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On Probability & Life’s Little Miracles
Phillip Hoffmann on the importance of the astonishingly improbable.
Above my desk I keep a copy of an article that made the news back in January, 1998. It concerns a game of whist played in Bucklesham, Suffolk, when the hand dealt after the deck had been properly shuffled was perfect, meaning that each of the players (four, including a dummy) had every card in a suit. That is, one player had all the hearts, another all the clubs, and so on. What are the odds of this happening? Glad you asked. It turns out one Horace Norton had already done the math for this back in 1939 and calculated that we should expect this to happen once in every 2,235,197,406,895,366,368,301,600,000 deals. To put this in some perspective, the article continued, even if a billion players played for 50 million years, dealing 100 hands per sitting at 400 sittings a year, the odds against a perfect deal would still be 100 million to one! This sounds mind-boggling, but what exactly is extraordinary about this event?
Each hand that is dealt from a properly shuffled deck is what statisticians call an equally likely outcome. In other words, the likelihood of any given deal is exactly the same as that of the perfect deal. So every time you play a game like whist or bridge, each deal is extraordinary in the sense that it’s very likely never to have been dealt before. Each hand, if you like, is a little miracle, and just as well, or else card games would soon become boring. What, then, makes the story about the whist game in Suffolk newsworthy? The answer is simple. As a species, we are, if nothing else, pattern-recognizers and pattern-seekers par excellence. A monkey sitting at a keyboard and typing gibberish is not news, but if one happens to type Hamlet, you can bet we’d hear about it before too long. And if the winning numbers for next week’s Lotto 6-49 turn out to be 1, 2, 3, 4, 5 and 6, this too would rate a mention on the BBC news. We are drawn to certain patterns and filter out very many other sensory inputs as noise, or garbage. Of course, it’s also possible that we routinely misinterpret real patterns as noise. Perhaps realizing that we have been doing so explains the ‘penny drops’ syndrome when we learn something new. And for all we know, some alien intelligence is patiently trying to alert us of its existence by sending out a signal encoding the decimal expansion of the square root of 17. But if we were first to pick up this signal only somewhere around the 900 trillionth decimal place of our number system, we might not recognize the signal as embodying anything intelligent, which would be our loss. But I digress.
Card games and lotteries involve outcomes that are equally likely, but of course in reality not all events are equally likely. You don’t need me to tell you that you are more likely to pass a course if you study hard and do the homework, and less likely to pass it if you repair to the pub every night instead. But what if life were just a huge collection of random events, and what if the appearance of order were just a function of the ways in which we impose order on these events by filtering out ‘garbage’? This strange possibility is allowed for by quantum theory, which implies that lots of random, even truly bizarre events can happen, but that the occurrence of most such events is extremely unlikely. More specifically, the phenomenon of quantum tunneling leaves open the theoretical possibility that you might simply vanish and reappear somewhere else almost instantaneously. Electrons do this sort of thing all the time, but quantum theory does not rule out the possibility that larger objects will do the same thing. The catch is that the probability that something like this will happen to, say, a human is, well, vanishingly small. But hey, perfect hands in whist shouldn’t get dealt either, so perhaps it isn’t crazy after all to entertain the possibility that you might quantum tunnel through a door one fine day.
There is a well-known interpretation of quantum theory called the many worlds interpretation. This interpretation predicts that tunneling and all other events allowed for by quantum theory actually do take place, somewhere, somewhen. In other words, not only does faeces happen, it has to happen. All of it. According to the many worlds interpretation, you really do tunnel through doors, but this happens only in very few of the worlds specified by the interpretation. From a subjective perspective, then, very few of us ever experience quantum tunneling through a door, just as very few of us ever have the subjective experience of being dealt a perfect hand of 13 clubs, or, alas, know what it feels like to win $10 million in a lottery. However, if everything that can happen does happen, then arguably this renders the objective unlikelihood of the events permitted by quantum mechanics to be a moot point. After all, the fact that it is virtually unheard of for someone to be struck by lightning twice in one day is of little consequence to anyone unfortunate enough to be the victim of two lightning strikes in one day. Reality might just be such stuff as trillions upon trillions of tiny miracles are made of. However, what we experience as actual in the enormously rich realm of quantum possibilities might, to make a kind of Kantian point, be primarily a matter of what we are capable of representing as real, given the cognitive machinery we happen to have as humans.
So while I don’t suggest you spend too much time patiently waiting to quantum tunnel out of the room you’re in next time you are stuck with a boring party guest, on the other hand I hope that the police don’t have you escorted away by people in white coats if you ever find yourself having to explain that the Jaguar you just demolished appeared from out of nowhere as you took the freeway exit. Honest it did, officer!
© Phillip Hoffmann 2005
Phillip Hoffmann practices his disappearing act at the DeVry Institute of Technology, in Calgary, Alberta, where he is Dean of Business and Systems. He is the author of Nothing So Absurd: An Invitation to Philosophy (Broadview Press, 2003).