Imagine Bob’s graph of health over time is sin(t) and his graph of exercise is cos(t), with negative values corresponding to being a couch potato. At first glance, health and exercise have nothing to do with each other, since their correlation is zero. At second glance, maybe exercise determines health with a π/2 lag. At third glance, maybe it determines health with a 3π/2 lag and a minus sign. At fourth glance, maybe exercise determines the derivative of health. You’ll find similar problems with any bounded functions over a long timespan, not just sin and cos.
II
Instead of correlation fishing, let’s investigate causation like real scientists, with graphs. Smoking causes tar in the lungs, tar is correlated with cancer, and for any fixed value of “tar” the values of “smoking” and “cancer” are conditionally uncorrelated. So there cannot be a trait that causes both smoking and cancer independently: the causation must go through tar, which we know is caused by smoking. Therefore smoking causes cancer.
But imagine there’s a trait that gives you a “set point” of X tar, continually adjusting your desire to smoke and compensating for external factors, and also gives you X risk of cancer. Then the above will still hold, but quitting smoking won’t help you.
III
Forget graphs. Let’s use the golden standard of determining causation: a randomized controlled experiment. Does skydiving increase risk of death? Yes, if we force a random half of all people to skydive, more of them will die than in the control group.
But now take a random half of all people and force them not to skydive. Those who didn’t skydive anyway will be unaffected, but those who skydived might change their behavior. What if they switch to something more dangerous, like basejumping, because getting the same thrill by safer skydiving is no longer available? Then this experiment also leads to more deaths, and our question about causation remains unanswered.
If we can’t trust correlations, graphs, or experiments—what can we trust? What, in the end, is causation?
Three more stories about causation
I
Imagine Bob’s graph of health over time is sin(t) and his graph of exercise is cos(t), with negative values corresponding to being a couch potato. At first glance, health and exercise have nothing to do with each other, since their correlation is zero. At second glance, maybe exercise determines health with a π/2 lag. At third glance, maybe it determines health with a 3π/2 lag and a minus sign. At fourth glance, maybe exercise determines the derivative of health. You’ll find similar problems with any bounded functions over a long timespan, not just sin and cos.
II
Instead of correlation fishing, let’s investigate causation like real scientists, with graphs. Smoking causes tar in the lungs, tar is correlated with cancer, and for any fixed value of “tar” the values of “smoking” and “cancer” are conditionally uncorrelated. So there cannot be a trait that causes both smoking and cancer independently: the causation must go through tar, which we know is caused by smoking. Therefore smoking causes cancer.
But imagine there’s a trait that gives you a “set point” of X tar, continually adjusting your desire to smoke and compensating for external factors, and also gives you X risk of cancer. Then the above will still hold, but quitting smoking won’t help you.
III
Forget graphs. Let’s use the golden standard of determining causation: a randomized controlled experiment. Does skydiving increase risk of death? Yes, if we force a random half of all people to skydive, more of them will die than in the control group.
But now take a random half of all people and force them not to skydive. Those who didn’t skydive anyway will be unaffected, but those who skydived might change their behavior. What if they switch to something more dangerous, like basejumping, because getting the same thrill by safer skydiving is no longer available? Then this experiment also leads to more deaths, and our question about causation remains unanswered.
If we can’t trust correlations, graphs, or experiments—what can we trust? What, in the end, is causation?