hard to tell for the earlier ones (my memory isn’t good enough to recall being a 9-month-old), but roughly speaking each of those eras seems to have an equal psychological weight.

And in the end it makes me wonder about parenting.  A lot of people talk as if the goal of parenting is to produce a healthy and productive adult.  Surely this is important: adulthood sure seems long and important.  But I can’t help but wonder whether it’s more important to give your offspring a happy childhood than to prepare them for a happy adulthood.  After all, by age 18 you’ve already lived about five and a half of your eight lifetimes!

My wife considers this to be a sad thought: we just got married and are supposed to have our whole lives ahead of us, but I’m telling her that we’ve already lived about 6 of our 8 lifetimes apart!  I prefer my phrasing: we have two entire lifetimes to share with each other: one as we grow to middle age, and another as we grow old.  I just like to think of how those early moments of childhood were so important, and so long.

As a final note, for the geekier of you who may be reading this post, it is of course possible to write a formula for the number of lifetimes lived as a function of time.  When some quantity grows proportional to its value we call it “exponential growth”, and when something slows down proportional to its value we call it “logarithmic growth.”  In this case, where the apparent passage of time is “slowing down” as a function of age, the number of lifetimes lived grows logarithmically with time.  Its simplest expression is probably this one:

$L(t) = 1 + \log_2 (t/t_L)$

where $t_L$ is the length of your “first lifetime” (here, 9 months).  Here it is in graphical form:

April 22, 2009 2:05 pm

It seems that the New York Times addressed a similar question this weekend: http://www.nytimes.com/2009/04/21/science/21qna.html (thanks Miriam!)
Their answer seems a little vague to me, but it brings up valid discussion points.

August 11, 2009 11:27 am

Lovely! If you care for evidence about the universality of your assertion (to first order, or so), I offer you The Bard, and his famous verse from As You Like It:

All the world’s a stage,
And all the men and women merely players:
They have their exits and their entrances;
And one man in his time plays many parts,
His acts being seven ages. At first the infant,
Mewling and puking in the nurse’s arms.
And then the whining school-boy, with his satchel
And shining morning face, creeping like snail
Unwillingly to school. And then the lover,
Sighing like furnace, with a woeful ballad
Made to his mistress’ eyebrow. Then a soldier,
Full of strange oaths and bearded like the pard,
Jealous in honour, sudden and quick in quarrel,
Seeking the bubble reputation
Even in the cannon’s mouth. And then the justice,
In fair round belly with good capon lined,
With eyes severe and beard of formal cut,
Full of wise saws and modern instances;
And so he plays his part. The sixth age shifts
Into the lean and slipper’d pantaloon,
With spectacles on nose and pouch on side,
His youthful hose, well saved, a world too wide
For his shrunk shank; and his big manly voice,
Turning again toward childish treble, pipes
And whistles in his sound. Last scene of all,
That ends this strange eventful history,
Is second childishness and mere oblivion,
Sans teeth, sans eyes, sans taste, sans everything.

August 11, 2009 11:54 am

Well, lifespans were a little shorter in Shakespeare’s time, so if he says seven lifetimes that sounds pretty good to me. : )

August 11, 2009 4:56 pm

Absolutely beautiful. Thanks for the wisdom and writing. I especially liked the Shakespearean coda contributed by a reader. Bravo

4. August 12, 2009 3:33 pm

I just have found this interesting link

Logtime: The Subjective Scale of Life
The Logarithmic Time Perception Hypothesis

http://web.archive.org/web/20071116094344/http://ourworld.compuserve.com/homepages/jmkenney/

August 12, 2009 4:23 pm

Wow, thanks.

I am invariably never the first person to have come up with any of my ideas.

5. August 12, 2009 5:27 pm

But you have derived interesting new things from it. That’s the point with good ideas 🙂

6. August 12, 2009 5:30 pm

By the way, I have stolen your graph for one of my posts . Of course citing your post.

7. August 13, 2009 4:13 pm

Great thinking. I guess for many the timing of the inverse half lives would vary according to events. Would an earlier entry into school bring forward one life or an extended stay at university push out another?

Oh – and you had a very smart mother!