“Lies, damn lies, and statistics”

Ours is the age of statistics; of number-crunching, of quantifying, of defining everything by what it means in terms of percentages and comparisons. Statistics crop up in every walk of life, to some extent or other, in fields as widespread as advertising and sport. Many people’s livelihoods now depend on their ability to crunch the numbers, to come up with data and patterns, and much of our society’s increasing ability to do awesome things can be traced back to someone making the numbers dance.

In fact, most of what we think of as ‘statistics’ are not really statistics at all, but merely numbers; to a pedantic mathematician, a statistic is defined as a mathematical function of a sample of data, not the whole ‘population’ we are considering. We use statistics when it would be impractical to measure the whole population, usually because it’s too large, and when we instead are trying to mathematically model the whole population based on a small sample of it. Thus, next to no sporting ‘statistics’ are in fact true statistics as they tend to cover the whole game; if I heard during a rugby match that “Leicester had 59% of the possession”, that is nothing more than a number; or, to use the mathematical term, a parameter. A statistic would be to say “From our sample [of one game] we can conclude that Leicester control an average of 59% of the possession when they play rugby”, but this is quite evidently not true since we couldn’t extrapolate Leicester’s normal behaviour from a single match. It is for this reason that complex mathematical formulae are used to determine the uncertainty of a conclusion drawn from a statistical test, and these are based on the size of the sample we are testing compared to the overall size of the population we are trying to model. These uncertainty levels are often brushed under the carpet when pseudoscientists try to make dramatic, sweeping claims about something, but they are possibly the most important feature of modern statistics.

Another weapon for the poor statistician can be the mis-application of the idea of correlation. Correlation is basically what it means when you take two variables, plot them against one another on a graph, and find you get a nice neat line joining them, suggesting that the two are in some way related. Correlation tends to get scientists very excited, since if two things are linked then it suggests that you can make one thing happen by doing another, an often advantageous concept, and this is known as a causal relationship. However, whilst correlation and causation are rarely not intertwined, the first lesson every statistician learns is this; correlation DOES NOT imply causation.

Imagine, for instance, you have a cold. You feel like crap, your head is spinning, you’re dehydrated and you can’t breath through your nose. If we were, during the period before, during and after your cold, to plot a graph of one’s relative ability to breath through the nose against the severity of your headache (yeah, not very scientific I know), these two facts would both correlate, since they happen at the same time due to the cold. However, if I were to decide that this correlation implies causation, then I would draw the conclusion that all I need to do to give you a terrible headache is to plug your nose with tissue paper so you can’t breath through it. In this case, I have ignored the possibility (and, as it transpires, the eventuality) of there being a third variable (the cold virus) that causes both of the other two variables, and this is very hard to investigate without poking our head out of the numbers and looking at the real world. There are statistical techniques that enable us to do this, but they are for another time.

Whilst this example was more childish than anything, mis-extrapolation of a correlation can have deadly consequences. One example, explored in Ben Goldacre’s Bad Science, concerns beta-carotene, an antioxidant found in carrots, and in 1981 an epidemiologist called Richard Peto published a meta-analysis (post for another time) of a series of scientific studies that suggested people with high beta-carotene levels showed a reduced risk of cancer. At the time, antioxidants were considered the wonder-substance of the nutrition, and everyone got on board with the idea that beta-carotene was awesome stuff. However, all of the studies examined were observational ones; taking a lot of different people, seeing what their beta-carotene levels were and then examining whether or not they had cancer or developed it in later life. None of the studies actually gave their subjects beta-carotene and then saw if that affected their cancer risk, and this prompted the editor of Nature magazine (the scientific journal in which Peto’s paper was published) to include a footnote reading:

Unwary readers (if such there are) should not take the accompanying article as a sign that the consumption of large quantities of carrots (or other dietary sources of beta-carotene) is necessarily protective against cancer.

