Wednesday, July 25, 2007

Subjective Life Span

When I was 7 years old, a year seemed a very long time. And indeed it was -- it was 1/7 of my life. Now that I'm 39, a year seems much shorter. But of course now a year is only 1/39 of my life. When I was 7, 30 minutes seemed a long time; now it doesn't seem nearly so long.

Let's suppose that subjective time is inversely proportional to life span. The subjective time of any period is then the integral of 1/x, which is to say the difference between the natural logs of the end and the beginning of the period.

(Most recent psychological work about "subjective time" tends to be about subjective estimations of clock time, or about comparisons of periods close together in time as seeming to go relatively more quickly or more slowly. These are completely different issues than the one I'm contemplating here. They don't get at the fundamental question of whether the clock itself seems to speed up over the life span -- though see Wittmann & Lehnhoff 2005.)

On this model, since 1/x approaches infinity as x approaches 0 (from the positive direction), it follows that our subjective life-span is infinite. We seem, to ourselves, subjectively, to have been alive forever. (Of course, I know I was born in 1968, but that's merely objective time.)

There's something that seems right about that result; but an alternative way of evaluating subjective life span might be to exclude the earliest years -- years we don't remember -- starting the subjective life span at, say, age 4.

Adopting that second method, we can calculate percentages of subjective life span. Suppose I live to age 80. At age 39, I've lived less than half my objective life span, but I've already lived 76% of my subjective life span ([ln(80)-ln(39)]/(ln(80)-ln(4)] = 0.76). At what age was my subjective life half over? 18. Whoa! I feel positively geriatric! (And these reflections about philosophers peaking at age 38 don't help either.)

Regardless of whether the subjective life span begins at age 0 or age 4, we can compare the subjective lengths of various periods. For example, the four years of high school (age 14-18) are subjectively 25% longer than the four years of college (age 18-22). Doesn't that seem about right? Similarly, it wasn't until I was teaching for 9 years (age 29-38) that I had been a teacher as long, subjectively, as I had been a high-school student; and it will take 'til age 60 for my subjective years of teaching to exceed my subjective years of high school, college, and grad school combined.

If we throw in elementary school, objective and subjective time get even more out of synch. Those 7 years (age 5-12) will be subjectively equivalent to the 42 years from age 30-72! And unless I teach until I'm 168 years old, I'll always have had more subjective time as a student than as a teacher. Is that too extreme? Maybe so. But I don't really know what it's like to be 168 years old; and I'm not sure how stable and trustworthy my judgments now could be about how long 3rd grade seemed to take. Is 6 times as long as a middle-aged year so unreasonable?

7 comments:

Keith Frankish said...

Nice post, Eric. The really interesting question here, I think, is why subjective time speeds up. One explanation, I suppose, is familiarity: the more familiar one is with life, the more quickly it seems to pass. But if so, then we could slow down subjective time by periodically changing our lifestyles, or (given the technology) erasing our memories. (I wonder, do amnesiacs report a slowing of subjective time -- assuming they can remember what it was like before?)

Another (not incompatible) explanation would be physiological: as the organism ages it becomes less alert, and proportionately more external stimuli are required to fill up the same span of subjective experience. But then no speeding up should occur until the end of adolescence, which is not the case.

There are also interesting epistemological issues here, similar to those raised in your recent discussion of Dennett. Judgements about subjective time are – presumably – introspective ones, but are they incorrigible or answerable to independent standards?

Genius said...

I presume it is related to the ability for your brain to make new connections which decreases over time. In that light a 0 yr old baby really is probably making a number of times more connections per hour than the adult.
Reminds me of the super nanny argument that you should give a child one minute in the corner for every year of life (or somthing like that)

Eric Schwitzgebel said...

Thanks for the comments, Keith and Genius! I agree that the next obvious question, if one accepts this view, is why time seems to speed up. I'm inclined to think (and this resonates with some remarks by Alison Gopnik on consciousness, attention, and time perception) that it may have to do with plasticity and learning -- this is your suggestion, too, Genius, no? The more we learn and the more our brain is changing, the greater the distance seems between week and week (although maybe moment-by-moment the effect is reversed?). As Gopnik notes, we can see this in miniature during travel: The three weeks in Japan -- when we're learning a lot quickly -- seem subjectively to be longer, and loom larger in our memory, than months at home in our usual routine.

Maybe.

You raise a nice point at the end, too, Keith. I'm inclined to think that there is a fact of the matter about whether subjective time speeds up, and by how much -- at least approximately -- but I very much mistrust our subjective judgments about it. On the other hand, no objective measure seems to get straightforwardly at the phenomenon either....

Keith said...

Eric -- The last bit of your reply is too intriguing to let pass. If there's a fact of the matter about subjective time, what kind of a fact is it (neurological?) and why can't we measure subjective time straightforwardly?

Eric Schwitzgebel said...

I'd say it's a phenomenological fact, which probably has a neural basis. For example, it might just be phenomenologically the case for me that a particular hour seemed to fly by very quickly; and hours (or days or years), in general, might go more quickly as I age.

I'm not sure, by the way, whether subjective time sums: Could every hour of a day go by quickly and yet the day seem to last forever? Could every day go by quickly yet the year seem interminable? Hmmm....

But I resolutely draw a line between phenomenal facts and our judgments about those facts (as you discuss in today's post); and I think our judgments are often wrong, especially retrospective judgments. At the same time, I see no straightforward way to determine whether a week goes faster for a 7-year-old than a 40-year-old.

Anonymous said...

An easier way to see the math is, and this allows one to calculate this for any ages.

If every year of your life is 1/(how many years old you are) then half your subjective life has passed once: let n be your age at the time, x be the age at which half your life has passed, and a be the age at which you die at.

thus integral of 1/n from 1 to x = 1/2 times the integral of 1/2 from 1 to a.

when you evaluate this integral you get ln(x)-ln(1)=1/2*ln(a)-1/2*ln(1)

thus ln(x)=1/2*ln(a)
ln(x)=ln(a^(1/2)) (this is a
property of logs)

x = sqrt(a) so if you life to be 80 years old then half your life has passed once you reach the age of the sqaure root of 80, or almost 9.

so according to your example:

ln(x)-ln(4)=1/2ln(80)-1/2ln(4)
ln(x/4)=ln(80^(1/2)/4^(1/2))
x/4=80^(1/2)/2
x=2*sqrt(80) which is almost 18!

Eric Schwitzgebel said...

Thanks for the clarification!