Knock on Wood

Jeffrey S. Rosenthal

• Publisher: HarperCollins Publishers
• Year: 2018
• ISBN:
  9781443453097
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Jeffrey S. Rosenthal, author of the bestseller Struck by Lightning: The Curious World of Probabilities, was born on Friday the thirteenth, a fact that he discovered long after he had become one of the world's pre-eminent statisticians. Had he been living ignorantly and innocently under an unlucky cloud for all those years? Or is thirteen just another number? As a scientist and a man of reason, Rosenthal has long considered the value of luck, good and bad, seeking to measure chance and hope in formulas scratched out on chalkboards.

In Knock on Wood, with great humour and irreverence, Rosenthal divines the world of luck, fate and chance, putting his considerable scientific acumen to the test in deducing whether luck is real or the mere stuff of superstition.

Chapter 1

Do You Believe in Luck?

As a university professor who specializes in the mathematics of probability and statistics, I am dedicated to spreading knowledge and wisdom about the workings of randomness and uncertainty. I have confidently answered questions about all sorts of probability-related subjects—lotteries, airplane safety, election polls, crime rates, gambling odds, sports statistics, medical testing, and more. But then, every once in a while, someone asks me if I believe in luck. An awkward pause follows, and then I try to eke out a reply.

Do I believe in luck? Well, sure, of course I do. Sometimes things work out well, and sometimes they don’t. Sometimes external forces make life difficult, and other times they come together just right. In my own case, I was lucky enough to be born into a middle-class family that valued education and started me on the path to success. I was lucky enough to grow up in a peaceful, safe, prosperous country. I was lucky enough to be admitted to top universities, leading to a good academic position with the job security of tenure. Of course I believe in luck!

Do I believe in luck? No, certainly not. Some people believe in such things as unlucky numbers, astrological predictions, and lucky charms, which all seem like bunk. There are no known physical laws that could produce a causal connection between actual life outcomes and any of these unusual items, nor have careful experiments ever shown any consistent relationship between them. Seriously believing in any of them seems a bit absurd. And just because good things have happened to someone so far does not mean that pattern will continue. The past does not predict the future, patterns are not set, and no one is guaranteed any luck at all. Of course I don’t believe in luck!

Do I believe in luck? In the end, it depends what you mean. Luck is one of those words that can be interpreted in many different ways. I once did a radio interview where they asked me to begin by giving a simple, short definition of luck.¹ I soon discovered that I couldn’t do that, and the entire interview got bogged down in a debate about what we were actually talking about.

If you say something happens “by luck,” then it is clear you are denying that it happened due to established scientific cause and effect (like a ball falling to the ground because of gravity), or due to hard work (like passing your final exam because you studied hard), or due to specific intent (like a bucket of water dumping on your head because your goofy friend left it balanced on top of your door). But if that is what luck isn’t, then what is it that luck is?

Sometimes people use the word “luck” to simply describe events that are outside of our control or prior knowledge, a sort of dumb luck or random luck. We cannot predict such luck, only notice it in hindsight—for example, you go to the store to buy sneakers and find that they are on sale this week, which you hadn’t known or suspected before leaving your house. Or you’re visiting a foreign city when terrorists attack, and you’re relieved to hear that their bomb went off on the opposite side of town from your hotel. These are indeed instances of getting lucky, but only in the sense of benefiting from a situation you could not influence or predict in any way. And if that is all there is to it, then it’s nothing but dumb, random luck.

On the other hand, sometimes people use the word “luck” to allude to certain special powers that magically affect the future—everything from lucky charms, like rabbits’ feet and four-leaf clovers, to supernatural “predictions” made by horoscopes, fortune cookies, and tea leaves, to “fate” about what just had to happen, to “karma” taking its sweet revenge, to simply being a magically lucky guy to whom good things must always happen. All of this implies a sort of forceful luck, a special kind of luck that can be predicted in advance and affects the probability of future events, based not on scientific laws or hard work or other fact-based explanations, but rather on other, ethereal causes.

So, which one is correct? Does “luck” refer to something that is dumb and meaningless, or to something that is forceful and magical?²

So many people believe in a special luck force, in one form or another. They scoff at my usual “scientific” approach to randomness and luck, incredulous that I could possibly imagine that probability and scientific causes are all there is. Could they be right and I be wrong? How can we truly measure and evaluate luck? How can we decide which predictions are accurate and which are nonsense? How can we figure out what causes what? How can we determine what really does govern the randomness all around us?

And how could I sort this all out? Well, maybe by writing a book.

In the pages that follow, I will discuss various examples of luck at work and try to sort out luck’s meaning—or lack thereof. Some of the questions I will ponder include:

