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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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on March 23, 2015
I've read a lot of books on statistics, both texts for work and more casual books for entertainment value. This is among the worst that I have read.

The examples are dull, recycled, and mostly uninteresting. The concepts seem too basic for the length of the book. And in the end it just is not interesting. Pass on this one.

When I read one star reviews, I often wish the reviewers would tell me what they did enjoy, so that I could calibrate their review and, potentially, so that I could find something better. So here I'll do that. Here are two books of similar nature, both of which are far better than The Improbability Principle:
1, The Drunkard's Walk, by Leonard Mlodinow
2, Fooled by Randomness, by Nassim Taleb
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on February 28, 2014
This is a book on statistics but without the mathematical details. The author explains the occurrence of events that one would expect to be extremely rare but, do in fact occur more frequently that anticipated. The author’s “improbably principle”, which is at the heart of this book, is composed of several strands: 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. These laws are each carefully explained by the author and several useful examples are presented to illustrate each one.

No formulas are used in this book. To be honest, I found that a bit disappointing being an avid mathematics enthusiast. However, it seems clear that the author’s objective is to drive his point home in the simplest and most widely accessible way possible. And in this he succeeds admirably.

The author, a professor of mathematics with specialization in statistics, writes very clearly in a friendly, engaging and often lively style. Because if its wide accessibility, I believe that this book can be enjoyed by any interested readers, no matter what their background. Science and mathematics enthusiasts, like me, although possibly disappointed by the lack of mathematical minutiae, should still be in for a treat. I enjoyed this book immensely.
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Our intuitive beliefs in the probability of various events are notoriously unreliable. In this book, the author David J. Hand, does a brilliant job of explaining how and why we get all this wrong. Chapter by chapter Hand explains various laws of probability that explain how seemingly improbable things happen and how they combine to virtually guarantee they happen. The anecdotes are interesting and the writing is well done.

This book has Amazon's "Look Inside" feature and I recommend you preview it's contents before buying.

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on March 14, 2014
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.
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on October 15, 2014
Hand is a competent writer and has some interesting things to say, but this book could have been better. For readers who have had ANY exposure to probability, I would begin with chapter 4. Hand, sensibly, starts his explanation of each concept with the simplest possible example, typically with dice. Too many of his examples to my taste, however, concern claimed psychic phenomena, and Hand's own personal experiences with coincidence are pretty dull, but there is much else of interest. Many readers will be unfamiliar with "regression to the mean", even if the term seems self explanatory, and you cannot be exposed too many times to this concept so that you recognize its implications when encountering them. I was unfamiliar with "scan statistics".

I believe Hand would have been better served to treat "the law of inevitability" as a special case of the law of large numbers. With large enough numbers of examples, an improbable event is likely to occur at least once. If a meteorite falls from the sky, and does not burn up, it has to land somewhere so now an improbable event, that it lands on a particular spot, is a certainty. Does inevitability of this kind need its own chapter? The chapter on "probability levers" I found a bit confusing. Also, in discussing the Cauchy distribution in that chapter Hand might have mentioned that its standard deviation is not finite - comparisons to the Normal therefore become problematical.

Hand discusses one phenomenon in two places, and I mention it only because a friend coined a word for it, an "aware-ity"; i.e. you encounter a word, possibly a proper noun like a place name, for the first time, and then it seems to keep cropping up. Of all Hand's explanations the one which helped me the most is that perhaps the word was not so rare in the first place, you just happened not to encounter it before, but sensitization may be the primary explanation.
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on March 18, 2014
This book was readable, which is probably an accomplishment for any book that at its core is about statistics. On the other hand, it was was organized as a collection of "laws" but each law seemed more like a tool for thinking about rare events. In the end, the disconnect between the book's claim of rigor and its anecdotal breeziness seemed vaguely disappointing.
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on October 22, 2014
This is an OK book, not a great book. The author fails to clearly identify a principle, but instead rehashes many of the issues common statistics present. It is an easy read, but is contrary to its title -- it does not prove nor address any principle.
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VINE VOICEon November 2, 2014
It goes without saying that most people have very little understanding of probability. Even as a teacher of mathematics, I find myself struggling with details of the subject. It’s just that the numbers so often seem to go against what our minds want to convince us is true. However, it’s important to understand the true impact chance has in our experience and Professor Hand does a pretty good job of explaining a difficult subject.

Take, for example, the law of truly large numbers. Basically, this law encapsulates the idea that, if the number of occurrences of an event is large enough, then events that are mathematically unlikely must happen. The lottery is a classic example of this. If hundreds of millions of people play the lottery it is likely that someone will win; however, the chances that the winner will be you is highly unlikely.

He also does a nice job of discussing how human beings warp the results of probability to force particular results. Studies of fortune-telling and ESP are examples of this. People who want to believe these things choose to take certain results as “hits” (the law of near enough) when they are not actually the specific result that was asked for.

Professor Hand’s prose is not always the smoothest when he’s in the midst of an explanation but he’s very good at using anecdotes to illustrate his propositions. He also invites unnecessary controversy with brief dovetails into evolution and the existence of god, which needed to be left out or detailed more fully. Still, for the most part, this is a nice exploration of why we shouldn’t be so surprised by coincidences and “unexpected” events.
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on November 19, 2014
In the last year, I've read four or five books on probability. This one is the best of the lot. It's clear, entertaining, and easy to understand.

People long for miracles. Everywhere you look there are charlatans ready to sell you a lottery ticket or a hot new stock and clean out your bank account. Even if no financial harm is involved, a belief in miracles and superstition can encourage an attitude of fatalism and passivity, diverting attention from real solutions to pressing problems.

This book is the antidote to that kind of ignorance and passivity. It should be required reading in every high school. Five stars.
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