Fluke: The Math and Myth of Coincidence

by Joseph Mazur

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.

Genres: Science, Nonfiction, Mathematics, Psychology, Philosophy, Audiobook, Business

288 pages, Kindle Edition

First published March 29, 2016

About the author

Joseph C. Mazur is Professor Emeritus of Mathematics at Marlboro College in Vermont. He earned his Ph.D. in algebraic geometry from MIT and has held visiting positions at MIT and the University of Warwick. A recipient of Guggenheim, Bellagio, and Bogliasco Fellowships, he has written widely on the history and philosophy of mathematics, with books translated into over a dozen languages.

Reviews

[Brucie · Rating 2 out of 5]

more math and less coincidence than I was looking for.

[Henry Mishkoff · Rating 2 out of 5]

About two-thirds of the way through the book, Mazur seems to run out of things to say about flukes and coincidences. I get the feeling that he rounded up a few previously written essays about marginally related topics, made a half-hearted effort to tie them to his subject, and tacked them on to the end of the book. It didn't ruin the book for me, but I kept waiting to see how he was going to tie everything together -- and when he didn't bother to do that, I was both puzzled and disappointed.

[Jennifer · Rating 3 out of 5]

This was a neither-here-nor-there book for me: a great deal of math, much of which I didn't understand, and moments that tried to be poetic but didn't really work for me. The subject is an interesting one--most people experience strange coincidences in life--and it was instructive to see how likely any particular fluke might be, when observed through the lens of mathematics. But I've read more useful discussions, particularly involving risk and the chances of something untoward happening.

[Mary · Rating 2 out of 5]

Math professor tries to use probability to illustrate how some unlikely coincidences are not as unlikely as you may think (e.g., there is a 50% chance that 2 people out any random group of 23 people will share the same birthday). While some of the examples are interesting, I think he stretches it a bit thin when he tries to give probabilities to such situations as finding a book one was looking to buy on a subway bench, or having a golden beetle at the window while someone is describing a dream about golden beetles (e.g., assume that there were x copies of the book published that year, y book stores within 2 miles of the subway stop in question, etc. or that the golden beetles come out in June, there are 30 days in June (with x hours of day light (assuming the story was told during the day in June....), then calculate what percentage of that time is 1 hour, etc. )). For those interested, the odds are 1:74,427 and 1:714, 285, respectively, for the above examples.

[Trike · Rating 3 out of 5]

This is pretty thin and Mazur sometimes does that aggravating thing so many people do when they can’t answer a question directly, they move the goalposts and answer something else instead. That said, some of the coincidences and explanations are interesting, so it’s not a total loss, and the stories themselves are entertaining. If this had been longer I would’ve down-rated it, but it doesn’t overstay its welcome.

I was hoping for a book version of the excellent YouTube channel Veritasium, which explores all kinds of cool things to do with science, math and physics. This isn’t that, so go try out some videos there: https://m.youtube.com/c/veritasium

Here’s a short one to get you going, which also applies to the ideas in this book about how we seek patterns due to our cognitive biases: https://youtu.be/vKA4w2O61Xo

[Beauregard Bottomley · Rating 1 out of 5]

All the math is sophomoric and the analysis is too simple. I already know Jungian synchronicity is pseudoscience and this book was not necessary to show me that.

[Bastian Greshake Tzovaras · Rating 3 out of 5]

tl;dr: Have a large enough sample and even rare things will happen, as such your freak coincidences aren't as unlikely as you think.

That could have been all the book, but instead the reader gets some anecdotes of coincidences, along with combinatorics 101. Unfortunately the book ends up neither here nor there: If you've been to high school and have ever heard of Bernoulli, then the combinatorics-part will bore you (and if you haven't been it might be too formalistic to understand). If you came for the anecdotes you'll find that there are too little of those.

recommended: for people who like to philosophize about coincidences without ever having picked up a book on chance.

[Kevinjwoods · Rating 2 out of 5]

The main problem is the way that he changes the stories in order to make the math work, for example in the Anthony Hopkins tale the actual coincidence is that a person who knew the author found a specific book that he was looking for and it was specifically owned by a the author, instead he does the math for ANY book being left in any park for someone to find, these include factors that are irrelevant to the story for example any book would include bestsellers that would have a greater chance of being left, for example more James Pattersons would be abandoned than Isaac Asimovs, add in the fact it was published 3 years before and the odds of that particular book being abandoned go up, so in all respects the chance of this book being found are different from the odds of any book being found by someone looking for it.
There are similar problems with each of his examples, he explains in great detail the various coincidences but has too often expanded the tales to the point where they are reliant on items that have no bearing or has done very little research (how often are 4 time lottery winners reported for example).
On the whole a good idea badly executed.

[Brandon Anderson · Rating 3 out of 5]

Meh. The whole point of the book is that coincidences and flukes aren't quite as mathematically unlikely as they seem. That part is true. The book itself is poorly written. I wished for more stories and less vague math talk.

