Subtract a Decade

Life is not as short as it used to be

Life is short. Still, it’s not as short as it used to be.

Of all the ways we’ve made progress, the leap in expected lifespan is probably the most personal.

That makes the following chart very good news.

While the data is worth perusing in full, the visual is abstract. Let’s make things concrete.

During the twentieth century, humans approached death by just seven months for every year they aged. That’s because as they moved through time, their allotted time itself was moving.

Every baby born in the last 150 years was gifted just over an extra year of life than a baby born a decade before. 1.17, to be exact, and that multiplier is growing.

So, relative to even our grandparents, we’ve secured an extra decade of life. And that without any technological or medicinal breakthrough that has truly changed the longevity game— which could very well come.

We’ll have time to wait. As the boost in lifespan increases, the gap between us and past generations widens daily. It may turn out that the fountain of youth is not a place, but a journey.

If you ask me, a change of expectations is in order. With new life should come new Einstellung (attitude). Einstellung, however, seems sticky — much like prices that don’t move in step with new economic information.

What would it look like if instead of following the crowd, we followed the math and subtracted a decade from our age?

Tradeoff

If you were turning twenty, instead of thirty, or thirty, instead of forty, what might be different about your approach to the next ten years? For most, the difference would be captured in the tendency to explore or exploit.

The explore/exploit tradeoff describes the strategical dilemma of maximizing gain from a series of options with unknown rewards. The multi-armed bandit problem — borrowed, as is the concept, from computer science — is a classic example.

Say you were a gambler in a casino facing down a metal sea of slot machines. Each slot machine has a different probability of reward, but you don’t know what it is.

Your first move is obvious. Pull a lever and see what happens. This is exploring, or trying new things. The second, third, and fourth moves are also easy: keep pulling levers, keep taking note of reward.

After a while, you’ve pulled the levers of many machines and have information about what their payoff-probabilities might be. Now you have a problem. Should you return, or exploit, machines that produced well or continue to explore by pulling new levers?

The question may feel academic, but it’s really quite quotidian. Whether it’s choosing what to wear, where to eat, or whom to date, any decision that involves a known benefit and unknown potential is a tradeoff between explore and exploit. We don’t often choose a strategy in explicit mathematical terms, but we choose one all the same.

What does all this have to do with age? A lot, it turns out, because the logic of explore/exploit changes as the end of an interval is neared.

Interval

In the classic multi-armed bandit problem, expected outcomes can be expressed mathematically as a series of payoff probabilities. This is called the Gittins index after John C. Gittins, who is credited with finding a solution to the basic multi-armed bandit problem in 1979.

In the index below, the column and row labels describe the number of wins and losses of a given slot machine. The cells contain the payoff probabilities of individual slot machines given those wins and losses.

The further northwest you go, the less trials you’ve observed. What’s fascinating is that unknown machines — that is, those whose lever you have pulled little or not at all— have a higher expected payoff than many for which you have information. This is captured by the increase in the payoff probabilities towards the upper left quadrant of the index.

That’s a very stuffy way of saying that given time and untested opportunity, exploring offers more benefit than exploiting. When we are new to a city, we stand to gain more from trying new restaurants. Such logic is generally abided.

However, the calculation changes when nearing the end of an interval. With time running out (say, due to a looming relocation), we eschew the unknown restaurant in favor of a greatest hits tour.

So it is with age. As we grow older and sense our time is dwindling, we prefer less novelty— fewer new friends, romantic partners, spontaneous vacations, edgy bands, fashion styles, you name it.

This sense of our age is intuitive, and it take its cues from the culture. In the greater interval of life, there are sub-intervals like “childhood,” “young adulthood,” “adulthood,” and “middle age” that, being culturally defined, remain contracted so long as Einstellung sticks.

As such, if cultural expectations are lagging behind the reality of burgeoning lifespan, we systematically shift to exploit sooner than we should, leaving much untouched, uncovered, and unexplored. The story of sticky Eintsellung is, in large part, one of opportunity cost.

Explore

It’s true that everything must come to an end. Waiting too long to accept greater responsibility and moving ungracefully through life’s phases is probably a greater error than moving too quickly.

However, per the math, both are errors all the same. There’s more to explore in the world than one person could possibly manage in a lifetime. Still, the extra years we’ve been gifted present an opportunity to do a little more — to take a little more risk, be a little more bold, and resist a little more the sense of closing doors as our calendar age creeps towards the benchmarks of our grandparents.

We should accept it. An expanding budget to explore means not only an extra berth of novel experience, but also a steadier foundation on which to eventually exploit.

So, here’s to subtracting a decade. There’s lots yet to do.