 In figure 10(a), we have the case of early preemption from  §1.2.1.  Here, c’s firing is a cause of e’s firing. In figure 10(b), we have a case of what Hall calls a “short circuit”. When c fires, it both initiates a threat to e’s dormancy (by making a fire) and neutralizes that very threat (by making d fire). Here’s a vignette with a similar structure (see Hall 2004, and Hitchcock 2001a): a boulder becomes dislodged and careens down the hill towards Hiker. Seeing the boulder coming, Hiker jumps out of the way, narrowly averting death. In this case, the boulder’s fall both initiates a threat to Hiker’s life and neutralizes that very threat (by alerting them to its presence). Hall contends that the boulder’s becoming dislodged did not cause Hiker to survive; and, in the case of the short circuit, c’s firing did not cause e to not fire. Intuitively, c accomplished nothing vis-a-vis e. But Hall notes that these two neuron systems are isomorphic to each other. We can make the point with systems of structural equations (see the entry on  causal models,  and  §3.2  below). Start with the case of early preemption, and use binary variables, A, B, C, D, and E for whether a, b, c, d, and e fire, respectively. These variables takes on the value 1 if their paired neuron fires, and they take on the value 0 if they do not. Then, we can represent the causal structure of early preemption with this system of equations: