In a thought provoking comment to my post Causation without Correlation is Possible James Bronzan wrote

To my uneducated eye, I’d say that even though correlation does not mean causation and causation does not mean correlation, they nonetheless travel very closely together. In other words: the instances in which causation results in correlation are far more frequent in the world than those in which it does not. (Maybe that’s why the examples had so much mathyness?)

Surely if X causes Y instances of X are more likely to hang around with instances of Y than not.

There’s a lot going on here. Let me try to unpack it. First of all, causation itself and any claim of it are theories or mental models, if you prefer that terminology. (A subsequent post will go more into this point.) However, causation and causal thinking has proven to be incredibly useful. No doubt it is an evolved modality of thought. Even if the world is not objectively causal in any sense I’m not ready to abandon causality. Let us say, if only as shorthand, causality exists and is ubiquitous. (As an exercise try for a moment to imagine any time and place in the universe where causality ceases. Good luck.)

I assert that there are far more things that are related by correlation than by causality. To build on an example from the prior post, among children, reading comprehension is correlated with, among other things, shoe size, mathematical ability, height, weight, and age. Yet only one of those plays a causal role (or so a reasonable person can believe). If causation exists and is ubiquitous, what do we say about correlation? It is hyper-ubiquitous. It is over-abundant. There is far too much of it to be useful. If we based inferences on correlation the universe would be over-determined. There’s just far too much of it.

That’s related to the fact that correlation is not as useful as we’d like to think. Or, rather, it is a very blunt tool, especially for causal inference. Using it is like trying to catch water with bare hands. It leaks out all over the place unless one carefully plugs all the holes. That’s not so easy to do, but it isn’t impossible to do a credible job. Sometimes we can hold just enough water to get a drink.

Very often we think correlation is carrying water when it is not. The conclusions of many studies on many subjects and much of what is believed in general (I can’t say how much) about many things are based on very casual causal inferences from correlations. I’d say we have a bias to think this way. It’s a sub-type of confirmation bias. We so adore our causal theories that we search for and believe correlations that support them. Sometimes we learn later how wrong we were. The history science is full of such stories (flat Earth, the Ptolemaic model, blood letting, and more recently, though less profound, arthroscopic knee surgery for arthritis, among many others).

But James’ point isn’t that correlation very often implies causation. Rather, his point is that if X really does cause Y, it is far more likely that X and Y are correlated than not. It certainly seems that way. But an honest look at this issue has to account for the bias in our minds and in our tools. We have very good tools for discovering correlation and certain other measures of relatedness. There could very well be (in fact must be) a class of causal phenomena that escape the detection of those tools. That is to say, our minds and tools are biased in favor of contemplation, detection, and study of evidence of correlation in support of causal inference. It is tempting to conclude that causation and correlation are frequently or tightly associated. But I don’t know how one could substantiate such a claim.

Nevertheless, correlations are useful in the study of causal phenomena. Though they do not by themselves confirm or reject causal assertions they do measure degree of relatedness. That is to say, if we take as given X causes Y, the next question is “to what extent?” Correlation provides an answer, though an incomplete one (being only one statistic).

So, to address James’ point directly, I think we do find that instances of causation to be associated with correlation. But that’s because that’s what we look for and that’s what we can see. The brightness of the street lamp tells us nothing about the extent of the universe it illuminates.