Skip to main content

The Fate of Schrodinger's Cat - James Stein ***

This is a difficult book to pin down. It covers a topic I find fascinating - probability and statistics, and specifically applications where these become counter-intuitive. Much of the book focuses on a particular kind of probabilistic outcome where introducing an extra, apparently irrelevant, factor makes seemingly impossible results occur (more on the specifics in a moment). There is no doubt that the result is mind-boggling, yet the way it is presented makes it difficult to get your head around. James Stein is a retired maths professor, and though he makes it clear he is a relative newcomer to statistics, he probably doesn't really understand just how opaque a mathematical discussion can be to the general reader.

The book starts with an old favourite, the Monty Hall problem. The problem itself is well covered by Stein, but he misses an opportunity to give it more bite by bringing in the controversy when Marilyn vos Savant brought this up in Parade Magazine in 1990 and a whole string of PhDs (almost entirely male) told her how wrong she was with her (correct) solution. Stein makes the outcome sound obvious, which it is when you are familiar with it, but most coming to the problem afresh still find it very challenging to get their head around.

With the Monty Hall problem, it is very easy to see what the proposition is, even though many have struggled to accept that it's true. But once Stein gets onto the core problem of the book, which will go on to appear in a range of variants (including the Schrödinger's cat example of the title), the proposition itself could have been explained more clearly. In the problem (Blackwell's bet) you are shown two envelopes with different amounts of money in them. You open one and then are given the opportunity to exchange the amount for the amount (unseen) in the other envelope. The surprising result is that, by comparing the contents of the envelope with an independent random number, such as the temperature, it is possible to make the decision on which envelope to choose and be right more than 50 per cent of the time.

Stein makes it clear that the maths involved to prove this outcome only requires high school algebra - it does - but in reality, getting your head around what the maths is doing, particular as more detail is added for the variants of the problem, is far beyond simple high school level. 

I absolutely love one aspect of this book. Stein makes a very strong argument as to why we should teach students simulation techniques (which are used several times in the book to demonstrate an outcome) rather than algebra. As he says 'Why so much emphasis on teaching something that's basically useless for most people, when learning how to construct models and program computers that teaches them equivalent skills, is far more useful and is about three orders of magnitude more fun.'

A smaller issue I have with a book is that a lot of the examples are taken from sport (which mostly means sports that only Americans play) and if you have no interest in sport, and particularly American sport, it rather puts a dampener on things. Half the time, I had no clue what the sports terminology meant.

Overall, rather too much of the book is focused on variants of the same thing, where I would have liked to see a broader range of challenges. Even so, there's no doubt that Blackwell's bet and its derivatives are truly fascinating, I just wish that they could be appreciated by a wider audience.

Paperback:    
Kindle:  
Using these links earns us commission at no cost to you
Review by Brian Clegg
Labels:

Comments

Post a Comment

Popular posts from this blog

The Antigravity Enigma - Andrew May ****

Antigravity - the ability to overcome the pull of gravity - has been a fantasy for thousands of years and subject to more scientific (if impractical) fictional representation since H. G. Wells came up with cavorite in The First Men in the Moon . But is it plausible scientifically?  Andrew May does a good job of pulling together three ways of looking at our love affair with antigravity (and the related concept of cancelling inertia) - in science fiction, in physics and in pseudoscience and crankery. As May points out, science fiction is an important starting point as the concept was deployed there well before we had a good enough understanding of gravity to make any sensible scientific stabs at the idea (even though, for instance, Michael Faraday did unsuccessfully experiment with a possible interaction between gravity and electromagnetism). We then get onto the science itself, noting the potential impact on any ideas of antigravity that come from the move from a Newtonian view of a...
Post a Comment
Read more

The World as We Know It - Peter Dear ***

History professor Peter Dear gives us a detailed and reasoned coverage of the development of science as a concept from its origins as natural philosophy, covering the years from the eighteenth to the twentieth century. inclusive If that sounds a little dry, frankly, it is. But if you don't mind a very academic approach, it is certainly interesting. Obviously a major theme running through is the move from largely gentleman natural philosophers (with both implications of that word 'gentleman') to professional academic scientists. What started with clubs for relatively well off men with an interest, when universities did not stray far beyond what was included in mathematics (astronomy, for instance), would become a very different beast. The main scientific subjects that Dear covers are physics and biology - we get, for instance, a lot on the gradual move away from a purely mechanical views of physics - the reason Newton's 'action at a distance' gravity caused such ...
Post a Comment
Read more

It's On You - Nick Chater and George Loewenstein *****

Going on the cover you might think this was a political polemic - and admittedly there's an element of that - but the reason it's so good is quite different. It shows how behavioural economics and social psychology have led us astray by putting the focus way too much on individuals. A particular target is the concept of nudges which (as described in Brainjacking ) have been hugely over-rated. But overall the key problem ties to another psychological concept: framing. Huge kudos to both Nick Chater and George Loewenstein - a behavioural scientist and an economics and psychology professor - for having the guts to take on the flaws in their own earlier work and that of colleagues, because they make clear just how limited and potentially dangerous is the belief that individuals changing their behaviour can solve large-scale problems. The main thesis of the book is that there are two ways to approach the major problems we face - an 'i-frame' where we focus on the individual ...
Post a Comment
Read more