Fluke: The Math and Myth of Coincidence by Joseph Mazur (PDF)

Description

A mathematical guide to understanding why life can seem to be one big coincidence-and why the odds of just about everything are better than we would think. What are the chances? This is the question we ask ourselves when we encounter the strangest and most seemingly impossible coincidences, like the woman who won the lottery four times or the fact that Lincoln’s dreams foreshadowed his own assassination. But, when we look at coincidences mathematically, the odds are a lot better than any of us would have thought. In Fluke, mathematician Joseph Mazur takes a second look at the seemingly improbable, sharing with us an entertaining guide to the most surprising moments in our lives. He takes us on a tour of the mathematical concepts of probability, such as the law of large numbers and the birthday paradox, and combines these concepts with lively anecdotes of flukes from around the world. How do you explain finding your college copy of Moby Dick in a used bookstore on the Seine on your first visit to Paris? How can a jury be convinced beyond a reasonable doubt that DNA found at the scene of a heinous crime did not get there by some fluke? Should we be surprised if strangers named Maria and Francisco, seeking each other in a hotel lobby, accidentally meet the wrong Francisco and the wrong Maria, another pair of strangers also looking for each other? As Mazur reveals, if there is any likelihood that something could happen, no matter how small, it is bound to happen to someone at some time. In Fluke, Mazur offers us proof of the inevitability of the sublime and the unexpected. He has written a book that will appeal to anyone who has ever wondered how all of the tiny decisions that happen in our lives add up to improbable wholes. A must-read for math enthusiasts and storytellers alike, Fluke helps us to understand the true nature of chance.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The “math and myth” subtitle is intriguing, but the book is somewhat disappointing. One part discusses the basic math of probability theory, and another part covers probability-related topics (DNA forensics, chance scientific discoveries, ESP experiments, stock markets), but all this has been discussed in many other “popular science” books. The “myth” part discusses Sir Gawain and the Green Knight and other fiction, but the author’s point is unclear to me: we all know that fiction often relies on coincidences or other unlikely events.What part is interesting to me? Well the standard rationalist explanation of coincidences is simply that there are gazillions of possible coincides that might happen, so even if each has only a 1-in-a-gazillion probability, then some will happen “purely by chance”. This is explained at length in the book

⭐by an academic statistician. However, such books rely on very simple “small universe of possibilities” models, such as the birthday paradox, which are quite different from what we perceive as remarkable coincidences in everyday life. To me, the interesting and novel part (about 50 small pages) of this book is the following. In chapter 2 the author devises 10 classes of coincidences — for instance “chance meetings” — and gives a true historical story to fit each class — for instance “In Miami a woman got into a taxi, and recognized the driver as her taxi driver from Chicago on one occasion 3 years earlier”. Then in chapter 10 he tries to estimate the probability of the coincidence in the story. This is what is actually needed to justify the rationalist explanation. So I applaud the attempt. But — as the author acknowledges — it is hard to do. In the story of the taxi driver, the chance (according to the author’s data — he gets the calculation wrong) is very roughly 1 in 2.5 million. But this is the chance “per event” where an event is (very roughly) “someone gets a taxi in some big city away from their big home city”. Now I’m not sure how often this event happens, but with more than 200,000 U.S. taxi drivers I guess the event happens several million times per week, in which case this coincidence will happen several times a month to some passenger. The key point, which the author fails to emphasize, is that one needs to think very carefully about all the other roughly similar coincidences which might have happened.

⭐I read a good review of this book in the WSJ and thought it sounded interesting. I was disappointed. First, there are errors. At location 746 of the kindle edition, he has two formulas with a + instead of an x. In table 6.1, for 900,000 flips, the result In the far right column drops a zero, making it 0.003 instead of 0.0003. He discusses this in his text, and his table makes his conclusion to appear ten times what it actually is.So that’s sloppy, but forgivable. My main problem is that he is flying by the seat of his pants, then applying numbers to his guesses to make them seem scientific. How many people in London a shopping for a specific book on any given day? Who knows? I do not need to disagree with his estimate to recognize that it is a wild guess. And if you string a bunch of wild guesses together, you have something that has no meaning, even if you have assigned a number to each guess. His conclusions then offered no real insight you could rely on. It was more like an academic exercise that some people might find interesting, but I found disappointing.I still went on, until his chapter on DNA evidence. He makes the point that DNA evidence is not as iron clad as generally assumed, and he discusses various miscarriages of justice with a decided slant in favor of the accused. Again, I don’t necessarily disagree. But this a) is getting a bit off topic for the book and b) seemed to me to be, again, mostly opinion. So I stopped reading. Maybe the rest of the book was great. If so, somebody please let me know.

⭐I have to wonder if some of the reviewers actually read the book. Fluke contains four distinct sections: One: describe a series of specific coincidences; Two: describe the basic math behind calculating probability; Three: deconstruct each of the coincidences in section One and attempt to calculate the actual probability of their occurrence, using the tools in section Two; and Four: a wildly disconnected set of meanderings that doesn’t seem to add value anywhere. Sections One through Three would be good enough to stand on their own if it weren’t that they contain an uncomfortable number of basic math errors and unsupported assumptions. Section Four seems to be there only to add volume. Professor Mazur is a startlingly competent teacher and mathematician, but Fluke makes me think he was short of cash and needed to pump out a volume to pay some bills.

⭐Loved it, because I have had so many similar experiences during the years when I was traveling the world (e.g, running into a man in Singapore whom I had only met the previous week in Chile).As an actuary, I used similar methods to Mazur’s to determine that for frequent international travelers the probability of such “Oh my God!” encounters was 50% per year.My most bizarre occurrence was when I mistakenly took someone else’s limousine at JFK (the driver was holding a sign with my last name on it) and then met the man a year later on the same London-NY flight. Given our unusual last names, it seemed incredible.What makes Mazur’s book so enjoyable is that he explains the math involved in an easily accessible way, so that the reader can get a feel for just how improbable (or not) some of these occurrences actually are.

⭐Interesting but not particularly exciting book. It describes several historical or personal coincidences and then attempts to construct statistical models or explanations of the probability of their occurring. The book investigates events such as the probability of the same person winning lotteries four times in 18 years, the size of a group of people such there is at least a 50% probability that two of them will share the same birthday, and the likelyhood that people will share the same DNA test structure even though they are not identical twins (answer: given the way DNA testing is performed, there are likely five or six people on the planet who share any given DNA structure; read the book to find out why this is so).

⭐Not uninteresting but not particularly thrilling either. It’s not deep enough if you are interested in the math and not light enough to be entertaining.

⭐Very enjoyable read with good examples that really fleshed out some of the more theoretical aspects. Recommend this.

⭐ok but a little too complex for me, as I don’t have a doctorate in higher mathematics!

⭐Overall this was a somewhat disappointing and scattergun review of the topic.

⭐Very rare subject, interesting read. I reached only first few chapters and going is good.

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