Hmm, maybe one can’t eliminate the [???] node. This is because non-causal-diagram information, such as observations, is conditioned on for all nodes, in the ordinary non-causal-diagram way. So the information encoded in diagram 1 really is causal, even if it’s unphysical. One could interpret this as a heuristic argument against diagram 1 - no unphysical causal nodes.
In general, you can remove the [???] node. Causal information can just be about how the wake on (day) node’s value is determined by the coin flip, it doesn’t necessitate another node. And even though this doesn’t fully determine the value of the wake on (day) node, our information still determines our probabilities.
Though if the causal picture of the universe is also true, the different undetermied choices are caused by either an extra causal factor ([???]) or un-tracked differences in the coin flip—just like how the different outcomes of the coin flip are caused by small differences in initial conditions.
If all coin flips are treated the same, this forces the decision to be made by some other sort of initial conditions. And it is a peculiarity of the Sleeping Beauty problem that this would be unphysical for diagram 1 - if we go back to the marble game, there’s any number of physical processes that work.
Hmm, maybe one can’t eliminate the [???] node. This is because non-causal-diagram information, such as observations, is conditioned on for all nodes, in the ordinary non-causal-diagram way. So the information encoded in diagram 1 really is causal, even if it’s unphysical. One could interpret this as a heuristic argument against diagram 1 - no unphysical causal nodes.
In general, you can remove the [???] node. Causal information can just be about how the wake on (day) node’s value is determined by the coin flip, it doesn’t necessitate another node. And even though this doesn’t fully determine the value of the wake on (day) node, our information still determines our probabilities.
Though if the causal picture of the universe is also true, the different undetermied choices are caused by either an extra causal factor ([???]) or un-tracked differences in the coin flip—just like how the different outcomes of the coin flip are caused by small differences in initial conditions.
If all coin flips are treated the same, this forces the decision to be made by some other sort of initial conditions. And it is a peculiarity of the Sleeping Beauty problem that this would be unphysical for diagram 1 - if we go back to the marble game, there’s any number of physical processes that work.