One in a million
People aren't very good at judging risk, and this is the principal driving factor behind much of the human capacity for extreme stupidity.
As can be seen here, there is not much inside a human's head.
Up until 10 000 years ago, people lived in groups of a few hundred at most, doing things very different to what most of us are doing today. The Cromagnon brain had been finely tuned by natural selection to judge what was foolhardy, and what was a sensible gamble by the simple expedient of letting nature kill off the brains that weren't so good at judging the risk of stealing honey from bees. Natural selection, in its shallow wisdom, wired into our forebearers the ability to judge risk based on a few simple rules, such as:
If you see someone you know doing something that ends up with them dead, then this is a risky thing to do.
And so Homo sapiens happily continued extant, noting the idiocies of her relatives and friends, and lived to a ripe old age by not pissing off the bees.
Then someone invented agriculture.
Within a few thousand years, Homo sapiens was living with thousands of other bald apes, doing things that had not even been invented the decade before, like ploughing, taming wild animals, and ingesting exciting extracts from borderline toxic plants. And so three billion years' worth of risk-judging evolution was undone in the geological blink of an eye. Homo sapiens was no longer a tribal hunter-gatherer, she was a farmer surrounded by a nation of farmers.
Unfortunately for us, our brains are still largely similar to those of our ancestors, and hence we judge risks in much the same sort of way. In today's world, if a sparrow farts in Wisconsin, we will probably hear about it, and if someone dies of necrotising fasciitis in Wales, we'll certainly hear about that (especially during the summer when the politicians are on holiday). Because the list of "people we know" now effectively includes anyone the media decides we should know, our heuristic for judging risk:
If you see someone you know doing something that ends up with them dead, then this is a risky thing to do.
has come to mean:
If you see anyone in the entire world doing something that ends up with them dead, then this is a risky thing to do.
This gives us a somewhat warped view of risk, because there are plenty of bee-molesting idiots in a population of six billion.
Three
The chances of someone winning the UK lottery are several millions to one, but because the media will hunt through world+dog to find that person and denounce him as a drug-addled adulterer, you now see someone win the lottery on a nearly weekly basis. And your incapable little Cromagnon brain will fall for it: "Someone wins the lottery every week, so maybe I can too!" Even though the chances are millions to one. Herein lies the problem: human brains are quite good at judging small numbers, but dreadful with big ones. You can probably recognise what three objects looks like without even counting them.
Many
See. But once you get above a thousand, most human brains reach a sort of plateau - a thousand, ten thousand, fifty million - could you really tell the difference? Obviously, we have attuned ourselves to hearing about millions of deaths, thousands of pounds, and so on, but how big a field would you need to fit a million people in? Do you really have a grasp of what a million of anything looks like? Quite possibly not. And if you do, it probably because at some point you've actually done the maths and turned the inconceivable number into a graspable one: one million people (assuming a square metre of standing space for each one) would entirely fill a square kilometre. That's a hell of a lot of people. It would take you 11 days to shake hands with every one of them, assuming no sleeping, and a shaking frequency of one person per second. Human brains are rubbish at intuitively dealing with these sorts of numbers, unless you deal with the routinely and have learnt how to translate them into something more manageable, like 'the price of a house', or 'the size of a field'.
A one-in-a-million chance of winning means that one person in a square kilometre swarming with people will win. You'd be lucky to spot the person with their hand up in that many people. The chances of that person being you are so small you may as well forget it.
So, when we try to get our heads round a one-in-a-million chance of dying from X we're talking about a number so tiny that you might as well forget about it. A one-in-a-million chance is the size of risk of death you experience very day from almost everything you do: eating a sweet, drinking a bottle of wine, cycling to work: these all carry a risk of death by choking, cirrhosis or accident of this sort of size. We all have an intuitive idea about how worrisome a one-in-ten chance of dying is (Russian roulette), but our brains simply aren't cut out for judging one-in-a-thousand, and one-in-a-million risks, which leads to our being blasé crossing the road, whilst being paranoid about getting vaccinated.
Hazardous risks are dangerous
Not only are we poor at judging risks, we don't really get our heads round what risk actually is. We have a tendency to squash danger, hazard and risk into one big homogenous blob, and leave it at that.