The editor’s footnote quickly proved a well-judged one; a study conducted in Finland some time afterwards actually gave participants at high risk of lung cancer beta-carotene and found their risk of both getting the cancer and of death were higher than for the ‘placebo’ control group. A later study, named CARET (Carotene And Retinol Efficiency Trial), also tested groups at a high risk of lung cancer, giving half of them a mixture of beta-carotene and vitamin A and the other half placebos. The idea was to run the trial for six years and see how many illnesses/deaths each group ended up with; but after preliminary data found that those having the antioxidant tablets were 46% more likely to die from lung cancer, they decided it would be unethical to continue the trial and it was terminated early. Had the Nature article been allowed to get out of hand before this research was done, then it could have put thousands of people who hadn’t read the article properly at risk; and all because of the dangers of assuming correlation=causation.

This wasn’t really the gentle ramble through statistics I originally intended it to be, but there you go; stats. Next time, something a little less random. Maybe

The Slightly Chubby Brigade

As the news will tell you at every single available opportunity, we are living through an obesity crisis. Across the western world (USA being the worst and Britain coming in second) our average national BMI is increasing and the number of obese and overweight people, and children especially, looks to be soaring across the board. Only the other day I saw a statistic that said nearly a third of children are now leaving primary school (ie one third of eleven year-olds) overweight, and such solemn numbers frequently make headlines.

This is a huge issue, encompassing several different issues and topics that I will attempt to consider over my next few posts (yeah, ‘nother multi-parter coming up), but for many of us it seems hideously exaggerated. I mean yes, we’ve all seen the kind of super-flabby people, the kind the news footage always cuts to when we hear some obesity health scare, the kind who are wider than they are tall and need a mobility scooter just to get around most of the time. We look at these pictures and we tut, and we might consider our own shape- but we’re basically fine, aren’t we. Sure, there’s a bit of a belly showing, but that’s normal- a good energy store and piece of insulation, in fact, and we would like to have a life beyond the weight-obsessed calorie counters that hardcore slimmers all seem to be. We don’t need to worry, do we?

Well, according to the numbers, actually we do. The average height of a Briton… actually, if you’re stumbling across this at home and you consider yourself normal, go and weigh yourself and, if you can, measure your height as well. Write those numbers down, and now continue reading. The average height of a Briton at the moment is 1.75m, or around 5’9″ in old money, and we might consider a normal weight for that height to be around 80 kilos, or 170 pounds. That might seem normal enough; a bit of a paunch, but able to get around and walk, and certainly no one would call you fat. Except perhaps your doctor, because according to the BMI chart I’ve got pulled up a 5 foot 9, 80 kilo human is deemed clinically overweight. Not by much, but you’d still weigh more than is healthy- in fact, one stat I heard a while ago puts the average Briton at this BMI. Try it with your measurements; BMI charts are freely available over the web.

This, to me, is one of the real underlying causes of ‘the obesity epidemic’- a fundamental misunderstanding of what ‘overweight’ consists of. Whenever our hideously awful everyone-dead-from-McDonalds-overdose etc. etc. diet is brought up on the news, it is always annotated by pictures of hanging bellies and bouncing flab, the kind of bodies that make one almost physically sick to look at. But, whilst these people certainly exist, there are not enough of them for the obesity issue to be even worth mentioning in everyday society; whilst the proportion of morbidly obese people is significant, it’s not seriously worth thought for most of us.

No, the real cause for all the chilling statistics we hear on the news is all the people who don’t look to be overweight. The kind whose diet isn’t appalling (no 24/7 McDonaldses), who are quite capable of exercise when it suits them, and who might take a rough glance at the dietary information of the stuff they buy in the supermarket. But these people are nonetheless hovering on the overweight borderline, pulling up the national average, despite the fact that they don’t consider anything to be wrong; in fact, some women who are according to the evil numbers overweight, may consider it almost dutiful to not become obsessed over shedding every pound and to maintain their curves. Having a bit of excess weight is, after all, still better than being underweight and anorexic, and the body image pressures some young women are coming under are just as much of an issue as national obesity. Even for those who don’t have such opinions, many of the slightly overweight feel that they don’t have any weight issues and that there’s surely no significant health risk associated with a ‘bit of meat on your bones’ (it’s actually muscle, rather than fat, that technically forms meat, but ho hum); as such, they have absolutely no motivation to get their weight down, as they don’t think they need to.

