In psychology, there's something called the broken-leg problem. A statistical formula may be highly successful in predicting whether or not a person will go to a movie in the next week. But someone who knows that this person is laid up with a broken leg will beat the formula. No formula can take into account the infinite range of such exceptional events.

THIS IS NOT, to say the least, an appealing prospect. People naturally prefer to avoid the subject of their decrepitude. There have been dozens of bestselling books on aging, but they tend to have titles such as Younger Next Year, The Fountain of Age, Ageless, or — my favorite — The Sexy Years. Still, there are costs to averting our eyes from the realities. We put off dealing with the adaptations that we need to make as a society. And we blind ourselves to the opportunities that exist to change the individual experience of aging for the better.

When you are young and healthy, you believe you will live forever. You do not worry about losing any of your capabilities. People tell you “the world is your oyster,” “the sky is the limit,” and so on. And you are willing to delay gratification — to invest years, for example, in gaining skills and resources for a brighter future. You seek to plug into bigger streams of knowledge and information. You widen your networks of friends and connections, instead of hanging out with your mother. When horizons are measured in decades, which might as well be infinity to human beings, you most desire all that stuff at the top of Maslow’s pyramid — achievement, creativity, and other attributes of “self-actualization.” But as your horizons contract — when you see the future ahead of you as finite and uncertain — your focus shifts to the here and now, to everyday pleasures and the people closest to you.

This is the consequence of a society that faces the final phase of the human life cycle by trying not to think about it. We end up with institutions that address any number of societal goals — from freeing up hospital beds to taking burdens off families’ hands to coping with poverty among the elderly — but never the goal that matters to the people who reside in them: how to make life worth living when we’re weak and frail and can’t fend for ourselves anymore.

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In fact, he argued, human beings need loyalty. It does not necessarily produce happiness, and can even be painful, but we all require devotion to something more than ourselves for our lives to be endurable. Without it, we have only our desires to guide us, and they are fleeting, capricious, and insatiable. They provide, ultimately, only torment.

Leonid Gavrilov, a researcher at the University of Chicago, argues that human beings fail the way all complex systems fail: randomly and gradually. As engineers have long recognized, simple devices typically do not age. They function reliably until a critical component fails, and the whole thing dies in an instant. A windup toy, for example, works smoothly until a gear rusts or a spring breaks, and then it doesn’t work at all. But complex systems — power plants, say — have to survive and function despite having thousands of critical, potentially fragile components. Engineers therefore design these machines with multiple layers of redundancy: with backup systems, and backup systems for the backup systems. The backups may not be as efficient as the first-line components, but they allow the machine to keep going even as damage accumulates. Gavrilov argues that, within the parameters established by our genes, that’s exactly how human beings appear to work. We have an extra kidney, an extra lung, an extra gonad, extra teeth.

The trouble is that we’ve built our medical system and culture around the long tail. We’ve created a multitrillion-dollar edifice for dispensing the medical equivalent of lottery tickets — and have only the rudiments of a system to prepare patients for the near certainty that those tickets will not win. Hope is not a plan, but hope is our plan.

Human beings have an ability to simply recognize the right thing to do sometimes. Judgment, Klein points out, is rarely a calculated weighing of all options, which we are not good at anyway, but instead an unconscious form of pattern recognition.

In medicine, we have long faced a conflict between the imperative to give patients the best possible care and the need to provide novices with experience. Residencies attempt to mitigate potential harm for supervision and graduated responsibility. And there is reason to think patients actually benefit from teaching. Studies generally find teaching hospitals have better outcomes than non teaching hospitals. Residents may be amateurs, but having them around checking on patients, asking questions, and keeping faculty on their toes seems to help. But there is still no getting around those first few unsteady times a young physician tries to put in a central line, remove a breast cancer, or sew together two segments of colon. No matter how many protections we put in place, on average these cases go less well with a novice then with someone experienced.