The math was really a waste of time anyway. To someone that knows math well, it added very little. Yet to someone that doesn't know in depth math, I think they'd get totally lost by all the language and notation here. The math sections- which were like half of the book and the whole point really- just seemed like a waste of time.

Interesting topic but poorly conveyed. It's hard to imagine there's not a better version of this book out there. Ultimately disappointing.

[Bob · Rating 3 out of 5]

The book has some interesting stories about what is a fluke or what is a coincidence, but it can't decide if it's a math book, a philosophy book, or a literature book. In theory, it's a mathematical look at flukes, but most of the pages are dedicated to telling us what we think are flukes aren't.

I preferred the The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every DayImprobability Principle much more to this one because it set out what kind of book it would be right away and stuck to it.

[Joseph · Rating 2 out of 5]

An interesting concept: take events that would seem to be coincidental, or maybe even "one-in-a-million," and show the true mathematics of the probability. Some great true stories of unlikely happenings throughout history, which were fascinating, but I'd already done the math in graduate school.

[Daniel Farabaugh · Rating 3 out of 5]

Large swaths of this book were very good. At the end when it begins to wax poetic about the nature of coincidence in science, etc. it got a little slow. But the sections that explains the math behind the apparent coincidences was very good.

[Stuart Smith · Rating 1 out of 5]

A rare 'did not finish'. A third of the way in and just a load of incomprehensible equations and probability ratios with not much of interest unless you love maths.

[Laura · Rating 2 out of 5]

Final review: Yeah, definitely not super impressed. The book really doesn't seem to have a thesis. The math section was kind of a fun thought-experiment but didn't really "prove" anything, in my opinion. I did enjoy the totally random passionate treatise on the Innocence Project and problematic incarceration rates in the US though. And there are definitely some fun tales told in the book.
It kind of feels like the syllabus for some kind of second-year elective that would be really fun to take but at the end of the term when you're reviewing for the exam you realize you're just left with an assortment of facts and stories; you didn't really learn anything substantial.

Interim review: I'm currently halfway through this book, and here's what I think so far. It's definitely an interesting topic, and it's reasonably well-written (even the math parts are easy to follow), but I have some problems.
1) In the first section he defines flukes and coincidences as different things (a distinction I agree with in this context), and then proceeds to use examples of flukes as illustrations of coincidences, so what was the point?
2) He seems to imply that until Cardano's Liber de ludo aleae was published in the 17th C, no one had ever even thought about the math behind chance, probability, and gambling. Just because no one else had published a paper on it doesn't mean some clever tavern-keeper hadn't spent hours idly doing sums while watching people play dice, I think.
3) He obviously talks a lot about odds, probabilities, etc. He also explains the weak law of large numbers, whereby in a large enough sample every possibility, no matter how improbably, is "bound to occur." And then he also points out that every thing that happens is governed by physical laws and can actually be predicted if we have fine enough tools. And he doesn't seem yet to see that these things seem to contradict each other.
Basically, at this point I don't know what he's trying to prove, and I feel like at the halfway point I should have a sense of where it's all going. I don't know if he's trying to prove that there's no such thing as coincidence, or that everything is just random chance, or what. I'll get back to you when I finish the book.

[Drew Van Gorder · Rating 4 out of 5]

This book had tons of cool information in it which I am grateful for concerning the math and science behind coincidence. I used to believe more in the magic of the coincidental until this book came along to prove most coincidences are merely rare circumstances which, given long enough, will occur no matter how improbable the chances were in the first place. Well worth my time and effort!

[Ben · Rating 3 out of 5]

The Fluke Ma(th)n

This is a fairly good book on mathematics and coincidence.

I did not find it too groundbreaking or earthshattering in the things I learned from it, but it was still a fun enough read.

I have definitely read better maths books, but I would still give this one a good rating!

3.1/5

[Sarah · Rating 3 out of 5]

Not sure of the point of the last chapter to be honest... and chapter 10 contained some confusing, conflicting statistics from different sources. But I enjoyed it overall and feel like I learned something

[pea. · Rating 2 out of 5]

potentially interested tho it lost my attention and have not yet bothered to find my way back to it... perhaps one day.

[SLADE · Rating 2 out of 5]

This book started well and ended interestingly enough, but oh my, the majority of it bored me with endless probability theory. I guess I should have known, based on the subtitle.

I was so ready to get done I finished it in just 3 days.

If you love probabilities, dive right in.

[Sarah · Rating 2 out of 5]

A random selection of subjects covered and not well written.

[Harold · Rating 2 out of 5]

Fluke, perhaps ironically titled, is a book that might not have been. It starts by telling the stories of a number of coincidences in great detail. They seem astonishing. Well perhaps not astonishing but they could have been interesting if my aunt told them with a twinkle in her eye about how surprising it was to have been there. As it was they sat on the page like a day old fried egg.

