A fascinating account of the breakthrough ideas that transformed probability and statisticsIn the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statisA fascinating account of the breakthrough ideas that transformed probability and statisticsIn the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact.Persi Diaconis and Brian Skyrms begin with Girolamo Cardano, a sixteenth-century physician, mathematician, and professional gambler who helped develop the idea that chance actually can be measured. They describe how later thinkers showed how the judgment of chance also can be measured, how frequency is related to chance, and how chance, judgment, and frequency could be unified. Diaconis and Skyrms explain how Thomas Bayes laid the foundation of modern statistics, and they explore David Hume's problem of induction, Andrey Kolmogorov's general mathematical framework for probability, the application of computability to chance, and why chance is essential to modern physics. A final idea--that we are psychologically predisposed to error when judging chance--is taken up through the work of Daniel Kahneman and Amos Tversky.Complete with a brief probability refresher, Ten Great Ideas about Chance is certain to be a hit with anyone who wants to understand the secrets of probability and how they were discovered....
|Title||:||Ten Great Ideas about Chance|
|Number of Pages||:||272 Pages|
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Ten Great Ideas about Chance Reviews
I probably set myself up for a fall with this one.For starters, I’m a big fan of Persi Diaconis. Not only is he Greek, not only did he teach Math at my alma mater, but he’s a proper, self-taught, genius. And he’s modest. Not once in the book does he mention that he’s the man who proved mathematically that a deck is random once you’ve shuffled seven times.Also, I’m a big big sucker for Probability, which I studied a fair bit both as an undergrad and as a graduate student. Indeed, if you go to amazon.co.uk you’ll see I have the definitive review (with errata and corrections to the homework problem solutions) for Capinski and Kopp’s “Measure, Integral and Probability.”And I’m an even bigger sucker for popular science and popular math. I devour popular science books whole, most recently Roger Penrose’s “Faith, Fashion and Fantasy” (no idea what that was all about, but it blew me away anyway) and Carlo Rovelli’s “Seven Brief Lessons in Physics,” which fooled me into thinking I understand General Relativity.On pages 115-116 the authors even dedicate a chapter to the work of a former role model of mine, my high school’s 1984 Valedictorian, John Ioannides! I still remember sitting in the audience as he was delivering his speech. It felt great to read about him in a book by Persi Diaconis.So I’m devastated to report that this is an underwhelming book.Don’t get me wrong: • the topics are expertly selected• the style is friendly• a story is told• there is a beginning and an end• you are left in no doubt of the beauty of the subject• the references are all there if you want to study the topics on your own• the authors’ love of Math is evidentHowever, and this is an enormous problem, if there is an idea you did not understand before you are extremely unlikely to get to terms with it by dint of having read this book. Indeed, there’s stuff I have in my life been an expert on that I read here and I was not able to recall it.The chapters are invariably a mix of 1. a trivial example that does not penetrate enough the intended topic because it contains too much of the familiar and too little of the topic that’s being introduced2. references to original texts that are nineteenth century translations into stilted English from eighteenth century originals written in French or German or Latin3. statements of complex results that would take fifty pages to arrive at if the proofs were shown4. cheerleadingSo what I re-lived by reading this book is my Freshman Year nightmare Math class where three times a week I’d follow the first five minutes of the lecture only to subsequently find myself furiously copying from the board so I can read my lecture notes later at home and try to make sense of them.And I got to remember the worst part of that package, which was that sometimes the teacher would make a mistake on the board, which of course would cost me hours of private desperation as I tried to see how that was compatible with everything else I’d copied down.Not saying there are mistakes in the main body of the book, but perhaps there are, because there’s at least a couple of absolute HOWLERS in the “probability tutorial” in the back.I’ll tell you one thing: the poor souls at Stanford who took this class as a distributional requirement learned absolutely nothing. That I promise you.Bottom line, after reading Rovelli I feel comfortable lecturing my mom on General Relativity, a topic I know nothing about. After reading this book I’m afraid to discuss Probability even with my colleagues at the startup I’m running. Dunno, perhaps I’m merely “confused about higher things.”All that said, this was the guided tour to the brain of a genius. Three-and-a-half stars from me ;-)
There are few topics that fascinate me as much as chance and probability. It's partly the wonder that mathematics can be applied to something so intangible and also because so often the outcomes of probability are counter-intuitive and we can enjoy the 'Huh?' impact of something that works yet feels so far from common sense.I think I ought to start by saying what this is isn't. It's definitely not an introductory book - the authors assume that the reader 'has taken a first undergraduate course in probability or statistics'. And though there's an appendix that claims to be a probability tutorial for those who haven't got this background, it's not particularly reader-friendly - in theory I knew everything in the appendix, but I still found parts of it near-impossible to read.As for the main text, if you pass that first criterion, my suspicion is that, like me, you will find parts utterly fascinating and other parts pretty much incomprehensible. The authors swoop between engaging philosophical discussions of the nature of probability and the frequentist v Bayesian debate and descriptions of pretty heavy duty mathematical thinking on specific aspects of probability and its applicability.Some of the 'ten great ideas' are fairly straightforward, whether we're talking the early work from Cardano or Bayes' theorem (though, again, the way it's presented here is really surprisingly impenetrable, when it could be covered for more accessibly). But others really strain the non-mathematician's brain. And these can come quite early. The second chapter opens 'Our second great idea is that judgements can be measured and that coherent judgements are probabilities.' Although I felt I ought to be able grasp what was going on here, I found that the way it was presented went totally over my head. It's just not very well written.So, unless you know much of this stuff already, the chances are you will find some parts hard going - but I found it well worthwhile using the old university student approach of 'just let it wash over you and you'll get to a bit where it starts to make sense again'. This, for me, was the way to cope and the parts I could get my head around were really interesting. I just wish there had been someone involved in the project who knew how to communicate to ordinary readers.
