# The Slippery Math of Causation

Pradeep Mutalik for Quanta Magazine: “You often hear the admonition “correlation does not imply causation.” But what exactly is causation? Unlike correlation, which has a specific mathematical meaning, causation is a slippery concept that has been debated by philosophers for millennia. It seems to get conflated with our intuitions or preconceived notions about what it means to cause something to happen. One common-sense definition might be to say that causation is what connects one prior process or agent — the cause — with another process or state — the effect. This seems reasonable, except that it is useful only when the cause is a single factor, and the connection is clear. But reality is rarely so simple.

Although we tend to credit or blame things on a single major cause, in nature and in science there are almost always multiple factors that have to be exactly right for an event to take place. For example, we might attribute a forest fire to the carelessly thrown cigarette butt, but what about the grassy tract leading to the forest, the dryness of the vegetation, the direction of the wind and so on? All of these factors had to be exactly right for the fire to start. Even though many tossed cigarette butts don’t start fires, we zero in on human actions as causes, ignoring other possibilities, such as sparks from branches rubbing together or lightning strikes, or acts of omission, such as failing to trim the grassy path short of the forest. And we tend to focus on things that can be manipulated: We overlook the direction of the wind because it is not something we can control. Our scientifically incomplete intuitive model of causality is nevertheless very useful in practice, and helps us execute remedial actions when causes are clearly defined. In fact, artificial intelligence pioneer Judea Pearl has published a new book about why it is necessary to teach cause and effect to intelligent machines.

However, clearly defined causes may not always exist. Complex, interdependent multifactorial causes arise often in nature and therefore in science. Most scientific disciplines focus on different aspects of causality in a simplified manner. Physicists may talk about causal influences being unable to propagate faster than the speed of light, while evolutionary biologists may discuss proximate and ultimate causes as mentioned in our previous puzzle on triangulation and motion sickness. But such simple situations are rare, especially in biology and the so-called “softer” sciences. In the world of genetics, the complex multifactorial nature of causality was highlighted in a recent Quanta article by Veronique Greenwood that described the intertwined effects of genes.

One well-known approach to understanding causality is to separate it into two types: necessary and sufficient….(More)”