The next section dealt in depth with the math of the coincidences in the stories, in great detail and with the formulae. But basically the math boils down to a simple concept. There are an enormous amount of people in the world and the odds of something unusual happening to someone somewhere are a lot higher than they seem. While the formulae are interesting, they hardly add the precision that they seem, since he estimates the data to apply the formula to. They do add an aura of precision, as well as an impassible 50 pages.

Then, as if you don't get the point, he tells the stories again, adding the formulae to the story to demonstrate that most of the coincidences are not really amazing, or even surprising. However a few are.

Then he finished with with another section which was about something and used the word fluke or coincidence a few times. The biggest fluke of all was that when I finished I found a more interesting book. No, on second thought, that wasn't surprising either.

[Marc · Rating 2 out of 5]

"When you need to knock on wood is when you realize the world is composed of vinyl, naugahyde and aluminum." Mazur realizes this fact too late or perhaps, not at all. This is a patchwork of essays and equations and connections not quite finished. There's an idea here, and a passion for that idea, but the end product is unorganized and a bit messy. Mazur follows in the heavy shadow of this topic's predecessor, David Hand's more superior work, "The Improbability Principle." Where Hand uses math to elevate and explore possibilities, Mazur feels bogged by it, mired by strings of numbers he never pauses to explain or develop. By the end, the steam is gone. By the end, we are subjected to summaries about myths and stories about coincidences giving the last few pages a feel of disjointed book report. By the end, meh. Knock, knock.

[Charlie Newfell · Rating 2 out of 5]

How unusual are coincidences? The main point of the book is that in a big world (7 Billion people and counting) coincidences are inevitable. Take the case of someone winning the lottery four times. Winning just once - the odds are inordinately high. Winning four times? Well, it's almost incalculable, but he shows the math that *someone* (certainly not me!) would win it that many times. Other examples have wild assumptions to them to display that they are inevitable, or nearly impossible. The last third of the book focusing on myths and fiction - why in a non-fiction book? In fiction you can make up anything. The author seems to run out of steam about a third a way through the slim volume - would have made a better paper.

[G · Rating 3 out of 5]

lots of math. not necessary to read through.
1. realization that though mathematics/probabilities/scientific theories are often tied & connected to physical events, there's no literal bond between the two. mathematics just helps us understand these physical events. our understanding of events are based on probabilities of outcomes - mathematically it is impossible to have 100% certainty re. any event.
2. literal randomness has a specific determinant. most events that seem random actually have a cause associated with. we have a hard time understanding the bigness or smallness of our world and our numbers and similarly often misunderstand the likeliness of events.

[Marsha · Rating 5 out of 5]

Joseph Mazur (the author) goes into so many different ways that chance and probability actually DO predict the totally unlikely, and he points out the POSSIBILITY and PROBABILITY of things that seem extremely unusual, unlikely, and downright freaky and magical occurring, thereby emphasizing the rationality of the world – and the IRRATIONALITY of pseudoscience, premonition, and ESP/psychic beliefs.
He goes into several realms: economy, weather, relationships, and day-to-day life for instance. Reality and probability are both amazing and surprising, and it's interesting to see demonstrated and described how they totally help to define our world and experiences without the need to go to magic!

[Karen S · Rating 2 out of 5]

I was pleased to receive a copy of Fluke from the Goodreads Giveaway. The author sets out to show the mathematical probability of coincidental events occurring. I though the premise was interesting, however, struggled to follow some of the maths, particularly when it seemed to me that he was guessing as to probability of things happening. The final section of the book did not reallly seem to follow on from the rest of the book and I have to admit to giving up at this stage. I would, however, return to the chapters that explained the maths - to prove to myself that I can get it!

[Lionkhan-sama · Rating 4 out of 5]

I LOVED this book. Such a new topic. So refreshing to read about something random with no clear significance. I mean, it doesn't really affect your life knowing why coincidences and flukes happen, but it sure is interesting.
This book is almost playful, in the way it tries to mathematically quantify anything "coincidence".
It is filled with a lot of great stories, followed by analysis and open-minded discussion.

A very entertaining and most interesting read.

[Emily · Rating 3 out of 5]

Interesting concept, but I'm not sure I fully agree with his 'results' in that everything can be explained by math. Even the case studies he presented were never fully explained. Perhaps I would have enjoyed it more if I fully understood the math, and he didn't jump around between topics so much at the end. Interesting read, but I'm not sold that coincidence is not coincidence.

[Brendan · Rating 2 out of 5]

I thought the book was a bit trivial. It went over some of the basic ideas behind statistics and probability and tried to apply them to various unusual circumstances. The methods and assumptions behind some of its conclusions was flawed, in my view. Would not recommend, unless you needed something to read

[Barry · Rating 4 out of 5]

May be hard to read for the math challenged, but very interesting premise and explanation. Mazur neither debunks nor encourages belief in coincidence, but shows how our thinking distorts many things into significance that are quite explainable statistically.