Wednesday, October 10, 2012

Fire burns cotton

This is from a casual note by Cosma Shalizi about graphical causal models. I'm publishing it here: 1) to park it where I can find it readily, 2) because it bears on a favorite example of Graham Harman's, and 3) sheds light on the 'tissue' of indirect causality (Harman's concept) that is the basis of my conception of Realm of Being:
Part of what we mean by "cause" is that, when we know the immediate causes, the remoter causes are irrelevant --- given the parents, remoter ancestors don't matter. The standard example is that applying a flame to a piece of cotton will cause it to burn, whether the flame came from a match, spark, lighter or what-not. Probabilistically, this is a conditional independence property, or a Markov property: a variable is independent of its ancestors conditional on its parents. In fact, given its parents, its children, and its childrens' other parents, a variable is conditionally independent of all other variables. This is called the graphical or causal Markov property. When this holds, we can factor the joint probability distribution for all the variables into the product of the distribution of the exogenous variables, and the conditional distribution for each endogenous variable given its parents.
Cf. remarks on visual notation in my post Harman's Ontology on a Single Level. Come to think of it, Arthur Stinchcomb's Constructing Social Theory makes occasional use of graph notation.


  1. Well, WmB, that's an interesting example for Shalidi to use, considering that the locus classicus for fire burning cotton, as far as I am aware, is in al-Ghazali's Incoherence of the Philosophers, problem xvii:

    The one who enacts the burning by creating blackness in the cotton, [causing] separation in its parts, and making it cinder or ashes, is God, either through the mediation of his angels or without mediation. As for fire, which is inanimate, it has no action. For what proof is there that it is the agent? They have no proof other than observing the occurrence of the burning at the [juncture of] contact with the fire. Observation, however, [only] shows the occurrence [of burning] at [the time of the contact with the fire], but does not shoe the occurrence [of burning] by [the fire] and that there is no other cause for it.

    Al-Ghazali, The Incoherence of the Philosophers, tr. Michael E Marmura. Provo: Brigham Young UP, 1997, p 177.

    Ghazali's position was nicely phrased for Western understanding by the eponymous Spengler in an article a while back for Asia Times:

    There are no intermediate causes, in the sense of laws of nature. Mars traverses an ellipse around the sun not because God has instituted laws of motion that require Mars to traverse an ellipse, but because Allah at every instant directs the angular velocity of Mars. … Allah is everywhere doing everything at all times. He sets the spin on every electron, measures the jump of every flea, the frequency of every sneeze.

    But that is not quite Shalizi's point, I think.

  2. Well, the interesting thing, Charles, is that Shalizi introduces the example as the "standard" one. HE didn't choose it as an example. Rather, it was chosen for him by tradition. And Shalizi is a statistician and physicist at Carnegie-Mellon. So what tradition is it that he refers to?

    I wonder if that particular tradition is continuous back to Al-Ghazali, which is probably where Harman gets the example. I know he says it is standard in Muslim medieval philosophy. According to Harman, Al-Ghazali's position on causation that example is known as occasionalism.

  3. Ah, okay, not being familiar with Harman I hadn't read of his connection with al-Ghazali -- now I see from Stellar Cartographies that it's a known known, just unknown by me.