Judea Pearl’s Causality

I want to quibble about some of Pearl’s points but so far do not want to argue with any of his main conclusions. In general the book is dense but fairly clear. Several parts (of those I have attempted) take more than one reading. He necessarily broaches several philosophical issues. I took graduate courses in probability in Berkeley in 1954 and my professor (Hodges) warned us that making decisions from statistical data was hard.

In the appendix there is a reprise of a talk he gave in 1996. In that talk he illustrates with a diagram of an adder circuit from a digital computer. This is indeed an excellent example of cause and effect where the two cannot be confused. There is no sense in which the outputs can effect the inputs of such a circuit. He says that this way of thinking is limited to diagrams and that equations lead to confusion as to input and output. This is simply not so. Important computers, such as the B5500, were designed with equations—Boolean equations. While there was an argument over which sort of representation was the most efficient of engineering effort, there was no argument concerning the equivalence of diagrams to equations. They meant the same thing and neither was time reversible. When Pearl argues equations are reversible he slips by linearizing the relations just at the same point as he switches to equations. Indeed linear equations as generally interpreted lack the distinction between cause and effect.

Most boolean equations are irreversible, but not all. The newish field of reversible computing is motivated by the observation that entropy must increase with irreversible computing components and this leads in turn to dissipation of more heat than may be necessary. I think that this field has made is a substantial reduction in the energy required by a class of computations. There seems always to be a substantial amount of irreversible computation needed to do the things we want computers for.

Gears, levers and pulleys are generally described with diagrams, and yet they do not distinguish cause and effect. Generally cause is ambiguous in equilibrium conditions where one might say that causes go both directions at once. A good deal of classic economic theory is about equilibrium. Such theories are unable to address non-equilibrium phenomena.

I think the argument for diagrams over equations is bogus, but that in turn does not impact Pearl’s other arguments. Diagrams are probably good pedagogically. His observations do support the idea that cause and effect are tied into entropy and the 2nd law of thermodynamics, which in its own realm violates time reversibility of the laws of physics.

Regarding intervention I am reminded of an idea from Dennet’s book “The Evolution of Freedom”. The philosophy of fatalism is merely determinism which omits you from the model. It seems clear to me that concepts of causality are biologically wired in because we survive by choosing between alternative actions with vital consequences. I suspect that causality was originally first person and unconscious. As we evolved a theory of mind it became 2nd and 3rd person. I do suspect that we may have said that rain caused wetness of grass for many thousands of years. I wonder if we used the same word, however.

Regarding f = ma, consider a train accelerating at one m/sec2. In the luggage compartment there is a 1000kg box on wheels. It is pressing against the box behind it with force 103 newtons (= 108 dynes). In this case I would say that the acceleration causes the force, but not in other applications of the formula.

These distinctions are like the What-is—How-to distinction.

I wonder about using information theory to study some of these issues. The information conveyed by the value of a continuously variable in infinite so this would have to be limited to discrete distributions. Mutual information is a critical idea here. I don’t see any new insights here necessarily but it might bring established techniques and plug into the intuition well.