I won’t waste much of my time on all the reasons for this statement, but unfortunately even this slight degree of overweight-ness will significantly increase your risk of major health problems somewhere down the line, particularly that of heart disease (which is going through the roof at the moment); diabetes isn’t likely to be a risk for the overweight unless they’re really overdoing things, but that’s also a potential, and very serious, health hazard. The trouble is that many of us find it hard to make this connection if we basically feel healthy. Despite what the doctor says and no matter how much we trust them, if we are capable of going for a nice walk and generally getting about without getting out of breath or feeling bad then we probably feel justified in thinking of ourselves as healthy. Our heart doesn’t seem about to give out, so why worry about it.

The thing to remember is that the heart is just a muscle, so if it isn’t stressed it will degrade just like any other. You know those triceps that haven’t done a press up in five years? Feel how small and weak they are? Yeah, that kind of thing can quite easily happen to the muscles that are responsible for keeping you alive. Your heart might be pumping all day long and be a different type of muscle, so the process will be slower, but give it twenty years and you might start to see the effects.

But anyway, I’m not here to lecture you about your health; that’s far too depressing and dull for my liking- the only point I was trying to make is that many of the accidental contributors to ‘the obesity epidemic’ are probably unaware that their health is in any way a problem, and not really through fault of their own. So whose fault is it then? Well, that one can wait until next time…

Big Pharma

The pharmaceutical industry is (some might say amazingly) the second largest on the planet, worth over 600 billion dollars in sales every year and acting as the force behind the cutting edge of science that continues to push the science of medicine onwards as a field- and while we may never develop a cure for everything you can be damn sure that the modern medical world will have given it a good shot. In fact the pharmaceutical industry is in quite an unusual position in this regard, forming the only part of the medicinal public service, and indeed any major public service, that is privatised the world over.

The reason for this is quite simply one of practicality; the sheer amount of startup capital required to develop even one new drug, let alone form a public service of this R&D, would feature in the hundreds of millions of dollars, something that no government would be willing to set aside for a small immediate gain. All modern companies in the ‘big pharma’ demographic were formed many decades ago on the basis of a surprise cheap discovery or suchlike, and are now so big that they are the only people capable of fronting such a big initial investment. There are a few organisations (the National Institute of Health, the Royal Society, universities) who conduct such research away from the private sectors, but they are small in number and are also very old institutions.

Many people, in a slightly different field, have voiced the opinion that people whose primary concern is profit are those we should least be putting in charge of our healthcare and wellbeing (although I’m not about to get into that argument now), and a similar argument has been raised concerning private pharmaceutical companies. However, that is not to say that a profit driven approach is necessarily a bad thing for medicine, for without it many of the ‘minor’ drugs that have greatly improved the overall healthcare environment would not exist. I, for example, suffer from irritable bowel syndrome, a far from life threatening but nonetheless annoying and inconvenient condition that has been greatly helped by a drug called mebeverine hydrochloride. If all medicine focused on the greater good of ‘solving’ life-threatening illnesses, a potentially futile task anyway, this drug would never have been developed and I would be even more hateful to my fragile digestive system. In the western world, motivated-by-profit makes a lot of sense when trying to make life just that bit more comfortable. Oh, and they also make the drugs that, y’know, save your life every time you’re in hospital.

Now, normally at this point in any ‘balanced argument/opinion piece’ thing on this blog, I try to come up with another point to try and keep each side of the argument at an about equal 500 words. However, this time I’m going to break that rule, and jump straight into the reverse argument straight away. Why? Because I can genuinely think of no more good stuff to say about big pharma.

