Causal language

Consider the following sentence: "You ate the blueberries because your fingers are stained." What is odd about it is that ordinarily, when we say "X because of Y" we mean "Y is the cause of X". For example, "The window broke because the baseball hit it" means that the baseball hitting the window caused it to break. But in this case, the sentence surely doesn't mean that your fingers being stained caused you to eat the blueberries. Now one might object that it's a weird sentence, and that instead it should be "I believe you ate the blueberries because your fingers are stained." But the original version is not confusing to an English speaker, and people sometimes do speak this way. Language is a complicated business. And language about causality is particularly tricky.

It is well known that correlation does not imply causation. But when scientific studies are reported in the media, this dictum is often forgotten. Professor Jon Mueller at North Central College in Naperville, Illinois has compiled a great set of links to news articles reporting scientific findings. Some of the headlines for these articles suggest causal relationships and some do not. Clicking through to the actual news articles shows that the purported causal relationships are often a stretch, to say the least. For example:

TV raises blood pressure in obese kids: study

The news article reports that:

The researchers found children who watched two to four hours of TV were 2.5 times more likely to have high blood pressure compared with those who watched less than two hours of television a day. Those who watched more than 4 hours per day were 3.3 times more likely to have hypertension.

In other words this was an observational study, which established a correlation between watching high amounts of TV per day and having high blood pressure. Contrary to the headline, the study did not show that the TV watching was the cause of the high blood pressure. For convenience let's rework the headline, while preserving its causal sense:

TV watching increases the probability of high blood pressure. (1)

The causal implication can be removed by writing:

TV watchers have higher probability of high blood pressure. (2)

In a wiki entry on causal language Gustavo Lacerda points out that action words often express causality. Note that in the present example, in order to remove the causal aspect of (1), it was necessary to change the verb "watching" into the noun "watchers" and the verb "increases" into the noun "higher".

Interestingly, there is a Bayesian formulation that sounds closer to (1):

Being a TV watcher increases the probability that a child has high blood pressure.

Note that this version has the verb "increases", like (1), but not the verb "watching". Instead it's expressed as "being a TV watcher", which indicates group membership rather than action or choice. It is this information about group membership that is used to update the probability of high blood pressure, following the Bayesian recipe.

Prediction and causality

Prediction can sound a lot like causation. Consider this statement:

If you exercise, you're less likely to have a heart attack. (3)

Does this mean:

People who exercise are less likely than people who don't to have a heart attack. (4)

or does it mean:

The act of exercising reduces your chances of having a heart attack. (5)

It seems quite ambiguous. On the one hand, "if you exercise" sounds like a statement about your choice simply to exercise instead of not exercising, which supports interpretation (5). On the other hand, "if you exercise" identifies you as a person who exercises, and that may predict your risk of heart attack, perhaps due to another behaviour common among people who exercise, such as healthy eating. This would support interpretation (4).

Natural language allows ambiguities. It's convenient to leave things out because everyone knows what we mean. Don't they? Not necessarily. Certainly, when it comes to causality, ambiguity can lead to a mess of trouble. In ordinary speech, the distinction between correlation and causation is often blurred. Statement (3) above is ambiguous about the comparator: less likely than whom to have a heart attack? Less likely than people who don't exercise? Less likely than you would be if you chose not to exercise?

It seems to me that causal language is almost a worst-case scenario. Many people would see the concern as unimportant. And yet evidence and beliefs about causation are at the foundation of any intervention, whether in health care, education, social programs, economics, what have you. The media and politicians routinely use misleading causal language. But it's difficult even when we try to be clear!

Sweetness and life

One of my favorite of Mueller's examples is:

Eat sweets, live longer.

All you have to do is juxtapose "eat sweets" and "live longer". Your mind does the rest.

Could you keep my place in line?

Line-ups are both eminently civilized and—really annoying! The first in first out (FIFO) principle is inherently egalitarian and respect for it is a sign of social order. But there's something crazy about using our bodies as place keepers in a queue, sometimes for hours on end.

Inevitably, after waiting some time in a lineup, someone will need to step out for a while. Rather than lose one's priority in the sequence, the convention is to ask someone (a complete stranger if need be), "Could you keep my place in line?"

The language here is metaphorical and indirect. The request is not really about keeping a place. It's about promising on the return of the person to vouch to any potential challengers that indeed this particular person was previously in line at this particular point in the sequence.

The fact is, complete strangers generally do agree to "keep your place in line". And that's a further sign of civil behaviour. Maybe line ups aren't so bad after all!

I bet there are lots of good stories about line-ups. I'd love to hear some. Then we could publish a book (I'm trying to think of a queued name for it ...)

P.S. I've tried to give equal time to the different spellings lineup / line-up / line up. I really don't know which is correct. Those who wish to correct me should form an orderly line.

It's the law!

There's been quite a lot of reaction to a New York Times op-ed by Paul Davies titled Taking Science on Faith. (I read about it first on Adventures in Ethics and Science.) Davies argues that, like religion, science is ultimately based on faith. My main interest is not in his argument per se (but see here for some scathing critiques).

What struck me about Davies' essay was his use of the term scientific law. He uses it again and again, whereas he refers to a theory only twice, and not once does he refer to a model.

If there are laws, then presumably there's a lawmaker, and the obvious candidate would be God. If we are able to discover these laws, then we have identified Truth. Who can then disagree? Who can go against the law?

This seems to me a very arrogant notion. In fact the history of science is littered with "laws" that have subsequently been overturned or shown to be special cases or approximations. For instance, Newton's laws of motion (one of which, incidentally—his 2nd law, F=ma—is actually a definition) were superceded by special relativity and quantum mechanics.

Aren't scientific "laws" more accurately described as theories, or—my preference—models? I've previously quoted statistician George E. P. Box:

All models are wrong, some are useful

I would concede that in principle, it may be possible to get a model exactly right, but except in the case of a computer simulation, it isn't possible to be certain that it's right! To me, Box's aphorism is humble, epistemologically wise, and profoundly scientific.

It is my impression that for many years now there has been a movement in science away from the word law, with its implicit suggestion that the Truth has been definitively uncovered, and that somehow any deviation from the law is improper or even unimaginable. Nevertheless, use of the term continues (see the Wikipedia entries for scientific law, physical law, and laws of science). It might be argued that I'm reading too much into the word law. But consider how it affects schoolchildren who are learning about science. Rather that encouraging the idea that science is about curiousity, observing, investigating, and testing, I think it suggests that science is about memorizing rules.

Laws of chance

There is another class of "laws" that aren't exactly scientific, but still have an empirical aspect. In probability and statistics, it was at one time common to refer to probability "laws", the most famous being the curiously-named normal law. Today we refer to it as the normal distribution, or better yet the Gaussian distribution. The term "normal law" is a bit of a double-whammy: to go against it you would have to be abnormal and lawless!

Two fascinating "laws" relating to probability distributions are Zipf's law and Benford's law. I think that what makes probability distributions seem like "laws" is that they often hold—at least approximately—under quite general real-world conditions.

Law-abiding citizens

Why are we so prone to label models (among other things) as laws? I think it might be related to our abhorrence of uncertainty. For a law-abiding citizen, laws are a source of security. Everything seems neat and tidy and safe and predictable. But every so often, the world is revealed to be a bit different from what we expected. Maybe the laws don't work so well after all ...