# jwdink comments on Reading Math: Pearl, Causal Bayes Nets, and Functional Causal Models - Less Wrong Discussion

4 05 December 2011 03:45AM

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Comment author: 05 December 2011 04:43:21AM 1 point [-]

The theory is supposed to describe ANY causal system-- otherwise it would be a crappy theory of how (normatively) people ought to reason causally, and how (descriptively) people do reason causally.

Comment author: 05 December 2011 05:53:30AM *  1 point [-]

The theory is supposed to describe ANY causal system.

No, it's not.

In particular, most of Pearl's work applies only under some sort of assumption that the underlying process is Markovian. The common criticism of Pearl is that this assumption fails if one assumes quantum mechanics is true. He addresses this in Causality, around chapter two or three. He also addresses extensions to possibly-cyclic diagrams, but the technicalities become annoying.

If you are okay with discretizing time, then Timeless Causality shows a "ladder"-like directed acyclic graph that will approximate the causal system.

Comment author: 05 December 2011 09:11:23AM *  1 point [-]

If his theory breaks in situations as mundane and simple as the gears example above, then why have common criticisms employed the vagaries of quantum mechanics in attempting to criticize the Markov assumption? They might as well have just used simple examples involving gears.

Comment author: 05 December 2011 09:25:38AM *  1 point [-]

I don't follow.

You made a claim of the form "For all causal systems, this theory ought to describe them." I demonstrated otherwise by exhibiting an explicit assumption Pearl makes at the outset, and that because of this assumption the theory applies only to a subset of causal systems. Gears are classical objects, and so a simple example involving gears doesn't elucidate the weaknesses of assuming all processes are Markov.

Then, I alluded to how one can hack around cycles in causal graphs by approximating them with "ladders".

As far as I can tell you're assuming some narrative between these points; there isn't one.

Comment author: 05 December 2011 07:48:15PM *  1 point [-]

Oy, I'm not following you either; apologies. You said:

The common criticism of Pearl is that this assumption fails if one assumes quantum mechanics is true.

...implying that people generally criticize his theory for "breaking" at quantum mechanics. That is, to find a system outside his "subset of causal systems" critics have to reach all the way to quantum mechanics. He could respond "well, QM causes a lot of trouble for a lot of theories." Not bullet-proof, but still. However, you started (your very first comment) by saying that his theory "breaks" even in the gears example. So why have critics tried criticizing his theory for breaking in complex quantum mechanics, when all along there were much more simple and common causal situations they could have used to criticize the theory for breaking under?

More generally, I just can't agree with your interpretation of Pearl that he was only trying to describe a subset of causal systems, if such a subset excludes such commonplace examples as the gears example. I think he was trying to describe a theory of how causation and counterfactuals can be formalized and mathemetized to describe most of nature. Perhaps this theory doesn't apply to nature when described on the quantum mechanical level, but I find it extremely implausible that it doesn't apply to the vast majority of nature. It was designed to. Can you really watch this video and deny he thinks that his theory applies to classical physics, such as the gears example? Or do you think he'd be stupid enough to not think of the gears example? I'm baffled by your position.

Comment author: 05 December 2011 09:30:55PM 2 points [-]

Hopefully the following clarifies my position.

In what follows, "Pearl's causal theory" refers to all instances of Pearl's work of which I am aware. "DAG theory" refers only to the fragment which a priori assumes all causal models are directed acyclic graphs.

Claim 1: DAG theory can't cope with the gears example. False.

For the third time, there exists an approximation of the gears example that is a directed acyclic graph. See the link in my second comment for the relevant picture.

Claim 2: Pearl's causal theory can't cope with the gears example. False.

If the approximation in claim 1 doesn't satisfy you, then there exists a messy, more computationally expensive extension of the DAG theory that can deal with cyclic causal graphs.

Claim 3: Pearl's causal theory describes all causal systems everywhere. False.

This is the only claim to which quantum mechanics is relevant.

Comment author: 05 December 2011 10:02:45PM 1 point [-]