(I wrote this post in April 2020 for a non-LW audience)
Causation is pretty cool. Even cooler than causation, causal models! If you haven't heard the news, the past few decades have produced big leaps in understanding causality and how to reason about it. There's also been great descriptive work on how humans already intuitively deal with causality. Causality is so baked into the human mind that causal relationships can often be experienced at the perceptual level, even before any higher level reasoning systems can act. We're very good at spotting causal relationships when they're present, so good that we sometimes even detect them when they aren't there :)
To get an understanding of the difference between causal models and predictive models we're gonna use the slogan "Correlation does not equal causation" as our entry.
To be fair, that graph isn't really even a good example. That's more "just because lines sorta match up on a graph, doesn't mean you should expect them to continue to math up." I'd totally bet that these variables wouldn't even be correlated if you picked a different time span.
Here's a better example of correlation not equaling causation (based on a true story, but simplified to make a point):
Your new study finds that people who listened to Mozart as a kid have higher SAT scores. Mozart makes you smarter! The meaning inherent in that claims is "If I intervene by playing Mozart for a kid, they will become smarter than they otherwise would have."
What could go wrong? Well it turns out that the actual causal graph looks more like this:
Different story. If you know someone listened to Mozart as a kid, it is still 100% legit an accurate to predict higher SAT scores, but now it's also clear that intervening on the Mozart variable won't affect one's SAT. Mozart is useful for predicting SAT because they are caused by the same variable. Mozart is evidence that their family is wealthy, and that causally affects SAT scores. But if you control for wealth, and the Mozart effect goes away.
(Also for completion, the causal graph probs looks more like this):
Moral of the story: if you do stats well, you'll have a good model that you can use to make robust predictions, but it can't inform intervention unless you have a causal model relating the variables.
So that's one nugget of wisdom that can be taken from "Correlation does not equal causation". But there's some interesting historical baggage with the sentiment expressed by that slogan. It seems like the early pioneers who coalesced statistics into it's modern form (Ronald Fischer, Karl Pearson) were so pissed by people incorrectly inferring causaility, and by their own inability to formalize causality, they said "Fuck it! We are only studying correlation, there is NO SUCH THING as causality, and no one gets to use that disgusting word in my house!" I won't get into the weeds, but The Book of Why covers this section of history, and this book review offers some alternative stories.
Whatever the reason for this taboo, it seems clear that there was a taboo. Explicitly talking about causality or trying to develop formal models and theories about causality just wasn't something one did in polite statistical society (and statistics had gained a lot of clout for it's impressive predictive powers, so the force of this taboo slightly leaked into other sciences).
Prediction is cool, but intervention is even cooler. So even though the formal doctrine banned causality, that didn't stop statisticians from thinking causally (just like the Behaviorists, who had a similar pact to just pretend like consciousness didn't exist, never stopped being conscious). They even developed randomized control trials, which are very useful for determining causal relationships. That must have been an interesting tension to live with. Intensely needing something to do anything useful, while denying that said something exists in the first place. Good thing you and I don't do that with anything! Ha! Ha...
Long story short, in the year 2020, causal models and causal discovery are rich developed fields that are gaining momentum, with plenty of interesting stuff still to figure out.