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Comment by Symmetry | Hacker News Reader

There's another way of looking for causality directly from data. If A and B are uncorrelated but both correlate with C then you know that C isn't causally upstream of either.

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So if you have an A and a C and want to figure out the causality you need to look for a B that correlates with C but not A?

How can two things not correlate with each other, but both correlate with a third thing? This seems like saying x=5, y=3, and that there's some variable z which x and y are both equal to?

The simplest way to explain is when when both cause C some % of the time. It's useful to run a simulation if you doubt it.

The number of people who like the taste of vanilla (I suppose) doesn't correlate with hours of sunlight in some area. Both correlate with amount of ice cream sold.

Interesting, is there a law or algorithm/equation for that?

Edit: sorry, instrumental variables do not describe what the original poster was talking about, but could be useful for understanding the connections between correlation and causation in other ways.

The concept of an instrumental variable

https://en.m.wikipedia.org/wiki/Instrumental_variable

covers some of it. Judea Pearl's book Causality summarizes lots of recent (past few decades) work in the area, with a focus on his theoretical framework. There are lots of algorithms for discovering the structural of causality for sets of variables larger than three. Having interventional data always makes these things easier, but it's not the only way to get at causality.

I always thought correlation was transitive.Isn't it? It is surely reflexive but I might have to go back and study more about those properties.

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