• Why am I, like so many others, attracted to fictional works like Macbeth and Shoeless Joe whose plot lines centre around concepts of luck, fate, and destiny? Why do we love magic in our stories? Are we rejecting scientific attitudes each time we read them? And should we then expect life to imitate art by following its own rules of destiny and magical meaning?
• If a friend tells me that sun rays shining through some tree branches were a “sign” to bring her comfort, is she onto something? Were those sun rays specially designed to cheer her up, or were they just random? And if they were random, does that make her comfort less real?
• When sports fans face the disappointment of their team losing, why are they so quick to blame it on superstitious curses? Does their belief fulfill some need? Is there any logic to their feelings?
• When terrible tragedies like nuclear explosions, hurricanes, and tsunamis kill thousands of people, is there a “reason” for it? Are the victims fulfilling their “destinies”? Or is it just dumb, horrible luck, causing suffering for no reason at all?
• How should I react to learning that I was born on a Friday the Thirteenth? Does that fact doom me to a life of failure and bad luck? Have my modest successes demonstrated that I “broke” the curse? Or was there never any curse to begin with?
• When evaluating my academic career success, should I feel proud of my accomplishments? Or should I just dismiss them all as meaningless, undeserved luck?
• When my student went on a blind date and discovered that both he and his date drove identical cars, was that a sign they were meant to be together? Did it guarantee love and bliss? Should it influence the decisions they make?
• What can we learn from amazing stories like the man who felt mysteriously drawn to a particular Hawaiian beach, where he happened to meet a half-brother he had never known, an encounter that ended up changing his life and rescuing him from his troubles? Was this destiny at work? Was it the hand of God? Or was it simply a random, lucky coincidence that could just as easily never have occurred?
• Why do so many people believe in astrological horoscopes, psychic predictions, fortune tellers, numerology, and other supernatural phenomena? Is there any basis for them? Are there scientific studies that evaluate the evidence for them?
• When we buy lottery tickets, gamble at a casino, or roll dice in a board game, is the randomness fixed, or is it subject to our influences? Is there anything we can do to improve our luck? Are some people inherently luckier than others?
• When we read a news story about the latest medical study, a new poll, or an astounding coincidence, should we trust it? Does it have meaning? How can we distinguish what is truly significant from what occurs just by luck alone?
• And most important of all, how can we answer these questions? What principles can help us distinguish between random, meaningless, dumb luck and true instances of meaning and significance and influence and destiny? What luck traps must we watch out for, to avoid drawing the wrong conclusions? How can we identify causes when they arise, without imagining them when they are lacking?

These questions don’t have easy answers. They have occupied me, and sometimes unsettled me, for years. My perspective is often at odds with those who surround me—when I am able to articulate my perspective at all. I had some misgivings about tackling these issues in book form, and yet here I am. Let the adventure begin.

Chapter 2

Lucky Tales

Our lives are constantly subjected to unexpected twists and turns that are beyond our direct control. Surprises that help us, hurt us, or confuse us. We can try to plan and prepare all we want, but the world may have other ideas for us. As the great Robbie Burns once put it:

The best-laid schemes o’ mice an’ men

Gang aft agley,

An’ lea’e us nought but grief an’ pain

For promis’d joy!¹

Can these twists and turns be dismissed as just random luck? Are they the result of simple science at work? Are they rooted in probability, odds, and outcomes? Many people do not think so. They insist that these events are somehow controlled by powerful supernatural forces such as superstition, ESP, divine intervention, and destiny.

Luckily for me, I haven’t had to search very hard to find examples to illustrate the latter point of view. They come up in my everyday conversations, with strangers, acquaintances, and friends alike.

The Scottish Play

A friend once hosted a party where each guest was supposed to recite a piece of poetry. I nervously selected a soliloquy from my favourite Shakespeare play, Macbeth. I chose the famous one that begins, “Is this a dagger I see before me?” which I had to memorize back in high school. I read it boldly, in my most ferocious Scottish accent, to moderate acclaim from my fellow partygoers. Not enough to quit my day job, but so far, so good.

Later, my friend made the mistake of bragging to another woman about the brilliance of my earlier Macbeth reading. The woman immediately became concerned. “You read Macbeth out loud?” she gasped. “But didn’t you experience bad luck afterwards?” She was referring to the superstition that misfortune is somehow caused by quoting Macbeth (or even naming it; hence alternative names like “The Scottish Play” and “The Bard’s Play” and “Mackers”). This superstition has its origins in a series of accidents that supposedly occurred during various productions of Macbeth, including a stabbing during a 1794 production.² Many of these misfortunes are poorly documented and difficult to verify, but that does not dissuade the true believers.

Surprised, I replied that no, I had not experienced any resulting bad luck. I mentioned, as mildly as I could, that I don’t actually believe in such superstitions. But this only provoked her to say more. “Oh, my daughter didn’t believe either,” she persisted. “So she quoted Macbeth too. Then, a week later, while preparing for a trip, she discovered that her passport had expired and had to be renewed!”

I began to realize that the woman was actually serious. Indeed, she was certain that her daughter’s passport woes were the result not just of simply random bad luck, but of some other, mysterious force. And nothing anyone said would change her mind. Why was she so convinced? Should I become convinced too?

Further enquiries revealed that the daughter’s passport had expired two years earlier, after being issued years before that. So I politely asked the woman how its expiration, the result of actions from long ago, could have been caused by events from the previous week. “It is not a question of cause,” she replied huffily as she walked off.

So much for my probabilistic diplomacy. Clearly this woman and I were coming from two very different perspectives. But who was right, and who was wrong? Is it even possible to say?

Disappearing Diamond

A friend once told me about the time, in the middle of a long drive, when she noticed that the diamond was missing from her wedding ring. Understandably upset, she searched the car high and low, without success. A religious person, she prayed for God to return the diamond to her. Some time later, she exited her car at a rest stop and the diamond emerged, unharmed, from a fold in her shirt.

This was proof, my friend assured me, of divine intervention. The fact that she had prayed for the diamond’s return and subsequently found it showed that her prayers had been answered, that God had intervened to bring her diamond back to her. She couldn’t understand how anyone could fail to believe in divine intervention after hearing her tale.

Considering the issue, I asked her why God had allowed her diamond to get lost in the first place. If God had really helped her recover the stone, ...