If anyone’s confused by the post, here’s my stab at a simpler version.
Assume we’re measuring random variables A and B at time moments 1 and 2, so we have many samples containing four values (A1,A2,B1,B2) each. We want to figure out whether moment 1 came before or after moment 2, using Eliezer’s assumption that the value of each variable at the later moment is independently probabilistically caused by the values of both variables at the earlier moment. Formally, if 1 came before 2, then A2 must be independent of B2 conditional on knowing A1 and B1, and if 2 came before 1, then A1 must be independent of B1 conditional on A2 and B2.
Let’s run through a simple example and see if we can figure out the direction of time. Let random() be a function that returns 0 or 1 with probability 50% each, and all calls to random() are independent. Our variables will be defined as follows:
A1 = random()
B1 = random()
A2 = A1 + B1 + random()/10
B2 = A1 + B1 + random()/10
Clearly, if we know A1 and B1, then additionally knowing A2 doesn’t give information about B2 or vice versa. But if we know, for example, that A2=1.1 and B2=1, then we know that A1+B1=1, so additionally knowing A1 would give information about B1 and vice versa. Therefore moment 1 must have come before moment 2.
Eliezer’s assumption of independent probabilistic causation seems to be doing most of the work here. I don’t know if that assumption applies very often in real life. For example, if A1 is allowed to probabilistically generate an intermediate value A1′ that’s used in the computation of both A2 and B2, we can’t figure out the direction of time using the proposed method.
One scenario where the method would work is if A2 and B2 are generated by two spacelike-separated generators, each of which receives the true values of A1 and B1. Or at least it should work with classical probability. I don’t know enough physics to tell if quantum entanglement tricks can screw up the method even when A2 and B2 are spacelike separated. Maybe someone could chime in?
If anyone’s confused by the post, here’s my stab at a simpler version.
Assume we’re measuring random variables A and B at time moments 1 and 2, so we have many samples containing four values (A1,A2,B1,B2) each. We want to figure out whether moment 1 came before or after moment 2, using Eliezer’s assumption that the value of each variable at the later moment is independently probabilistically caused by the values of both variables at the earlier moment. Formally, if 1 came before 2, then A2 must be independent of B2 conditional on knowing A1 and B1, and if 2 came before 1, then A1 must be independent of B1 conditional on A2 and B2.
Let’s run through a simple example and see if we can figure out the direction of time. Let random() be a function that returns 0 or 1 with probability 50% each, and all calls to random() are independent. Our variables will be defined as follows:
A1 = random()
B1 = random()
A2 = A1 + B1 + random()/10
B2 = A1 + B1 + random()/10
Clearly, if we know A1 and B1, then additionally knowing A2 doesn’t give information about B2 or vice versa. But if we know, for example, that A2=1.1 and B2=1, then we know that A1+B1=1, so additionally knowing A1 would give information about B1 and vice versa. Therefore moment 1 must have come before moment 2.
Eliezer’s assumption of independent probabilistic causation seems to be doing most of the work here. I don’t know if that assumption applies very often in real life. For example, if A1 is allowed to probabilistically generate an intermediate value A1′ that’s used in the computation of both A2 and B2, we can’t figure out the direction of time using the proposed method.
One scenario where the method would work is if A2 and B2 are generated by two spacelike-separated generators, each of which receives the true values of A1 and B1. Or at least it should work with classical probability. I don’t know enough physics to tell if quantum entanglement tricks can screw up the method even when A2 and B2 are spacelike separated. Maybe someone could chime in?