Risk is not the same as hazard. A hazardous substance is one that will cause disease or death if you eat it, inhale it, or bathe in it. Let us take the example of sulfuric acid. This substance is inherently hazardous: it causes burns in contact with skin. However, people in labs are perfectly happy to handle this substance. Are they mad? Well, no. Although sulfuric acid is hazardous, we wear gloves to prevent it getting on our skin, and makes sure we use only dilute solutions whenever possible. Hence, it is quite safe to handle it having taken suitable precautions. By taking precautions, we reduce the risk of exposure. Far from being the same thing, danger, hazard and risk are quite distinct:
Danger = Risk × Hazard
We only consider something dangerous if it is inherently hazardous (arsenic, sulfuric acid, β-radiation), and if the risk of our coming in contact with it is high. These two things can be separated quite readily. Something highly hazardous (cyanide) requires only small amounts to cause death; something slightly hazardous (salt) requires huge amounts to cause death. However, if the risk of your eating a vast amount of salt is high, it is just as dangerous as a small risk of ingesting a little cyanide. Would you rather eat ten apple pips (which contain highly hazardous cyanide, but the chances of them containing enough to kill you is negligible), or a kilogram of 'innocuous' table salt? I know where I'd take my chances.
Whenever you hear that something is dangerous, you need to find out whether this is because the something is inherently very hazardous, or because the risk of your being exposed to it is very high.
The wrong sort of life
We have been naturally selected to live in much smaller groups than we currently inhabit, and to have an intuitive grasp only of small numbers. Since our inbuilt risk-ometer is calibrated on only knowing a few hundred people, this means we are not too good at judging risk any more.
Unfortunately, we no longer even experience the same sorts of hazard that hunter-gatherers had to put up with either! When was the last time you had to worry about being eaten by a hyena? We are quite good at comprehending some hazards, but increasingly, we are exposed to hazards that we have not the wit of. There is nothing in human evolutionary history to give us a visceral understanding of the hazard posed by sulfuric acid: the concentrated stuff looks quite innocuous, rather like oil, until it eats through your hand. We are not very good at spotting these novel hazards, and we are even worse at dealing with invisible, intangible hazards like radiation and pesticide residues. These are the sort of hazards that recall in our little ape brains the terror of the half-glimpsed movement in the dark.
Much research has been done on this, all of it pointing to the fact that people are happy to deal with hazards that either evolution, or their upbringing have introduced them to, hence we have a good grasp of how hazardous fast moving objects (cars) and things with big teeth (hyenas) are, but we are still scared to death of:
- Things that are new
- Things that are unknown
- Things that are invisible
- Things where cause and effect are separated in time
- Things where we don't understand the hazard at all
I have listed these not because they are surprising, nor because I find them silly, but because most people's metacognitive ability is appalling: you might be worried about mobile phone masts destroying your brain, but the least you could do is recognise that this is in no small part due to the fact that mobile phones are new(ish), microwaves are invisible, and you may well not have the foggiest idea what a microwave actually is anyway. Examining your own brain processes to understand why you think what you do generally seems lacking from the hysterical reactions you see to the siting of mobile phone masts, traces of pesticides in food, etc. The fact that the same hysterics are happy to drive cars, cross roads, and eat junk food is testament to the blind spot people have for hazards they are used to.
So not only are we dreadful at judging risk, we are also terrible at judging most of the hazards we are now exposed to, because there is nothing in our history to prepare us for them. This means we either under- or over-estimate the hazards of driving cars, using mobile phones, and drinking tap water.
Lymnaea, a snail often parasitised by trematode worms.
The executioner's art
The final nail in the coffin of our ability to judge risk is that natural selection does such a great job of finding an optimum risk aversion strategy, no matter how horribly complex the dangers involved are. The great thing about natural selection is that no matter what you do, if it's seriously the wrong thing, you'll end up dead or sterile. There is a certain species of aquatic snail (Lymnaea) that has to put up with a trematode parasite that bores into its shell and can kill it. So should the snail grow a thicker shell, to reduce the risk of being parasitised? Not necessarily, because being heavier means it's more difficult to escape predators. So should the snail grow a thinner shell? Maybe, but that means it's more exposed to the risk of being smashed against a rock and killed by a wave. So a thicker shell is in order? Well yes, unless this reduces its fertility by diverting calcium from it's reproductive organs. If we sat down and tried to work out the optimum shell thickness, we would find it nightmarishly difficult. However, natural selection just does it all automatically: a snail with a shell of thickness X will be exposed to certain dangers during its lifetime, and will run a certain risk of dying. No matter how complicated the risks, there will likely be a single optimum shell thickness at a given point in time, and natural selection will home the snail genepool in on this.
