If the world is built from computation rather than causal arrows, how do you get to causal arrows?

I had to do a bit of searching, but it seems that Eliezer (or at least Eliezer_2008) considers causal arrows to be more fundamental than computations:

And, if we have "therefore" back, if we have "cause" and "effect" back—and science would be somewhat forlorn without them—then we can hope to retrieve the concept of "computation". We are not forced to grind up reality into disconnected configurations; there can be glue between them. We can require the amplitude relations between connected volumes of configuration space, to carry out some kind of timeless computation, before we decide that it contains the timeless Now of a conscious mind.

So here's my understanding of Eliezer_2008's guess of how all the reductions would work out: mind reduces to computation which reduces to causal arrows which reduces to some sort of similarity relationship between configurations, and the universe fundamentally is a (timeless) set of configurations and their amplitudes.

Interestingly, Pearl himself doesn't seem nearly as ambitious about how far to push the reduction of "causality" and explains that his theory

takes the physical notions of “mechanisms”, “variables”, “measurements” and “interventions” as the basic primitives.

which bears almost no resemblance to Eliezer's idea of reducing causality to similarity.