Do Dice Play God?: The Mathematics of Uncertainty by Ian Stewart (PDF)

Description

A celebrated mathematician explores how math helps us make sense of the unpredictableWe would like to believe we can know things for certain. We want to be able to figure out who will win an election, if the stock market will crash, or if a suspect definitely committed a crime. But the odds are not in our favor. Life is full of uncertainty — indeed, scientific advances indicate that the universe might be fundamentally inexact — and humans are terrible at guessing. When asked to predict the outcome of a chance event, we are almost always wrong. Thankfully, there is hope. As award-winning mathematician Ian Stewart reveals, over the course of history, mathematics has given us some of the tools we need to better manage the uncertainty that pervades our lives. From forecasting, to medical research, to figuring out how to win Let’s Make a Deal, Do Dice Play God? is a surprising and satisfying tour of what we can know, and what we never will.

User’s Reviews

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

⭐Having a degree in a mathematics with an interest in Probability and Statistics, once in a while, I’m drawn to a book about this subject, When I read the review for this book in the Wall Street Journal, which wasn’t great, I thought, let’s give this book a try. After reading it, I’ll say that the best word to describe it is interesting, but not for everyone.The book starts out inauspiciously, in my opinion, going through how everything in the world is uncertain, and laying out the six phases of human dealing with uncertainty. But, then the author states “except for climate change which is clearly certain”. Hmm… Interesting. Maybe he’ll go into that more later. Of course, there are hints that those who don’t believe this are stupid including a certain US administration.Then, in the second chapter, the book lays out how people dealt with uncertainty initially by killing lambs (or other animals) and reading their livers (or other part of the inner bodies). With this, he degrades to some level faith and believing in anything except science. Hmm… Interesting. Let’s see how he handles this one later.In the next number of chapters, the book picks up and is in fact, really interesting. Here, the author describes the history of the development of probability and statistics. Nothing new here for a math major like myself. Going from probability statements regarding games of chance (dice, flipping coins and cards) to trying to understand the movement of planets better (astronomy), mathematicians developed some useful tools like conditional probability, least squares, binomial and normal distributions, and Bayesian statistics. All very useful and may be of interest to the lay reader. The author also provides examples of use. The use of Bayesian statistics in the court room was of special interest to me.Then he goes into thermodynamics and uncertainty, the human brain and uncertainty and weather forecasting. Some of this was interesting, and some bordered on the esoteric. In his chapter on weather forecasting, he described how hard it is forecast weather going one day out and even harder further out. Makes sense. Then, he went into the certainty of climate change. I wondered what is this doing in a book on uncertainty. He did, however, provide the best argument that I’ve heard for the certainty of climate change. Climate is different that weather. Weather is like individual observations (from a statistical sense) and climate is the mean of the mean of those observations. OK, I get it, this is why it is easier to forecast this, and then of course all of observations of the ice melting, etc. to support. Much like the observation of smoking causes cancer because of the statistics, but not the proof. But, when we found a carcinogen in the cigarette. Ah, ha.Now, I’ve never been a climate denier. I’ve just been caught in the “religious fervor” of climate change folks. And, we need to do something about it, but there are no answers in my opinion, except driving us into the dark ages so we won’t go into the dark ages. Of course, there is nuclear, but the same people who push climate change, say oh no, we can’t do that. And, then there is China and India, the biggest polluters on the planet and we aren’t doing anything about them. The author, of course, has no answers for this, just that the current US administration is stupid for getting out of the Paris climate accords.I don’t like it when mathematics professors from England get political about the US. I’m sorry, but I don’t.In the next chapters, he goes down the quantum path. And, there are there good quotes from Feynmann – if you think that you know quantum theory, then your don’t know quantum theory, from Einstein – there is something spooky going on in the distance, and the author himself: “We’re here because we’re here because we’re here”. This last statement is very profound (only kidding). As I read this, the Bible story of the Tower of Babel became clear to my mind. You know the one. These people who thought that they were smart, built a tower to show their intelligence so that they could become like God. Face the facts, in quantum theory, these scientists are chasing their tails finding answers and talking to each other and us in “babel” – useless language. Science has limits – oh no, he said it. We can not understand the infinite, no matter how hard we try.Back when the author covered the brain, he talked about how we all get into our own “bubbles” to try to make sense of the world. This was profound. I’m in mine. I’m a Catholic and believe in God. It is called faith. This author is in his own scientific bubble – believing that science provides the answer to everything. Good luck with that one. I won’t be reading another book from this author. It was interesting to get inside his “bubble” for a bit, but I don’t want to return (and waste my time).

⭐Chaos theory changed the world, and those who ignore chaos theory do so at their own peril. Do Dice Play God introduces chaos theory from a mathematical and narrative perspective and looks how the world is ruled by chaos if not randomness outright. Great for forecasters of all sorts. Interesting branch of applied mathematics.

⭐It’s a good book with Stewart’s usual gift for clarifying heady concepts. For what it’s worth, though, it didn’t feel quite as engaging to me as several other introductory texts (like “The Drunkard’s Walk,” I believe it’s called) or even some of Stewart’s own past works. His metaphors tend to work, but some of the concepts are so complicated they just fail to connect with the lay man. On average (you’re welcome), a good read.

⭐Gift purchase.

⭐No ones explains math concepts so clearly.

