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Years ago my wife was looking through the books at a Goodwill store, and for a gag gift for my birthday she bought me a volume of poems by Rod McKuen, whose work I do not like. Helen brought it home and was going to wrap it when she looked inside. There was a dedication in the book signed by the author himself: “To Rob - May you always sleep warm. --Rod McKuen.” Now I have a volume of McKuen’s poetry I cannot throw away, but more to the point, how is it possible that completely by chance that she should pick up such a book bearing a dedication to someone of the same name? It just does not seem that such a thing could happen. It’s the sort of story told many times in _The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day_ (Scientific American / Farrar, Straus and Giroux) by mathematician David Hand. Hand knows that it is tough to write about mathematics for the layman, perhaps even more so for probability which he says “is renowned for its counterintuitive nature, more than any other area of mathematics. Even the most eminent mathematicians have been tripped up by it.” Yet there are few equations here, there are many astounding stories, and many of Hand’s explanations are drawn from tossing a humble die.
The book starts with its main contradiction, only a seeming contradiction and one of many explained away within these pages: How is it possible that extremely unlikely things happen, and not only happen, but happen over and over? Hand gives satisfying answers, but besides being a book about extraordinarily improbable events, this is also a book that explains probability in general. Take the law of inevitability: Something has to happen. In a lottery, each possible ticket has so tiny a chance of winning that you might think it a miracle if yours is the one chosen. But what _is_ certain is that some ticket will be picked to win (or if not, the stakes will be raised for the next draw when there will be a winner). It is thus dead certain that an improbable event will occur. There’s the law of truly large numbers: if there are enough possible opportunities, any outrageously unlikely event can happen. If you toss a coin enough times, and have a near-eternity to do so, you will get a run of a hundred heads; it simply has to happen. These are understood strictly with probability theory, but we have also to supplement our “understanding” of rare events by human foibles. The law of selection, for instance, says that you can make probabilities as high as you like, in retrospect. It’s like shooting arrows into the side of a barn and then painting bullseyes around each one. All of us are liable, too, to confirmation bias; we notice events that reinforce what we wish to believe and we disregard data that does not fit. Prophets and astrologers harness this tendency all the time. And sometimes we use bad equipment for our research. Federal law has specific and strict rules for every die thrown in a casino, but dice you get in a Monopoly set are far from such strict engineering and they have bias; research into psychokinesis, the ability to control die tosses, has been criticized because it used ordinary dice.
Readers of Hand’s book will have a happy tour of many aspects of probability, delivered by a guide who is knowledgeable and funny. Even if some of the math gets by you, the astonishing stories are sure to impress you, like the ones about people who have won the lottery more than once. Spare a little sympathy, however, for Maureen Wilcox, who in 1980 bought lottery tickets in both the states of Massachusetts and Rhode Island. She picked all the right numbers, too. Except the numbers she picked for Rhode Island won in Massachusetts, and vice versa.
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The Improbability Principle begins by recounting what David Hand calls the simply unbelievable coincidence of three unrelated events: (1) In November 1971, author George Peifer gives an annotated copy of his novel The Girl from Petrovka to a friend. (2) His friend loses the copy in Bayswater, London. (3) In the summer of 1972, actor Anthony Hopkins waiting for an underground train at Leicester Square tube station, sees a discarded book lying on the seat next to him. It is Peifer's annotated copy of The Girl from Petrovka. Hopkins had been unsuccessfully searching London bookstores for the book. As if that was not coincidence enough, more was to follow. When he had a chance to meet the author, Hopkins told him about his find. A quick check of the annotations in the copy Hopkins found showed that it was the very same copy that Peifer's friend had mislaid.
Hand explains that theses and similar coincidences are explained by the ‘improbability principle’, which he elaborates upon in the book. He asserts that extremely improbable events are commonplace; a consequence of a collection of more fundamental laws which all tie together to lead inevitably and inexorably to the occurrence of such extraordinarily unlikely events. According to these laws, and the improbability principle, the universe is in fact constructed so that these coincidences are unavoidable: the extraordinarily unlikely must happen; events of vanishingly small probability will occur. In The Improbability Principle Hand endeavors to resolve the apparent contradiction between the sheer unlikeliness of such events, and the fact that they nevertheless keep on happening.
Hand admits that improbability principle is not a single equation, such as Einstein's famous equation, but a collection of strands which intertwine, braiding together and amplifying each other, to form a rope connecting events, incidents, and outcomes. The main strands are the law of inevitability, the law of truly large numbers, the law of selection, the law of the probability lever, and the law of near enough. Putatively, anyone of these strands is sufficient, by itself, to produce something apparently highly improbable, but it is when they combine and work together that their real power takes hold. Hand insists in the Epilogue that when these laws - the intertwining strands - are put together, virtually every simply unbelievable coincidence may be explained.
Just at the point where one expects Hand to illustrate intertwining of the strands, and event connections, he quickly concludes the book by merely listing a number of extraordinary events by which we should be unsurprised, given the improbability principle. He disappoints by abdicating an expected detailed example of at least one illustrative instance of how various strands may braid together to connect exemplary unrelated events. His detailed expositions of the law of inevitability, the law of truly large numbers, the law of selection, the law of the probability lever, the law of near enough, their apprehension by the human mind lay the foundations for the expectation. This reviewer has found one such illustration - but prefers to await the author’s genius to produce several better ones.
In the recent book My Universe - A Transcendent Reality author Alex Vary describes ‘impossible loops’ that may underlie and explain the inevitability of remarkable coincidences. In Gödel, Escher, Bach: an Eternal Golden Braid, Douglas Hofstadter expounds on the intricate coincidences of and recursive interplay of mind, matter and universe. David Hand may well have considered how the improbability principle explains Hofstadter’s paradox which he entitles 'which came first - the ribosome or the protein?' Hofstadter observes that in order for a ribosome to be made, certain kinds of proteins must be present, and rRNA must be present. Of course, for proteins to be present, ribosomes must be there to make them. Each ostensibly pre-exists the other. This and similar coincidence paradoxes are resolvable when they are considered in the context of communication, interplay and exchanges engendered by impossible loops, perhaps in concert with the improbability principle.