Followup to: Causality: The Fabric of Real Things

Previous meditation:

"You say that a universe is a connected fabric of causes and effects. Well, that's a very Western viewpoint - that it's all about mechanistic, deterministic stuff. I agree that anything else is outside the realm of science, but it can still be real, you know. My cousin is psychic - if you draw a card from his deck of cards, he can tell you the name of your card before he looks at it. There's no mechanism for it - it's not a causal thing that scientists could study - he just does it. Same thing when I commune on a deep level with the entire universe in order to realize that my partner truly loves me. I agree that purely spiritual phenomena are outside the realm of causal processes that can be studied by experiments, but I don't agree that they can't be real."

Reply:

Fundamentally, a causal model is a way of factorizing our uncertainty about the universe.  One way of viewing a causal model is as a structure of deterministic functions plus uncorrelated sources of background uncertainty.

Let's use the Obesity-Exercise-Internet model (reminder: which is totally made up) as an example again:

We can also view this as a set of deterministic functions F_i, plus uncorrelated background sources of uncertainty U_i:

This says is that the value x₃ - how much someone exercises - is a function of how obese they are (x₁), how much time they spend on the Internet (x₂), plus some other background factors U₃ which don't correlate to anything else in the diagram, all of which collectively determine, when combined by the mechanism F₃, how much time someone spends exercising.