⭐This is the book that I was very eager to read because of the subject: the mathematics of uncertainty. I read it in parallel with The Art of Statistics by David Spiegelhalter because I felt the combination of the two books on similar topics from two different directions would make the reading experience more complete as the two books should complement one another. It was mentally challenging to read both books together, but I am glad I did because my goal was accomplished: they were indeed complementary. There were certain areas where the books overlapped but it was good retrieval practice to go over some of those areas at spaced intervals.The book comprises of 18 chapters. The first two chapters sets the tone for Stewart. By defining the six ages of uncertainty in Chapter One, Stewart proceeds to converse about some of the things that humankind has been using to deal with uncertainty and to predict the future. He follows that initial setting of the stage with a qualitative discussion of the idea of probability and statistics. It is a difficult task because it is easier to discuss probability and statistics in terms of the equations. Even with that caveat, Stewart did an excellent job of explaining quantitative concepts qualitatively, it takes someone who deeply understands the ideas, in all their glory, to be able to pull it off, and Stewart did so. This is not to say that the book is completely devoid of numbers and figures, but it was enlightening to be reading about these concepts without equations and mathematics.The book then proceeds into many topics about uncertainty and randomness. He shares an abundance of examples and evidence which demonstrates the idea. It sometimes feel like an unrelenting onslaught of different cases in different areas, regarding different problems. The examples come from mathematics, biology, medicine, physics, numerical systems, and many more, which gives proper perspective to the reader as well elicits an understanding about the universality of uncertainty in our reality. The main topics that I had struggles with, and that is true of Spiegelhalter’s book as well, is the section on the Bayesian probability, even though Stewart did a masterful job of explaining it. I understand Baysian ideas after having read both but I am still easily confused when trying to apply the idea.Stewart lost me with his explanation of quantum mechanics and the counter intuitive ideas from quantum mechanics. It was a difficult section to read, even though I was exposed to the idea when I was a young engineering student. On the other hand, when Stewart expounded on the ideas of dynamical systems, he made perfect sense, as I was thinking about Lorenz attractors when I was studying dynamical systems as a graduate student. Since I had understood those equations as equations, it was not much of a leap for me to understand them as applications which made the mathematics more sensible.As the reader work their way through the book, they will find themselves doing many mental gymnastics with the mathematics that he does present, but he does an excellent job of explaining why these concepts are so important to us.The last chapter is the magnum opus chapter that Professor Stewart uses as his platform to summarize his intention with the book. His key intent is to make the general audience become aware and comfortable with the fact that uncertainty is a normal part of life. Professor Stewart has work diligently throughout the book to chip away at our enduring and grossly erroneous belief that our lives are deterministic, and that any uncertainty that we admit or accept is not something that we overcome easily or can be disregarded because the uncertainty plays a very large role in how our lives will often result.A quick summary of all the topics that that had been discussed ends the book. In returning to these topics while reading these short pages, the reader realizes the extensive number of topics that Professor Stewart had discussed; more importantly, the reader finally understands the lessons that Professor Stewart is trying to teach us. He started with the basic ideas of how human beings dealt with uncertainty. As humanity progressed along the timeline, we got better at rationalizing some of the uncertainties, and we thought we were able to minimize the uncertainties. We invented tools like statistics and probability; we deliberately tested and experimented to arrive at what we thought was the truth. Even though this book is not the definitive history of uncertainty in our world, this book does very well in filling some of the obvious gaps in our thinking and dispels enough biases to make the readers at least accept the fact that life itself is uncertain and full of mystery.I thought the book was a marvelous read even though it was particularly challenging. Professor Stewart explained many different concepts very well, some better than others, but the overall effect is that the reader can gain a much better understanding of how little and how much we know about our world and appreciate how much guessing we are doing on a daily basis.

⭐I read Prof Stewart’s ‘Does God play dice?’ several years ago and thoroughly enjoyed it, therefore I was really looking forward to the follow-up.I’ll have to admit that I struggled with this book, which is far more a criticism of my rusty maths and stats skills than of the book itself. I’m going to read it again to see if I can grasp a bit more from the many sections I didn’t fully understand.As one other reviewer has rightly pointed out, you’ll need at least an undergraduate level of maths to get the most out of this book.This would’ve been a 5-star review but for a couple of gripes. First is the author’s lapse into soap-boxing about man-made climate change. Whatever your views on the degree to which man-made CO2 may be affecting the climate, I found the preachy tone out of place in a book like this. Secondly, the chapter on securities pricing is very misleading in that it starts by looking at the random walk theory of equity pricing and then jumps without warning to talking about option pricing and the hazards of assuming that risk is normally distributed. There’s big gap between option pricing models that don’t use a normally distributed measure of implied volatility (there are plenty of variants on Black-Scholes that don’t make this assumption), and the monster that is the Cauchy distribution – the latter is where black swans, blind archers and other statistical chimera make their nests. This chapter also doesn’t make it clear that cash equities, bonds (credit instruments and government securities) and derivatives such as CDOs, CDSs and vanilla exchange-traded options all have very different risk and pricing models.

⭐Interesting stuff, but a difficult read. Also nothing really new; must of the stuff I had read in other books. Not worth the effort.

⭐In this book, the author, a mathematician and well-known popularizer of science and mathematics, explores the subject of uncertainty in a variety of domains. These include the usual probability distributions, coin flips and dice throws as well as various fallacies and paradoxes. But also included are fascinating discussions on thermodynamics, chaos theory, weather forecasting, climate change, Bayes’s Theorem, quantum uncertainty and many more topics involving uncertainty.I found this book very interesting. I particularly enjoyed the section on climate change; I found it quite informative and well done. The author’s prose, I thought, was generally clear, authoritative, often even riveting and quite engaging. I do admit that some passages were a bit tough going for me and required more than one reading. However, the wealth of information contained in this book makes reading it immensely enriching. I suspect that serious science enthusiasts will likely be the ones who will enjoy it the most.

⭐Nice

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