on 30 July 2010
As an unlikely (but still possible) opening event to my contact with this book, I reveived it through the mail from Amazon without having ordered it and with no invoice. Having read it I was suitably impressed with it's historical accuracy, depth, and interesting viewpoint. Indeed, randomess is an aspect of scientific theory that experimentation's biggest challenge is dialing out. We have always been taught to try and avoid it as vehemently as possible in order to deepen the trust we bear on our randomness-free research results. Mlodinow's whole viewpoint is one of understanding randomness and tailoring our understanding to embrace it rather than avoid it, and as such it offers an enriched and amusing new perspective on the application of modern scientific method, and life in general.
As a beautiful side-effect of reading this book, you'll:
1) Stop trusting or believing bankers, hi-risk investors, market analysts or people who predict anything related to systems which aren't rigidly understood (financial markets, success of the film industry, fashion).
2) Realize there is so little correlation between which team is superior and which team wins the game that you'll practically lose interest in any kind of sporting contest which involves randomness-prone factors (namely people).
3) Learn to question the potential of false-positives whenever confronted by a member of the medical profession concerning any bad news you're given, particualrly when dealing with extreme cases of numerical disparity. This is not a criticsm towards doctors; more a statement that their understnding of statistics is lacking. (And understandably so, there's enough medicine for them to learn without teaching them statistics too)
An excellent book with almost no scientific background required. Easy to read through, very little bias in ideology or viewpoint, with plenty of highly informative examples from antiquity to the modern days. A must buy.
Alternatively, you can trust in wild chance to make one literally fall into your lap, like I did. Such is the nature of randomness!
on 8 October 2008
I was surprised to learn that the Greeks did not have a theory of probability. Their belief "that the future unfolded according to the will of the gods" and their taste for "absolute truth" did not encourage the study of chance. Where pristine philosophy failed, the more grubby pastime of gambling succeeded in motivating probability theory. And, in true statistical style, it only took a handful of gamblers out of a large enough sample to get things going.
Today we might as well be Greeks for all that we understand or even recognize uncertainty. Even if we do not share the view that everything happens for a reason, it is still easy to ignore the role chance plays in our lives. We humans, with our big brains and clever language and propensity for story telling, are well equipped for this kind of failure. When it comes to recognizing randomness, we can be "outperformed by a rat". If this fact piques your curiosity or lowers your self-esteem, read on, and this superb book should satisfy one and restore the other. It is anything but a drunkard's walk through an intellectual maze. Mathematics, the social sciences, psychology, economics, brain studies, all contribute to the modern understanding of this fascinating area. By the end, several important ideas should have become straightened out into the intellectual equivalent of broad, tree-lined avenues, and you might agree with a quotation from Max Born: "Chance is a more fundamental conception than causality."
First off, do not panic. Even a Harvard professor specializing in probability and statistics admits we're not cut out for this kind of thinking - which makes Mlodinow's achievement in writing an entertaining book from which you can actually learn something all the more remarkable. For example, I've come across the Monty Hall problem before, and thought I'd understood it, sort of, although it was like having to read a novel by following the words with my finger. This time, it was easier, partly to do with the way in which Mlodinow introduces the concept of the sample space and breaks down the problem into manageable pieces, and partly because his style is so engaging. It helps that he writes in the first person, and is neither afraid to draw on personal experience nor cringe making when he does so.
One major theme is the "fundamental clash between our need to feel we are in control and our ability to recognize randomness." Research by scientists like Kahneman and Tversky shows how deep-rooted this is. Most of us have been duped by optical illusions, but while these "seldom have much relevance in our everyday world" cognitive biases or systematic errors, on the other hand, "play an important role in human decision making." For example, confirmation bias occurs when we attempt to prove our ideas correct instead of searching for ways to prove them wrong, and "it presents a major impediment to our ability to break free from the misinterpretation of randomness."
Abstract notions are never allowed to wander far before being pinned down by concrete illustrations, often taken from remarkably current affairs. There are two graphs - proper sciency pictures with numbers and axes and everything - which are striking in their portrayal of a startling truth: they show the performance of fund managers over two five-year periods, and while one is a nice orderly ranking from good to bad, the other looks "like random noise". You could have no better illustration of the small print that past performance is no guide to future returns - so why do we pay huge fees to these so-called experts to manage our money, when a large chunk of their "performance" is down to luck? It is salutary to learn that even Wall Street superstars cannot consistently beat the average market return. "People systematically fail to see the role of chance in the success of ventures": the CEO of Merrill Lynch could one year "be celebrated as the risk-taking genius responsible" for the company's success and then, "after the credit market collapsed, derided as the risk-taking cowboy responsible" for its failure. These are important lessons to learn, especially now that even red-blooded capitalists are beginning to question the stratospheric pay packets of financiers.
