omens -- 5/6/21
Today's encore selection -- from The Canon: A Whirligig Tour of the Beautiful Basics of Science by Natalie Angier. Things often happen that seem like omens or fateful coincidences -- the pianist at the bar starts playing a song you'd just been thinking of, or you pass the window of a pawnshop and see the heirloom ring that had been stolen from your apartment eighteen months ago, or a long-lost friend calls just after you learn of a personal tragedy. Natalie Angier explains that, often, the things we view as omens are instead reasonably probable outcomes:
"The more one knows about probabilities, the less amazing the most woo-woo coincidences become. ...
"John Littlewood, a renowned mathematician at the University of Cambridge, formalized the apparent intrusion of the supernatural into ordinary life as a kind of natural law, which he called 'Littlewood's Law of Miracles.' He defined a 'miracle' as many people might: a one-in-a-million event to which we accord real significance when it occurs. By his law, such 'miracles' arise in anyone's life at an average of once a month. Here's how Littlewood explained it: You are out and about and barraged by the world for some eight hours a day. You see and hear things happening at a rate of maybe one per second amounting to 30,000 or so 'events' a day or a million per month. The vast majority of events you barely notice, but every so often, from the great stream of happenings you are treated to a marvel: the pianist at the bar starts playing a song you'd just been thinking of, or you pass the window of a pawnshop and see the heirloom ring that had been stolen from your apartment eighteen months ago. Yes, life is full of miracles, minor, major, middling C. It's called 'not being in a persistent vegetative state' and 'having a life span longer than a click beetle's.'
"And because there is nothing more miraculous than birth [Professor] Deborah Nolan also likes to wow her new students with the famous birthday game. I'll bet you, she says, that at least two people in this room have the same birthday. The sixty-five people glance around at one another and see nothing close to a year's offering of days represented, and they're dubious. Nolan starts at one end of the classroom, asks the student her birthday, writes it on the blackboard, moves to the next, and jots likewise, and pretty soon, yup, a duplicate emerges. How can that be, the students wonder with less than 20 percent of 365 on hand to choose from (or 366 if you want to be leap-year sure of it)? First, Nolan reminds them of what they're talking about -- not the odds of matching a particular birthday, but of finding a match, any match, somewhere in their classroom sample.
"She then has them think about the problem from the other direction: What are the odds of them not finding a match? That figure, she demonstrates, falls rapidly as they proceed. Each time a new birth date is added to the list, another day is dinged from the possible 365 that could subsequently be cited without a match. Yet each time the next person is about to announce a birthday the pool the student theoretically will pick from remains what it always was -- 365. One number is shrinking, in other words, while the other remains the same, and because the odds here are calculated on the basis of comparing (through multiplication and division) the initial fixed set of possible options with an ever diminishing set of permissible ones, the probability of finding no birthday match in a group of sixty-five plunges rapidly to below 1 percent. Of course, the prediction is only a probability, not a guarantee. For all its abstract and counterintuitive texture, however, the statistic proves itself time and again in Nolan's classroom a dexterous gauge of reality.
"If you're not looking for such a high degree of confidence, she adds, but are willing to settle for a fifty-fifty probability of finding a shared birthday in a gathering, the necessary number of participants accordingly can be cut to twenty-three."