One of my favorite posts on this blog so far has been the one about my eight lifetimes.  In it, I postulated that we measure time relative to our age, and as a result each length of time wherein our age doubles carries an equal psychological weight.  There’s nothing scientific about this discussion — it’s just an idea.  But it has absolutely changed the way I think about my life and the process of getting older.  At the risk of being a shameless self-promoter, I highly recommend reading it.

The argument about “my eight lifetimes” can be summarized this way: in your life you will undergo roughly eight major transformations.  That is, you get eight “lifetimes” during which you become a new and different person.  If you’re reading this blog, chances are that you’re already on your sixth or seventh.  This is not to say you have one foot in the grave: having an entire lifetime ahead of you is still a big deal.  For me, a 25-year-old, the two remaining lifetimes are the transformation from a 20-something-year-old to a middle aged man, and then from middle age to an old man.  Both of those time periods are a big deal, and each of them contains plenty of living to be done.  I just imagine that the time period between age 6 and age 12 was a similarly big deal.

All of this brings me back to the Gompertz Law of human mortality.  The Gompertz Law is already an extraordinarily fair statement: no one escapes mortality, which becomes exponentially more probable in old age.  But if you subscribe to my idea of time progressing relative to itself (of life being composed of “lifetimes”), then the consequence of the Gompertz Law is an almost extreme level of fairness.  Look at it this way: about 96% of people survive to age 48 (the beginning of the “eighth lifetime”), but only 4% make it to age 96 (the end of the eighth lifetime).  If you try to come up with an equation for probability of survival vs. number of lifetimes lived, you get an almost absurd exponential within an exponential within an exponential.  And the result looks like this:

That, in my book, is extreme fairness.  Virtually all of us get to live to the end of our seventh lifetime, but almost none of us get to complete the eighth.

$\hspace{10mm}$

$\hspace{10mm}$

It may seem that this argument is somehow making light of mortality among older people.  That I am claiming the difference between living to age 55 and living to age 80 doesn’t matter because it only constitutes half a “lifetime”.  This is certainly not my intention.  The difference between living to 55 and living to 80 is a huge deal.  In my way of thinking, each of us is allotted nearly eight lifetimes before we die, and when someone is deprived of some number of those eight, it is a tragedy.

Of course, what this post really highlights is that there is nothing more tragic than death during childhood.  If a 40-year-old man dies, he is deprived of the chance to live out his life and become a new kind of person.  When an infant dies, he or she is deprived of seven such chances.  My wife is working in a pediatric hospital these days, and the stories she tells about shaken baby syndrome are almost cripplingly sad.

1. August 13, 2009 10:43 am

First, a general compliment on your blog, I really enjoy what you’re doing here.

Second, about your conclusion “that there is nothing more tragic than death during childhood”; you’re certainly correct given the metric that you’ve laid out.

What is implicit in your methodology, however, is an individualistic perspective which I think is worth exploring further. Indeed, there is nothing more tragic than the death of an infant from the perspective of the infant. S

From a societal — or “objective, economic” — perspective, however, I believe that a different conclusion must be drawn. From this external point of view, the ages 0-25 are a period of intense, societal investment in the individual. Parents must take care of the child in the early years. The older child then (usually) goes to series of publicly-funded schools, building his capacities while making a negligible contribution to society. Finally, around age 25, the individual joins the workforce and begins providing society with the return on investment it’s been after all along. This productive period continues until the age of 65, roughly, at which point the individual retires and either lives off of savings or a government-sponsored pension, no longer making an economically productive contribution.

From the societal (perhaps “objective, economic” is a better modifier) perspective, then, the most tragic age at which to die is 25 (or thereabouts), when the maximum of investment has been made and the individual has yet to realize any return. The most “preferable” moment for death would then be the day of retirement (maximum return on investment, before the individual goes back on the dole). The death of an infant is only mildly negative in that there was relatively little investment lost.

Of course, I personally find this view abhorrent, but I think it is interesting on two counts:
It demonstrates the limits of certain versions of economics or utilitarianism which consider only the aggregate good.
It forces us to consider the implications of a shift between the individual and societal perspectives. This has deeply practical applications. Indeed, the balance between the desires of the individual and the needs of the society is perhaps the most basic element of politics and we see it being played out in the current debate shouting match in the US on end-of-life decisions.

My ideas aren’t fully developed on this issue so I apologize for any lack of clarity on my part, though I’d love to hear any comment you may have.

August 13, 2009 10:53 am

No, you were quite clear. I like your point a lot. From a practical economics standpoint, this argument about “maximum return on your investment” is pretty indisputable. But the great disparity between practical optimization and our sense of moral correctness is very interesting to note.

I wonder whether there could be such a thing as “moral economics”, wherein our moral beliefs and ideas are given quantitative measures. This post, for example, suggests that the degree to which death is a bad thing, in a moral sense, varies like 1/(1 + log2(t/(9 months))). Would there really be any value to using such a numerical assessment? It somehow sounds awful to “put a numerical value on human life”, but maybe this approach could be useful for weighing moral alternatives in less extreme cases.

August 16, 2009 10:43 pm

Here’s a hypothetical question that comes to mind. This is a variation on the old “trolley problem” http://en.wikipedia.org/wiki/Trolley_problem .

Imagine that a train is hurtling out of control down a track, and that you are standing at the switchboard with the ability to divert the train down a different track. If you let the train go down track A, then two people will die. If you divert the train down track B, then one person will die. Which track should you let the train go down? Usually the answer is track B.

Now imagine that down track A are two 25-year-olds, and down track B is a three-year-old. Which option do you choose then?