If I may just digress a little; in the UK & USA (I think, anyway) a patent for a drug or medicine lasts for 10 years, on the basis that these little capsules can be very valuable things and it wouldn’t do to let people hang onto the sole rights to make them for ages. This means that just about every really vital lifesaving drug in medicinal use today, given the time it takes for an experimental treatment to become commonplace, now exists outside its patent and is now manufactured by either the lowest bidder or, in a surprisingly high number of cases, the health service itself (the UK, for instance, is currently trying to become self-sufficient in morphine poppies to prevent it from having to import from Afghanistan or whatever), so these costs are kept relatively low by market forces. This therefore means that during their 10-year grace period, drugs companies will do absolutely everything they can to extort cash out of their product; when the antihistamine drug loratadine (another drug I use relatively regularly, it being used to combat colds) was passing through the last two years of its patent, its market price was quadrupled by the company making it; they had been trying to get the market hooked onto using it before jacking up the prices in order to wring out as much cash as possible. This behaviour is not untypical for a huge number of drugs, many of which deal with serious illness rather than being semi-irrelevant cures for the snuffles.

So far, so much normal corporate behaviour. Reaching this point, we must now turn to consider some practices of the big pharma industry that would make Rupert Murdoch think twice. Drugs companies, for example, have a reputation for setting up price fixing networks, many of which have been worth several hundred million dollars. One, featuring what were technically food supplements businesses, subsidiaries of the pharmaceutical industry, later set the world record for the largest fines levied in criminal history- this a record that persists despite the fact that the cost of producing the actual drugs themselves (at least physically) rarely exceeds a couple of pence per capsule, hundreds of times less than their asking price.

“Oh, but they need to make heavy profits because of the cost of R&D to make all their new drugs”. Good point, well made and entirely true, and it would also be valid if the numbers behind it didn’t stack up. In the USA, the National Institute of Health last year had a total budget of $23 billion, whilst all the drug companies in the US collectively spent $32 billion on R&D. This might seem at first glance like the private sector has won this particular moral battle; but remember that the American drug industry generated $289 billion in 2006, and accounting for inflation (and the fact that pharmaceutical profits tend to stay high despite the current economic situation affecting other industries) we can approximate that only around 10% of company turnover is, on average, spent on R&D. Even accounting for manufacturing costs, salaries and such, the vast majority of that turnover goes into profit, making the pharmaceutical industry the most profitable on the planet.

I know that health is an industry, I know money must be made, I know it’s all necessary for innovation. I also know that I promised not to go into my Views here. But a drug is not like an iPhone, or a pair of designer jeans; it’s the health of millions at stake, the lives of billions, and the quality of life of the whole world. It’s not something to be played around with and treated like some generic commodity with no value beyond a number. Profits might need to be made, but nobody said there had to be 12 figures of them.

NUMBERS

One of the most endlessly charming parts of the human experience is our capacity to see something we can’t describe and just make something up in order to do so, never mind whether it makes any sense in the long run or not. Countless examples have been demonstrated over the years, but the mother lode of such situations has to be humanity’s invention of counting.

Numbers do not, in and of themselves, exist- they are simply a construct designed by our brains to help us get around the awe-inspiring concept of the relative amounts of things. However, this hasn’t prevented this ‘neat little tool’ spiralling out of control to form the vast field that is mathematics. Once merely a diverting pastime designed to help us get more use out of our counting tools, maths (I’m British, live with the spelling) first tentatively applied itself to shapes and geometry before experimenting with trigonometry, storming onwards to algebra, turning calculus into a total mess about four nanoseconds after its discovery of something useful, before just throwing it all together into a melting point of cross-genre mayhem that eventually ended up as a field that it as close as STEM (science, technology, engineering and mathematics) gets to art, in that it has no discernible purpose other than for the sake of its own existence.

This is not to say that mathematics is not a useful field, far from it. The study of different ways of counting lead to the discovery of binary arithmetic and enabled the birth of modern computing, huge chunks of astronomy and classical scientific experiments were and are reliant on the application of geometric and trigonometric principles, mathematical modelling has allowed us to predict behaviour ranging from economics & statistics to the weather (albeit with varying degrees of accuracy) and just about every aspect of modern science and engineering is grounded in the brute logic that is core mathematics. But… well, perhaps the best way to explain where the modern science of maths has lead over the last century is to study the story of i.