We need to move beyond "the deterministic view of the marketplace" in which "it is mainly the intrinsic qualities of the person or the product that governs success." The "nondeterministic view" - not confined to the stock market - holds that "there are many high-quality but unknown books, singers, actors, and what makes one or another come to stand out is largely a conspiracy of random and minor factors - that is, luck. In this view the traditional executives are just spinning their wheels." Such a wholesale change in our thinking seems too much to hope for, given how much "we rely on gut instinct" in everyday life and how tempting it is to see purpose where there is none, to "pay lip service to the concept of chance" but to "behave as though chance events are subject to control."
Uncertainty is a modern sin that dare not speak its name. There are always pundits on hand to explain the past and prophesy the future, to nurture some of society's "shared illusions". If you want to "learn to view both explanations and prophecies with skepticism" then the "Drunkard's Walk" is an excellent introduction.
on 12 October 2010
This book gives an excellent overview of probability. It explains with good humour and precise research, the way in which probability was discovered by the most unlikely of characters throughout history. It explains quite complicated ideas in an incredibly simple way.
The author is careful to avoid any heavy mathematics, which makes this book suitable for all levels of maths ability. (If only I had read this book in my first year of university, it would have saved much anguish.)
The last chapter really pulls together all the theories discussed throughout the book to give a new perspective and provokes thought long after you put the book down.
on 28 February 2011
I bought this on a whim based on an Amazon-recommendation, and I wasn't disappointed. Mlodinow gives a very apporachable introduction to the science of randomness, and pitches the subject matter at the right level.
Unlike other books that have dated badly, the examples that the author uses to illustrate his points are recent and relevant, and communicated with a light-hearted sense of humour that turns a dry subject matter into something surprisingly engaging. I got through it quite happily in a couple of sittings.
It loses a star as occasionally Mlodinow does go into a little too much detail on the history of probability and the personal lives of the mathematicians on whose theories this book is based. I didn't think this was necessary (or particularly interesting) and would have liked to have seen this space filled instead with wider content. Nevertheless, the vast majority of the book is abosrbing and so is well worth picking up.
Have you ever flipped a coin 100 times to see the sequence of heads and tails that comes up? If you have, you know that there can be long streaks of heads and tails. Random results that end up 50-50 don't look that way in the short term.
Human perception is such that we like to find patterns where none exist. I remember the CEO of a company I worked for would draw a trend line through one data point with great authority, totally unaware of what he was doing.
More often, we judge by samples of behavior and time that are too short to be representative. Professor Mlodinow does a good job of showing how executives are often fired just before they get their best results, and how seldom the new executive does any better than the prior one.
In sports, we get all excited about streaks. Professor Mlodinow dampens that enthusiasm by pointing out that like streaks can occur randomly. We need to check to see if the streak exceeds the expected degree of variation before deciding that something significant has taken place. (But don't stop cheering on your favorite team and players.)
The book also provides lots of thumbnail sketches of the human side of those who have advanced the science and math behind our ability to measure and understand randomness. In fact, I don't recall a book on this subject with better anecdotes about the scientists and mathematicians. That's the reward in this book if you already know about randomness.
If you know nothing on the subject, this book is the gentlest possible introduction.
on 24 June 2008
If you wonder about the relevance of the statistics and 'proof' that inundate our lives then this book puts them in their place. With a nice bit of history about probability up to the present and how outcomes are not as predictable as we would like to think. It certainly added to my own feeling that with our politicalisation of 'statistical proof' in society that the wool maybe being pulled over our eyes. Everyone aught to know about probability and randomness. And this is a good place to start - an enjoyable read.
As a lecturer of statistics to a non-maths audience I often have problems getting students to engage with the subject. Here is a book that makes it entertaining in a clear and interesting way. There are no equations to get in the way and only a few graphs to look at. but the explanations are clear and the historical context brings the subject to life.
There are two small gripes. The first is that the Bayes chapter is not as clear as some of the others and it could refer back to the earlier ideas about probability of compound events as conditions make a difference. The second is that for me chaos is deterministic - we cannot know what will happen but something is caused by an unknown current state, rather than non-deterministic - completely random in a non-causal way. But this is hair splitting.