People often wonder why, after swimming all that way upstream to spawn, salmon die of exhaustion immediately afterwards. "What a terrible waste", they say. No: it's not! The thing is it's bloody difficult to swim all that way, and natural selection has judged that it is more sensible not to bother with the return journey. So, say the people who think nature should be cute and fluffy, why don't the salmon swim around for a week or two, bathing in a postorgasmic glow before they die? The reason is that if the salmon didn't die of exhaustion immediately, they will be wasting energy better spent on semen or eggs than on frivolities like living. Natural selection is splendidly good at weighing up all the possibilities, and chosing the best of the bunch. It is so good at this, not because it is amazingly clever, but because it is stupefyingly dumb: simply put, the salmon that makes the best 'choice' makes the most offspring, which come to dominate the population. Eventually everyone is doing as-near-as-damn-it the best possible thing they can to produce offspring.
This poses us a few problems. Firstly, we are no longer baby-making machines, and these days we're often more interested in survival than breeding. Secondly, whatever exquisitely complex environment natural selection has blindly attuned us for, it's not the one we live in now. And thirdly, we have generally left it to natural selection to find the best strategy in a horribly complex and interdependent environment. These days we have to use our brains instead, and that's a lot harder. When you worry about the risk that mobile phone masts might give you cancer, you also need to worry about the risk that a lack of mobile phone connectivity will end up with you dead in a ditch in the middle of nowhere. Weighing up all these little risks is much harder for brains than it is for natural selection: natural selection would just run a few generations of town planners and mobile phone users, and automagically balance the miniscule costs and tiny benefits to produce the optimum mobile coverage.
Risky behaviour
The upshot of all this is that we are terrible at judging risk, poor at evaluating the magnitude of novel hazards, and hence exceptionally bad at judging danger. Furthermore, most dangers are so horribly mixed up with other dangers, there's not a hope our unaided brains will be able to pick them apart.
Pigeon in a Skinner box
There's an interesting, if rather unethical, experiment you can perform on pigeons. Pigeons can be trained to peck a button to receive food, when placed in a Skinner box, which is simply a cage with a button and a food chute in it. If you put a pigeon in such a box, at some point it will peck the button for want of anything better to do, and food will be delivered. By simple reinforcement, the pigeons learn that button equals food. This is not particularly surprising.
All sorts of nasty things can be done in Skinner boxes: rats can be trained to be frightened of the floor by the simple expedient of electrifying it, and so on. However, by far the strangest thing that can be done in one of these things is to instil superstition. All you need to do for this is to arrange for food to be delivered randomly when the button is pecked: sometimes it comes, other times it doesn't. By adding this element of chance to the reinforcement, you can get some pigeons to do a very odd thing: they begin to develop religious ceremonies. The way it works is that e.g. the pigeon happens to turn around before pecking the button, and on this occasion, it gets fed. If this happens a few times by pure chance, the pigeon begins to 'learn' that spinning round makes the food arrive, even if it doesn't make the slightest bit of difference. Soon, it always spins round before it pecks the button, and may incorporate ever more elaborate rituals into the pecking in the mistaken 'belief' that they decrease the risk that pecking will not get them fed. Humans do exactly the same thing: do rain-dances make it rain? Of course not. But our inability to properly analyse risk, probability and chance means that rain-dances get performed. The pigeon would be much better off not doing its little food dance: it's a waste of energy, and hence she is wasting the very food she is trying to magic out of the chute. The rain-dancer would be much better off spending his time finding a river than appeasing the sky. He'd be even better off doing a controlled experiment to see if rain-dances made it rain more often, but superstition and ritual have an interesting way of inveigling themselves deep into a culture, so that no amount of contrary evidence will overturn those first few experiences when the rain-dance seemed to work.
