Five men to twenty! though the odds be great,
I doubt not, uncle, of our victory.
Many a battle have I won in France,
When as the enemy hath been ten to one:
Why should I not now have the like success
— Shakespeare, Henry VI, Part III
Very recently, my daughter and her husband and their two small children moved in with my wife and me, into our home in Concord Massachusetts. They had been living in Brooklyn NY, the epicenter of the coronavirus. After 8 weeks of toughing it out, during which they didn’t dare venture out of their house, their cabin fever finally reached an unbearable level.
Now that our social ecosystem had grown to include six people, we began discussing rules of engagement with the outside world: Could we go into local grocery stores wearing face masks and rubber gloves, or would we shop only by delivery? How close could we get to fellow joggers? What was the procedure for scrubbing down mail and packages left at our doorstep? Could another relative, who had been sheltering in place, come for a visit to see the grandchildren?
Very quickly, it became evident that each one of us had a different tolerance for risk. In the new social ecosystem that we had just created, the group would have to follow the wishes of the least risk-tolerant among us.
Our families are privileged. We can work from home and still receive an income. Others face much more dire decisions. Meat packing workers must weigh the risk of infection against losing their jobs. As do health care workers and factory workers and grocery store workers and many others in shops and stores that are beginning to reopen. How does one weigh the risk of illness and possibe death against needed livelihood? What chances are we willing to take? Consciously or unconsciously, each of us is performing our personal risk-benefit analysis. Added to the unsettling nature of this dilemma is the fact that the risk is not fully known.
And even when the risk is known, converted to a definite probability, how does a person weigh that probability of infection against the value of health and livelihood?
A psychiatrist friend, Dr. Nicholas Browning, recently responded to my question about the psychological territory of such decisions:
Interestingly, “certainty” in the context of science means something remarkably different than it does in the context of psychology. In the world of science, certainty refers to something that is known to an extremely high degree of probability. The period of the earth’s rotation around the sun, for instance,.
In the study of experienced life, that is the study of psychology however, we should recall Yeats’ famous line, “…the worst are full of passionate intensity.” In the face of uncertainty, as is the case now with our frightening pandemic as well as other profound threats to human life on earth, orthodoxy thrives. Ambiguity and the difficulty of knowing what we will have to cope with tomorrow or next year becomes terribly difficult for most of us. Orthodoxy is a form of psychological certainty, a refuge from an unpredictable world, but it is very different than the certainties of science.
I am here simply trying to separate two experiences of certainty or uncertainty: the careful detached certainty of scientific confirmation from the highly unreliable internal experience of conviction.
I would interpret Nick’s comments to mean that probabilities, although very useful in science, are not at all definitive when making decisions about our personal lives. Each one of us has a unique mental landscape — different memories, different past experiences, different values, different commitments and convictions. Thus two people with the same bodily health, working exactly the same job, with the same financial obligations, might make different decisions when confronted with a risky situation.
Let me briefly sketch out the meaning of “probability” in the inanimate world before showing why it is almost irrelevant in the world of the mind.
When we say that the flip of a coin has a 50% chance of coming up heads and a 50% chance of tails, what we mean is that in billions of flips, heads would come up half the time. However, in a small number of flips, we will not always get 50% heads. Most of the time we won’t. If you are pressed for time, there is a nifty online site that does the flipping for you instantly. Using this site, I recently got the following results: With 10 flips of the coin, I got 6 heads (60%). With 100 flips, I got 53 heads (53%). With 1000, 505 heads (50.5%). As you can see, as the number of flips gets larger and larger, the fraction of heads gets closer and closer to 50%. Probability, as used in math and science, has meaning only when we have many many identical trials or events. If we don’t have identical events, or if we don’t have lots and lots of events, probability loses its meaning.
I promise that I am moving towards considering risk and human decision making — just bear with me a bit longer. Scientists use probabilities all the time in the construction of digital devices, for example, where the behavior of the device depends on the behavior of a very large number of identical atoms or electrons (subatomic particles). The behavior of only a few atoms or electrons is not at all predictable (like the flip of a coin only a few times), but the behavior of zillions of atoms is highly predictable.
Before returning to risk and the coronavirus, let me mention two familiar situations in which we human beings make personal decisions on probabilistic events in an unscientific manner. Consider the purchase of lottery tickets. Mathematically speaking, the odds are never in our favor to purchase a lottery ticket. In the Texas Lotto, for example, you pick 6 out of 54 numbers, and you can’t choose any number twice. Using a bit of arithmetic, you can calculate that the probability of getting any particular group of 6 numbers is 1 in 25,827,165. The Texas lottery commission will pay you $5 million for getting all 6 numbers right. Mathematically and scientifically, each ticket should cost $5 million/25,827,165 = 19 cents. That is, if you played the lottery lots and lots and lots of times and paid 19 cents for each ticket, you should come out even in the long run. So, mathematically speaking, 19 cents or less is a fair price for a ticket. However, each ticket actually costs $1. It makes no logical sense to play the Texas lottery. Why do people do it? Because of the thrill of taking a chance, the pleasure in imagining yourself with $5 million, the sheer hope and optimism that is a lovely part of human nature.
Similarly, why do people buy life insurance? The odds are always in favor of the insurance companies. They have to make money. If they paid out as much as they took in, they would be out of business. So why do people buy insurance? For peace of mind. To take care of loved ones in case of an unlikely accident and untimely death.
In both of these examples, we see the obvious thing: even when people know (or suspect) that the odds are against them, they will make bets based on unquantifiable feelings, spawned by “the experience of lived life,” to use Dr. Brownings words.
Finally, let’s get back to weighing risks with the coronavirus, and health risks in general. Suppose that the probability for your age group of getting infected in the next few years, without sheltering in place, were 0.01, and suppose that the probability of dying if infected were 0.01. That means that 1 out of 100 people in your age group will contract the virus and 1 out of 100 of those will die. Here is the critical point: There is only 1 of you. You cannot repeat the trial with 100 different lifetimes, as you would with 100 flips of a coin, or 100 different versions of yourself, as you would measuring the disintegration rate of 100 atoms of uranium. You cannot go into 100 parallel universes. You live in only 1 universe, and there is only 1 of you. So mathematical probabilities do not matter so much to you as an individual person. What matters far more are all the personal and psychological considerations mentioned earlier, and those will vary greatly from one person to the next.
Sometimes I have wondered why it is that each of us has her or his own mind, totally disconnected from all the other minds on the planet. One might imagine a universe in which all of our minds were connected in some mental cyberspace so that, in effect, our individualities would be blended together. Such a situation would not be far from having many copies of ourselves. And, in that case, laws of probability would apply more aptly to our decisions. But, for better or for worse, that is not the universe we live in. Each of us has a unique mind. Each of us is a unique individual, with unique memories and life experiences and personal passions. That is, perhaps, one reason why each life is so precious.