It is definitely a book I will recommend to my students and anyone else who wants a gentle introduction to the strange world of probability.
on 31 December 2014
I have seen the odd review or two which criticise Mlodinow for his lack of "mathematical maturity" . As a previous reviewer has pointed out, there is an obvious trade off between maintaining rigor and providing a book which is easily accessible. The latter approach characterises the essence of this book, it is a book for the average reader who does not have much or any prior knowledge of the topics discussed.
If anything, this book is a history of randomness, designed to whet your appetite. Mlodinow does a good job of illustrating the very counter intuitive nature of probability and why we aren't hardwired to understand it.
From the stock market to Hollywood, we habitually underestimate the effects of randomness.
If you want to see the mathematics behind stochastic processes, look elsewhere.
If you would like a non-technical introduction to the concept of randomness, look no further.
on 2 November 2010
I was first introduced to the writing of Leonard Mlodinow when I read Euclid's Window as an undergraduate in mathematics. It was (and still is) one of the most delightful books on maths I have ever read. So it was with great anticipation that I looked forward to the Drunkard's Walk.
The subtitle, How Randomness Rules Our Lives, is probably a more apt description for the book, as the question of the Drunkard's Walk is not really discussed. If you are unaware of it, it relates to the probability that a drunk person, staggering around randomly will eventually return to where they started from. Given enough time, this probability tends towards 100% if they travel in two dimensions, but not if they travel in three dimensions. So if you're looking for an explanation of why, this is not the book for you.
Rather, this is about probability and statistics. The mathematics in it is not particularly technical, although there are some concepts in it that seem to go against common sense. In fact, common sense is a running theme throughout the book; but only insofar as how unreliable common sense can be (here I am distinguishing between "common" sense and "good" sense). The book takes us on a wide and varied journey through history, sports, finance, gambling and medicine, amongst other things, looking at the way in which chance events are commonly understood, how they should be understood and getting to grips with the consequences of what happens when there is a gap between the two.
It is written in a highly engaging way, with enough humanity in it to keep the lay reader interested and just enough technical detail for the more mathematically minded to stay the course. There are, however, a few small points to pick up on. Mlodinow himself is a physicist, not a statistician . This results in a couple of explanations appearing a little muddled. For example, his explanation of why the probability of two independent events both occurring should be multiplied together may not be clear to someone without any maths knowledge beyond GCSE level.
The slightly bigger issue is in his philosophical interpretation of randomness. There is very little discussion over different interpretations of randomness and of what probabilistic measures mean. The conclusion that Mlodinow seems to reach is that it applies to unpredictability. However, in various places throughout the book, he seems to get this confused with purposelessness, which leads to a few unjustified conclusions on specific matters.
That said, this is a minor distraction in an otherwise excellent book.
As somebody whose main purpose in my school years was to save others from the fate of being bottom of the class, I never would have seen myself even reading books for pleasure, much less books on the history of maths. Another reviewer is correct in using this description of the subject matter. I had no conception that different civilisations were advancing at such different rates in their knowledge of maths. For instance, I didn't realise how late some societies were in acquiring the number zero. They weren't so tardy about bringing in zero hours contracts though but that's another story. If some readers are turned off by the idea of maths history as a book subject, let me assure you that the book is both entertaining and informative. It is not just informative in a fascinating and enlightening way. We make so many decisions on hunches, probabilities and possibilities that we owe it to ourselves to be better educated.
The author breaks complex material down into relatively easy and well-explained examples and I am relieved to know that even Maths Professors have been known to misunderstand probability. He cites a newspaper sindicated columnist named implausably "Von Savant" who gave a correct solution that was nevertheless ridiculed over a theory, even though real world data proved beyond doubt that she was right. More shockingly million's to one Dna evidence is undermined by lab error rates of possibly 1%. We have all read about once in a hundred year weather events. I am either older than I think, or perhaps some of that data is questionable too. If nothing else the book will leave you more informed about probability than is good for us. (if ignorance truly is bliss).
The book does for statistics what Super Freakonomics does for Economics which is to share and open up the subject to people like me. It enabled me to be in awe of people like Galileo (who I thought just looked at stars) and Newton (who I thought just invented gravity soon after working out that apples usually fell downwards. It also documents an extraordinary contemporary of Leonardo Da Vinci, who despite a tragic life was responsible for some remarkable work which others were able to build upon and become better known for. Some of the gambling stories also show the power of knowledge and our capacity to be fooled.
In my view this is a book well worth reading.