One of the most basic functions we are able to perform to a number is to multiply it by something- a special case, when we multiply it by itself, is ‘squaring’ it (since a number ‘squared’ is equal to the area of a square with side lengths of that number). Naturally, there is a way of reversing this function, known as finding the square root of a number (ie square rooting the square of a number will yield the original number). However, convention dictates that a negative number squared makes a positive one, and hence there is no number squared that makes a negative and there is no such thing as the square root of a negative number, such as -1. So far, all I have done is use a very basic application of logic, something a five-year old could understand, to explain a fact about ‘real’ numbers, but maths decided that it didn’t want to not be able to square root a negative number, so had to find a way round that problem. The solution? Invent an entirely new type of number, based on the quantity i (which equals the square root of -1), with its own totally arbitrary and made up way of fitting  on a number line, and which can in no way exist in real life.

Admittedly, i has turned out to be useful. When considering electromagnetic forces, quantum physicists generally assign the electrical and magnetic components real and imaginary quantities in order to identify said different components, but its main purpose was only ever to satisfy the OCD nature of mathematicians by filling a hole in their theorems. Since then, it has just become another toy in the mathematician’s arsenal, something for them to play with, slip into inappropriate situations to try and solve abstract and largely irrelevant problems, and with which they can push the field of maths in ever more ridiculous directions.

A good example of the way mathematics has started to lose any semblance of its grip on reality concerns the most famous problem in the whole of the mathematical world- Fermat’s last theorem. Pythagoras famously used the fact that, in certain cases, a squared plus b squared equals c squared as a way of solving some basic problems of geometry, but it was never known as to whether a cubed plus b cubed could ever equal c cubed if a, b and c were whole numbers. This was also true for all other powers of a, b and c greater than 2, but in 1637 the brilliant French mathematician Pierre de Fermat claimed, in a scrawled note inside his copy of Diohantus’ Arithmetica, to have a proof for this fact ‘that is too large for this margin to contain’. This statement ensured the immortality of the puzzle, but its eventual solution (not found until 1995, leading most independent observers to conclude that Fermat must have made a mistake somewhere in his ‘marvellous proof’) took one man, Andrew Wiles, around a decade to complete. His proof involved showing that the terms involved in the theorem could be expressed in the form of an incredibly weird equation that doesn’t exist in the real world, and that all equations of this type had a counterpart equation of an equally irrelevant type. However, since the ‘Fermat equation’ was too weird to exist in the other format, it could not logically be true.

To a mathematician, this was the holy grail; not only did it finally lay to rest an ages-old riddle, but it linked two hitherto unrelated branches of algebraic mathematics by way of proving what is (now it’s been solved) known as the Taniyama-Shimura theorem. To anyone interested in the real world, this exercise made no contribution to it whatsoever- apart from satisfying a few nerds, nobody’s life was made easier by the solution, it didn’t solve any real-world problem, and it did not make the world a tangibly better place. In this respect then, it was a total waste of time.

However, despite everything I’ve just said, I’m not going to decide that all modern day mathematics is a waste of time; very few human activities ever are. Mathematics is many things; among them ridiculous, confusing, full of contradictions and potential slip-ups and, in a field whose age of winning a major prize is younger than in any other STEM field, apparently full of those likely to belittle you out of future success should you enter the world of serious academia. But, for some people, maths is just what makes the world makes sense, and at its heart that was all it was ever created to do. And if some people want their life to be all about the little symbols that make the world make sense, then well done to the world for making a place for them.

Oh, and there’s a theory doing the rounds of cosmology nowadays that reality is nothing more than a mathematical construct. Who knows in what obscure branch of reverse logarithmic integrals we’ll find answers about that one…