This book straddles a tricky middle ground, given that it introduces topics from scratch and goes into some very specific details of them in a relatively few pages, before jumping onto the next. On starting to read it, I was skeptical of how this could possible work, but by the end of it I believe that I saw the real utility of a book like this. The audience is quite specific, but for them it will be a gem.The book covers a huge range of ideas related to chance, from the underlying mathematics of probability, to the psychology of decision making, the physics of chaos and quantum mechanics, the problems inherent in induction and inference and much more besides.The book is taken from a long-running course at Stanford which the authors taught for a number of years, and they have tried to condense down the most important aspects of it to a relatively light book. At 200 pages, a great deal is packed into this, and as such, anyone without a good foundation in mathematics will certainly find a great deal of it too advanced. As I was reading it however, I realised that a first or second year mathematics or physics student (or even more advanced), taking a course in statistics would find this a perfect addition to their course notes or prescribed text book.The book covers the history of ideas which have shaped our understanding of chance, stretching back millennia, and including research which is ongoing, as well as contentious, and as such will beautifully contextualise what is learned in a lecture course which is unlikely to give quite the grounding that this book gives. The biographical and historical insight from economists, philosophers, psychologists, mathematicians and physicists, amongst other people, will give a far better framework to the ideas which in my experience helps to give a deeper understanding of how everything fits together.And perhaps that is really the idea of this book. Though the chapters are not specifically contiguous, it really is a book about how these very disparate topics fit together, often in surprising ways, historically as well as mathematically.If I have a slight criticism of the book it is that in a few places, ideas are introduced in slightly awkward ways, and then used without giving quite the understanding necessary to follow the details. If used in conjunction with a course which covers similar topics however, this will not be a problem. The clearest example of this for me was in one of the first chapters, where the idea of a Dutch Book is introduced, without quite explicitly stating what it is…. though perhaps this is my own lack of knowledge showing through. In the same chapter, some of the mathematical writing is slightly sloppy, but as this is not a text book, this can also be forgiven.All in all, I would recommend this to any student studying or having studied anything statistics related at university, if only to give a much wider perspective than would be given in a course. It is so often useful to have both the forest and the trees, and this provides precisely the map of the interlinking forests which would certainly have been very satisfying for me as an undergraduate student first coming across these ideas.
A book that will appeal to the maths and science geeks at first glance, considering ten of the past major breakthroughs that brought change to statistics and probabilities, yet something that can appeal to the curious, generalist reader too. These changes have been quite pivotal, having a very broad impact, and within the book the authors subject them to technical and philosophical scrutiny.To a non-mathematician this was a particularly fascinating topic to consider. The book brings to life many ‘everyday’ things, such as chance and probability – something that one takes for granted without knowing the back story or deeper implication. For a more involved specialist, they may form an entirely different connection, since the book manages to be attractive to both audience groups through its informed, accessible and engaging writing style. A few myths and misunderstandings may even be corrected along the way.This can be one of those books that you hadn’t considered you needed, but you will be glad you have read. It certainly can be a book that is hard to put down. If you are not particularly au fait with mathematics, some of the book may appear unfathomable, but fortunately the accompanying text can come to your aid and you can always skip a bit of the ‘deep maths stuff’ without affecting your enjoyment of the story-at-hand.Christmas is coming. This may deserve a space in a Christmas sack or two!
As a layperson (by trade I am only a physician), I find parts of this book incomprehensible. Topics covered include (I think): expectation is the correct measure of value; coherent judgmental strengths are probabilities; the psychology of chance and the logic of chance are different subjects; probability can be mathematized; inference from frequencies to chances is different from inference from chances to frequencies; symmetry/exchangeability is the basis of ergodicity; randomness is defined in terms of computability and algorithmic compressibility; nature is in a sense both deterministic and statistical. Advanced mathematics is certainly required to understand some of its arguments. Overall it is still a profitable read.