It’s not often that I come across a book which I think everyone should read.

Risk: The Science and Politics of Fear, by Dan Gardner, is one such book.

Risk tells us about how we are constantly misled in every day life about how dangerous things are — drugs, cancer, paedophiles, knife crime, terrorism — without actually understanding what likely risk each of them pose. We assume that because they are big and scary emotive things that they have a considerably higher risk than they actually have. And similarly we downplay the risk of things like diabetes which frankly aren’t as interesting.

Basically, the world is an awful lot safer than we feel it is. And he goes on to explain why our perception is wrong.

Dan talks about how the brain works, how we have two control systems (which he terms ‘gut’ and ‘head’) which work in different ways. ‘Gut’ is a more immediate reaction, based on three main things, and ‘Head’ is the more considered verdict, based on conscious reasoning.

The three things that power Gut with relation to the likelihood of something occurring:

1. How easily can I think of an example?
2. What number did I first think of? Gut then takes this as an anchor which head will tend to revise up or down
3. What do I consider is typical consequence?

That’s not a perfect explanation, but without giving all the examples Dan does, it’s difficult to get the point across. The consequence rule he described as “The Law of Typical Things”, but I think a better term would be the Law of Typical Consequences.

If there is an 70% probability Event A will lead to Event B, and that has an 70% probability of leading to event C…. to event F, we will see event F as a likely outcome, because each step seems typical of what we would expect, so the whole seems typical. Whereas of course if were to actually work out the probability of this (or even think about it with ‘Head’ rather than ‘Gut’), we’d find that the likelihood of event F is just under 17% — it’s still plausible, but not the most likely outcome.

If Saddam Hussein has the intention to develop weapons of mass destruction in Iraq, if he then succeeds in this, if he gave them to terrorists, if the terrorists had the capability to mount an attack, if the terrorists did mount an attack, and if it wasn’t foiled, there could have been a major terrorist incident.

Anyone remember this justification that Dan quotes? I’ve got no idea what the actual probabilities of each step are, but you can see that the first link in the chain does not inevitably lead to the last.

I’ll use another one of his examples to explain the anchoring rule:

Was Gandhi older or younger than 9 when he died? Of course, that’s a silly question. The answer is obvious. It is also irrelevant. Please forget I asked.

Let’s move along to another question. How old was Gandhi when he died? Now if you actually know how old Gandhi was when he died, you are excused from this exercise.

Risk, p40-41, Dan Gardner

Answer the question in your head before moving on. What did you come up with?

Statistically, the average answer for people being asked that — after being presented with the ’9′ question first — is 50. If people are asked whether he was older or younger than 140 when he died, the answer comes back as 67 on average. In both cases, your ‘Gut’ has started with a number which has been revised up or down as appropriate, but obviously is not independent of that initial number, because a different starting number gives a different result.

Oh, and it turns out, Dan announces in the notes section at the back, that both results were wrong. He was actually seventy-nine. I’m sorry Dan, but you are wrong too. He was seventy eight. You’ve made the mistake of subtracting his birth year from his death year without actually working out whether or not he’d had his birthday that year…

Irrespective of nit-picking corrections, this is an important, and indeed an interesting point. Did you know your brain worked that way? No, me neither. Dan suggests that there is some evidence that — particularly with statistics — the more numerate you are, the more ability you have to revise this anchor figure.

But it’s also interesting how the use of figures evolves without seemingly anyone being able to back up the original figure with any sources.

Dan points out that a story saying that there may be ‘as many as’ 50,000 paedophiles online appeared in The Independent. Yet by the time this figure was being used in Dallas Child, it was being stated that 50,000 paedophiles were on myspace.com at any one time. Similarly, a measure of relative deprivation in Canada (“one in six families are substantially worse off than average”) ended up morphing into something suggesting one in five Canadian children are so poor that they go to bed hungry.

Possibly without anyone actually being aware of it, an unsupported figure has been plucked out of the air, and then the wording around it has evolved over time to make the story even more threatening, to make you more likely to want to buy cyber-safety products, or not let your child use the internet unsupervised, throw bread to ducks Canadians or whatever.

Then there are the times when a report by a perceived authority is supressed, simply because what they are saying is not politically palatable. For example a study was carried out by the World Health Organisation in 1995 into cocaine use.

Among its findings: ‘Occasional cocaine use,’ not intensive or compulsive consumption, is ‘the most typical pattern of cocaine use’ and ‘occasional cocaine use does not typically lead to severe or even minor physical or social problems’Risk, p142, Dan Gardner

Funny that we’ve never heard about it, isn’t it? To find out why the report was pulled (and I’ll give you a clue: it wasn’t because their findings were proved incorrect), you’ll need to read the notes in the back of Dan’s book.

Dan covers a wide variety of topics: crime, the environment, the media, and so on, but the next one to catch my eye was a personal bugbear of mine. Health statistics.

Carson’s statement that cancer ‘accounted for 15 per cent of the deaths in 1958 compared with only four per cent in 1900′ makes the common mistake of simply assuming that the disease’s larger share of the total is the result of risinng rates of the disease.Risk, p265, Dan Gardner

Thank you, Dan. Finally, someone who understands. If more people are dying from cancer now (or in 1958, in this case) than used to before, it is because people aren’t dying of something else.

Life, so far as I can tell, has a mortality rate of 100%. As Dan points out, if you eliminate tuberclosis, diptheria, typhoid fever, whooping cough, cholera, measles and scarlet fever as major killers in the developed world, something else will end up taking a higher proportion of deaths.