Our manhandling of probability and risk contributes to superstitious behaviour. Pseudoscience is a huge exercise in superstitious behaviour, and religion arguably even more so. A belief in psychics is in no small part due to our misunderstanding of how risk and probability work. Say someone tells you that you will meet a short, blonde, ugly stranger. In a small tribe, the chances of your meeting a stranger are rather low. The chances of her being short, blonde and ugly are vanishingly small. However, a simple stroll along a crowded urban road will almost certainly take you past several short, blonde, ugly people, especially if you are specifically looking out for someone you can equate (however tenuously) with the description the 'psychic' gave you. This is not an indication the charlatan was right, but that you have seriously misjudged the risk of bumping into short, blonde, ugly people.
A new hope?
So what can we do to make up for our uselessness at judging probabilities, risk and danger? The only method we have so far come up with is mathematical modelling, and in particular, that dreaded word, statistics.
Statistics is how scientists judge risks. We know that our intuition is a grotesquely unreliable tool, so we invented a slightly less unreliable tool to better it. Statistics is not a panacea, and it is all too easy to be taken in by shoddy statistics, but it is all we have. This is most certainly not to say that you should blindly belive statistics thrown at you by scientists, the media or the government. It is always possible to pick out some good news amongst a lot of horror. The headmaster at my secondary school had thoroughly dishonest approach to statistics: we were forever being told that the exam grades of girls in years 8 and 9 had improved, when you knew that the flip side to this coin was probably a catastrophic collapse in grades in every other group. You should always take stats with a pinch of salt: at the very least, find out from what sample size the stats were taken, and which statistics have been left carefully uncalculated. But we must also realise that while stats may hide a multitude of sins, out intuition is likely to be even more unreliable. The catalogue of food scares, contraceptive pill scares, child-molester-round-ever-corner scares and vaccination scares served up on a daily basis to a credulous public riding high on the infallibility of intuition is a sorry sight to behold.
It has been said that when you have no food to eat, you only have one problem, but when you have lots of food, you have many problems. Our world is increasingly a place where intuition doesn't work, because the risks we are dealing with are so small, complex and intangible. When you have nothing to eat, you really do run a significant risk of dying from starvation, but when you have a lot to eat, the things to worry about are not the unfamiliar and lethal botulism and the insidious and invisible pesticide residues, which are one-in-a-million risks, but the very real risk (one-in-ten or so) of dying of coronary artery disease from overconsumption of fats and salt.
Measles virus - this will kill about one in every thousand children
it infects. MMR will kill about one in every million children
immunised with it (…a risk so small you may as well forget
about it…), but it certainly will not cause autism.
Worrying about pesticide residues in a McDonald's hamburger is rather missing the point. The current hysteria over the new and 'unproven' MMR vaccination and its possible link to scary and unfamiliar autism is quite likely to lead to an epidemic of measles in the UK in the next few years. At least the parents who refused to get their kids immunised will have the consolation that measles is quite familiar and 'natural' when their kids are running a small, but very real risk of brain damage from the virus.
Messing up risk even applies to our belief (or otherwise) in the reliability of statistics. Because of the excessively low risk threshold brought on by people thinking they still know only two hundred people, bad stats have a disproportionate effect on our thinking:
If you see someone you know making a statistical mistake that ends up with people dead, then this it is a risky thing to believe statisticians.
A statistical mess over calculating the risk of death from eating BSE infected beef reflects very badly on the technique. We also tend to miss the very important point that it's mathematical modelling, and the use of stats that makes sure the that planes very rarely fall out of the sky, your food's best-before-dates are reasonably accurate, and condoms don't split on a daily basis.
Diarrhoea is a gut reaction too
In all these cases, intuition wins, but in all these cases, it is almost certainly we that will be losing out. It's about time we started asking if asking our intuition about hazards that it has never met, and risks that it is ill-adapted to calculate, is any more sensible than asking a dentist to perform heart surgery.
"Well, I know roughly where all the bits are, and I'm quite handy with the anaesthetic. I'll reckon I can take a good stab at it. Now, how do you open a chest up with a drill?"