Implicit in this “eight lifetimes” idea is the notion that each lifetime is equally valuable. So if you really believe it, then your choice in this particular scenario is clear. You save the three-year-old, who has 5 lifetimes left to live, instead of the 25-year-olds, who combined have only 4. I have to admit that if I were placed in this situation with such a terrible choice to make, I would probably believe this reasoning and save the three-year-old. But maybe that would only be a way of rationalizing a choice that would feel awful either way. If track B had a seven-year-old (less than 4 lifetimes left) instead of a three-year-old, though, the answer would be different.

So is there something inherently wrong with the fact that I used a mathematical formula to make my ethical choices for me? Is there something immoral about describing my moral opinions with mathematical statements? I’m not sure.

August 17, 2009 4:34 pm

People of an older generation who heard of the death of a child tended to ask whether the parents were young enough to have another. That might imply that the felt burden depends on the age (and presumed fertility) of the parents.

August 18, 2009 6:58 pm

Many academic and research economists apply numerical values to life, namely monetary values, through a variety of methods. One clear example of this is a paper by Ashenfelter and Greenstone, titled Using Mandated Speed Limits to Measure the Value of a Statistical Life. This paper analyzes the 1987 policy to raise the cap on speed limits from 55 mph to 65 mph, this raised average speeds and in turn accident fatalities. They calculated that a specific amount of time was saved per additional fatality, and multiplied this time by the average wage to get the value of a statistical life; their figure was $1.54 million. Here is another analysis of the value of a statistical life based on government policies. Levitt and Donohue did a paper on The Impact of Legalized Abortion on Crime, made famous by Levitt’s Freakonomics. The dataset they used indicated that abortions reduced crimes, theoretically by reducing the number of unwanted children that tend to grow up in bad situations and may turn to crime. I don’t believe that this was in the paper, but later analysis applied the cost to society of the crime by the number of crimes reduced by an abortion and valued an abortion as a positive$20,000 (I can’t find the citation for this, but I believe this is approximately what they found). Applying this to your adjusted trolley problem, this three year old likely had no parental supervision and could potentially become more of a cost to society than the two 25 year olds.

In wrongful death litigation, a plaintiff (i.e. spouse of deceased) is often paid the net present value of their spouses potential income by the defendant. I don’t see the defendant arguing against additional cost burdens of the spouse and expecting to get paid themselves–take for example an old man with heart disease who died at the hands of a careless doctor, this doctor saved his spouse potentially thousands of dollars in future medical costs. This example only works one way and even feels wrong–potentially equating a spouses life to his/her earnings.

To answer your question about putting a value on life, you can definitley put a quantitative value on life but the dataset you use and the assumptions you make to calculate this can vary wildly. The morality of this also questionable, but this research is quite intriguing (to me at least)–the morality issue is all about how you apply the numbers. You could come up with a conditional function applying a different cost/benefit equation to each section of life using things like public education expenditures and health care as costs and wages as benefits for each of the eight groups.
E(life) = { -(cost of day care)*age if x=1
{ -(cost of education)*age if x=2
{ ….
{ (wages)*age – costs if x=6
{ -(healthcare costs)*age if x=7
This is definitely over simplified but I think you probably get the point here. It would be quite difficult to develop these costs and benefits but I suppose it could be modeled this way.

4. August 19, 2009 1:42 pm

Isn’t there an assumption that all these lifetimes are equally valuable? Also, I think when faced with a moral dilemma like this, voting on which track to take i.e. consensus of opinion, will take the moral burden out of a single person’s shoulders and place it on the group.

I believe that there is no right/wrong or moral/immoral thing as such. Why not talk about the percentage that you feel confident on the morality of your decision.

Asking mathematical formulas to make your ethical choices may release the burden off your shoulders and place it on the equations. What if somebody later comes up with a better mathematical theory of ethics and prove your decision wrong?

5. September 15, 2009 6:04 am

Following up on this thread, I saw a review of a book called “The Time Paradox” on Ben Casnocha’s blog: http://ben.casnocha.com/2009/09/book-notes-the-time-paradox-by-zimbardo-and-boyd.html

Quoting from Casnocha (who quotes from the book):

The authors assert that people usually fall into one of a handful of “time perspective types.” Here’s an overview of each time perspective. They are: present-oriented, present-hedonistic, present-fatalistic, future-oriented, past-oriented. While I didn’t fill out the various surveys in the book, I think I trend toward being future-oriented, which would mean I am especially good at delaying immediate gratification for long term reward, employing probabilistic thinking, being health conscious, goal oriented, and a few other things. Future-oriented people struggle with being able to “enjoy present, transient, consumable activities and experiences.”

Below are my favorite nuggets. All are direct quotes, per usual.

How Sense of Time and Its Passage Affects Decisionmaking
After adolescence chronological age becomes a less reliable predictor of motivation, thought process, and emotional response. Recently, leading psychologists have begun to explore whether your chronological age—time passed since birth—is as relevant as your sense of the time remaining until your death.

When you imagine that you have a lot of time left, you use it to learn more about the world, meet new people, and experience novelty. When a life’s time is short, its goals become short-term. The mantra of those who anticipate a long-term future is “More is better,” and they generally look to spend time with a lot of different people and new acquaintances. The mantra of those who anticipate a short future is “Quality, not quantity,” and they choose to spend quality time with fewer people.

September 15, 2009 3:49 pm

‘It somehow sounds awful to “put a numerical value on human life”, but maybe this approach could be useful for weighing moral alternatives…’

Richard Dawkins – The Selfish Gene.

Our genetics unconsciously make this decision for us all the time based on the percentage of shared genes.