Statistically, if we reduce the proportion of deaths to cancer, we’ll increase the number dying of heart disease. Not because it akes the nation’s hearts unhealthier, but because something is going to kill you in the end, and some of those people who would previously have died from cancer will now die from heart disease instead.

When I was reading this book, by the time I had got to the end of the first couple of chapters, I had already decided that I must tell people about it, and encourage them to buy it (ideally using one of the Amazon affiliate links I have provided, but so long as you read it somehow, I’ll settle for that). So I flicked back through the first chapters and turned the corner of a few pages which had points I considered important, or interesting, or worthy of mention in the review.

By the time I had finished reading the book, there were about thirty points that I specifically wanted to include in this review. I therefore had to somewhat hack this number down considerably, and I have been unable to get across to you a lot of the important ideas contained within this book. You will therefore have to buy this book for yourself to read them.

Dan is very much an ideas man. These are big ideas, well presented, and they encourage us to challenge the statistics and mental imagery we are presented with. So I did.

In fact, today, we have technology that can dissect the components of drinking water to the level of one part per billion — equivalent to a single grain of sugar in an Olympic size swimming poolRisk, p273, Dan Gardner

“A billion?” I thought. “That doesn’t sound very many. I bet you can fit more grains of sugar in an Olympic sized swimming pool than that…”.

So I checked it out.

Normal granulated sugars for table use: typically they have a grain size about 0.5 mm acrossWikipedia: Granulated Sugar

Okay, we’ll make this a little larger, to allow for them not being perfectly stacked. Even allowing them to be 40% larger per side — 0.7mm per side, this gives each grain a volume of 0.000000000343m³ (some 270% larger by volume than they would be at 0.5mm/side).

The specifications for an Olympic size swimming pool are publicly available: 50m long, 25m wide, with a minimum depth of 2m. Which works out at 2500m³.

Which means that you could fit 7,288,629,737,609 grains of sugar into an Olympic sized swimming pool, even if the grains were 40% larger than usual, and the swimming pool was the minimum allowed depth.

How many billion is that? Well, if you are reading the book in a country which uses the short-scale billion (1000 million), you could fit about 7288 billion large grains of sugar in a swimming pool. So one part per billion would be the equivalent of 7,288 grains of sugar in that pool Considerably more than one, although obviously still not enough to make the water sweet.

Officially, most English speaking countries use the short-scale billion: the UK (yes, despite the term ‘British billion’ sometimes being used to describe the long-scale billion), the US, Australia, Ireland, South Africa, and the English-speaking parts of Canada.

Using the long scale however, it’s around 7.2 billion. Which, as I’ve established that Dan Gardner is Canadian, seems to suggest that he’s maybe meaning the long billion. In which case, despite him being very critical of other statistics and coloured examples, he himself has given an example which is out by a factor of more than seven. And were you to assume — as you probably would — that as the book is in English, and you’ve probably bought it in one of the countries which officially uses the short-scale billion, that a billion means a thousand million.

In which case you then start wondering about the use of terms like ‘billion’ have been used elsewhere in the book, which billion has Dan meant? Since he seems to use the long-scale billion, does he realise most statistics from English speaking countries will use the short-scale billion? Or was the whole ‘swimming pool’ things just a throwaway line?

Even if it was intented as a throwaway, I feel it’s legitimate comment that a book which criticises other statistics for the way they are portrayed or represented ought to get its own statistics right… (mutter mutter, typical lazy journalist)

Of course, what actually makes this funny is that Dan himself says…

How many of us make that effort [to become numerate] isn’t clear. A Canadian polling company once asked people how many millions there were in a billion. Forty-five percent didn’t knowRisk, p112, Dan Gardner

One of those being Dan himself, presumably! The wikipedia article on long and short scales would suggest that English-speaking Canadians use short scale, and French speaking Canadians use long scale. If this is correct (because just finding it on the internet doesn’t necessarily make it so), then it’s little wonder so many Canadians are confused!

But neither that, nor Dan’s inability to work out Gandhi’s age, detracts from the central message of the book. It tells us how we are being misled (whether or not intent is present) by ourselves, by the media, by our society, by advertisers. It shows us what we need to watch for and gives us some of the tools with which to critically analyse what we are told. Even by the person who is telling you to critically analyse what you are told.

And that includes those very tools with which I criticise the book — not accepting something at face value and checking the statistics for yourself. Question what you are told. Just from today’s news on the BBC I can ask:

• why is the headline ‘significant’ fall in gun crime not one of the top stories, when a significant increase would lead to a frenzy?
• when you say ‘too many’ cannot read and write, how many do you mean? For me, I would assume even a handful is too many. But it turns out that this relates to school leavers without an English and/or Maths GCSE. Failure to pass a test may be indicative of an inability to read, write, or be numerate, but this is not the same as saying that these people cannot read or write.
• Or what about Chemicals ‘may reduce fertility’? Which chemicals? How much do they reduce it, and in what concentration do you have to encounter them? And even if there is a correlation, this does not prove causation. What would be the consequence of no longer using those chemicals?

This should be mandatory reading for everyone old enough to grasp the subject matter. Irrespective of your beliefs on any one of the subjects — on crime, on chemical/natural, on the environment, on terrorism — this book will help you question not only the way in which information is imparted to you, but why that information is imparted. Buy this book.

Just on the off-chance that I’ve convinced you, here’s that Amazon affiliate link again: Risk: The Science and Politics of Fear

PS did anyone spot the supraliminal message?