The Land of the Red

Nowadays, the country to talk about if you want to be seen as being politically forward-looking is, of course, China. The most populous nation on Earth (containing 1.3 billion souls) with an economy and defence budget second only to the USA in terms of size, it also features a gigantic manufacturing and raw materials extraction industry, the world’s largest standing army and one of only five remaining communist governments. In many ways, this is China’s second boom as a superpower, after its early forays into civilisation and technological innovation around the time of Christ made it the world’s largest economy for most of the intervening time. However, the technological revolution that swept the Western world in the two or three hundred years during and preceding the Industrial Revolution (which, according to QI, was entirely due to the development and use of high-quality glass in Europe, a material almost totally unheard of in China having been invented in Egypt and popularised by the Romans) rather passed China by, leaving it a severely underdeveloped nation by the nineteenth century. After around 100 years of bitter political infighting, during which time the 2000 year old Imperial China was replaced by a republic whose control was fiercely contested between nationalists and communists, the chaos of the Second World War destroyed most of what was left of the system. The Second Sino-Japanese War (as that particular branch of WWII was called) killed around 20 million Chinese civilians, the second biggest loss to a country after the Soviet Union, as a Japanese army fresh from an earlier revolution from Imperial to modern systems went on a rampage of rape, murder and destruction throughout the underdeveloped northern China, where some war leaders still fought with swords. The war also annihilated the nationalists, leaving the communists free to sweep to power after the Japanese surrender and establish the now 63-year old People’s Republic, then lead by former librarian Mao Zedong.

Since then, China has changed almost beyond recognition. During the idolised Mao’s reign, the Chinese population near-doubled in an effort to increase the available worker population, an idea tried far less successfully in other countries around the world with significantly less space to fill. This population was then put to work during Mao’s “Great Leap Forward”, in which he tried to move his country away from its previously agricultural economy and into a more manufacturing-centric system. However, whilst the Chinese government insists to this day that three subsequent years of famine were entirely due to natural disasters such as drought and poor weather, and only killed 15 million people, most external commentators agree that the sudden change in the availability of food thanks to the Great Leap certainly contributed to the death toll estimated to actually be in the region of 20-40 million. Oh, and the whole business was an economic failure, as farmers uneducated in modern manufacturing techniques attempted to produce steel at home, resulting in a net replacement of useful food for useless, low-quality pig iron.

This event in many ways typifies the Chinese way- that if millions of people must suffer in order for things to work out better in the long run and on the numbers sheet, then so be it, partially reflecting the disregard for the value of life historically also common in Japan. China is a country that has said it would, in the event of a nuclear war, consider the death of 90% of their population acceptable losses so long as they won, a country whose main justification for this “Great Leap Forward” was to try and bring about a state of social structure & culture that the government could effectively impose socialism upon, as it tried to do during its “Cultural Revolution” during the mid-sixties. All this served to do was get a lot of people killed, resulted in a decade of absolute chaos, literally destroyed China’s education system and, despite reaffirming Mao’s godlike status (partially thanks to an intensification in the formation of his personality cult), some of his actions rather shamed the governmental high-ups, forcing the party to take the angle that, whilst his guiding thought was of course still the foundation of the People’s Republic and entirely correct in every regard, his actions were somehow separate from that and got rather brushed under the carpet. It did help that, by this point, Mao was now dead and was unlikely to have them all hung for daring to question his actions.

But, despite all this chaos, all the destruction and all the political upheaval (nowadays the government is still liable to arrest anyone who suggests that the Cultural Revolution was a good idea), these things shaped China into the powerhouse it is today. It may have slaughtered millions of people and resolutely not worked for 20 years, but Mao’s focus on a manufacturing economy has now started to bear fruit and give the Chinese economy a stable footing that many countries would dearly love in these days of economic instability. It may have an appalling human rights record and have presided over the large-scale destruction of the Chinese environment, but Chinese communism has allowed for the government to control its labour force and industry effectively, allowing it to escape the worst ravages of the last few economic downturns and preventing internal instability. And the extent to which it has forced itself upon the people of China for decades, forcing them into the party line with an iron fist, has allowed its controls to be gently relaxed in the modern era whilst ensuring the government’s position is secure, to an extent satisfying the criticisms of western commentators. Now, China is rich enough and positioned solidly enough to placate its people, to keep up its education system and build cheap housing for the proletariat. To an accountant, therefore,  this has all worked out in the long run.

But we are not all accountants or economists- we are members of the human race, and there is more for us to consider than just some numbers on a spreadsheet. The Chinese government employs thousands of internet security agents to ensure that ‘dangerous’ ideas are not making their way into the country via the web, performs more executions annually than the rest of the world combined, and still viciously represses every critic of the government and any advocate of a new, more democratic system. China has paid an enormously heavy price for the success it enjoys today. Is that price worth it? Well, the government thinks so… but do you?